Field Guide to Astronomical Instruments [Spi ed.] 1628411775, 9781628411775

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Field Guide to

Astronomical Instrumentation

Christoph U. Keller Ramon Navarro Bernhard R. Brandl

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SPIE Terms of Use: This SPIE eBook is DRM-free for your convenience. You may install this eBook on any device you own, but not post it publicly or transmit it to others. SPIE eBooks are for personal use only. For details, see the SPIE Terms of Use. To order a print version, visit SPIE.

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Library of Congress Preassigned Control Number Data Keller, Christoph U. Field guide to astronomical instrumentation / Christoph Keller, Ramon Navarro, Bernhard Brandl. pages cm. – (The field guide series ; FG32) Includes bibliographical references and index. ISBN 978-1-62841-177-5 (alk. paper) 1. Astronomical instruments–Handbooks, manuals, etc. I. Navarro, Ramón II. Brandl, Bernhard R. III. Society of Photo-optical Instrumentation Engineers. IV. Title. QB86.K45 2014 5220 .87–dc23 2014009876 Published by SPIE P.O. Box 10 Bellingham, Washington 98227-0010 USA Phone: 360.676.3290 Fax: 360.647.1445 Email: [email protected] www.spie.org Copyright © 2015 Society of Photo-Optical Instrumentation Engineers (SPIE) All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means without written permission of the publisher. The content of this book reflects the thought of the author(s). Every effort has been made to publish reliable and accurate information herein, but the publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon. Printed in the United States of America. First printing.

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Introduction to the Series Welcome to the SPIE Field Guides—a series of publications written directly for the practicing engineer or scientist. Many textbooks and professional reference books cover optical principles and techniques in depth. The aim of the SPIE Field Guides is to distill this information, providing readers with a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena, including definitions and descriptions, key equations, illustrations, application examples, design considerations, and additional resources. A significant effort will be made to provide a consistent notation and style between volumes in the series. Each SPIE Field Guide addresses a major field of optical science and technology. The concept of these Field Guides is a format-intensive presentation based on figures and equations supplemented by concise explanations. In most cases, this modular approach places a single topic on a page, and provides full coverage of that topic on that page. Highlights, insights, and rules of thumb are displayed in sidebars to the main text. The appendices at the end of each Field Guide provide additional information such as related material outside the main scope of the volume, key mathematical relationships, and alternative methods. While complete in their coverage, the concise presentation may not be appropriate for those new to the field. The SPIE Field Guides are intended to be living documents. The modular page-based presentation format allows them to be updated and expanded. We are interested in your suggestions for new Field Guide topics as well as what material should be added to an individual volume to make these Field Guides more useful to you. Please contact us at [email protected]. John E. Greivenkamp, Series Editor College of Optical Sciences The University of Arizona

Field Guide to Astronomical Instrumentation

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The Field Guide Series Keep information at your fingertips with the SPIE Field Guides: Adaptive Optics, Second Edition, Robert Tyson & Benjamin Frazier Atmospheric Optics, Larry Andrews Binoculars and Scopes, Paul Yoder, Jr. & Daniel Vukobratovich Diffractive Optics, Yakov Soskind Digital Micro-Optics, Bernard Kress Displacement Measuring Interferometry, Jonathan D. Ellis Fiber Optic Sensors, William Spillman, Jr. & Eric Udd Geometrical Optics, John Greivenkamp Holography, Pierre-Alexandre Blanche Illumination, Angelo Arecchi, Tahar Messadi, & John Koshel Image Processing, Khan M. Iftekharuddin & Abdul Awwal Infrared Systems, Detectors, and FPAs, 2nd Edition, Arnold Daniels Interferometric Optical Testing, Eric Goodwin & Jim Wyant Laser Pulse Generation, Rüdiger Paschotta Lasers, Rüdiger Paschotta Lens Design, Julie Bentley & Craig Olson Lidar, Paul McManamon Linear Systems in Optics, J. Scott Tyo & Andrey Alenin Microscopy, Tomasz Tkaczyk Nonlinear Optics, Peter Powers Optical Fabrication, Ray Williamson Optical Fiber Technology, Rüdiger Paschotta Optical Lithography, Chris Mack Optical Thin Films, Ronald Willey Optomechanical Design and Analysis, Katie Schwertz & James Burge Physical Optics, Daniel Smith Polarization, Edward Collett Probability, Random Processes, and Random Data Analysis, Larry C. Andrews & Ronald L. Phillips Radiometry, Barbara Grant Special Functions for Engineers, Larry Andrews Spectroscopy, David Ball Terahertz Sources, Detectors, and Optics, Créidhe O’Sullivan & J. Anthony Murphy Visual and Ophthalmic Optics, Jim Schwiegerling Field Guide to Astronomical Instrumentation

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Field Guide to Astronomical Instrumentation This Field Guide to Astronomical Instrumentation is the one book that the three of us would want to carry with us if we had to single-handedly design an astronomical instrument on a remote mountain top. To keep it concise, it focuses on the ultraviolet to infrared wavelength range. The Field Guide is not intended to serve as a textbook, but as a handy desktop reference to be found in the labs and offices of instrument builders. This book contains information on a wide range of topics, from fundamental physics to project management, and from technical concepts to material properties. Only the most important concepts and equations are presented here. In many areas, dedicated SPIE Field Guides discuss particular topics in much more detail. While we tried to maintain consistency with other volumes in this series, we wrote this Field Guide in the language that instrumental astronomers use, which might sometimes look strange to people working in other areas. A Field Guide that strives to cover such a wide variety of topics will naturally overlook some potentially relevant topics. We look forward to suggestions from our readers on how to improve this Field Guide for its next edition. Last but not least, we greatly appreciate the continuous support of our families in this endeavor. Christoph U. Keller Leiden Observatory, Leiden University, The Netherlands Ramon Navarro NOVA Optical & Infrared Instrumentation Division at ASTRON, The Netherlands Bernhard R. Brandl Leiden Observatory, Leiden University, The Netherlands

Field Guide to Astronomical Instrumentation

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vii

Table of Contents Glossary of Symbols and Acronyms General Optics Refraction, Reflection, and Transmission Polarization Brewster Angle and Total Internal Reflection Images, Pupils, and Beams Aberrations Diffraction Point-Spread Function Modulation Transfer Function Spectral Transfer Function

xi 1 1 2 3 4 5 6 7 8 9

Optical Elements Windows Lenses Mirrors Filters Colored Glass Filters Interference Filters Coatings Astronomical Bandpass Filters Prisms Gratings Polarizers Crystal Polarizers Waveplates Optical Fibers

10 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Detectors Detector Overview Intrinsic Photoconductors CCD and CMOS Detectors Extrinsic and Stressed Photoconductors BIB Detectors and (Avalanche) Photodiodes Bolometers Coherent (Heterodyne) Detectors CCD and CMOS Readouts Infrared Array Readouts

24 24 25 26 27 28 29 30 31 32

Field Guide to Astronomical Instrumentation

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viii

Table of Contents Detector Noise and Artifacts Detector Radiation Effects in Space Detector Flat Fielding

33 34 35

Telescopes and Imagers Telescopes Correctors and Wide-Field Imagers Focal Reducers Reimaging Optics High-Resolution Imagers

36 36 37 38 39 40

Spectrographs Spectrograph Overview Single-Slit Spectrometer Echelle Spectrometers Slitless Spectrometers Fabry–Pérot Interferometer Fourier Transform Spectrometer Integral Field Spectrometer Multi-object Spectrometer OH-Suppression Spectrographs Spectral Data Analysis

41 41 42 43 44 45 46 47 48 49 50

Polarimeters Rotating Waveplate Polarimeters Liquid Crystal Polarimeters Spectral Modulation Polarimeters

51 51 52 53

Interferometers Interferometer Principle and Angular Resolution Delay Lines Beam Combiners Fringe Visibility Fringe Tracking and Closure Phase Aperture Synthesis and (u,v) Plane Field of View and Sensitivity Image Processing

54 54 55 56 57 58 59 60 61

Field Guide to Astronomical Instrumentation

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ix

Table of Contents Coronagraphs Focal-Plane Coronagraphs Pupil-Plane Coronagraphs Space Coronagraphs

62 62 63 64

Adaptive Optics Adaptive Optics Atmospheric Turbulence: Seeing Wavefront Sensors Deformable Mirrors Adaptive Optics Control Laser Guide Stars Operation Modes

65 65 66 67 68 69 70 71

Optical Design Optical Design Principles Design Approach Ray Tracing Optimization Tolerance Analysis Stray Light Control and Baffles

72 72 73 74 75 76 77

Optomechanics Packaging Optics Mounts Mechanisms Actuators and Motors Sensors Mechanical Engineering for Space

78 78 79 80 81 82 83

Vacuum and Cryogenics Dewars Cooling Methods Thermal Models Thermal Effects in Space

84 84 85 86 87

Software and Electronics Control Instrument Control System

88 88 89

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Instrumentation

x

Table of Contents Data Handling Data Transfer from Space Data Analysis Overview Electronics: Cabling Shielding

90 91 92 93 94

Systems Engineering Systems Engineering: Requirements Definition Block Diagrams Interface Control Error Budgets Noise and its Distribution Signal-to-Noise Ratio Instrument Sensitivity and Integration Time Signal Sampling Project Management Technology Development Risk Management Quality Management

95 95 96 97 98 99 100 101 102 103 104 105 106

Manufacturing, Assembly, Integration, and Testing Optics Manufacturing Optics Testing Alignment Instrument Commissioning Operations and Maintenance

107 107 108 109 110 111

Appendices Optical Material Properties Mirror Substrate Material Properties Mechanical Material Properties Material Selection ISO 10110 Optical Drawing Standard ECSS

112 112 113 114 115 116 117

Equation Summary

118

Bibliography

125

Index

127

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xi

Glossary of Symbols and Acronyms 1D, 2D, 3D 4QPM A A A Aðu; vÞ AC ADC ADC AG AIT AIV AO APD APP AR B B BIB BLIP BS CC CCD CMOS CNC CP CTE CTE CWL d D d D d d d D DC

One-, two-, or three-dimensional system Four-quadrant phase mask Absorption Surface area Telescope aperture Amplitude of aperture function Alternating current Analog-to-digital converter Atmospheric dispersion corrector Aplanatic Gregorian Assembly, integration, and testing Assembly, integration, and verification Adaptive optics Apodizing phase plate Avalanche photodiode Anti-reflection Baseline of an interferometer Bias frame Blocked-impurity-band (detectors) Background-limited performance Beamsplitter Closed cycle cooler Charge-coupled device Complementary metal-oxide semiconductor Computer numerical control Closure phase Charge transfer efficiency Coefficient of thermal expansion Center wavelength Actuator spacing Dark frame Diameter Diameter Distance Grating groove spacing Lens thickness Telescope diameter Direct current Field Guide to Astronomical Instrumentation

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xii

Glossary of Symbols and Acronyms DHS DQE DSN E E e e ECSS Eg ELT EMC EMI ESA ESO ETC F F F f F f F F 1!2 FDR FEM FFBD fG FLC FSR FTS FWHM g G gD gI gP GLAO gP

Data handling system Detective quantum efficiency Deep space network Electrical field Energy Error signal Jones vector European Cooperation for Space Standardization Bandgap energy Extremely Large Telescope Electromagnetic compatibility Electromagnetic interference European Space Agency European Southern Observatory Exposure time calculator Finesse Flat-field frame Flux Focal length Focal ratio, f-number Frequency Fresnel number View factor Final design review Finite element model Functional Flow Block Diagram Greenwood frequency Ferro-electric liquid crystals Free spectral range Fourier transform spectrometer Full width at half maximum Gain Strehl ratio gain Derivative gain in a PID controller Integral gain in a PID controller Proportional gain in a PID controller Ground-layer adaptive optics Proportional gain in a PID controller

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xiii

Glossary of Symbols and Acronyms GR h H HEB HGA I I IBF ICD ICS ID IFS IFU IR IRR J J J0 J1 JWST k K K K k kn L L L2 LCVR LGS LHe LN2 LO LSST LVDT m M mbar

Generation-recombination Height of turbulence layer Near-IR atmospheric band Hot electron bolometer High-gain antenna Image Intensity Ion beam figuring Interface control document Instrument control system Dirty image Integral field spectrometer Integral field unit Infrared Integration readiness review Jones matrix Near-IR atmospheric band Zeroth-order Bessel function First-order Bessel function James Webb Space Telescope Angular frequency Conic constant Near-IR atmospheric band Temperature in Kelvin Wave number Normalized angular frequency Grating width Maximum path length difference Second Lagrangian point Liquid crystal variable retarders Laser guide star Liquid helium Liquid nitrogen Local oscillator Large Synoptic Survey Telescope Linear variable differential transformer Grating order, order of diffraction Mueller matrix Millibar pressure Field Guide to Astronomical Instrumentation

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xiv

Glossary of Symbols and Acronyms MCAO MEMS MKID MLI MOAO MOS MTF n n N N n N NA NASA neff NGS nm np ns o OCS OPD OTCCD OTF P p P P PðvÞ Pðx; mÞ PDR PEM PIAA PID PL PS PSF

Multi-conjugate adaptive optics Micro-electro-mechanical system Microwave kinetic inductance detector Multi-layer isolation Multi-object adaptive optics Multi-object spectrometer Modulation transfer function Index of refraction Noise Number of actuators Number of illuminated grooves Number of photons Number of telescopes Numerical aperture National Aeronautics and Space Administration Effective index of refraction Natural guide star Index of refraction of medium number of photons per m2 Index of refraction of substrate Object Observatory control system Optical path difference Orthogonal-transfer CCD Optical transfer function Degree of polarization Point spread function Poke matrix Pressure Instrumental profile Probability for value x around a mean m Preliminary design review Piezo-elastic modulator Phase-induced amplitude apodization Proportional-integral-derivative Degree of linear polarization Point source (diffraction limited) Point spread function

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xv

Glossary of Symbols and Acronyms Pt100, Pt1000 PTF PVA Q Q QA QC QMS r R R R R R&D r0 RAM RAMS RC RFI RMS ROI rp rs RVDT RX , RY , RZ S s S s SH Si SIS SL SNR STEP STF SUR T t

Platinum temperature sensor Phase transfer function Polyvinyl alcohol Heat transfer Stokes Q Quality assurance Quality control Quality management system Radial distance Radius of curvature Reconstructor Reflectivity Spectral resolution Research and development Fried’s parameter Risk assessment matrix Risk assessment and method statement Ritchey–Chrétien (telescope) Radio frequency interference Root mean square Region of interest Reflection amplitude for p-polarization Reflection amplitude for s-polarization Rotary variable differential transformer Rotation around X , Y , Z coordinates Science frame Sensor data Signal Stokes vector Shack–Hartmann wavefront sensor Silicon Superconductor–insulator–superconductor Seeing limited Signal-to-noise ratio Standard for exchange of product data Spectral transfer function Sample-up-the-ramp Temperature Thickness

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xvi

Glossary of Symbols and Acronyms t T T1, T2 TCS tD TDRSS TES tF TIR TIS TLR TMA tp TRL tS ts TX , TY , TZ u ðu; vÞ U UV V V v VPH W WBS WFS Wi x X, Y, Z y y Y z z a a a

Time Transmission Telescopes Telescope control system Dark frame exposure time Tracking and data relay satellite system Transition edge sensor Flat-field frame exposure time Total internal reflection Total integrated scatter Top-level requirements Three-mirror anastigmat Transmission amplitude for p-polarization Technology readiness level Science frame exposure time Transmission amplitude for s-polarization Translation in X , Y , Z coordinates Control signal Coordinates in Fourier space Stokes U Ultraviolet Fringe visibility Stokes V Wind speed Volume phase hologram Watt Work breakdown structure Wavefront sensor Weighting coefficient Path-length difference X , Y , Z coordinates Actuator position Distance from field center Yield strength Surface zag Zenith angle Linear polarization orientation Absorption coefficient Prism apex angle

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xvii

Glossary of Symbols and Acronyms a b g d d d d D DlFWHM Dl  h h u u u uB uB ui ui0 uisoplanatic uo ur ut l lB lc lc lfsr mm n s s s2control s2DM s2offaxis s2total s2WFS t

Incident angle on grating Reflected angle on grating Groove center to edge phase difference Phase change on total internal reflection Retardation in birefringent material Dispersion angle Angle of linear polarization OPD in an interferometer Filter transmission profile FWHM Spectral resolution element Emissivity Relative grating efficiency Throughput Half-angle Position or rotation angle Angular resolution in radians Brewster angle Blaze angle Angle of incidence Refracted angle of incidence Isoplanatic angle Angle of dispersed beam Angle of reflected beam Angle of transmitted beam Wavelength Blaze wavelength Center wavelength Cutoff wavelength Free spectral range micrometer Frequency Stefan Boltzmann constant Standard deviation Control system lag induced variance Fitting error induced variance Anisoplanatism wavefront variance Total wavefront variance Wavefront sensor induced variance Internal transmission Field Guide to Astronomical Instrumentation

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xviii

Glossary of Symbols and Acronyms t ti ts t0 f0 fobs fatmos fs wðu; vÞ w v

Frequency in Nyquist sampling Internal transmission Servo lag time Atmospheric coherence time Intrinsic phase Observed phase Phase shifted by atmospheric effects Angular slit width Phase of aperture function Wedge angle Angular frequency

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General Optics

1

Refraction, Reflection, and Transmission Much of optics relies on refraction and reflection at interfaces between media with different indices of refraction n1 and n2 . The incoming and reflected rays have the same angle with respect to the normal to the interface, ur ¼ ui . Snell’s law relates the angles of the incoming and refracted transmitted rays: n1 sin ui ¼ n2 sin ut The Fresnel equations define the (complex) amplitude transmission and reflection for s-polarized (electric field perpendicular to plane of incidence) and p-polarized (electric field parallel to plane of incidence) light. ts ¼

2 sin ut cos ui sinðui þ ut Þ

tp ¼

2 sin ut cos ui sinðui þ ut Þ cosðui  ut Þ

sinðui  ut Þ sinðui þ ut Þ

rp ¼

tanðui  ut Þ tanðui þ ut Þ

rs ¼

Arbitrarily polarized light with the electric field vector at an angle a to the plane of incidence has intensity reflectivity R and transmission T . R ¼ jrp j2 cos2 a þ jrs j2 sin2 a T¼

jn˜ 2 j cos ut ðjt j2 cos2 a þ jts j2 sin2 aÞ jn˜ 1 j cos ui p

In general, R þ T þ A ¼ 1, where A is the absorption at the interface. If the indices of both materials are real, there is no absorption at the interface. The internal transmission t of a homogenous material with absorption coefficient a and thickness t is described by the Beer–Lambert law, t ¼ eat . The internal absorption of optical materials is typically listed in terms of the internal transmittance ti (measured for a thickness ti ). The internal transmission of a homogeneous material ðtt Þ

can then be calculated as T internal ¼ ti i . Field Guide to Astronomical Instrumentation

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2

General Optics

Polarization The electrical field vector of an electromagnetic wave is E ¼ E x ex þ E y ey with unit vectors ex;y in the x and y axes. If the phase difference between E x and E y is 0 deg or a multiple of 180 deg, the wave is linearly polarized. A phase difference of 90 deg implies left or right circularly polarized light. Polarization is mostly described in terms of Jones or Stokes vectors. The complex Jones vector e contains the two complex electric field components E x and E y and describes fully polarized light. It cannot be measured directly. The addition of Jones vectors corresponds to the coherent superposition of waves.
 Ex e¼ Ey Stokes vectors can be measured directly and can describe partially polarized light. Stokes I is the intensity, Stokes Q corresponds to the difference between linear polarization at 0° and 90°, Stokes U is the difference between linear polarization at 45° and 135°, and Stokes V is the difference between left and right circularly polarized light. 3 0 1 2 E x E x þ E y E y I B C 6 E E  E E 7 BQC 6 y y 7 s ¼ B C ¼ 6 x x 7 @ U A 4 E x E y þ E y E x 5 iðE x E y  E y E x Þ V The addition of Stokes vectors corresponds to the incoherent superposition of quasi-monochromatic light waves. The qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 degree of polarization is defined as P ¼ ðQ þUI 2 þV Þ, where P ¼ 1 is fully polarized light, and P ¼ 0 is unpolarized light. The influence of a sequence 1: : : n of optical elements on polarized light is described by Jones matrices Ji or Mueller matrices Mi that act on Jones and Stokes vectors e and s, respectively, according to e 0 ¼ Jn Jn1 : : : J2 J1 e ⇌

s 0 ¼ Mn Mn1 : : : M2 M1 s

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General Optics

3

Brewster Angle and Total Internal Reflection When the incident beam is at the Brewster angle uB , tan uB ¼ n2 = n1 , the reflected light is completely s-polarized, and the transmitted light is moderately polarized. This occurs when the reflected wave is perpendicular to the transmitted wave, i.e., ui þ ut ¼ 90 deg. If a beam goes from a higher-index medium (n1 ) to a lowerindex medium (n2 ), total internal reflection (TIR) occurs for sin ui $ n1 =n2 . All light is reflected and none is transmitted. TIR induces a phase change d ¼ ds  dp between s- and p-polarized light. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
 tan

d ¼ 2

cos ui

sin2 ui 

n1 n2

2

sin2 ui

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4

General Optics

Images, Pupils, and Beams Astronomical object points at infinity come to a focus in the image plane where the object information is encoded in the position. A field stop limits the size of the image in subsequent image planes.

The aperture stop, aperture, or stop limits the rays that can pass through the optical system. A pupil is an image of the aperture. Light in one pupil point comes from different object points. In a pupil, the object information is encoded in the angle, not in the position. The entrance and exit pupils are the images of the aperture as seen from the object space and image space, respectively. The focal ratio or f-number is the focal length f divided by the aperture diameter D and is commonly written as, e.g., f =11 for a focal ratio of 11. For a cone of light with a maximum half-angle of u in a medium with index n, the numerical aperture NA is defined as NA ¼ n sin u. Vignetting describes the variation of the geometrical beam throughput as a function of the field position. It typically occurs when parts of an off-axis beam are blocked by something that is not in a pupil plane. In a converging beam, the rays come to a focus. In a diverging beam, the rays fan out as if they originated from a virtual focus. In a collimated beam, all rays coming from one object point are parallel. In a telecentric beam, the exit pupil is at infinity, and the image size is independent of the focus position.

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General Optics

5

Aberrations Aberrations are the departure of the exit pupil wavefront from a perfect spherical wave due to imperfections in the system. Aberrations are often characterized by the exit pupil wavefront error, the optical path difference (OPD), and are commonly described in terms of a superposition of fundamental modes, such as the third-order (Seidel) aberrations or the Zernike polynomials. The third-order aberrations can be divided into on-axis aberrations (focus, spherical) that occur for all image points and off-axis aberrations that only occur for image points away from the field center. The latter degrade the image quality (coma, astigmatism) and distort the image (field curvature, distortion). The third-order aberrations scale with the focal ratio or f-number F and the distance y from the field center.

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6

General Optics

Diffraction An aperture modifies a plane wave by multiplying its electric field amplitude and phase by a complex aperture function Aðu; vÞeifðu;vÞ , where u and v are the coordinates in the pupil. The amplitude A of the aperture function is often either 0 or 1. The phase f is the optical path difference introduced in the aperture. The Fresnel number F determines the resulting diffraction pattern, where F ¼ D2 =ðlzÞ, D is the diameter of the aperture, l is the wavelength, and z is the distance between the aperture and the point at which the beam is studied. In the near field, where F .. 1, Fresnel diffraction applies, a pattern that changes rapidly with distance from the aperture. In the far field, where F ,, 1, Fraunhofer diffraction applies.

In most astronomical instruments, it is sufficient to consider Fraunhofer diffraction because the instrument images the far field onto the focal plane, not because the image plane is physically far away from the exit pupil. In high-contrast imaging instruments, Fresnel diffraction effects can become important. If a plane wave falls onto the aperture, the scalar complex electrical field in the image plane is given by the Fourier transform of the complex aperture function. ZZ 2p Eðx; y; zÞ ¼ Aðu; vÞeifðu;vÞ ei lz ðxuþyvÞ dudv

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General Optics

7

Point-Spread Function The point-spread function (PSF) of an optical system is the image that it generates for a point source. Everything between the source and the image influences the PSF. The image i of an extended source can be determined by convolving the object o with the PSF p, if the PSF does not vary significantly over the image, ZZ iðx; yÞ ¼ o  p ¼ iðx 0 ; y 0 Þpðx  x 0 ; y  y 0 Þdx 0 dy 0 where * is the convolution operator. The PSFs due to diffraction at the most important types of apertures with x; y ¼ 2pdx;y sin u=l, u being the angle of incidence in the image plane, and l being the wavelength, are shown in the table.

In addition to diffraction, aberrations in the optical system, the Earth’s atmosphere, and scattered light contribute to the PSF. A frequently used radial profile is the Moffat PSF model: 
2 b r iðrÞ ¼ 1 þ a where a is a scaling factor and b is a shape factor. Single or multiple Gaussian profiles can also often approximate real PSFs. Field Guide to Astronomical Instrumentation

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8

General Optics

Modulation Transfer Function The optical transfer function (OTF) is the Fourier transform of the PSF and also the auto-correlation of the complex aperture function. With FT being the Fourier transform operator, and  the correlation operator,

OTF ¼ FTðPSFÞ ¼ FT½jFTðAeif Þj2  ¼ Aeif  Aeif The absolute value of the OTF is the modulation transfer function (MTF). Its value as a function of angular frequency indicates the reduction in amplitude of a sinusoidal image when passing through the optical system. For an unobscured, round aperture with diameter D, the MTF as a function of the normalized angular frequency kn ¼ klf =D (k being the angular frequency, l the wavelength, f the focal length, and D the aperture diameter) is

OTFðkn Þ ¼

2 ðcos1 kn  kn p

qffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1  k2n Þ

A central obscuration with diameter «D reduces the MTF at mid-frequencies and enhances it close to the cutoff frequency. The MTF of a good optical system can often be approximated by the product of the MTFs of the individual subsystems (e.g., telescope, fore-optics and camera optics). The approximation is precise if each individual subsystem acts upon an incoherent image. The argument of the OTF is the phase transfer function (PTF) such that

OTF ¼ MTF · ei·PTF Field Guide to Astronomical Instrumentation

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General Optics

9

Spectral Transfer Function The spectral transfer function (STF) is the equivalent of the optical transfer function (OTF) in the wavelength dimension. The STF is the Fourier transform of the slit function, which is the spectrum of a monochromatic light source. The STF is most useful in interpreting observed spectra in terms of real and instrument-induced signatures. The total STF of an incoherently illuminated spectrograph has contributions from the entrance aperture, the collimator and camera optics, the dispersing element, and the detector. If the slit function is symmetric, the STF is real.

The ideal spectral transfer function for a spectrograph that is limited by diffraction at the aperture of the collimator or the disperser is given by a triangle function that is zero beyond the cutoff frequency. If the size of the entrance slit limits the spectral resolution, the triangular STF is multiplied by a sinc function, which transmits beyond the first zero in the STF, even with the inverse sign. This can lead to spurious spectral effects, in particular when observing spectra with periodic spectral lines such as molecular spectra. The Fourier transform spectrometer has a top-hat STF.

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10

Optical Elements

Windows Windows are designed to minimize their influence on the transmitted light and separate environments that differ in composition, pressure, or temperature. Most windows are plane-parallel to avoid beam deviations, but lenses can also serve as windows. Surface coatings maximize the transmission. The wavelength range, diameter, mechanical properties, and cost determine the window material. Pressure differences and gravity are common forces that determine the diameter d to thickness t ratio (aspect ratio) d=t. To
 qffiffiffiffiffi Y avoid fracture with a safety factor of 4, choose dt , DP , where DP is the pressure difference (DP ¼ 0.1 MPa for vacuum), and Y is the window material yield strength (≈ 50 MPa for most glasses). Transmitted wavefront requirements may demand even smaller aspect ratios. Multiple reflections between the surfaces of a window lead to ghost images and spectral fringes (Fabry–Pérot effect). Antireflective coatings and/or a slight wedge reduce those effects. A wedge angle f will deviate a ghost image by an angle 3f=n.

Dl ¼ tðn2 –1Þ=ð8F 2 n3 Þ ðn2  1Þ=n3 .

and

A plane-parallel window of thickness t and glass with index n laterally moves the focus of a converging beam with f-number F by Dz ≈ tðn  1Þ=n, laterally displaces the beam by Dx ≈ ut ðn  1Þ=n, and introduces lateral spherical aberration of lateral astigmatism of Dl ¼ tu2

Temperature non-uniformities and stress birefringence in a window will introduce aberrations.

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Optical Elements

11

Lenses Lenses are transparent refracting optical elements made of glass or crystals. The wavelength range, the index of refraction, and the required diameter determine the lens material. Most lens surfaces have thin-film coatings to maximize transmission and minimize reflections.

The focal length ƒ of a spherical lens with index of refraction n in air, radii of curvature R1 and R2 , and center thickness d is given by the thick-lens equation.

  1 1 1 ðn  1Þd ¼ ðn  1Þ  þ f R1 R2 nR1 R1

The same focal length f can be achieved with different combinations of R1 , R2 , and d. Spherical aberration is minimized for conjugate points s 0 and s when

R1 ¼

2f ðn  1Þ qþ1

R2 ¼

2f ðn  1Þ q1

q¼

2ðn2  1Þ s 0  s · 0 nþ2 s þs

Lenses made of different materials can be combined to achieve better performance. Achromatic lenses minimize the focal length variation over a given wavelength range and almost always have better imaging properties than a single lens, even at a single wavelength. Athermal lenses keep the focal length stable over a large temperature range. Wide-angle lenses consist of several elements to reduce the off-axis aberrations of a single lens. Lenses change their properties with wavelength, temperature, and the index of refraction of the ambient medium. Field Guide to Astronomical Instrumentation

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12

Optical Elements

Mirrors Mirrors are reflective optical elements that change the direction and/or wavefront of a beam. Common mirror substrates are glass, aluminum, beryllium, and silicon carbide. The mirror coating determines the reflectivity. All optical properties of mirrors except for the reflectivity are independent of the wavelength and ambient medium. Compared to lenses, mirrors have only a single surface, and the surface tolerances are about two times more stringent. To minimize system aberrations, most mirrors are aspheric. Common surface shapes are conic sections, where the sag z of the mirror surface is a function of the conic constant K , radius of curvature R, and the distance r from the vertex.

0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 11 r2 @ r2 1 þ 1  ð1 þ K Þ 2 A z¼ R R

Conic mirrors image an on-axis object at infinity onto a point that is R=2 away from the vertex and perfectly image their far focus onto their near focus, and vice versa. Conic Section

Conic Constant K

Near Focus

Sphere Paraboloid Ellipsoid Hyperboloid

0 1 1 , K , 0 K , 1

R ½R pffiffiffiffiffiffiffiffi R=ð1 þ K Þ pffiffiffiffiffiffiffiffi R=ð1 þ K Þ

Far Focus

R infinity pffiffiffiffiffiffiffiffi R=ð1  K Þ pffiffiffiffiffiffiffiffi R=ð1  K Þ

Off-axis mirrors, in particular parabolas, are useful to avoid beam obscuration. Two or more mirrors with conic surface shapes can be combined to minimize off-axis aberrations in reflective systems.

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Optical Elements

13

Filters Filters are optical elements that change their transmissive, reflective, or absorptive properties as a function of wavelength. The filter transmission spectrum identifies them as bandpass filters, longpass filters, and short-pass filters. Dichroic filters are used at non-normal incidence in both transmission and reflection to separate two wavelength ranges. The following quantities are typically specified when ordering custom bandpass filters: • ambient medium, • temperature, • angle of designed),

incidence

(as

• center wavelength (CWL), • peak transmission (maximum percentage transmission within passband), • blocking (degree of attenuation outside of transmission band), and • full-width at half maximum (FWHM, width of the bandpass at one-half of maximum transmission).

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14

Optical Elements

Colored Glass Filters Colored glass filters are primarily used as long-pass and fairly broad bandpass filters between 300 and 1000 nm. Short-pass applications are limited to suppressing nearinfrared light. Schott, Corning, and Hoya produce most of the commonly used glass filters. Glass-filter properties are independent of the angle of incidence, temperature, and humidity.

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Optical Elements

15

Interference Filters Interference filters use thin-film coatings, often combined with a colored substrate, and provide great design freedom for the filter transmission, reflection, and polarization as a function of wavelength. Regular interference filters deteriorate due to humidity, show strong temperature dependence, and have limited peak transmission and blocking. Filters manufactured with ion-assisted deposition (IAD) have better performance in every respect, but come at a higher price. Interference filters are sensitive to the angle of incidence u, temperature T , and humidity. The change in central wavelength Dlc for u , 30 deg in a medium with index nm can be used to tune narrow-band interference filters with effective index neff and temperature sensitivity dl=dT (typically 0.01  0.2 nm=K ). ffi  sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  nm 2 2 1 DlðuÞ ¼ lc sin u  1 neff

­l Dlc ðDT Þ ¼ c DT ­T

Narrow-band interference filters are constructed from a number of Fabry– Pérot cavities. The filter profile as a function of the number of cavities can be approximated by T ðlÞ ¼

 1þ

2ðl  lc Þ DlFW HM

2n

cavities

1

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16

Optical Elements

Coatings Coatings are applied to optical elements to improve their reflection and transmission characteristics.

 R¼

Anti-reflection coatings are used on transmitting surfaces to minimize reflection at interfaces. For uncoated, common glass in air, there is a loss of about 4% per surface. The reflectivity of a bare substrate is given by

nm  ns nm þ ns

2

The narrower the wavelength range over which transmission must be controlled the smaller the reflectivity can be made. An optimal singlelayer coating has an optical thickness of l=4 with a material with an index of pffiffiffiffiffiffiffiffiffiffiffi refraction of n ¼ nm ns . Reflective coatings are mostly metallic. Aluminum, gold, and protected silver work over a large wavelength range. Purely dielectric, reflective coatings can have extremely high reflectivity over a relatively narrow wavelength range. Different coating materials are used for dielectric thinfilm coatings depending on the desired wavelength range.

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Optical Elements

17

Astronomical Bandpass Filters Most astronomical instruments use well-defined color bandpass filters to classify stars (Johnson, Cron-Cousins, Bessel), determine stellar properties (Stromgren) or classify faint galaxies (Thuan-Gunn, SDSS).

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18

Optical Elements

Prisms Prisms are glass wedges with a large apex angle a to maximize the dispersion. They are often used for low-resolution spectroscopy and as predispersers or cross-dispersers in high-resolution grating spectrographs. The angular dispersion of a prism is ­d sin a ­n ¼ · ­l cos uo cos ui0 ­l

sin ui0 ¼

sin ui n

sin uo ¼ n sinða  ui0 Þ

The spectral resolution R is maximized by using highdispersion (large dn=dl) glass. R¼

l ­d ¼ D2 Dl ­l

D2 cos ui0 cos uo ¼ D1 cos ui coso0

Prisms can be arranged such as to cancel the dispersion and provide anamorphic magnification or image rotation (Dove prism, K-prism).

Prisms using total internal reflection can be used to fold a beam with minimal losses. Combinations of prisms with different materials are used to compensate the dispersion of the Earth’s atmosphere (atmospheric dispersion corrector). Grisms are prisms with a grating on one of the surfaces where the prism and grating dispersions compensate each other for one particular wavelength. In a collimated beam, an image is replaced with its spectrum without deviating the beam. Field Guide to Astronomical Instrumentation

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Optical Elements

19

Gratings Gratings are transmitting or reflecting optical elements that disperse the light by diffraction on periodic structures. Maximum throughput is achieved by only changing the phase of the incoming wavefront. Reflection gratings have a periodic surface relief, while transmission gratings have a surface relief or a periodic change in the index of refraction [volume phase hologram (VPH) gratings]. For a given wavelength l and order m, the angles of the incoming beam a and outgoing beam b are related by the grating equation, from which one derives the angular dispersion db=dl and the spectral resolution R, which is proportional to the grating width L. ml ¼ dðsin a þ sin bÞ

db m ¼ dl d cos b

R¼m

L d

Grooves can be shaped (blazed) to maximize the throughput, which is achieved at the blaze angle ub and the blaze wavelength lb . ub ¼

aþb 2

lb ¼

2d sin ub cosða  ub Þ m

The grating efficiency (or throughput) is a function of wavelength and polarization and is often available from the manufacturer. At some wavelengths, the grating may be a complete linear polarizer (Woods anomaly). A rough approximation of the relative grating efficiency for a ≈ b is h¼

sin2 g g2

g ¼ 2pa

cos ub sinða  ub Þ l

Immersion gratings are on the backside of a high-index material, and increase the resolution for a given physical grating size. Echelle gratings have large groove spacing and are used in high orders (e.g., m ¼ 42). Field Guide to Astronomical Instrumentation

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20

Optical Elements

Polarizers Polarizers produce light with linear, circular, or elliptical polarization from unpolarized light. Wire-grid polarizers consist of parallel conducting wires with a spacing that is less than the wavelength. Wires are evaporated on a substrate or are freestanding. The transmitted polarization is linearly polarized perpendicular to the wires. Dichroic sheet polarizers consist of stretched polyvinyl alcohol (PVA) treated with iodine. The elongated iodine complexes act as small, conducting wires. Polarcor™ consists of glass with metallic, elongated nanoparticles that act as small, conducting wires. Crystal polarizers use the birefringence of specific crystals for the highest-quality linear polarizers. Polarizing cube beamsplitters use thin-film coatings to separate orthogonal linear polarization states. type

Crystal Polarcor Dichroic Cube Wiregrid

extinction ratio

.105 .104 150–104 .500 .100

pol. transmission

.90% .80% .75% .90% .90%

bandpass (nm)

full 150 200 200–400

acceptance angle (deg)

,8–25 ,20 ,20 ,10 ,20

The Jones and Mueller matrices of an ideal linear polarizer at position angle u are   cos u sin u cos2 u Jpol ðuÞ ¼ cos u sin u sin2 u 1 0 1 cos 2u sin 2u 0 1 B cos 2u sin 2u cos 2u 0 C cos2 2u C Mpol ðuÞ ¼ B 0A sin2 2u 2 @ sin 2u sin 2u cos 2u 0 0 0 0 The extinction ratio of a polarizer is defined as the ratio of intensities for two identical crossed and aligned linear polarizers. Field Guide to Astronomical Instrumentation

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Optical Elements

21

Crystal Polarizers Crystal polarizers rely on the anisotropy of the index of refraction to separate the incoming beam into two beams with precisely orthogonal linear polarization states. They can be constructed for ultraviolet UV to mid-infrared (IR) (16 mm) wavelengths. The Wollaston prism consists of two uniaxial crystal prisms with crossed optic axes. The divergence angles for a Wollaston with a prism apex angle V and birefringence (ne –no ) is deo ¼ 2ðne  no Þ tan V. It is most frequently used close to a pupil. A Savart plate consists of two birefringent crystal plates with their optic axes at a finite angle to the entrance surface. The second plate is rotated by 90 deg around the optical axis with respect to the first plate. It splits the beam into two parallel beams and is most frequently used close to a focal plane. The splitting is about 7.5% of the thickness for calcite and 0.42% for quartz. The crystal astigmatism in a converging beam can be compensated for with a half-wave plate between the two plates and a cylinder lens. The Foster prism consists of two crystal pieces with parallel optic axes. One polarization state passes without deviation, while the other beam is strongly deviated. In contrast to the Wollaston and the Savart plate, the beam divergence of the Foster prism is independent of the wavelength.

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22

Optical Elements

Waveplates Waveplates, also called retarders, delay the phase of one polarization state (linear, circular, or elliptical) with respect to the orthogonal state. Linear retarders are by far the most common and use birefringent crystals, stretched plastics, and TIR in prisms. The Jones and Mueller matrices for a linear retarder are

 Jr ðdÞ ¼

d

ei 2 0

0 d ei2



0

1 B0 Mr ¼ B @0 0

0 1 0 0

0 0 cos d sin d

1 0 0 C C sin d A cos d

Frequent retardation values are quarter-wave plates (d ¼ 90 deg, transforming linear into circular polarization, and vice versa) and half-wave plates (d ¼ 180 deg, rotating linear polarization without affecting circular polarization). These retardations require very thin birefringent materials, which are true zero-order retarders. To simplify manufacturing, most crystal waveplates are compound zero-order retarders that use two thicker plates with orthogonal crystal axes such that the effective retardation is the difference between the two plates. Achromatic retarders can be constructed by combining two different materials (bi-crystalline retarders) or by combining two or more plates of the same material with their crystal axes in different orientations (Pancharatnam retarders). Super-achromatic retarders combine the two approaches. Fresnel rhombs are highly achromatic as they use TIR. type

quartz MgF2 mica polymer Fresnel

accuracy (%)

0.4 0.4 4 0.6 2

wavelength range (nm)

180–2700 140–6200 350–1550 400–1800 240–2000

bandpass (nm)

100 100 100 100 330–1000

acceptance angle (deg)

,3 ,3 ,10 ,10 ,2

Variable retarders can be constructed from liquid crystals or be based on the Faraday, Kerr, or Pockels effects. Piezoelastic modulators (PEMs) work with stressed glass.

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Optical Elements

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Optical Fibers An optical fiber is a thin, flexible, transparent fiber made of high quality glass or plastic. The fiber consists of a core surrounded by a cladding layer with a lower index of refraction. Light is kept in the core by TIR, causing the fiber to act as a waveguide.

The numerical aperture (NA) of the fiber is the maximum acceptance angle and is related to the critical angle for TIR. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n2core  n2cladding NA ¼ sin umax ¼ nair Single-mode fibers have a narrow core of only a few wavelengths in diameter and can conserve polarization. It is easier to insert the light from astronomical targets observed with a large telescope in a multi-mode fiber with a relatively wide core. Bending and twisting the fiber might induce stress, which causes focal ratio degradation (FRD). FRD causes the light cone leaving the fiber to be broader than the light cone entering the fiber. Time-varying speckle patterns from a multi-mode fiber can cause problems in radial velocity observations. A uniform, stable light distribution can be achieved at the fiber output with a fiber scrambler. Insertion losses and attenuation determine the transmission of a fiber. Fiber ends must be aligned in both angle and position. Attenuation in fiber optics is caused by scattering and wavelength-dependent absorption.

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24

Detectors

Detector Overview Detectors of electromagnetic radiation are key elements of almost any astronomical instrument. Most modern detectors are electronic devices made of multiple photonsensitive detector elements (pixels). The most important criteria concerning detectors are as follows: • detective quantum efficiency (DQE): number of photons converted into signal/number of incoming photons, • wavelength range over which the detector is responsive, • format and number of pixels, • energy resolution, • temporal stability, • linearity of the response and full well capacity, and • polarization sensitivity. Based on their physical principle, detectors can be subdivided into two categories: direct photon detectors, which respond directly to individual photons, and coherent detectors (such as heterodyne receivers), which respond to the electrical field strength. Direct photon detectors can be further subdivided into quantum detectors (photoconductors, like CCDs and photodiodes) and thermal detectors (bolometers). The sensitive material of photoconductors is based on either intrinsic or extrinsic semiconductor materials. Numerous materials and detection principles are available to cover a wide range, from x-rays to radio waves.

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Detectors

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Intrinsic Photoconductors While, historically, the photographic plate has been the detector of choice for many decades, it has been replaced by solid state devices, which provide much higher quantum efficiencies. Photoconductors are being used from x-ray to infrared wavelengths and respond directly to individual photons. Almost all intrinsic photoconductors are crystals with diamond lattice structure, in which each atom bonds to four neighbors. Such crystals can be formed by elements with four valence electrons (group IV of the periodic table, e.g., Si, Ge), as well as III-V semiconductors (e.g., GaAs, InSb) and II-VI semiconductors (e.g., CdTe). Since the atomic wave functions in a semiconductor overlap, the discrete energy levels split, due to the Pauli principle, in energy bands. In its ground state, the valence band is completely filled (eight valence electrons of each atom in the diamond lattice). The conduction band, the next higher energy band, is unoccupied and energetically separated by a bandgap E g . If a photoconductor absorbs a photon with energy hv . E g , an electron can be lifted from the valence to the conduction band. Once in the conduction band, the electron is only loosely bound, and applying an electric field to the photoconductor (pixel) will drive the electron to an electrode where it can be detected. The amount of collected charge is then proportional to the detected photon flux. However, a photon with energy hv , E g cannot produce a photocurrent, and the width bandgap E g defines the cutoff wavelength lc of the photoconductor according to lc ¼

hc 1.24 mm ¼ Eg E g ½eV

Cutoff wavelengths for some materials include GaAs Silicon Germanium InSb

common photoconductor 0.9 1.1 1.9 4.9

mm mm mm mm

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26

Detectors

CCD and CMOS Detectors Charge coupled devices (CCDs) are the most common detectors in astronomical instruments. They are based on intrinsic silicon photoconductors collecting the photo-electrons in potential wells, and work from x-rays to the silicon bandgap at 1.1 mm. The quantum efficiency, in particular at blue wavelengths, is maximized by back-illuminated CCDs. The longer distance to the depletion region (compared to front-illuminated CCDs) requires the CCD to be thinned. Antireflection coatings on the silicon further increase the quantum efficiency. An important performance parameter of CCDs is the charge transfer efficiency (CTE) at which charges are transported from one pixel to the next during the readout. CMOS (complementary metal-oxide semiconductor) detectors are the norm in consumer and even professional photography products and are starting to show up in astronomical instruments and form the basis for the multiplexers in infrared arrays. Like CCDs, CMOS devices can be thinned and illuminated from the backside to provide high quantum efficiency. Advantages of CMOS over CCD: • Less expensive due to standard semiconductor fabrication • Much lower power consumption • Faster readout due to on-chip camera electronics • Random access to regions of interest • Higher tolerance to pixel saturation • Higher radiation tolerance Advantages of CCD over CMOS: • Higher quantum efficiency, reaching close to 100% • Larger full-well depth for larger dynamic range • Sub-electron readout noise with electron-multiplying CCDs (EM-CCD) • Binning of electrons Field Guide to Astronomical Instrumentation

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Detectors

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Extrinsic and Stressed Photoconductors The wavelength coverage of photoconductors can be extended to longer wavelengths by reducing the width of the bandgap. This can be achieved by doping an intrinsic group IV photoconductor with group III or V atoms at very low concentration in a controlled process. Replacing a small amount of silicon or germanium atoms in the crystal lattice with group V atoms (five valence electrons) will add “surplus” electrons at a state just below the conduction band, and we get an n-type photoconductor. Similarly, doping with group III atoms (three valence electrons) will create an energy state just above the valence band in the p-type crystal lattice. As the gaps between these states and the corresponding bands are much smaller than the gap between the bands themselves, a lower-energy photon is required to create a mobile charge (electron or hole). Since these properties are determined by the impurities, we speak of extrinsic photoconductors. The resulting cutoff wavelengths for extrinsic Si- and Ge-based photoconductors are typically one to two orders of magnitude longer than for intrinsic materials: Si∶As 23 mm Si∶Sb 29 mm

Ge∶Ga Ge∶Sb

115 mm 129 mm

In order to achieve responsivities beyond 130 mm, physical stress of several hundred N=mm2 can be applied on the crystal (preferentially along the [100] axis of the diamond lattice), which further reduces the energy required to “break” the bonds in a p-type photoconductor. Applying physical stress to a Ge:Ga photoconductor will extend its cutoff wavelength from 115 mm to about 200 mm. Unfortunately, mobile charges can also be created by thermal excitation within the photoconductor itself. This strongly temperature-dependent effect creates an undesired dark current, which increases with smaller bandgaps. Hence, most extrinsic photoconductors require efficient cooling to operating temperatures of only a few K. Field Guide to Astronomical Instrumentation

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Detectors

BIB Detectors and (Avalanche) Photodiodes A fundamental problem of extrinsic photoconductors is their low absorption coefficient due to the low doping levels. However, increasing the doping levels would substantially change their electrical properties and lead to high dark currents. Blocked-impurity-band (BIB) detectors use different layers to optimize the optical and the electrical properties independently. The photons are absorbed in the heavily doped IR-active layer, which is attached to a thin blocking layer of high purity (intrinsic photoconductor). Common devices are Si∶As or Si∶Sb BIBs. Photodiodes are based on a junction between two oppositely doped zones that create a depletion region with high impedance. Photons will be absorbed in either the p- or n-type region. A bias voltage drives the resulting photoelectrons across the depletion region, creating a photocurrent. Common devices are Hg1x Cdx Te arrays, where the relative amount of Hg=Cd is varied to tune the cutoff wavelength lc . Common cutoff wavelengths are 1.75 mm, 2.5 mm, 5.3 mm, and 12 mm. Avalanche photodiodes (APDs) use a high bias voltage that accelerates the photo-electrons to kinetic energies that generate additional electron–hole pairs by collision, which in turn are also accelerated. Hence, the number of photo-electrons created per absorbed photon is much larger than unity. Since the charge collection occurs very quickly, APDs are often used when high temporal resolution is important. Other important types of detectors for submillimeter wavelengths, based on superconducting materials, are transition edge sensors (TES) and microwave kinetic inductance detectors (MKIDs).

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Detectors

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Bolometers Bolometers thermalize the kinetic energy of an absorbed photon. Since there is no distinct minimum energy, bolometers have no physical cutoff wavelength and are thus common detectors at far-infrared and submillimeter wavelengths. A bolometer has two functional components: a photon absorber with high cross-section, and a sensitive thermometer.

The absorber, typically a highly doped semiconductor, is connected via a weak thermal link to a heat sink that provides the reference temperature. In order to measure the temperature, an electronic system detects the absorber resistance, which depends on the temperature, which depends on the absorbed photon flux. While small absorbers with low heat capacity provide the strongest signal, small sizes lead to low quantum efficiencies. One solution is composite bolometers, which use a physically larger absorber of small heat capacity (e.g., blackened sapphire or a metal film) to which the thermometer is attached. The bolometer design has been revolutionized by precision etching techniques in silicon, which make it possible to produce bolometer arrays with hundreds to thousands of pixels. Although bolometers have no physical wavelength cutoff, the detection of photons becomes increasingly difficult with longer wavelengths (lower energies), and most bolometers require very low operating temperatures of typically only a few hundred mK.

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Detectors

Coherent (Heterodyne) Detectors Coherent detectors (or heterodyne receivers) are mainly used at submillimeter and radio wavelengths. Unlike direct photon detectors, they respond to the electrical field strength and preserve the phase information.

The source signal of frequency vS is combined with a reference wave of similar frequency vLO . The reference wave is provided by a local oscillator (LO). The beam combination produces a down-converted intermediate or beat frequency at the difference frequency vS  vLO (and vS þ vLO ), which is typically several orders of magnitude lower and can be handled by existing electronics. The signal is extracted by a so-called mixer, a nonlinear device that converts the power from the original frequencies to the beat frequency. Suitably fast devices that can be used as mixers are Schottky diodes, superconductor– insulator–superconductor (SIS) junctions, and hot electron bolometers (HEBs). Since the power of the LO can be controlled, the resulting down-converted signal can be easily amplified. While the bandwidth is limited to less than one octave per channel, heterodyne receivers are by design ideally suited for highresolution spectroscopy. Since the beam combination depends on the polarization of the signal wave with respect to the LO, many heterodyne receivers have two receivers per frequency band, one for each linear polarization.

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CCD and CMOS Readouts CCDs collect the photo-electrons in potential wells during the exposure. During the readout, these potential wells move the electrons physically, step-by-step along the pixel rows to one or more readout capacitors at the edge of the array. [A special case is orthogonaltransfer CCDs (OTCCDs), which can move the charges in any direction]. A readout always terminates an exposure. The charge-moving capability also enables binning, where charges from several pixels are combined before the readout. By covering one-half of a CCD with an opaque layer, an image can be read out while the next image is being exposed (frame transfer). An EM-CCD has an electron-multiplying stage before the readout that multiplies the number of electrons and thereby provides higher signal-to-noise ratios. Unlike CCDs, each pixel of a CMOS array contains its own charge-to-voltage conversion and reset electronics. Each pixel can be individually controlled and addressed via row and column selection lines, which allows the definition of complex regions of interest (ROIs) during the readout. Binning of electrons is not possible. CMOS detectors often include analog-to-digital converters (ADCs) and drivers to operate the device as a detector array, and form the basis for the multiplexers in infrared arrays.

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Detectors

Infrared Array Readouts Unlike CCDs, which are based on monolithic silicon structures, most infrared arrays are hybrids, consisting of a photoconductive layer and a multiplexer that are “sandwiched” together. Very similar to CMOS detectors, the multiplexer circuit enables direct reads and resets of individual pixels. In order to speed up the readout, larger arrays are subdivided into quadrants or up to 64 channels, which are operated in parallel by separate electronics. An important feature of the direct access is the possibility to read a pixel value repeatedly or nondestructively during an exposure, enabling several common readout schemes: Single sampling simply resets the pixel and reads its charge at the end of the exposure. It measures the absolute signal level (which may be important close to saturation) but does not remove the reset noise. Reset-read-read resets the pixel, reads its initial state, and reads the value at the end of the exposure. The difference between the two reads eliminates the reset noise but requires frame storage. For CCDs, a similar improvement can be achieved by subtracting a “bias” frame. “Fowler sampling” is similar to reset-read-read, but both reads are repeated n times consecutively. The signal is simply the difference between the two means of p the ffiffiffi two multiple reads, which reduces the read noise by n with respect to single reads. Sample-up-the-ramp reads the pixels value n times at a constant rate during the exposure. A linear fit to the read values yields the slope, which represents the signal. In pffiffiffi addition to reducing the read noise by n, the fitting can be used to detect and remove spurious events, like cosmic ray hits, which alter the pixel value during an exposure. Hence, sample-up-the-ramp is particularly important for detectors in space, but requires long exposure times and produces large data volumes.

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Detector Noise and Artifacts Generally, detectors suffer from fundamental and devicespecific sources of noise. The main sources of noise are: Generation-recombination (G-R) noise, which is the fundamental statistical noise due to the Poisson statistics of the photon arrival times and is transferred into the statistics of the photo-electrons. Johnson or kTC noise is the fundamental thermodynamic noise due to the thermal motion of the charge carriers and is also called read or reset noise. 1=f noise describes a frequency-dependent noise component that has many sources such as crystal defects, JFETs, temperature fluctuations, bad electrical contacts, surface damage, etc. To achieve the best possible background-limited performance (BLIP) in a given astronomical observation, the noise introduced by the detector should be less than the fundamental noise given by the photon statistics: hI 2GR i .. hI 2J i þ hI 21=f i In addition, numerous detector artifacts and imperfections contribute to the noise: The charge transfer efficiencies (CTEs) in CCDs describe how efficiently charges are transported from pixel to pixel. CTEs below 100% result in lower SNR. Dead, hot, and rogue pixels provide either no or very unreliable information. Mitigation involves redundant measurements and reduced detector bias voltage. Dead pixels in CCDs lead to dead pixel rows or columns. Residual or latent images result from local overexposures and require wait time, frequent resets, and, if possible, detector annealing. Very bright sources often lead to pronounced stripes and bands, referred to as pulldown and banding. Detectors in spectrographs often show fringing when the light reflects off of the back surface of the detector and interferes with the incoming light, leading to a regular interference pattern along the dispersion direction. Field Guide to Astronomical Instrumentation

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Detector Radiation Effects in Space The harsh radiation environment in space can cause two main effects in sensitive detectors and electronics: first, the passage of a particle leads to ionization, which increases the number of trapped charges (i.e., the signal); and, second, the energetic particles collide with atoms of the crystal lattice (displacement damage). While ionization can be calibrated out to some extent by median-filtering many exposures or using nondestructive sample-up-the-ramp (SUR) readout modes, displacement damage typically leads to an increase in dark current (hot pixels) or decreased CTE. In about 80% of these cases, hot pixels can be repaired by annealing, i.e., heating the detector significantly above the operating temperature. Reducing the bias voltage also improves the cosmetic quality of the detector, albeit at the cost of lower quantum efficiency. The radiation consists of charged energetic particles (protons, electrons, heavy ions) from the Sun, and cosmic rays from energetic sources in our Galaxy. Most of the near-Earth radiation is confined to the Van Allen radiation belt, where electrons and protons of energies of 0.01–500 MeV, with mean particle energies 50 MeV, spiral around the Earth’s magnetic field lines. The Van Allen belt reaches its maximum at 1–3 REarth (Earth radii) with several thousand protons=cm2 =s having energies above 100 MeV. At larger distances from Earth, e.g., at the Sun–Earth Lagrangian L2 point (1.5 · 106 km from Earth), the radiation environment is much weaker, but still noticeable at approximately five primary energetic particles=cm2 =s. Shielding with aluminum of thicknesses up to 25 mm reduces radiation effects. Thicker shielding is counterproductive as it generates more secondary particles of lower energy inside the shield, leading to an increased particle density. A very massive shield of thick lead is usually ruled out by the required opening angle of the optical system and requirements on minimum launch mass for space missions. Field Guide to Astronomical Instrumentation

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Detector Flat Fielding The achievable sensitivity of any observation depends largely on how well the individual pixel response is known. The relative correction factors to account for pixel-to-pixel variations is called flat field and can be derived from the difference of two exposures with different flux levels F 1 and F 2 , normalized by the median flux level: 1  F1  F2 flat field ¼ medianðF 1  F 2 Þ The different flux levels are commonly provided as dome flats (observing an illuminated screen within the telescope dome), twilight flats (observing the sky twice during sunrise or sunset), or sky flats (where F 1 is the “sky” from the observations and F 2 can be a “dark” frame).

Good flat fields provide a detector flatness at the level of 10–3 to 10–4 . Further improvements in flatness can be achieved by dithering the field of view with small offsets between exposures, and averaging the aligned, stacked images. Generally, for technical reasons, the longer the wavelength range for which the detector has been designed, the lower the time stability of the flat field. While CCD flat fields are constant over long time periods, gain instabilities in infrared detectors may require more frequent measurements, e.g., by beam chopping.

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Telescopes and Imagers

Telescopes Instruments and telescopes form a unit. Telescopes also define the optical interface for instruments that are attached to them. To design instruments, one needs to understand the telescope optics. Furthermore, telescopelike optics is also useful to collimate or focus a beam. Simple mirror telescopes contain only a parabolic primary, which provides an image free of spherical aberration but suffers from off-axis coma. This also holds for Cassegrain/ Gregorian telescopes, which use parabolic primary mirrors and hyperbolic/elliptical secondary mirrors to significantly magnify the image. The Ritchey–Chrétien (RC)/aplanatic Gregorian (AG) uses slightly hyperbolic/elliptical primaries to simultaneously eliminate spherical and coma aberration and enlarge the field of view by about a factor of two compared to the classic Cassegrain. Most modern telescopes are of the RC type, as the AG design has a larger secondary obscuration and is physically longer. Three-mirror anastigmats (TMA) provide even larger fields of view by eliminating the off-axis astigmatism of RC/AG telescopes. TMAs are found in modern, compact instruments such as collimators and camera optics. All of these designs can also be used off-axis when an unobscured aperture is required.

From an instrument designer’s point of view, the most important aspects of a telescope are the f-number, the focal length, the field curvature, the instrument location (prime focus, Cassegrain, Nasmyth, coudé), and the telescope pupil shape. Field Guide to Astronomical Instrumentation

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Telescopes and Imagers

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Correctors and Wide-Field Imagers Catadioptric telescopes combine reflecting and refractive components to achieve very large fields with compact designs. The Schmidt design uses a full-aperture, aspherical corrector and a spherical primary, while the Maksutov design uses a spherical meniscus corrector. The glass corrector limits the achievable aperture size and wavelength range.

For large apertures, the transmitting correctors or field lenses are located in the converging beam close to the focus. In two-mirror telescopes, corrector lenses can significantly reduce the off-axis astigmatism, field curvature, and distortion and can even produce almost telecentric beams, which greatly simplifies the design of spectrographs and narrowband imagers. Instruments that require a very large field of view are most often located in the prime focus of a telescope where the magnification is small. As the primary mirror of a two-mirror telescope is almost always slightly hyperbolic, a prime-focus corrector needs to correct the spherical and coma aberrations of the primary mirror in addition to the off-axis astigmatism and field curvature. Field curvature and distortion are easily corrected by a field lens close to an image plane, which does little except for compensating for the field curvature and the distortion of the telescope. To correct other aberrations, the lenses need to be strongly curved due to their proximity to the focus. The design of correctors is simplified when aspherical surfaces can be manufactured.

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Focal Reducers Instruments often do not require diffraction-limited angular resolution. As detector size is a major cost driver for imagers, it is often useful to reduce the image scale of the telescope with a focal reducer. In addition, a focal reducer may also act as a corrector to provide better image quality over a larger field of view. Focal reducers consist of a collimator that reimages the telescope pupil and a camera that focuses the image onto the detector. Both collimator and camera optics may consist of several transmitting elements or mirror telescopes. The focal reduction is given by the ratio of the focal lengths of the collimator to the camera optics.

The intermediate pupil image where the beam is collimated provides an excellent location for filters, grisms, polarization optics, and atmospheric dispersion correctors. The ray angles in the pupil plane are magnified compared to the telescope entrance pupil. The magnification is given by the ratio of the diameters of the telescope entrance pupil and the pupil image in the focal reducer. Focal reducers should always be designed with at least two optical elements. While a single lens or elliptical mirror could be used to reduce the focal length, this would lead to the exit pupil and the final image being very close together. With two optical elements, the exit pupil location can be controlled and aberrations can be reduced.

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Reimaging Optics Instruments often require transfer or reimaging optics to bring an image to another location such as the outside of an instrument where a detector can be attached, to provide an intermediate pupil plane where a cryogenic cold-stop can be inserted, or to adapt the image scale to the pixel size of a detector. Focal reducers and magnifiers are particular types of reimaging optics. As the reimaging often requires little or no change in magnification, specific solutions have been developed for that case. The double-Gauss design consists of two identical, mirrored combinations of a positive lens and a negative meniscus lens. The system’s symmetry and the distribution of power over four surfaces provide good image quality even for fast beams. Many more-complex versions of this basic design with more surfaces exist. An excellent reflective reimager is the Offner relay, an arrangement of two spherical mirrors. The Offner design is particularly attractive for rectangular fields, as the image quality is constant on circles around the symmetry axis of the Offner. Elliptical mirrors reimage one focus of the ellipse to the other focus, an approach often used in illumination applications. When the field of view is considerable, TMAs provide excellent performance. If the magnification in two orthogonal directions needs to be different, such as in a spectrograph, anamorphic magnification can be provided by prism pairs.

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Telescopes and Imagers

High-Resolution Imagers High-resolution imagers look at very small fields of view with diffraction-limited angular resolution. As the field is small, intrinsic aberrations are negligible and parabolic mirrors, often used off axis, provide diffraction-limited collimation, magnification, and focusing independent of wavelength. As atmospheric seeing is typically the limiting factor, high-resolution imagers include adaptive optics.

High-resolution imaging requires the correction of the atmospheric dispersion, which is induced by the differential refraction of air and depends on the wavelength, the zenith angle of the object, the temperature, the pressure, and the humidity. An atmospheric dispersion corrector (ADC) compensates for this variable dispersion. The most common ADC design employs two identical prism combinations that rotate against each other to adjust the amount of correction. Each prism combination consists of two prisms made from different materials such that the central wavelength is not deviated.

The longitudinal or linear ADC design consists of two wedge plates where one is close to the focus and the other is moved along the optical axis to adjust the amount of correction. Field Guide to Astronomical Instrumentation

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Spectrographs

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Spectrograph Overview A spectrograph (or spectrometer or spectroscope) is a device that disperses the incoming light into a wavelength or frequency spectrum. The main components of most spectrometers are: • a slit in the focal plane onto which the light to be analyzed is being focused, • a collimator, which produces a collimated, quasi-parallel beam, • a disperser, an optical element like a prism or grating that spectrally disperses the light, and • a camera, which focuses the dispersed light onto a detector (i.e., it provides a dispersed image of the slit on the detector).

The main characteristics of a spectrometer are: • its spectral resolution or spectral resolving power: l R ¼ Dl , where Dl is called a spectral resolution element, • its instrumental profile PðvÞ, which broadens the intrinsic line width I 0 ðvÞ to the observed line width: IðnÞ ¼ PðnÞ  I 0 ðnÞ, which determines the spectral resolution element Dl, ðnÞ , which is often only  10% • its throughput, hðnÞ ¼ IIout in ðnÞ due to the large number of optical components.

For unresolved lines ½I 0 ðvÞ , PðvÞ, the line-to-continuum pffiffiffiffi ratio, and hence the signal-to-noise ratio, increases with R. Inserting a disperser in the optical system may change the image scale in the dispersion direction, leading to anamorphic magnification. Field Guide to Astronomical Instrumentation

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Spectrographs

Single-Slit Spectrometer The simplest concept of a spectrometer uses a single narrow slit that produces data products with spatial information in one dimension along the slit and spectral information in the dispersion direction, usually orthogonal to the slit major axis. The disperser can be a grating, a prism, or a grism. The achievable spectral resolution of a grating spectrometer is given by R ¼ lmN Dfs , where l ¼ wavelength, m ¼ order of diffraction, N ¼ number of illuminated grating grooves, D ¼ telescope aperture diameter, and fs ¼ angular size of the slit on the sky. For a given fs (e.g., seeing-limited) and constant resolution R, the size of the spectrometer increases proportionally to the telescope diameter D. For telescopes operating at the diffraction limit (slit size l=D), this does not apply. Large spectrographs are often located at the coudé or Nasmyth focus to provide a gravity-stable rest, at the expense of image rotation as the telescope tracks. The spectral calibration of single-slit spectrometers is relatively simple since the long slit usually covers spectra of the background “sky” to be subtracted, and the source can be placed in different locations along the slit, improving the flat fielding. Sometimes, a so-called Dekker mask is used to cover certain parts of the slit. Single-slit spectrometers are popular because they are relatively simple and have high throughput, but they provide spectra for only a one-dimensional cut across the target of interest, which, in many cases is rather inefficient in time and usage of detector pixels.

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Echelle Spectrometers m According to the grating equation db dl ¼ a cos b, one can obtain high dispersion by either operating the grating at very high diffraction orders (m $ 50), or decreasing the factor a cos b, which requires high groove density (small groove spacing a, while a must be larger than l) and large angles of incidence (b ! 90 deg). Gratings operated under large angles of incidence are called Echelle gratings.

For high efficiency, the incoming and the reflected ray should have about the same angle (a ≈ b ≈ u). Under these conditions, the spectrometer operates in Littrow configuration and the grating equation becomes mlB ¼ 2a sin u. A fundamental quantity of spectrometers is the free spectral range (FSR), which is the maximum Dl for which successive orders do not overlap and is given by l lfsr ¼ max mþ1 At high orders m, lfsr becomes too small. However, the spectral overlap can be avoided by spatially separating the diffraction orders by means of a so-called pre-disperser, a lowdispersion prism or grating. Since the predispersion direction is perpendicular to that of the primary disperser, it is also called a cross-disperser. The design must ensure that the spectral overlap of the orders at their ends is sufficient to reconstruct a continuous spectrum. Echelle spectrometers uniquely provide high spectral resolution and efficient use of detector pixels, but their more complex optics yields more scattered light and lower efficiency. Field Guide to Astronomical Instrumentation

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Spectrographs

Slitless Spectrometers A slitless spectrometer does not preselect the input to the dispersing element (typically a low-dispersion element like a prism or grism) by a slit or mask. Hence, each point in the field is being dispersed, and the spectra overlap. Slitless spectrometers are well suited for observations of targets for which the position is not sufficiently known. In particular, “blind surveys” for objects with a strong emission feature (e.g., the Ha line) or objects with unusual spectra use slitless spectrometers. However, slitless spectrometers have several fundamental limitations. Since the spectra overlap, these spectrometers can only be used for fields with low source density. Also, because objects outside the center of the field provide sufficient spectral coverage, the number of resolution elements must be much smaller than the number of detector elements. As a result, the angular dispersion and spectral resolution are small. Furthermore, due to the spectral overlap, an extended source will show lower spectral resolution than a point source since the width of a strong emission line will be broadened by the spatial extent of the source. Finally, slitless spectrometers are only suitable for low-background applications. If the flat spectrum of a source contains n resolution elements spread over 2n pixels, each pixel will see the source signal but also 2n times the background flux, requiring the source to be brighter than the background times the spectral resolution. One can distinguish between objective and non-objective prism spectrographs as follows. In objective prism spectrographs, a prism is placed directly in front of the telescope objective, which requires a dispersing element the size of the aperture and is only possible for small telescopes. In a non-objective prism spectrograph, the dispersing element is placed in the converging beam near the focal plane. Both concepts provide relatively low dispersion.

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Fabry–Pérot Interferometer If the spectral information is of interest for objects over a larger field but only for a narrow spectral range (e.g., one spectral line), one may consider spectral interference filters, preferentially placed in a collimated beam near the pupil. However, the resolving power l=Dl of interference filters is typically only a few hundred, and the narrow bandpass is defined by design. A more flexible solution, which also provides higher spectral resolution, is the Fabry–Pérot etalon. Here, a pair of partially reflective, flat optical plates (of reflectivity R and transmission T ¼ 1  R), which are slightly wedged, are separated by a distance d. In a Fabry–Pérot interferometer, the distance d, and hence the operating wavelength l, can be tuned. Light that is being reflected numerous times between the inner surfaces of the two plates will experience constructive interference (and maximum transmission) when 2d cosðui Þ is an integer multiple of the wavelength l. Due to the small free spectral range lfsr , a Fabry–Pérot interferometer requires pre-sorting filters. The ratio between free pffiffiffi spectral range and line width is called finesse, F ¼ p1RR and the corresponding spectral resolution is given by l=Dl ¼ m · F, where m is the order of the interferometer. Fabry–Pérot interferometers are best suited for single-line spectroscopy of an extended object or multiple objects within the field of view. However, a fundamental problem is that the transmitted wavelength shifts with the angle of incidence ui . In a collimated beam, different angles ui correspond to different field points. Hence, the central wavelengths l varies across the field of view. Since line scans require different settings of d, the emission line and the adjacent spectral continuum are recorded at different times, which may cause calibration issues. Field Guide to Astronomical Instrumentation

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Spectrographs

Fourier Transform Spectrometer A Fourier transform spectrometer (FTS) is a classical Michelson interferometer with a variable path length L and detectors and beamsplitters appropriate for the considered spectral range. The change in path length occurs with constant velocity or by stepping, the latter enabling imaging FTS instruments. Hence, an FTS measures one Fourier component of the spectrum at a time. For a source with a spectrum BðkÞ between k1 and k2 and wave number k ¼ 2p=l, the intensity at the output of the FTS as a function of the path-length difference x between the two arms is Z Z 1 k2 1 k2 BðkÞ cosðkxÞdk I0 ¼ BðkÞdk IðxÞ ¼ I 0 þ 2 k1 2 k1 The FTS output has a constant offset I 0 , an intensity that is averaged over the spectrum, and a term that is modulated by the path-length difference. The spectrum BðkÞ is recovered from the Fourier transform of IðxÞ  I 0 . An FTS yields absolute wavelength measurements, limited only by the accuracy of the path-length difference measurement. The spectral resolution R of an FTS is determined by its largest path-length difference L and given by: R¼

2L l

It is independent of the size of the entrance aperture. An FTS has high throughput and can provide spectral information on multiple sources within the field of view simultaneously.

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Integral Field Spectrometer An integral field spectrometer (IFS) provides spectral information l for each spatial element within a contiguous, but usually small, two-dimensional field ðx; yÞ. Since the information density of ðx; y; lÞ is high and the optics is complex, an IFS typically covers fields of view of only a few arcseconds in size. However, IFSs are ideally suited to take spectra of extended objects with varying physical properties. Consider a single-slit spectrometer where the slit is offset by one slit width between subsequent exposures. Instead of stepping time-wise across the object, which requires absolute stability of the instrument and observing conditions, the IFS simultaneously records the spectra from the various slit offsets and optically rearranges the input spectra before sending them to the disperser. This integral field unit (IFU) can work in three ways: 1. An array of lenslets subdivides the field and focuses the sub-images onto the disperser, which is tilted with respect to the lenslet orientation to avoid overlapping spectra. 2. An array of lenslets subdivides the field and feeds the sub-images into optical fibers. The output of the fibers is aligned in one dimension, resembling a long slit, before dispersion. This option enables more efficient packaging, and all field points are dispersed with the same [l2  l1 ]. 3. An image slicer, which is a stack of rectangular, slightly tilted (with respect to each other) mirrors in the focal plane, cuts the image in small slices. A second array of mirrors realigns the slices along one dimension before dispersion. Both mirror assemblies require very accurate alignment. Field Guide to Astronomical Instrumentation

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Spectrographs

Multi-object Spectrometer A multi-object spectrometer (MOS) enables simultaneous spectroscopy of multiple compact objects within the field of view. This multiplexing advantage, which has become possible with the advent of large-format detector arrays, allows for large spectral surveys, particularly of faint targets, which require long integration times. Since the location of the target of interest varies, the input focal plane of an MOS needs to be configured for a given observation. The selection of targets can be accomplished in different ways: • By fixed mini-slits that are cut into a fixed-slit mask. Formerly mechanically drilled, masks are nowadays often laser cut and host hundreds of slits. This option is optically simple and allows accurate calibration but requires pre-machined equipment for one-time usage. • Microshutter arrays, which cover the focal plane with an array of adjacent microshutters. An opened microshutter acts as a mini-slit. Alternatively, one can use a row of robotic movable slits for one object per line. Both schemes allow real-time configurations of the input focal plane at the expense of added complexity. • Small pick-off mirrors, which redirect the light to the disperser. The optical subsystems served by robotic reconfigurable pick-offs may contain IFUs, combining the advantages of MOS and IFS. • Optical fibers, which are either mounted to a fixed, pre-machined plate, or placed in the focal plane by a fiber positioner and kept in place by “magnetic buttons.” The ends of the hundreds of fibers are arranged in one dimension to form a “long slit” before sending the light to the disperser. A challenge for accurate spectral calibration is the lack of adjacent “sky” spectra. Fiber spectrographs are often located on a fixed platform, and the flexible fiber bundles, tens of meters in length, compensate for the relative motion between the telescope focal plane and the spectrograph.

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OH-Suppression Spectrographs More than 95% of the sky background in the near-infrared J and H bands (1.15 , l , 1.8 mm) originates from emission of the OH radical (“airglow”) in the upper atmosphere. The narrow emission lines are widely spread across the J and H bands and cannot be easily filtered out. An OH-suppression spectrograph produces a spectrum at an intermediate focal plane, where a mask will block the wavelengths corresponding to the OH line emission while the non-affected wavelengths are passed to a re-imaging system, which recombines the light to a lower spectral resolution or even broadband imaging. A spectral resolution R of approximately 3000 is required to separate and filter the OH lines in the spectrum.

An OH-suppression spectrograph is fundamentally different from other spectrographs in that its main purpose is not to measure the spectral properties at medium resolution but to increase sensitivity by suppressing the background. The gain in sensitivity is typically about two astronomical magnitudes. The disadvantage of this concept is the added complexity, which leads to light losses and reduced gains. With the advent of large-format, low-read-noise, infrared detector arrays, the need for OH suppression spectrographs has diminished as the dispersed spectrum can be recorded directly and rebinned in software. A novel approach to this concept uses fiber Bragg gratings in the optical fibers of the spectrograph, utilizing periodic variations in the refractive index of the fiber core. Field Guide to Astronomical Instrumentation

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Spectral Data Analysis The step from the dispersed, two-dimensional, raw detector format to a calibrated one-dimensional spectrum is nontrivial and requires several important steps. The standard procedures for dark/bias/sky subtraction and correction for detector nonlinearities are similar to the procedures for imaging systems. However, the twilight sky, commonly used to provide flat fields for imaging cameras, displays a high density of emission and absorption lines and requires a spectrally and spatially flat source, or a source with an exactly known spectrum to calibrate the pixel-to-pixel responsivity of the spectrograph. In a properly sampled spectrograph, one spectral resolution element covers more than one detector pixel. Furthermore, some spectrographs record the same wavelength in several diffraction orders. Combining the detected signal C from i different pixels with a weighting coefficient W i  ðSi =N i Þ2 is called optimal extraction. The signal S, given the background B, and summed over all pixels is: P SðlÞ ¼

i W i ðlÞ

· ½C ðlÞ  BðlÞ P i W i ðlÞ i

Accurate wavelength calibration, usually to within a small fraction of one resolution element, can be achieved by comparison to a spectral lamp, gas cell, or the sky spectrum, of which the wavelengths of the spectral lines are well known. A complication arises when the slit is wider than the FWHM of the source, causing the wavelength calibration to depend on the exact position of the source within the slit, and, consequently, yielding a different spectral resolution between point and extended sources. Absolute flux calibration requires a calibration source with accurately known flux density over the relevant Dl.

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Polarimeters

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Rotating Waveplate Polarimeters Many different types of polarimeters have been built for different applications. The simplest polarimeters are rotating waveplate polarimeters, where a rotating waveplate is followed by a linear polarizer or a polarizing beamsplitter. The measured intensity I 0 as a function of waveplate retardance d and rotation angle u for an incoming beam with Stokes vector ðI; Q; U ; V Þ is I Q I 0 ¼ þ ½ð1 þ cos dÞ þ ð1  cos dÞcos 4u 2 4 U V þ ð1  cos dÞsin 4u  sin d sin 2u 4 2 A waveplate with d ¼ 126.8 deg at the wavelength of interest has equal modulation amplitudes and sensitivity for Q, U , and V . The rotation can be continuous with eight equally long integrations per rotation or stepped to four or more discrete angles. The signals S produced by a polarimeter with a modulator having states 1 and 2 followed by a polarizing beamsplitter producing images l and r can be combined in the dual-beam exchange equation to remove effects due to transmission changes, detector gain variations, and image motion:     1 Sl1 Sr2 1 V1 V2  1 ¼ þ I2 4 Sl2 Sr1 2 I1 Field Guide to Astronomical Instrumentation

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Liquid Crystal Polarimeters The mechanically rotating waveplate in a polarimeter can be replaced with one or several nonmoving, electrically controlled liquid crystal retarders, which can change either their retardation (nematic liquid crystals) or their fast axis orientation (ferro-electric liquid crystals). These liquid crystal devices are often combined with fixed retarders to achieve good performance over a large wavelength range. Liquid crystal variable retarders (LCVRs) based on nematic liquid crystals have a fixed fast axis orientation but change their retardance as a nonlinear function of the applied voltage and temperature. Maximum modulation frequencies are about 50 Hz. Since the retardance is controlled by the electric field, LCVRs can be tuned to different wavelengths. Ferro-electric liquid crystals (FLCs) have a fixed retardation (generally l=2). Their fast axis orientation can be electrically switched between two angles. Maximum modulation frequencies reach 10 kHz. The switching angle depends on temperature.

Liquid crystal polarimeters that measure all four Stokes parameters with four measurements can be built with two LCVRs or two FLCs and two fixed retarders, followed by a linear polarizer or a polarizing beamsplitter. Field Guide to Astronomical Instrumentation

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Spectral Modulation Polarimeters While rotating waveplate and liquid crystal modulators sequentially measure different polarization states, spectral modulation polarimeters change the polarization state as a function of wavelength, which enables spectropolarimetric measurements with a single spectrum. One or several retarders with many waves of retardation in combination with a linear polarizer transfer the polarization information into an amplitude modulation of the spectral intensity. The thick retarder is very sensitive to temperature; combinations of crystals can make the modulation athermal. For measuring linear polarization only, a combination of an achromatic quarter-wave plate, a thick retarder with retardance dðlÞ, and a polarizer measures the complete linear polarization information. The degree of linear polarization P L ðlÞ is encoded in the amplitude of the modulation. The orientation of the linear polarization is encoded in the phase of the modulation. The observed spectral intensity I 0 ðlÞ is     IðlÞ 2pdðlÞ I ðlÞ ¼ þ 1 þ P L ðlÞ cos þ 2wðlÞ 2 l 0

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54

Interferometers

Interferometer Principle and Angular Resolution An astronomical interferometer is a device that combines the beams from two or more telescopes coherently (in phase) to produce an interferogram. Its main purpose is to provide higher angular resolution with respect to what could be practically achieved with a large single-dish telescope. The angular resolution u of an interferometer is determined by interference, which does not require a contiguous aperture. Analogous to Young’s double-slit experiment, the interference fringes become narrower for larger baselines (wider slit separations). As a first-order approximation (for a filled aperture), the achievable angular resolution is determined by the baseline B as u 5 1.22 · l=B However, for an “unfilled aperture” the actual angular resolution is higher, analogous to a single-dish telescope with a very large central obscuration. Considering that only rays from parts of distance B contribute to the interference, the angular resolution u (as given by the first minimum of the PSF) of a two-element interferometer with Earth-rotation synthesis is u 5 0.764 · l=B The Earth-rotation synthesis converts the original twotelescope arrangement into partially filled apertures (aperture synthesis). In this case, the PSF is described by the Bessel functions J 0 ðxÞ, rather than 2J 1 ðxÞ=x as in the case of a filled aperture. Field Guide to Astronomical Instrumentation

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Interferometers

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Delay Lines Within an interferometer, delay lines are needed to compensate the optical path difference between the beams before combining them to interference. The optical path difference D depends on the zenith angle z simply as D 5 B · sinðzÞ, where B is the baseline between the apertures. For large baselines, this can result in path differences of tens of meters that need to be optically compensated, usually by adding an adjustable, back-reflected path to each telescope beam, with a length of half the maximum path length to be compensated. The length must be aligned to within a fraction of one wavelength and needs to be continuously adjusted while the telescope is tracking the object on the sky. This requires typical dynamical ranges of 1079 . Under seeing-limited conditions with Fried parameter r0 and for baselines shorter than the outer scale of the atmospheric turbulence, the amplitude of the wavefront pffiffiffiffiffiffiffiffiffiffi B 56 fluctuations is given by s 5 6.88 r0 rad RMS. In order to interfere, the wavefront errors must be much smaller, which requires accurate beam combiners and adaptive optics to correct for atmospheric turbulence. For most radio interferometers, the delay is introduced by an electronic circuit that adds a phase shift, or by recording the signal with respect to an absolute phase reference. Due to the higher frequencies of a few hundred terahertz of optical light, optical interferometers require optical delay lines.

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Beam Combiners There are several ways to combine coherent optical beams from different telescopes in interferometry. A coaxial beam combiner uses a 50% beamsplitter mirror to combine two coherent pupils from different telescopes, creating two beams with varying intensity, depending on the phase difference between the incoming beams. This is similar to a Michelson interferometer. Photonic integrated circuits, or integrated optics, allow optical systems to be made more compact and with higher performance than with discrete optical components. Beam combiner chips are directly fed by single-mode fibers from each telescope, providing instantaneous pairwise combination of all baselines for multiple telescopes, including phase shifting. Coherent optical beams can be combined under an angle, creating an interference pattern. The pupils of multiple telescopes are reimaged side by side, and all pupils together form an image on a single camera. It is possible to combine multiple telescopes by carefully selecting the distances between the pupils of all telescopes. A Fizeau interferometer works in a similar way, but here the size and distance of the pupils resemble the physical layout of the telescopes. Therefore, the Fizeau interferometer can produce images directly.

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Fringe Visibility In the simplest case of a two-element interferometer, the resulting signal is an interferogram of alternating maxima and minima (fringes) with corresponding intensities I max and I min . One can define the fringe visibility as I min V 5 II max . max þI min

The fringe visibility is the Fourier transform of the object’s brightness distribution and is given by the amplitude of the fringes. The phase determines the position of the fringes. If the dark regions in the fringe pattern go to zero, the object is unresolved and the visibility is V 5 1. If the visibility goes to zero, then there are no fringes, and the object is completely resolved. The visibility provides direct information on the angular size of an object.

If the baseline B is reduced, one may observe an increase in visibility as the object moves from a spatially resolved to a spatially unresolved state. In the more practical case of polychromatic “white” light, the interferogram consists of colored fringes. The term whitelight fringe refers to the central fringe.

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Fringe Tracking and Closure Phase Small phase shifts introduced by the atmosphere or small fluctuations in the optical alignment of the interferometer will lead to moving fringes in the focal plane on time-scales that can be as short as the atmospheric coherence time.

In order to integrate for a longer time and build up sufficient signal-to-noise ratio, the fringes need to be actively tracked, and their motion needs to be compensated. The tracking requires tracking fluctuations within a small fraction of wavelength in real time, which can only be done with a bright reference source (guide star) within the isoplanatic angle. Interferometers with three (or more) telescopes will provide three sets of fringes: (1-2), (2-3), and (3-1). In this case, the phase can be determined by summing up the phases from all three baselines. This method, called closure phase (CP)—or self-calibration in radio aperture synthesis imaging— cancels out the (mostly atmospheric) wavefront aberrations, which are common to all three telescope beams: Fobs ð1  2Þ 5 F0 ð1  2Þ þ ½Fð2Þ  Fð1Þatmos Fobs ð2  3Þ 5 F0 ð2  3Þ þ ½Fð3Þ  Fð2Þatmos Fobs ð3  1Þ 5 F0 ð3  1Þ þ ½Fð1Þ  Fð3Þatmos ) CPð1  2  3Þ 5 F0 ð1  2Þ þ F0 ð2  3Þ þ F0 ð3  1Þ Field Guide to Astronomical Instrumentation

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Aperture Synthesis and
u;v Plane A two-element interferometer, consisting of two telescopes separated by the baseline B, provides only one baseline and an interferogram that resembles a double slit. At the other extreme, each point on a large mirror could be seen as one element of an interferometer with an infinite number of baselines, yielding an Airy function. An interferometer with N telescopes will provide NðN–1Þ=2 baselines. Each baseline adds a new Fourier component (or fringe spacing) in the Fourier or
u;v plane. Since the resulting point spread function (PSF) is the Fourier transform of the ðu; vÞ plane, an accurate reconstruction of the object’s intensity distribution requires good coverage of the ðu; vÞ plane. Any nonredundant baseline will add new information to the image formation. This technique, called aperture synthesis, was pioneered by Martin Ryle at radio wavelengths. The limited sampling of the ðu; vÞ plane can be further expanded by moving the telescopes to change the baselines or by using the Earth’s rotation (and thus the apparent rotation of the sky) to fill the ðu; vÞ plane.

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Field of View and Sensitivity The maximum field of view umax of an astronomical interferometer is limited by the strict requirements to maintain coherence across the field of view and the physical sizes of the elements of the complex transfer optics, resulting typically in only a few arcseconds. The signals S1 and S2 from two telescopes depend on their respective aperture areas A1 and A2 as hS1 · S2 i ∝

pffiffiffiffiffiffiffiffiffiffiffi A1 A2 5 Aeff

The effective area of an interferometer Aeff with two identical elements is only the area of one of the elements. Since the noise from the two elements is uncorrelated, p the ffiffiffi noise output from the correlator is reduced by a factor of 2. In other words, thepsignal-to-noise ratio of a two-element ffiffiffi interferometer is 2 times higher than that of a single aperture of area A. An array of N identical telescopes can be treated as NðN  1Þ=2 two-element interferometers, for which the signal-to-noise ratio scales as   S ∝ ½NðN  1Þ1=2 N With respect to the visibility V of an interferometer, the signal-to-noise ratio in the background-limited regime (infrared) photon-limited regime (visible), respectively, is given by   S ∝n · V N bkgrdlim   pffiffiffi S ∝ n·V N photonlim where n represents the number of source photons per coherence volume A · t0 (where t0 is the atmospheric coherence time).

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Image Processing For a densely covered ðu; vÞ plane, the measured fringe intensities Iðu; vÞ will approximate the intensity distribution I as imaged with a filled-aperture telescope: ZZ Iðx; yÞ 5 Iðu; vÞei2pðuxþvyÞ dudv For a sparsely sampled ðu; vÞ plane, described by the sampling function Sðu; vÞ, the gaps in the ðu; vÞ plane add undesired artifacts, resulting in a so-called dirty image I D : ZZ Iðu; vÞSðu; vÞei2pðuxþvyÞ dudv ID 5 The dirty image I D is given by the true image I, convolved with the PSF that representes the dirty beam: ZZ Sðu; vÞei2pðuxþvyÞ dudv I D ðx; yÞ 5 Iðx; yÞ  A common method to remove the artifacts introduced by the incomplete ðu; vÞ plane is deconvolution with the PSF given by the particular interferometer configuration. Iterative algorithms like CLEAN (Högbom 1974) are commonly used to reduce the “dirty beam.” Most submillimeter and radio interferometer arrays allow the observer to choose the weights at which the different baselines contribute to the image formation. Uniform weighting gives an equal weight per unit ðu; vÞ plane and provides a clean PSF and intermediate resolution. Natural weighting gives every data point (telescope) the same weight, irrespective of their distribution in the ðu; vÞ plane, which typically leads to poorer resolution but the highest signal-to-noise ratio for point sources. Gaussian weighting suppresses the longer baselines, leading to low resolution and low signal-to-noise ratio but a very clean PSF with almost no sidelobes. A weighting that includes only the longest baselines provides the best resolution but at the expense of poor signal-to-noise ratio and a complex PSF. As an alternative to image reconstruction, one can fit model parameters describing the astrophysical object to the measured visibilities. Field Guide to Astronomical Instrumentation

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Coronagraphs

Focal-Plane Coronagraphs A focal-plane coronagraph has an amplitude mask and/or a phase mask in a focal plane that blocks the light coming from a bright, central object to enable the study of the faint, close-by environment. An optional amplitude mask apodizer in a pupil plane in front of the focal plane masks the sharp telescope aperture edges with a smooth variation in transmission, strongly reducing the diffraction rings. A Lyot stop, a pupil mask after the focal plane, blocks the light diffracted at the edges of the telescope aperture.

The Lyot coronagraph consists of an opaque amplitude mask (occulter) in the center of the field of view, which blocks the light from the central object. An apodized Lyot coronagraph with an amplitude apodizer in a preceding pupil plane has much better performance. The four-quadrant phase mask (4QPM) coronagraph has adjacent quadrants with a phase delay of p, which results in destructive interference of the central object in the final focal plane. The vortex coronagraph uses an azimuthal phase ramp from 0 to 4p and can be implemented using regular, scalar phase plates or spatially varying retarders that work with polarized light. Phase-mask coronagraphs are particularly useful when looking very close to a bright point source. Amplitude mask coronagraphs can be very simple to implement. Focal-plane coronagraphs are very sensitive to the precise position of the bright object on the mask.

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Pupil-Plane Coronagraphs A pupil-plane coronagraph has an amplitude or phase apodizer in an intermediate pupil plane to significantly reduce the diffracted light coming from a bright, central object to enable the study of the faint, close-by environment. A focal plane mask may follow to block unwanted light.

An amplitude apodizer in a pupil plane creates a pointspread function with minimum intensity in at least part of the focal plane. It can have a complex binary aperture shape or replace the sharp telescope aperture edges with a smooth variation in transmission. The simplest implementation is a radially varying neutral-density filter. To avoid light losses due to absorption, the phase-induced amplitude apodization (PIAA) uses a pair of steeply aspheric mirrors to concentrate the light toward the center of the pupil. After the focal-plane mask, a remapping optics restores the original pupil to produce sharp off-axis images. A phase apodizer modifies the wavefront to create a point-spread function with minimum intensity in a part of the focal plane. The apodizing phase plate (APP) coronagraph moves all diffracted light into one-half of the focal plane and is dark in the other half. The phase modification can be introduced with shaped glass plates or spatially varying retarders using polarized light. Pupil-plane coronagraphs can be added to any instrument that has an intermediate pupil plane, but the apodizer can be challenging to manufacture. Pupil-plane coronagraphs are insensitive to the precise position of the bright object in the focal plane.

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Space Coronagraphs Most coronagraphs in space observe the solar corona. Since the sun is an extended object, the telescope focal plane contains an internal occulter, which is a focalplane mask that absorbs or reflects the light from the solar disk. As with other focal-plane coronagraphs, a Lyot stop removes light diffracted at the edge of the aperture. While solar coronagraphs suppress light from the 0.5deg-diameter solar disk, coronagraphs for the direct imaging of exoplanets suppress the diffraction rings around a point source. The absence of seeing makes it possible to actively compensate minuscule wavefront amplitude and phase aberrations by using electric field conjugation or a self-coherent camera directly in the science focal plane and achieve extreme contrasts of .1010 . Coronagraphs that look at the outer, much fainter parts of the solar corona use an external occulter, a system of disks mounted in front of the telescope. As the external occulter is not in a focal plane, the occulter must be oversized. Light diffracted at the edge of the external occulter is blocked by an internal occulter. A Lyot stop in an image of the aperture blocks the light diffracted at the telescope aperture.

External occulters are also considered for exoplanet imagers. A starshade spacecraft far away from the telescope blocks the light from a star. In contrast to a solar coronagraph with an external occulter that blocks the light from an extended object, the starshade’s outer edge is highly structured to minimize the effects of diffracted light from the starshade’s edge. Field Guide to Astronomical Instrumentation

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Adaptive Optics

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Adaptive Optics Adaptive optics (AO) systems correct aberrations induced by the Earth’s atmosphere (seeing), the telescope, and fore-optics in real time. AO systems consist of a wavefront sensor, a deformable mirror, and a control system. The deformable mirror (DM) modifies the incoming wavefront. The wavefront sensor (WFS) measures the residual aberrations, and the control system adjusts the deformable mirror accordingly. The performance of an AO system depends primarily on the telescope diameter D, the seeing r0 ðlÞ, the number of DM degrees of freedom N, and the brightness of the source used for wavefront sensing. In case of a fast AO system looking at a bright star, the AO performance can be described in terms of the Strehl ratio (S) gain G ¼ SAO =SnoAO and the residual wavefront variance s2N : 
5 
2 D D 3 5 exp 0.3 N6 G ≈ 0.5 r0 r0 pffiffiffiffiffiffi
D 53 2 sN ¼ 0.3 N 3=2 ½rad2  r0 When the source itself is too faint to sense the wavefront, lasers can generate artificial laser guide stars. The total residual wavefront variance can be expressed as a sum of variances for the different subsystems: s2DM from mismatches between the achievable DM shape and the wavefront, s2W FS from wavefront sensor noise, s2control from delays in the control system, and s2offaxis from off-axis wavefront changes when the guide star and the science target are not identical. s2total ¼ s2W FS þ s2DM þ s2control þ s2offaxis Field Guide to Astronomical Instrumentation

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Atmospheric Turbulence: Seeing Seeing is the colloquial term for the wavefront aberrations induced by the Earth’s atmosphere, which are due to index-of-refraction fluctuations of air produced by turbulent temperature fluctuations. The Kolmogorov turbulence theory is often employed to model these index fluctuations. The turbulence strength as a function of height h is described by the refractive-index structure constant C 2n ðhÞ, which typically has major contributions from 0 km (ground layer) and 7–12 km. The Fried parameter r0 depends on the wavelength l and the zenith angle z: 
2  3 Z 5 2p sec z C 2n ðhÞdh ½m r0 ¼ 0.423 l The angular size of a point source at wavelength l is uFWHM ≈ l=r0 ðlÞ rad. r0 varies with wavelength as l6=5 and uFWHM as l1=5 . The corresponding wavefront variance with and without image motion compensation is
5
5 D 3 D 3 2 2 2 ½rad  sseeing ¼ 1.02 ½rad2  snoMotion ¼ 0.134 r0 r0 Given a wind profile vðhÞ or a constant wind velocity vw , temporal fluctuations in the aberrations are characterized by the Greenwood frequency: 3  Z 5 v 5 65 2 3 f G ¼ 2.31l sec z C n ðhÞv ðhÞdh ½Hz ¼ 0:43 w ½Hz r0 Wavefront aberrations are highly correlated over angular scales of the isoplanatic angle uisoplanatic , which is Z Z 3 5 0.3r0 5 2 2 3 ½rad H ¼ sec z C n ðhÞh dh u0 ≈ C n ðhÞdh ½m H If an AO system perfectly corrects on axis, off-axis objects at an angle u exhibit an additional wavefront variance:
5 u 3 2 ½rad2  soffaxis ¼ u0

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Wavefront Sensors A wavefront sensor (WFS) measures the remaining aberrations in real time with a minimum of photons. The Shack–Hartmann (SH) WFS is easy to implement but not necessarily optimal. Lenslets in a pupil image divide the aperture into subapertures, each of which makes an image of the guide target such that the image displacement is proportional to the wavefront tilt averaged over the subaperture. The curvature wavefront sensor uses images in front of and behind the focus. The difference between the two images is proportional to the wavefront curvature. Nonlinear curvature sensing uses two more images farther out of focus and a nonlinear algorithm to reconstruct the wavefront. The pyramid WFS has a transparent pyramid in the focal plane with the guide star image on its apex. A lens makes four separate pupil images, and the differences between the images are proportional to the wavefront gradient. The pyramid may be vibrated in both axes to increase its linear range. The rooftop prism WFS uses a beamsplitter with a rooftop prism and a lens in each arm to also provide four pupil images. If the WFS is limited by photon noise and seeing, the WFS error variance contribution s2WFS for np photons=m2 in the aperture for all modes together is s2W FS 

ðl=r0 Þ2 ½rad2  np

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Deformable Mirrors Astronomical AO systems work over a broad wavelength range using deformable mirrors (DMs) to correct the largely achromatic aberrations introduced by the atmosphere. Most DMs consist of a thin, continuous face sheet attached to actuators, which translate an electrical signal into a small mechanical motion by using piezo-electric, electro-static, electro-strictive, or voice-coil actuation. DMs can be assembled from individual actuators or actuator modules and a face sheet, or as an integrated manufacturing process using micro-electro-mechanical systems (MEMS) technologies. The choice of DM technology is driven by the required number of actuators, the actuator pitch (distance between actuators, typically 0.3 to .5 mm), the actuator stroke (maximum deformation induced by one actuator, typically 1 to 50 mm), and the speed with which the DM shape can be changed (typically 1 kHz and faster). Other crucial performance parameters are the amount of hysteresis, which can be as large as 10%, the coupling between actuators (typically 10%), and the percentage of nonfunctional actuators. A deformable secondary mirror in a telescope provides AO-corrected images without additional optics, which is particularly advantageous in the infrared. The DM can fit the actual wavefront error only to a certain degree due to the limited spatial frequencies it can influence. For an actuator spacing of d, the remaining wavefront error variance is s2DM ≈ 0.3


5 d 3 ½rad2  r0

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Adaptive Optics Control The adaptive optics control system transforms the wavefront sensor data into commands for the deformable mirror. In the simplest case, the wavefront sensor data s and the DM actuator positions y, including additive noise n with zero mean, are linearly related through the poke matrix P: s ¼ Py þ n The poke matrix P is determined by measuring the WFS signal s as a function of DM actuator position y. The reconstructor R performs the inverse operation during closed-loop operation and estimates the actuator position y based on the measured WFS signal s. In the simplest case, the reconstructor is a matrix. The AO control system applies the correction with some gain g and delay Dt, which can be represented as an integrator: yðt þ DtÞ ¼ yðtÞ þ gRs The reconstructor removes the piston term, may split off the tip/tilt signals to a separate tip/tilt mirror, reduces the influence of WFS noise, removes mirror modes that are invisible to the WFS, optimizes the gain, and may control the dynamical performance of the DM and the tip/tilt mirror. The loop update rate, the rate at which WFS measurements are acquired and the DM actuators are moved, needs to be 10 to 20 times faster than the maximum frequency at which the DM is expected to correct. Typical update rates range from 0.5 to 3 kHz. The remaining wavefront error variance s2control due to the AO control system is dominated by the servo lag ts : s2control


5 t 3 ¼ s ½rad2  t0

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Laser Guide Stars Artificial laser guide stars (LGSs) can be produced by scattering laser light off of molecules in the Earth’s atmosphere at a height of up to 20 km (Rayleigh scattering) or off the 5-km thin atomic, neutral sodium layer at a height of 90 km (resonant scattering). This enables AO correction over the full sky. As Rayleigh scattering occurs over the whole atmosphere, a pulsed laser and gated WFS are used for observing the laser pulse only when it passes through a thin layer of the upper atmosphere. Lasers are typically launched from a separate launch telescope, often situated behind the secondary mirror, to avoid fluorescence on the telescope optical surfaces. LGSs suffer from the cone effect, which is due to the finite height of the LGS: astronomical and LGS light do not travel through the same parts of the higher atmospheric layers. The cone effect becomes particularly troublesome for large telescopes and short wavelengths. It is mitigated by using several LGSs around the astronomical object. LGSs are also insensitive to tip-tilt wavefront errors as the laser light travels through the same atmospheric layers on the way up and on the way back down to the telescope. Hence, natural guide stars (NGSs) must be used to determine the tip and tilt of the wavefront. Those stars can be much fainter than stars used for wavefront sensing, as one needs to only determine their position in the sky.

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Operation Modes Current adaptive optics systems in astronomy come in a variety of AO operating modes. The classical single-conjugate adaptive optics (SCAO) mode uses a single source for the wavefront sensing and a single deformable mirror. It is most suited to obtain very high image quality for the object that is also used for the wavefront sensing. Ground-layer adaptive optics (GLAO) uses several guide stars for wavefront sensing to determine the aberrations introduced by turbulence close to the ground, which has a correspondingly large isoplanatic angle. Multi-conjugate adaptive optics (MCAO) uses several wavefront sensors and multiple deformable mirrors that are conjugated to several layers in the atmosphere. MCAO corrects the turbulent volume and provides a larger corrected field of view than SCAO and better correction than GLAO. Multi-object adaptive optics (MOAO) provides an even larger field for a few objects by using several wavefront sensors to drive a deformable mirror for each object. While MCAO operates in closed loop, MOAO operates in open loop because the wavefront sensors are not located behind the deformable mirrors.

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Optical Design

Optical Design Principles The optical design of astronomical instruments is not a linear process. The close coupling between optical, mechanical, electrical, controls, and software design and the science requires an iterative design process. The optical design is the first design effort that provides a glimpse at how the final instrument will look. Prioritization of requirements and a tightly integrated design team accelerate the design process. Requirements that have a large influence on the optical design are site characteristics (seeing and temperature statistics), telescope properties, instrument location (fixed or variable gravity vector, space, and weight limits), angular and spectral resolution, field of view, wavelength range, detector pixel size, stability, and repeatability. Optical design principles for optical instruments: • Minimize the number of optical components. Additional elements increase design freedom and can improve theoretical performance but add cost and problems such as ghost reflections and scattered light. • Maximize the radii of curvature to reduce aberrations and ease manufacturing and alignment. • Maximize the allowed tolerances to simplify the manufacturing, mechanical design, and operational requirements. • Place components close to a focus if they introduce wavefront aberrations. • Place components close to a pupil if all field points should pass the same part of the component. • Place components in a collimated beam if all rays from one field point should pass the component under the same inclination angle. • Place components in a telecentric beam if the component is sensitive to the inclination angle. • Oversize optical elements because optical manufacturing quality is always worse at the edge. Field Guide to Astronomical Instrumentation

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Design Approach

The requirements review identifies unnecessary, incompatible, and omitted requirements, and ensures that all requirements can be verified and traced back to scientific needs. The derived optical design requirements set the boundary conditions for the optical design in terms of optical quantities. First-order optical designs use ideal optical elements (e.g., paraxial surfaces), rays from central and extreme field points along with image and pupil locations to establish the general configuration. Often based on existing designs, they can be sketched on paper or in a spreadsheet. They provide an initial idea of the size of different designs. Realistic optical designs replace ideal optical elements with real optical elements. Their performance is analyzed with optical design software, and they are modified until basic requirements, such as image scale and image/pupil locations, are met. Other requirements that critically depend on the exact shape of optical elements (e.g., image quality) are unlikely to be met at this stage. Realistic designs can be compared, and a single design may be chosen for further refinement. Modern optical software can automatically produce an optimized design by adjusting parameters of optical elements (e.g., position, radius of curvature, glass type). This produces the best possible design, given the optical elements and the order in which the light passes them. Tolerancing determines the accuracy with which the design must be realized, and the analysis verifies that the optimized design meets all requirements. If it does not, one needs to modify the realistic or first-order design or even the requirements and repeat the design process. Field Guide to Astronomical Instrumentation

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Optical Design

Ray Tracing Ray tracing is based on the geometrical optics approximation where wavefronts are locally flat. Rays, the normals to the locally flat wavefronts, are traced from the source to the image plane according to Snell’s law and the Fresnel equations. Sequential ray tracing traces rays according to a predetermined sequence of optical elements. Non sequential ray tracing is considerably slower and determines, at each step, the next surface a given ray will reach.

Chief rays go from the edge of the field through the center of the aperture stop. At the location of pupil images the chief ray intersects the optical axis. Marginal rays go from the center of the field of view through the edge of the aperture stop. The marginal ray intersects the optical axis at image planes. Skew rays do not intersect the optical axis or are parallel to it.

Results of ray tracing calculations are often presented in the form of spot diagrams, which show the intersections of the traced rays with an image plane, and in the form of the optical path difference (OPD), which shows the difference in the optical path length of each ray in the exit pupil with respect to the chief ray. Raytracing does not include the effects of diffraction and interference, making it very fast. Ray tracing is usually sufficient for optimization and tolerancing.

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Optimization Automatic optimization built into most optical design software can much improve the performance of initial optical designs. The declaration of variable parameters of the optical design, e.g., radii of curvature of optical surfaces, spacing between elements, conic constants, and glass thicknesses, defines the degrees of freedom of the automatic optimization process. The optimization can go as far as changing the glass type to achieve a better performance as a function of wavelength or temperature. A merit function, defined by the optical designer based on the design requirements, mathematically defines the performance: the design is optimal when the merit function reaches a global minimum. The merit function is a function of the optical design parameters (restrictions on diameters, thicknesses, etc.), the system parameters (f-number to be achieved, overall system length, etc.), and the aberration parameters (such as the RMS wavefront aberration, field curvature, etc., often as a function of field angle and wavelength). Local optimization will look for a local minimum in the merit function: the optimized design will stay close to the starting point, and the optimization is fast. Global optimization will look for the global minimum, which is the best design achievable given the set of variable parameters and the definition of the merit function. It is much slower than local optimization and may easily lead to unacceptable designs if the merit function does not sufficiently penalize unacceptable designs. Optimization generally does not insert new optical elements and will not change the order of elements in sequential ray tracing. If the optimized design does not meet the requirements, changes to the design must be made manually. When working with lenses, one can split a lens into two with their flat surfaces touching and then re-optimize their radii of curvature and separation.

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Optical Design

Tolerance Analysis The tolerance analysis determines the tolerances to which the optical elements have to be manufactured and positioned, and the degree to which environmental parameters such as temperature must be controlled. It needs to consider all design parameters that are subject to errors. Different optical designs may have the same performance, but one may be much more demanding on the manufacturing and/or alignment than another design. The tolerance analysis is based on a merit function, which describes the optical performance with a single number and may be the same merit function as the optimization. The sensitivity analysis is the simplest form of a tolerance analysis and reveals the sensitivity of the merit function with respect to an assumed error in each design parameter such as known manufacturing limits. The inverse sensitivity analysis determines the maximum allowed error in a design parameter for a given maximum change in the merit function. It provides a first approximation to the tolerances that should be specified. It does not consider the coupled effect of simultaneous errors in all design parameters. The Monte Carlo tolerance analysis provides a realistic estimate of the expected performance by using statistical distributions of the expected errors and allowing for simultaneous errors in all parameters. Compensators are design parameters and/or instrument components that can be adjusted to compensate for some errors in manufacturing and/or alignment, such as the position of an image plane to compensate for a defocus. Tolerance balancing can often reduce the cost of an instrument. The tolerances on one element can make that element extremely expensive to manufacture or position. By tightening tolerances that are easy to achieve on other elements, one can often reduce the cost-driving tolerances without affecting the expected instrument performance.

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Stray Light Control and Baffles The performance of an imaging system is generally limited by (1) the quality of its optical elements, (2) the alignment of its optomechanical components, and (3) the efficiency with which unintended reflections (ghost images) and diffuse stray light can be suppressed before reaching the focal plane. Ghost images are often caused by internal reflections (e.g., screw heads, fasteners, optics mounts) and lead to image artifacts. Stray light will produce an additional background to the signal, which is often difficult to remove. To suppress unwanted reflections, the surfaces surrounding the optical system can be either coated with black paint or anodized. A black surface reduces reflection within a limited wavelength range by means of absorption. For handling reasons, black anodization (90% absorption) is often preferred over black paint, which generally provides better absorption (95%) and can be more easily redone after remachining or repair. However, both black paint and anodization are inefficient when light enters at grazing incidence. A well-designed cylinder baffle can reduce the stray light by five orders of magnitude. In such a baffle, vanes within the tube prevent light from outside the entrance aperture to reach the focal plane by trapping it inside small cavities defined by the vanes. The vanes are usually beveled to avoid specular reflections at their ends.

Dedicated software packages that can model stray light in an optical system are available. Field Guide to Astronomical Instrumentation

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Optomechanics

Packaging Optical systems can be one dimensional or multi-dimensional, referred to as 1D, 2D, 2.5D, or true 3D. A set of lenses, such as in a camera, is a 1D system. It is practical to fit the optical components in a barrel. The barrel can be a solid tube or an open structure based on struts. 2D optical systems are often designed in a horizontal plane on an optical table. When vertical beams are present to generate multiple horizontal layers, this is referred to as 2.5D. A standard optical table works fine in a stable lab environment or if it is fixed to the Nasmyth platform of a telescope. At the telescope Cassegrain focus, the gravity direction changes when the telescope moves. This is also the case for an instrument co-rotating with the sky on a Nasmyth port. A changing gravity direction causes flexure in optomechanics. Vibrations during launch can restrict use of optical tables in space. In these cases, a dedicated instrument structure can be designed to optimize flexure or vibration issues using finite element model analysis. A rigid sandwich of optical tables works well for 2D systems. Folding mirrors or right-angle prisms reduce the size of a structure, especially if it is elongated. 3D systems often need a dedicated structure, or instrument box, to mount the optical components under specific angles. Alignment of 3D systems is relatively difficult, so additional alignment references are necessary for test purposes. Thermal effects of both the optics and the mechanics must be analyzed. Common materials for the structure are steel, aluminium, silicon carbide, and low-CTE materials such as Invar or ZERODUR®. Structures can be light weighted and machined with accurate optical interfaces. Manufacturing tolerances can be compensated using shims.

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Optics Mounts A rigid body has six degrees of freedom: translations in X, Y, Z and rotations in X, Y, Z (also called tip, tilt, and rotation). A flat mirror is optically insensitive to translations or rotation in the mirror plane and has only three degrees of freedom. A rotationally symmetric lens has five degrees of freedom.

A kinematic mount constrains all degrees of freedom exactly once using point contacts. An underconstraint system allows unwanted motion or play in the optics. An overconstraint system can cause stress and distortion or needs tight tolerances. A semi-kinematic design is a practical implementation allowing some overconstraint by using line and area contacts instead of point contacts. Optical components and mounts made of different materials can cause problems at different temperatures due to CTE effects. An isostatic mount allows for relative size variations between the optical component and the mount, without affecting the semi-kinematic principles. For example, a lens mounted using 3 spring leaves at 120 deg. A monolithic design uses the same material for the (reflective) optical components and the mount. This makes the system insensitive to static temperature variations. Even a monolithic design might need isostatic mounts to withstand temperature gradients.

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Optomechanics

Mechanisms In many systems, mechanisms are used to position optical components. A mechanism contains these elements: • a system of constraints that allows motion only in the desired degree(s) of freedom, • an actuator that drives the mechanism, • an encoder to measure motion of the mechanism, or another method of obtaining position feedback, and • a lock (optional) to maintain its position. Mechanism requirements include degrees of freedom, travel range, load capacity, speed, lifetime and cost. There are many effects that limit the accuracy: resolution, repeatability, stability, etc. The requirements analysis needs to evaluate the performance of and constraints on the degrees of freedom. Selection mechanisms can place several optical components in the optical beam at a single position. These mechanisms can be based on rotation or translation mechanisms, e.g., a filter wheel or a slit slider. Alignment mechanisms are generally based on focus, tip-tilt, X-Y, or tip-tilt-focus mechanisms. They require high resolution and stability to maintain alignment when power is switched off. High-precision, piezo-driven stages are available off the shelf. Error sources for rotation stages include eccentricity, axial runout, and wobble. Preload forces on bearings enable better positioning and repeatability tolerances. Flexure stages provide precision motion but typically have a small travel range. Some optical shutters, such as diaphragm shutters, blade shutters, and curtain shutters, are available off the shelf. The exposure time is most accurate and uniform for a curtain shutter placed in the pupil plane or image plane. Field Guide to Astronomical Instrumentation

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Actuators and Motors Mechanisms can be driven by gravity, for instance, a cantilever with a balance mass. Such mechanisms have no external control loop. The vast majority of mechanisms are driven by electric motors, i.e., a device that converts electrical energy into mechanical motion. Motors can drive mechanisms directly, or use a gear to slow down the motion (worm gear, planetary drive). Motors can be placed outside the vacuum, using a vacuum feedthrough. An AC motor is ideal for high-power, fixed-speed motion. In a DC motor, the driving voltage controls speed, and the driving current controls torque. A brushless DC motor has a high efficiency and is maintenance free. A stepper motor is a brushless DC electric motor that divides a full rotation into a number of equal steps. The motor’s position can then be commanded to move and hold at one of these steps without any feedback sensor. A servomotor is an actuator that allows for precise control of angular position, velocity, and acceleration. It is not a specific class of motor. A servomotor is often used to refer to a motor coupled to a sensor for position feedback and is suitable for use in a closed-loop control system. A linear motor produces a linear voice coil linear and is well known

is an ‘unrolled’ electric motor that force instead of a torque (rotation). A motor has a fast positioning response for the loudspeaker application.

The operation of a piezoelectric motor, or piezo motor, is based on the change in shape of a piezoelectric material when an electric field is applied. Micrometer-sized steps can be made at a high frequency, using stick-slip effects or more sophisticated walking devices. A solenoid is an electromechanical device that can actuate (e.g., a valve). Solenoids can be bistable and do not require an active control loop to maintain their position.

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Sensors A variety of sensors is used in astronomical instrumentation for system monitoring and use in automated feedback loops. Electrical switches break or activate electrical contact in a certain position of mechanical motion. They are used as end switches before mechanisms hit a mechanical motion limit, or for initialization of mechanisms. A linear or rotary variable differential transformer (LVDT/RVDT) is an electro-magnetic sensor used for measuring linear or rotary displacement to better than micrometer-level accuracy. They are passive, robust, frictionless devices that can be used in harsh environments. Temperature sensors are used in an active feedback control loop with heaters or for temperature limit monitoring. Depending on temperature and accuracy, Pt100, Pt1000, and Si diodes are used. Thermostats like Klixon® cut the electrical current above a threshold temperature and are used as a passive backup system to prevent overheating. A photocell detects the amount of light that hits its surface and can be used to detect mechanical motion and distance. Quad cells have four photosensitive quadrants and can be used for (active) alignment of optical beams. Actively illuminated optical sensors, such as optical encoders, must be well shielded in astronomical instrumentation, because of possible contamination of the faint scientific optical signal collected by the telescope. Nevertheless, such systems can provide extreme precision impossible to achieve otherwise; a fiber optic interferometer can detect motion to nanometer-level accuracy.

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Mechanical Engineering for Space Rocket launchers generate extreme noise, wide-spectrum random vibrations, and (acoustic) shocks on the launcher and payload. Earthquakes and transport cause similar effects. Exposed to a spectrum of random vibrations, a system resonates in its corresponding natural frequencies. The amount of energy per unit frequency determines if the system excites, and damping determines the ability to dissipate energy. The remaining energy and motion in the system causes internal stresses. The natural frequencies need to be higher than the noise frequencies (increase stiffness, avoid excitation) or the system should be able to withstand the induced stresses (increase strength). The material properties and the particular design or shape of a construction determine its mass distribution, stiffness, and natural frequencies. Compact and low-mass constructions have higher stiffness and higher natural frequencies; however, low damping in metallic constructions results in higher stresses. Finite element model (FEM) analysis is the first step in assessing the vibration response of a system. Vibration tests are the final step in vibration qualification; a spectrum of random vibrations and (acoustic) shock tests is applied while monitoring the response of the system. Low-density materials and light weighting allow designs to fit within the strict size and mass limits for satellites. Light weighting is the removal of as much redundant material as possible while maintaining specifications such as high strength and stiffness. The coefficient of thermal expansion (CTE) is the tendency of matter to change in volume in response to a change in temperature. CTE values vary drastically between materials and in different temperature regimes. Large temperature differences can result in harmful dimensional differences inside a construction.

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Vacuum and Cryogenics

Dewars Cooling is essential to detect infrared radiation and to limit certain temperature-induced effects in optical and infrared focal plane arrays. The table shows typical temperatures for the optics and the detector. System

optical near infrared thermal infrared

Wavelength

l , 1 mm 1 mm , l , 2.5 mm l . 2.5 mm

Temp. Optics

Temp. Detector


300 K
100 K


180 K ,80 K


30 K


6 K

The detector—or the entire optical system—is placed in a vacuum tank called a dewar or cryostat. There is no thermal convection in vacuum, and heat transport is via radiation and conduction only. A heat shield or radiation shield with multilayer isolation (MLI) is used to limit radiation heat transport between the hot (300 K) vacuum wall and the cold instrument. The cryostat is connected to vacuum pumps, valves, and a cooling system. These systems induce vibrations. A rough vacuum pump reaches ,0.1 mBar level, then a turbo pump takes over and reaches ,105 mBar before cooling. After cooling, a vacuum of 107 mBar is typically reached. A sorption pump limits the effect of material outgassing. The optical beam from the telescope enters the cryostat through an optical window that is closed vacuum tight with an O-ring.

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Cooling Methods Various cooling methods are regularly used in astronomical instrumentation. Each technique has its own performance parameters, most noticeably the achievable temperature and the complexity of the system. Peltier cooling: Thermoelectric cooling uses the Peltier effect to create a heat flux between the junction of two different types of materials. This cooling technique does not induce vibrations. Single-stage Peltier cooling can reach 50 K below environmental temperature. This can be increased somewhat by using multiple stages. Liquid nitrogen (LN2 ) is relatively inexpensive and does not generate vibrations. Bath cryostats need regular LN2 refills; alternatively, continuous-flow cryostats create a steady flow of LN2 from a large dewar. The temperature of liquid nitrogen is
77 K. Liquid helium (LHe) has a boiling point of 4.2 K and can be supercooled under vacuum to achieve lower temperatures. Closed cycle coolers (CC) use adiabatic expansion of helium that is recuperated or regenerated. These devices include: Gifford–McMahon, pulse tube, Stirling, Joule– Thomson and Brayton. These devices have two stages, reaching temperatures down to 30 K and 4 K, but generate mechanical vibrations. Temperatures colder than 1 K can be achieved by dilution (Dil) or magnetic refrigeration. Cooling

Temp.

Peltier LN2 LHe CC Dil

.230 K .77 K .2 K .2 K ,0.1 K

Typical Power


100 mW @ 40 K delta T
1 W @ 80 K
100 mW @ 4 K
100 W @ 80 K &
20 W @ 20 K
0.2 mW @ 0.1 K

Vibr.

No No No Yes Yes

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Vacuum and Cryogenics

Thermal Models All materials emit thermal radiation. A body with emissivity «, surface area A and temperature T will emit energy at a rate of E ¼ «sAðT Þ4 where s is the Stefan-Boltzmann constant (5.673 108 Wm2 K4 ). A blackbody corresponds to « ¼ 1. Many materials have an « close to 1 in the thermal infrared. An « as low as 0.03 is achieved for gold or electrolytic polished copper or aluminium. The view factor from a surface A1 to another surface A2 at distance r is given by cos u1 cos u2 A2 F 1!2 ¼ pr2 The radiative heat transfer Q between two surfaces is Q¼

sðT 41  T 42 Þ 2 þ A1 F11!2 þ 1« A2 «2

1«1 A1 «1

A thermal model of a cryostat is a simplified scheme to model the effects of conduction, radiation, and convection between the different temperature levels in the cryostat. From the thermal model, a mathematical model with nodes is created in thermal simulation software to simulate cool-down, static operation, and warm-up.

Thermal properties of materials such as conductivity and specific heat can vary by an order of magnitude or more depending on the temperature. This makes thermal models highly nonlinear. Field Guide to Astronomical Instrumentation

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Thermal Effects in Space The space operational environment can result in temperatures approaching absolute zero in the shade; in contrast, there is a high thermal load on parts directly exposed to the sun. A reflective heat shield (MLI) limits the impact of these radiation effects. A radiator is a passive device that provides cooling by emitting many infrared photons into the night sky, while absorbing only a few photons from the cold night sky. Radiators are black, have a large surface, and must be permanently located in the shade. A heat pipe is a heat-transfer device that combines the principles of both thermal conductivity and phase transition to efficiently manage the transfer of heat between two solid interfaces.

Temperature cycling is the process of cycling through two temperature extremes, typically at relatively high rates of change. It is an environmental stress test used in evaluating product reliability. The thermal behavior of a satellite is verified in a space simulator: a large vacuum tank with black walls cooled by liquid nitrogen and illuminated by a powerful lamp. Outgassing is the release of a gas that was dissolved, trapped, frozen, or absorbed in some material. The released gas can condensate on optical components, deteriorating the optical performance. Most condensation occurs on the coldest parts of a system. Materials for use in vacuum show a very low rate of outgassing in vacuum and are tolerant to bake-out temperatures. Bake-out is an artificial acceleration of the process of outgassing.

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Software and Electronics

Control Astronomical instruments require control of adjustable elements such as motors and coolers. These low-level control functions are often implemented on specialized hardware that is programmed in its own language. The state of a mechanism is its position, velocity, or the force it applies. Piezoelectric actuators are position controlled, as an output voltage is needed to hold a required position. Regular motors are velocity controlled, as an output current will change the velocity of the mechanical motion. Voice-coil actuators are force controlled. An open-loop controller’s commands are based only on a mathematical model of the adjustable element and its current state. Stepper motors are often controlled in open loop.

A closed-loop controller has a sensor to determine the true state of an adjustable element. Its commands are based on a mathematical model of the adjustable element and the error between the desired and the true state.

Many adjustable elements can be controlled with a simple PID (proportional-integral-derivative) controller, where the control signal uðtÞ is the sum of terms that are proportional to the error signal eðtÞ itself, its integral, and its derivative with respect to time.

Z

uðtÞ ¼ g P eðtÞ þ g I

eðt 0 Þdt 0 þ g D ­eðtÞ=­t

The best choice for the three gains gP , gI , and gD depends on the dynamic properties of the adjustable element and the statistical properties of the error signal, and is determined by tuning. Field Guide to Astronomical Instrumentation

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Software and Electronics

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Instrument Control System An instrument control system (ICS) is a hardware and software layer on top of the low-level controls that controls individual, adjustable elements. Above the ICS is the observatory control system (OCS) that coordinates the telescope through the telescope control system (TCS) and the instruments through the ICSs to execute observing sequences. An operator or observer typically only interacts with the OCS.

An ICS has the following functions: • receiving commands from higher levels and generating sequences of commands for individual low-level controllers, • providing actual state information to higher levels, • controlling and reading out detectors and sending data to higher levels, • synchronizing instrument components in time, • detecting, recovering, and reporting errors, • protecting the instrument from damage, and • logging. An ICS can be implemented on standard computers with real-time operating systems. Observatories often provide a software infrastructure that prescribes a software architecture and provides the building blocks or components. This reduces the software efforts for the instrument builders as well as the commissioning and operating efforts for the observatory. Field Guide to Astronomical Instrumentation

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Software and Electronics

Data Handling Data handling is an integral part of an astronomical instrument and is closely linked to the observatory infrastructure. The data handling within the instrument moves the digital data from the camera(s) to the data handling system (DHS) provided by the observatory. Important aspects of the data handling capabilities inside the instrument are • real-time data preprocessing such as combination of nondestructive readouts and averaging of frames, • average and peak data rates defining the bandwidth requirements, • maximum latency of DHS to receive data defining the data buffer size in the instrument, • average and peak data volumes per day/night, • collection and transfer of logging and metadata including actual values of all instrument parameters. The observatory’s DHS consists of hardware and software having the following tasks: • receive data from instrument, • archive data, • retrieve data, • process data, • display real-time and quick-look data, • provide quality assurance, and • provide connection to virtual observatories.

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Data Transfer from Space The ever-increasing number of pixels of focal plane detectors and deep astronomical surveys leads to everincreasing data volumes that need to be transferred, processed, stored, and archived. For example, the Large Synoptic Survey Telescope (LSST), with its 3.2 billion pixels in the focal plane, will create 2.6 Gb=s or 12 TB of data per 10-hour night. While the data transfer via fiber links is not the limiting factor for ground-based instruments, the downlink of data from instruments in space is challenging. Most distant space observatories have both a low and a high gain antenna (HGA). The latter provides high amplification (data rates) but only within a small opening angle, which requires accurate pointing (i.e., stopping normal operations) for that data downlink. Different downlink schemes are in use, depending on the distance from Earth and the type of orbit. Observatories in Earth orbit, like the Hubble Space Telescope (HST), can send their data via HGA (up to 0.5 Mb=s) to a geosynchronous tracking and data relay satellite system (TDRSS), which then downlinks the data. More distant observatories on solar orbits (e.g., Spitzer) or at the Lagrangian L2 point [e.g., James Webb Space Telescope (JWST) and Herschel space telescope] make use of NASA’s Deep Space Network (DSN). The DSN provides three radio antennae with 120 deg longitudinal spacing near Goldstone, Madrid, and Canberra. To handle the 235 GB=day that JWST will produce, the DSN has to switch to the Ka-band (26 GHz), increasing the maximum data rate from 5 to 10 Mb=s. Unlike geostationary satellites, which have straightforward satellite-to-Earth communications, the contact between L2 and Earth is limited to about four hours per day. Many distant space observatories hence reduce the data volume onboard by lossless data compression, which provides a typical gain of a factor of two or less.

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Software and Electronics

Data Analysis Overview Data analysis occurs in steps from raw data to the final science result. Often the following processing levels are distinguished: Level 0 Level 1

Level 2

Level 3

Raw data from instrument is obtained. Standard data reduction steps are applied (bias, dark, flat, sky background), timing and ancillary information added, and calibrations applied (e.g., wavelength solution). Images are transformed into the sky coordinate system, spectra are extracted, and wavelengths are calibrated. Astronomical quantities are derived from Level-2 data (e.g., aperture photometry, spectral line properties).

Level-1 data for instruments with CCD or CMOS detectors are obtained from the raw Level-0 data by applying calibration data: • science frame S, exposure time tS , • dark frame D, exposure time tD , • bias frame B, zero exposure time, and • flat field frame F, exposure time tF . The corrected (calibrated) image S 0 is then given by 0

S ¼

S  ttDs ðD  BÞ  B F  ttDF ðD  BÞ  B

The denominator F  ttDF ðD  BÞ  B is often normalized to unity such that the mean of S 0 equals the mean of S. Processing to Level 1 may also include the removal of bad pixels, cosmic ray artifacts, and the sky background. Processing to Levels 2 and 3 is highly dependent on the particular instrument.

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Electronics: Cabling Electrical cables significantly contribute to the heat transfer between the ambient temperature vacuum wall and the cryogenic part of the instrument. Therefore, relatively long cables are used that are temperature synchronized at various levels by connectors or potting. This prevents radiative hot points inside cold structures. The maximum current in electrical cables in a cryostat is limited as they heat up because of the lack of convection. Several wire materials are available, with distinct thermal and electrical properties, applicable for specific use and temperature range. The wire insulation material should not cause outgassing.

Material

Copper Phosphor bronze Manganin Nichrome

Electric resistivity [mV cm] @300 K

Thermal conductivity [Wm1 K 1 ] @300 K

1.7 11 48 120

400 48 22 12

Cryogenic Thermal conductivity [Wm1 K 1 ]

1100 @ 20 K 5 @ 10 K 0.006 @ 0.1 K 0.7 @10 K

Heaters require a lot of power for emergency warm up. There are voltage limits and current restrictions per pin in electrical vacuum feed throughs. This increases the number of required pins on a connector. It is good practice to use pin savers on expensive vacuum feed throughs. CAUTION: The breakdown (discharge) voltage in a low pressure system can be just over 100 V at pressures in the mBar range. Cryostats operate at much lower pressures and are tested at ambient pressure where electronic discharge occurs at much higher voltages. For safety reasons, however, voltages in cryostats are limited to 48 V. If higher voltage cannot be avoided, these systems must be automatically switched off during depressurization and repressurization.

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94

Software and Electronics

Shielding Electromagnetic compatibility (EMC) and radio frequency interference (RFI) control the unintentional generation and the susceptibility of electronics at radio frequencies. EMC is important in power supplies, microcontrollers, and pulsed electronics such as solenoids. There are four basic coupling mechanisms: conductive, capacitive, magnetic or inductive, and radiative.

EMC controlling measures include: • shielded housing with RF fingerstock, • shielded cables that are surrounded by a conductive layer grounded at one or both ends, • star earthing schemes and ground planes to avoid ground loops, • RF chokes at critical points such as cable entries to reduce RFI effects, and • avoidance of fast switching. Stepper motors can cause electrical spikes that compromise weak electrical signals from sensors. In particular, data cables from the CCD detector must be well shielded to avoid cross talk.

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Systems Engineering

95

Systems Engineering: Requirements Definition Requirements analysis in systems engineering is the task of determining performance requirements, goals, and conditions for an instrument. The technical requirements definition process is used to transform the stakeholder expectations (input) into unique, quantitative, and measurable technical requirements (output).

Requirements come from various stakeholders and can be conflicting. Prioritize requirements by identifying top-level functional requirements and derived requirements. Requirements are expressed as “shall” statements that can be used for defining a design solution and enabling technology developments. Goals are optional and are expressed as “should” statements. Performance requirements describe the extent to which a function must be executed; they are measured in terms of quantity, quality, coverage, timeliness, and readiness. During requirements analysis, performance requirements are interactively developed across all identified functions. The requirements should be defined to a level of detail sufficient for system design, and should be documented, actionable, measurable, testable, and traceable to identified needs or opportunities. Requirements are fixed and can only be changed by approval of a change control board after careful investigation of the consequences of the proposed change. The requirements document provides a baseline against which compliance can be measured.

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Systems Engineering

Block Diagrams A block diagram is a diagram of a system in which the principal parts or functions are represented by blocks connected by lines that show the relationships between the blocks. The block diagram is typically used for a higherlevel, less-detailed description, aimed more at understanding the overall concept and less at understanding the details of implementation.

A functional flow block diagram (FFBD) is a multi-tier, time-sequenced, step-by-step flow diagram of a system’s functional flow. Each function should be represented by a single box and should be a definite, finite, discrete action to be accomplished by system elements.

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97

Interface Control An interface control drawing or interface control document (ICD) describes the interface or interfaces between subsystems or between a system and subsystem. Several types of interfaces are common in astronomical instrumentation: optical, mechanical, electronic, thermal, and data.

Interfaces are described in text in a document, however, elaborate mechanical interfaces are better documented in a 3D drawing, e.g., in universal STEP file format. Both the nominal situation of the interface and the acceptable tolerance range are described. An ICD complements the requirements specification in describing the external references of a work package. An ICD is fixed and can only be changed by approval of a change control board after careful investigation of the consequences of the proposed change.

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Systems Engineering

Error Budgets Uncertainty propagation or error propagation is the quantification of uncertainties in system output(s) propagated from uncertain inputs. Uncertainty propagation modeling methods include Monte Carlo simulations and Taylor series. An error budget provides an estimate of all potential errors within a (sub)system that lead to deviations from the desired status or performance. System performance is ensured if all error sources are in their allocated budget. Error budgets are used in advance of the comprehensive design effort as a method to evaluate the ability of a proposed system configuration to meet the desired specifications. Reducing potential errors early in the design phase also reduces any compensation effort that might be subsequently required. Tolerances in error budgets can be specified as 1s values, 3s values, or rejection criteria. Not all errors follow a normal distribution. Large optical components are polished until the wavefront error meets specifications, which, in practice, results in components just meeting rejection criteria.

The equation for a normal or Gaussian distribution can be found on the next page.

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Noise and its Distribution Noise is the unwanted signal underlying the true signal. In astronomical instruments, it may have various origins, from the detector system (read noise, dark current noise, flatfielding uncertainty) and environmental factors (cosmic rays, electromagnetic interference, atmospheric effects) to noise in the source signal itself (e.g., photon shot noise). Apart from specific systematic noise, the most fundamental noise in astronomical instruments usually falls in one of three categories: Poisson noise, Gaussian noise, or 1/f noise. A Poisson distribution describes the probability Pðk; mÞ of a number of events k occurring in a fixed period of time for a process with a known average rate m: Pðk; mÞ ¼

mk em k!

An example is an average photon flux m from a light source per unit time interval; Pðk; mÞ is often called shot noise and describes the probability that the detected number has pffiffiffiffi a certain value. The standard deviation of m is m. A Gaussian (or normal) distribution describes the probability Pðx; mÞ to measure a value of x around a mean of m for a number of uncorrelated measurements:   1 ðx  mÞ2 p ffiffiffiffiffiffi exp  Pðx; mÞ ¼ 2s2 2ps Pðx; mÞ is symmetric around m. The likelihood that a value x lies within 1, 2, or 3 standard deviations s is 68%, 95%, and 99.7%, respectively. An example for a Gaussian distribution is detector readout or flat-field noise. For a large number of events, Poissonian and Gaussian distributions become very similar. Finally, 1/f (or pink) noise describes a common process in nature in which the power per unit frequency is inversely proportional to the frequency to some power a: const P¼ a f Field Guide to Astronomical Instrumentation

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Systems Engineering

Signal-to-Noise Ratio The signal-to-noise ratio (SNR) is the ratio between signal power S and the underlying background noise N. The SNR is the standard unit to quantify the statistical significance (or probability of being real) of a detected signal, either spatially (point source), spectrally (spectral line) or temporally (pulse). To calculate the SNR correctly, both signal and noise must be measured for the same bandwidth and time interval. Generally, the detection of a signal is considered likely to be real (with 99.7% confidence) if SNR . 3 (i.e., above 3s of the noise for a Gaussian noise distribution), or certain if SNR . 5 (Rose criterion). In the ideal case of a signal S that is spread over npix detector pixels, and where the relevant noise consists only of noise from the sky background B, detector read noise R, and dark current noise D, the achievable SNR in m exposures of time t can be approximated with the CCD equation: pffiffiffiffiffiffiffiffiffiffi S m·t SNR ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2 S þ npix B þ D þ Rt One has to distinguish two fundamental cases: a. The sky- or background-limited case when B .. 2 D þ Rt and B . S, which is typically given for IR astronomy. 2 b. The detector noise-limited case when Rt .. B þ D, which is typically given for optical astronomy. Note that in case (b) the SNR increases linearly with exposure time t, while in case (a) the SNR increases with pffiffi t. In case (a) the SNR has a natural limit given by the shot noise of the background. It is a common design goal to reduce the detector noise to this fundamental limit to reach background-limited performance (BLIP).

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Instrument Sensitivity and Integration Time The sensitivity of an astronomical instrument is essentially defined by the required observing time to reach a certain SNR. The sensitivity depends on many parameters, such as the detector read noise, dark current noise, background noise, source brightness, transmission of instrument and atmosphere, detector quantum efficiency, bandwidth, pixel sampling, and the quality of image formation (atmospheric turbulence and performance of the optical system). Most important for planning the observation, however, are the integration time and telescope aperture. For a background-limited (photon shot noise dominant) signal pffiffiffiffi B, the 1s noise is B; hence, increasing the integration time pffiffiffiffiffiffiffi tint will increase the SNR by tint . For a detector-noise-limited system, the SNR will increase with tint . Using a larger telescope aperture, D will increase the source flux S in proportion to D2 , as will the sky background B, but the pffiffiffiffi background noise will only increase by B. In the case of a point source observed at the diffraction limit, the pixel sampling is usually fixed to the FWHM of the source, which shrinks with D and leads to another pffiffiffiffi reduction of the (spatially uniform) background noise by B, while keeping S constant. Combining these relations, we find that tint scales with D as follows [depending on whether the source is a diffractionlimited point source (PS), a seeing-limited (SL) point source, or an extended source]: tint /

PS

SL

Background lim. detector noise lim.

D4 D2

D2 D2

The steep scaling of tint / D4 for point sources is a major driver for the construction of diffraction-limited extremely large telescopes (ELTs). Most instruments provide online exposure time calculators (ETCs), which estimate the required tint or the achievable SNR for a given source brightness, wavelength, and atmospheric condition.

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Systems Engineering

Signal Sampling Sampling is a term used in signal processing that describes the determination of a signal value from a series of discrete measurements. Sampling can be done in the spatial, spectral, or temporal domain, and is necessary, as no real detector system can provide infinite resolution. In order to recover the full information in the signal, the sampling process must satisfy certain criteria. The Shannon Nyquist theorem states that if a signal function jðxÞ contains no frequencies higher than t, the signal can be completely determined by sampling at values xi , which are 1=ð2tÞ or less apart. Systems that satisfy this criterion are often called Nyquist sampled. Practical examples of signals are an unresolved source or a spectral line of which the full width at half maximum (FWHM), corresponding to 1=t, must be sampled at least twice, e.g., by two or more pixels. Measurements with higher or lower sampling rates are called oversampled or undersampled, respectively. Oversampling provides redundant measurements at the expense of additional bandwidth or detector pixels, or lower sensitivity in the case of detector-noise-limited measurements. However, oversampling might be desirable if the detector has noisy pixels or if higher frequencies than t (e.g., substructure of a spectral line) are expected. Undersampling can lead to aliasing when a periodic frequency component above t=2 is indistinguishable from an associated lower frequency component.

Typical effects of undersampling in astronomical instruments are loss of spatial or spectral resolution to less than what the telescope or spectrograph could provide.

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Systems Engineering

103

Project Management A work breakdown structure (WBS) is a deliverableoriented decomposition of a project into smaller work packages that can be executed by different teams.

A stage gate process is a project management technique in which a project is divided into stages or phases, separated by gates. At each gate the progress of the project is evaluated by a review committee, who can also decide on the continuation of the process. Reviews force a project to meet review requirements simultaneously for all work packages. This ensures that any work package has sufficient information from other work packages and that there are no omissions. Space mission projects are organized as follows: Phase 0: Mission Analysis. Phase A: Feasibility. Phase B Preliminary Definition. Phase C: Detailed Design. Phase D: Production and Qualification. Phase E: Utilization. Phase F: Disposal.

A Gantt chart illustrates a project schedule. It shows start and finish dates of individual tasks and the relation between them, revealing the critical path and the duration of the entire project. Field Guide to Astronomical Instrumentation

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Systems Engineering

Technology Development Research and development (R&D) is the creation of knowledge to be used in products or processes. Technology development is the process of research, creation, and improvement of technology. Technology is the use of knowledge tools and machines to solve a problem. Technology readiness levels (TRLs) are measures used to assess the maturity of evolving technologies (devices, materials, components, software, work processes, etc.) during their development. The primary purpose of using technology readiness levels is to help management in making decisions concerning the development and transitioning of technology. It provides a common understanding of technology status over multiple disciplines. NASA, ESA, and ESO have somewhat different criteria for meeting a certain technology readiness level.

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Risk Management Risk management is the identification, assessment, and prioritization of risks, followed by coordinated and economical application of resources to minimize, monitor, and control the probability and/or impact of unfortunate events. Risks can be ranked in a probability-impact matrix. Risk ¼ probability 3 impact Risk mitigation strategies include: avoid, reduce, transfer, and accept, but monitor risk and reserve budget. A risk assessment and method statement (RAMS) is a tool for gathering information to prioritize assets, identify mitigation needs, and develop preparedness, response, and recovery plans. It consists of several steps: • identify functions and processes, • determine criticality, • determine recovery time, • identify threats, • determine vulnerability, and • select action plans. The risk assessment matrix (RAM) provides a systematic method for assigning a hazard level to a failure event based on the severity and frequency of the event. Risk categories differentiate credible high-hazard threats that may result in loss of life and property from less probable risks.

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Systems Engineering

Quality Management Quality control (QC) is the most basic level of quality management. QC is typically an inspection before delivery of a product. If the product does not pass QC, this is called nonconformity. Quality assurance (QA) is aimed at preventing nonconformities/defects. QA includes management of the quality of raw materials, assemblies, products and components, services related to production, management, and inspection processes. Quality audits are performed to verify conformance to standards through review of objective evidence. A quality management system (QMS) is a collection of business processes focused on achieving quality objectives. ISO 9001 is an international standard defining all of the elements that should exist in a sound quality management system. This standard specifies that the organization shall issue and maintain the following documented procedures: control of documents, control of records, internal audits, control of nonconforming product, corrective action, and preventive action. QA is useful at any stage in a project. For example: Planning

Design Production Operational

To ensure that the product can be operated comfortably and that the quality responds to expectations. To confirm the safety of the product and the degree of achievement of quality targets. To verify the safety of the product and to ensure the quality level. To ensure the proper usage of the product.

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Manufacturing, Assembly, Integration, and Testing

107

Optics Manufacturing Common steps in optics manufacturing are: • optical glass blank manufacturing, including mixing, casting and annealing, • subsequent rough shaping, generating, and fining for creating the shape of the optical component from the initial blank, with only submillimeter oversize, • polishing and figuring of optical surfaces to create a specular surface with nanometer-level accuracy, • cleaning and possibly cementing to form doublets (two lenses) or triplets (three lenses). This process works well for spherical surfaces. Alternative processes have been developed to handle aspheric and freeform surfaces with reduced cost and improved accuracy. Single-point diamond turning involves mechanical machining of precision elements using machines equipped with diamond-tipped tool bits. Computer numerical control (CNC) diamond turning is used to manufacture aspheric optical elements. Precision glass molding is a replicative process that allows the production of optical components from glass by heating the glass and pressing it against a mold. Ion-beam figuring (IBF) uses an ion stream to locally “polish” optical surfaces and achieve better surface figure. For smooth surfaces, the total integrated scatter (TIS) due to RMS surface roughness Rq is  TIS ≈

Rq 4p l

2

An optical coating comprises one or more thin layers of material deposited on an optical surface in order to change its reflection and transmission for certain wavelengths. Common coatings are anti-reflection (AR), high-reflector, and dichroic thin-film optical filters. Field Guide to Astronomical Instrumentation

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Manufacturing, Assembly, Integration, and Testing

Optics Testing Optics testing provides error feedback in the final stages of the optics manufacturing process. Newton (test plate) interferometry is a quick method to monitor the surface figure as it is being shaped and figured. The Foucault knife-edge test measures conic shapes of optical mirrors, with error margins of a fraction of the wavelength of light. In phase-shifting interferometry, multiple interferograms are analyzed with the reference optical surface shifted by a precise fraction of a wavelength between each exposure. Computer software analyzes the collected intensity data from every point of the test optics. Aspheres can be tested in the same interferometer setup if the deviation from a spherical surface is only a few micrometers and individual fringes can be distinguished. Auxiliary optics such as computer-generated holograms are necessary to test stronger aspheres. A spectrometer (spectrophotometer, spectrograph, or spectroscope) measures the intensity of light over a specific portion of the electromagnetic spectrum. It is used to test the performance of coatings. Surface imperfections are localized blemishes on the surface of an optical element, such as scratches and digs. Specifications are in the ISO 10110 norm or MIL standard. A profilometer quantifies the roughness of a surface. Contact profilometers use a stylus, and noncontact profilometers use optical measurement techniques. Crossed induced) between mounted

(90 deg) linear polarizers can reveal (stress birefringence in an optical element placed the polarizers, visualizing, e.g., local forces in optics.

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Alignment Alignment is the art of placing optical (and mechanical) components at the intended position and orientation. Collimating a telescope means lining up its optical components (lenses, mirrors, eyepieces) in their proper positions. Several tools are used to facilitate alignment of an optical system. An alignment telescope creates a line of sight that can be used as a reference to align optical components. Lasers are also used to create a reference optical beam. In both cases, reference targets are used at predetermined positions to set and check the alignment. Retroflectors such as a corner cube prism return an optical beam, independent of the alignment of the retroreflector. A penta prism is a five-sided prism that deflects the optical beam 90 deg, independent of the alignment of the pentaprism. A penta beamsplitter has an additional wedge to allow the beam to pass undeviated. An autocollimator is an optical instrument for measurement of angles by projecting an image onto a target mirror and measuring the deflection. A theodolite is a surveying instrument that measures vertical and horizontal angles. Similarly, a laser tracker operates by steering a laser beam to home in on the reflection from a sphere-mounted retroreflector. Focusing is positioning at best focus, e.g., by using intrafocal and extrafocal images. Point source illumination and a Bahtinov mask indicate the direction of best focus. Keep track of every pupil and focus position in alignment.

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Manufacturing, Assembly, Integration, and Testing

Instrument Commissioning After successful construction of the instrument and testing in the lab, following the plan for assembly, integration, and verification or testing (AIV or AIT), the instrument must be commissioned at the telescope. Usually, the commissioning consists of two phases: the functional testing and the science verification. The functional testing checks the functions and instrument modes and the basic performance of the instrument and its subsystems. These activities follow a detailed, pre-defined commissioning plan and require ground- or space-based calibration sources. An important component is the verification of the instrument top level requirements (TLRs); a checklist will reveal which requirements have been met and in which areas the instrument is not performing to specifications. The latter cases usually require additional activity, either by modifications of the instrument hardware or by finding solutions in the data processing software. The aim of the science verification (SV) phase is to demonstrate the scientific performance and capabilities of the instrument. The SV uses astronomical space-based targets and representative, standard observing modes. If successful, SV may not only lead to several press releases, but also improve the quality and accuracy of the scientific calibration of the instrument and the associated data pipeline. Many observatories make the data from the instrument commissioning immediately public, i.e., offer them to the interested communities.

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Operations and Maintenance After the commissioning and science verification of a new instrument on the telescope, the operations phase (phase E) begins. For a smooth, efficient, and long-lasting operations phase, numerous aspects are relevant and should already be considered during the design phase of the instrument (the relative importance of these aspects varies from facility to facility, and, in particular, between ground- and space-based observatories): • reliability of the instrument under normal operating conditions; a measure of reliability is the mean time between failures (MTBF), • the degradation (wear and aging) of key components, which may determine the lifetime of the instrument until decommissioning, • simplicity of operation and maintenance, keeping in mind that, in general, the operation is performed by a different group than the team of people who designed and built the instrument, • ease of access to those components that require regular maintenance or upgrades, • handling of the instrument (size, weight, robustness) during transport, integration, regular instrument changes, and alignment procedures, • safety procedures that need to be followed to avoid risks to personnel and instrument, • cost and availability of consumables needed for the continuous operation of the instrument and its electronics, such as electricity and cryogenics, • a complete set of detailed documentation of all aspects of the instrument to facilitate maintenance and allow for instrument refurbishments, • simplicity of the optical, mechanical, electrical, and thermal interfaces to the telescope, • data rates, which need to be processed and stored, • required daytime support, e.g., calibration procedures and refilling with liquid coolants, and • special requirements on the control of the instrument, (e.g., remote control or location of the control room). Field Guide to Astronomical Instrumentation

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112

Appendices

Optical Material Properties

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Appendices

113

Mirror Substrate Material Properties

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Appendices

Mechanical Material Properties

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Material Selection This plot is helpful in selecting materials for optomechanical instrumentation. The specific stiffness (Young's modulus/density) is plotted against the thermo-mechanical stability (thermal conductivity/CTE). Triangles represent metals, diamonds represent glasses, and circles represent special materials.

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116

Appendices

,62  2SWLFDO 'UDZLQJ 6WDQGDUG ISO 10110 is a 13-part standard describing the drawings for optical elements and systems.

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117

ECSS The European Cooperation for Space Standardization (ECSS) is an initiative established to develop a coherent, single set of user-friendly standards for use in all European space activities. ECSS publishes handbooks and technical memoranda on the following subjects: • project management • product assurance • engineering • sustainability

More information can be found on the ECSS website: http://www.ecss.nl/

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118

Equation Summary Fresnel reflection and transmission amplitudes for s and p-polarized light: 2 sin ut cos ui sinðui þ ut Þ 2 sin ut cos ui tp ¼ sinðui þ ut Þ cosðui  ut Þ sinðui  ut Þ rs ¼ sinðui þ ut Þ tanðui  ut Þ rp ¼ tanðui þ ut Þ ts ¼

Reflectivity and transmission at interface for arbitrary linear polarization orientation: R ¼ jrp j2 cos2 a þ jrs j2 sin2 a T¼

jn˜ 2 j cos ut ðjt j2 cos2 a þ jts j2 sin2 aÞ jn˜ 1 j cos ui p

Normal-incidence reflectivity: 
nm  ns 2 R¼ nm þ ns Phase change on total internal reflection (TIR): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 cos ui sin2 ui  nn21 d tan ¼ 2 sin2 ui Focus shift and image displacement of tilted, planeparallel plate: Dz ≈

tðn  1Þ n

Dx ≈

utðn  1Þ n

Thick lens equation: 
1 1 1 ðn  1Þd ¼ ðn  1Þ  þ f R1 R2 nR1 R2 Field Guide to Astronomical Instrumentation

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Equation Summary Radii of curvature for best-form lens: R1 ¼

2f ðn  1Þ qþ1

R2 ¼

2ðn2  1Þ s 0  s q¼ · 0 nþ2 s þs

2f ðn  1Þ q1

Surface sag of conic surface: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 
r2 r2 1 þ 1  ð1 þ K Þ 2 z¼ R R Central wavelength shift of interference filter due to angle of incidence and temperature: ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
 ­lc nm 2 2 1 DT DlðuÞ ¼ lc sin u  1 Dlc ðDT Þ ¼ ­T neff Multicavity bandpass filter transmission profile:     2ðl  lc Þ 2ncavities 1 T ðlÞ ¼ 1 þ DlFWHM Numerical aperture of a fiber: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðn2core  n2cladding Þ NA ¼ sin umax ¼ nair Angular dispersion of a prism: ­d sin a ­n ¼ 0 · ­l cos uo cos ui ­l

sin ui0 ¼

sin ui n

sin uo ¼ n sinða  ui0 Þ Grating equation, angular dispersion, and spectral resolution: ml ¼ dðsin a þ sin bÞ

db m ¼ dl d cos b

R¼m

L d

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Equation Summary Grating blaze angle and blaze wavelength: aþb 2

ub ¼

lb ¼

2d sin ub cosða  ub Þ m

Grating efficiency in Littrow configuration: h¼

sin2 g g2

g ¼ 2pa

cos ub sinða  ub Þ l

Spectral resolution of grating spectrometer: R¼

lmN Dws

Finesse of Fabry–Perot: pffiffiffiffi p R F¼ 1R Intensity at output of Fourier transform spectrometer: IðxÞ ¼ I 0 þ

1 2

Z

k2

BðkÞ cosðkxÞdk

k1

I0 ¼

1 2

Z

k2

BðkÞdk

k1

Optimal extraction of spectrum: P W ðlÞ · ½C ðlÞ  BðlÞ SðlÞ ¼ i i P i W i ðlÞ i

Jones and Mueller matrices of an ideal, linear polarizer:
 cos u sin u cos2 u Jpol ðuÞ ¼ cos u sin u sin2 u 0 1 cos 2u sin 2u 01 B cos2 2u sin 2u cos 2u 0 C 1 B cos 2u C Mpol ðuÞ ¼ B C 2 A 2B 2u 0 sin 2u sin 2u cos 2u sin @ 0 0 0 0

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Equation Summary Jones and Mueller matrices retarder: 0 1 
d B0 0 ei2 Mr ¼ B Jr ðdÞ ¼ d @0 0 ei2 0

of an ideal, linear 0 1 0 0

1 0 0 0 0 C C cos d sin d A sin d cos d

Output of rotating waveplate polarimeter: I Q þ ½ð1 þ cos dÞ þ ð1  cos dÞcos 4u 2 4 U V þ ð1  cos dÞsin 4u  sin d sin 2u 4 2

I0 ¼

Dual-beam exchange polarimetry data reduction: 

 1 Sl1 Sr2 1 V1 V2  1 ¼ þ I2 4 Sl2 Sr1 2 I1 Output of spectral modulation polarimeter:     IðlÞ 2pdðlÞ 0 þ 1 þ P L ðlÞ cos þ 2wðlÞ I ðlÞ ¼ 2 l Optical transfer function for an unobscured aperture: OTFðkn Þ ¼

2 ðcos1 kn  kn p

qffiffiffiffiffiffiffiffiffiffiffiffiffiffi klf 1  k2n Þ kn ¼ D

Image as a function of object intensity distribution and point-spread function: ZZ iðx; yÞ ¼ o  p ¼

iðx 0 ; y 0 Þpðx  x 0 ; y  y 0 Þdx 0 dy 0

Moffat point-spread function model:
2 b r iðrÞ ¼ 1 þ a 

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Equation Summary Angular resolution of interferometer: u ¼ 0.764 ·

l B

Visibility definition: V ¼

I max  I min I max þ I min

Closure phases: Fobs ð1  2Þ ¼ F0 ð1  2Þ þ ½Fð2Þ  Fð1Þatmos Fobs ð2  3Þ ¼ F0 ð2  3Þ þ ½Fð3Þ  Fð2Þatmos Fobs ð3  1Þ ¼ F0 ð3  1Þ þ ½Fð1Þ  Fð3Þatmos ⇒ CPð1  2  3Þ ¼ F0 ð1  2Þ þ F0 ð2  3Þ þ F0 ð3  1Þ Interferometer Signal to Noise:
 S / ½NðN  1Þ1=2 N



S N

bkgrd{lim

S N photon{lim

/n·V pffiffiffi / n·V

Dirty image in aperture synthesis interferometry: ZZ I D ðx; yÞ ¼ Iðx; yÞ 

Sðu; vÞei2pðuxþvyÞ dudv

Fried parameter: 
2  3 Z 5 2p sec z C 2n ðhÞdh ½m r0 ¼ 0.423 l Greenwood frequency:  f G ¼ 2.31l

65

3

Z sec z

5 C 2n ðhÞv3 ðhÞdh

5

½Hz ¼ 0:43

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vw ½Hz r0

123

Equation Summary Adaptive optics Strehl ratio gain and residual wavefront errors: G ≈ 0.5


2 5 5 D 0.3ðrD Þ3 N 6 0 e r0

pffiffiffiffiffiffi
D 53 s2N ¼ 0.3 N  3=2 ½rad2  r0

Wavefront variance due to atmospheric turbulence: s2seeing ¼ 1.02


5
5 D 3 D 3 ½rad2  s2noMotion ¼ 0.134 ½rad2  r0 r0

Isoplanatic angle: u0 ≈

0.3r0 ½rad H

Z Z 3 5 5 H ¼ sec z C 2n ðhÞh3 dh C 2n ðhÞdh ½m

Wavefront error variance due to off-axis source position:
5 u 3 2 ½rad2  soffaxis ¼ u0 Wavefront error variance due to photon noise in wavefront sensor:
2 l =np ½rad2  s2WFS ≈ r0 Wavefront error variance due to deformable mirror fitting error:
5 d 3 2 ½rad2  sDM ≈ 0.3 r0 Wavefront error variance due to control-system lag: s2control


5 t 3 ¼ s ½rad2  t0

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Equation Summary Radiative heat transfer: sðT 41  T 42 Þ Q ¼ 1«1 1«2 1 A1 «1 þ A1 F 1!2 þ A2 «2 Proportional-integral-derivative controller: Z uðtÞ ¼ g P eðtÞ þ g I eðt 0 Þdt 0 þ g D ­eðtÞ= ­t Cutoff-wavelength of a photoconductor: lc ¼

hc 1.24 mm ¼ Eg E g ½eV

Detector data reduction: S0 ¼

S  ttDs ðD  BÞ  B F  ttDF ðD  BÞ  B

Signal-to-noise ratio of CCD exposure: pffiffiffiffiffiffiffiffiffiffi S m·t SNR ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
 R2 S þ npix B þ D þ t Total integrated scatter (TIS):
TIS ≈

Rq 4p l

2

Poisson and Gaussian distributions: Pðk; mÞ ¼

mk em k!

  1 ðx  mÞ2 Pðx; mÞ ¼ pffiffiffiffiffiffi exp  2s2 2ps

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Bibliography Bass, M. (Ed.), Handbook of Optics Volume I–V, McGraw Hill, New York (2009). Born, M. and E. Wolf, Principles of Optics, 6th Ed., Cambridge University Press, Cambridge, UK (1997). Breckinridge, J. E., Basic Optics for the Astronomical Sciences, SPIE Press, Bellingham, WA (2012). Donabedian, M., Spacecraft Thermal Control Handbook. Volume II: Cryogenics, The Aerospace Press, El Segundo, CA (2003). Gilmore, D., Spacecraft Thermal Control Handbook. Volume I: Fundamental Technologies, The Aerospace Corporation, El Segundo, CA (2002). Greivenkamp, J., Field Guide to Geometrical Optics, SPIE Press, Bellingham, WA (2004). Haniff, C., “An introduction to the theory of interferometry”, New Astronomy Reviews, Proc. of the EuroSummer School 51(8–9), (2007). “Observation and Data Reduction with the VLT Interferometer” Hearnshaw, J., Astronomical Spectrographs and their History, Cambridge University Press (2009). Hecht, E., Optics, 4th Ed., Addison-Wesley, Upper Saddle River, New Jersey (2002). Högbom, J. A., “Aperture Synthesis with a Non-Regular Distribution of Interferometer Baselines.” Astr. Astrophys. Suppl., 15, 417. (1974). Huber, M. C. E., A. Pauluhn, J. L. Culhane, J. G. Timothy, K. Wilhelm, and A. Zehnder (Eds.), “Observing Photons in Space,” ISSI Scientific Report SR-009, International Space Science Institute (2010). Léna, P., D. Rouan, F. Lebrun, F. Mignard, and D. Pelat, Observational Astrophysics, Springer (2012). Macleod, H. A., Thin-film Optical Filters, Institute of Physics Publishing, London (2001). Field Guide to Astronomical Instrumentation

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Bibliography McLean, I. S., Electronic Imaging in Astronomy: Detectors and Instrumentation, Springer Praxis Books, Chichester, UK (2008). Rieke, G. H., Detection of Light: From the Ultraviolet to the Submillimeter, Cambridge University Press (2002). Rieke, G. H., Measuring the Universe: A Multiwavelength Perspective, Cambridge University Press (2012). Schroeder, D. J., Astronomical Optics, Academic Press, (1999). Tinbergen, J., Astronomical Polarimetry, Cambridge University Press, Cambridge (1996). Tyson, R. K., Principles of Adaptive Optics, CRC Press, Boca Raton, FL (2010). Wolfe, W. L. and G. J. Zissis, The Infrared Handbook, In-frared Information Analysis (IRIA) Center, Environmental Research Institute of Michigan (1989). Wolfe, W. L. (Ed.), Optical Engineer’s Desk Reference, OSA & SPIE (2003). Yoder, P. and D. Vukobratovich, Opto-Mechanical Systems Design, Fourth Edition, Two Volume Set: Opto-Mechanical Systems Design, Fourth Edition, Volume 2: Design and Analysis of Large Mirrors and Structures, CRC Press, Boca Raton, FL (2015).

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Index 1=f noise, 33, 99 aberration parameters, 75 aberrations, 5 absolute wavelength, 46 absorber, 29 absorption, 1 absorption coefficient, 1 AC motor, 81 achromatic lens, 11 achromatic retarder, 22 actuator, 68, 80–81 actuator pitch, 68 actuator stroke, 68 adaptive optics, 40, 55, 65 adaptive optics control, 69 aliasing, 102 alignment, 109 alignment references, 78 alignment telescope, 109 alignment mechanisms, 80 amplitude, 63 amplitude apodizer, 63 amplitude mask, 62 anamorphic magnification, 41 angle of incidence, 15 angular dispersion, 18–19 angular resolution, 54 annealing, 34 anodized, 77 anti-reflection coatings, 16 aperture, 4 aperture stop, 4 aperture synthesis, 54, 59 aplanatic Gregorians, 36 apodized Lyot coronagraph, 62 apodizer, 62

apodizing phase plate, 63 aspect ratio, 10 aspherical corrector, 37 aspheres, 107, 108 assembly, integration, and verification, 110 astigmatism, 5 astronomical interferometer, 54 athermal lens, 11 atmospheric dispersion, 40 atmospheric dispersion corrector, 18, 40 audits, 106 autocollimator, 109 avalanche photodiode (APD), 28 back-illuminated, 26 background-limited, 100 background-limited performance (BLIP), 33, 100 Bahtinov mask, 109 bake-out, 87 bandgap, 25 banding, 33 bandpass filters, 13, 17 barrel, 78 baseline, 54 beam combiner, 55 beat frequency, 30 bi-crystalline retarder, 22 bias voltage, 34 BIB, 28 binary aperture, 63 binning, 31 birefringence, 108 black paint, 77

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Index blaze angle, 19 blaze wavelength, 19 block diagram, 96 blocking, 13 blocking layer, 28 blocked-impurity-band, 28 bolometers, 24, 29 Brewster angle, 3 brushless DC motor, 81 calibration, 42, 110 camera, 41 Cassegrain, 36 catadiotropic telescope, 37 center wavelength (CWL), 13 central obscuration, 8 change control board, 95 charge transfer efficiency, 26, 33 charge coupled device (CCD), 26, 31, 100 chief ray, 74 chopping, 35 circular polarization, 2 closed-loop controller, 88 closure phase, 58 closed cycle cooler, 85 CMOS, 26, 31 CNC diamond turning, 107 coaxial beam combiner, 56 coatings, 16 coefficient of thermal expansion, 83 coherent detector, 24, 30 collimated beam, 4 collimator, 41 colored glass filter, 14

coma, 5 commissioning, 110–111 complex aperture function, 6 compliance, 95 composite bolometer, 29 compound zero-order retarder, 22 compensator, 76 conduction band, 25 cone effect, 70 conic constant, 12 conic sections, 12 consumables, 111 control, 88 control of the instrument, 111 control system, 65 controller, 88 converging beam, 4 coronagraphs, 64 correctors, 37-38 cost, 111 coudé, 42 cross-disperser, 43 cryostat, 84 crystal polarizers, 20-21 current restrictions, 93 curvature wavefront sensor, 67 cutoff wavelength, 25 cylinder baffle, 77 dark current, 27 data handling system, 90 data pipeline, 110 data rates, 111 data volumes, 91 data analysis, 92

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Index data handling, 90 daytime support, 111 DC motor, 81 Deep Space Network, 91 deformable mirror, 65, 68 deformable secondary mirror, 68 degree of polarization, 2 degrees of freedom, 65, 79 Dekker mask, 42 delay line, 55 design parameters, 75 design requirements, 75 detective quantum efficiency, 24 detector noise-limited, 100 detectors, 24, 26 dewar, 84 diamond turning, 107 dichroic filter, 13 dichroic sheet polarizer, 20 diffraction pattern, 6 direct photon detector, 24 dirty beam, 61 dirty image, 61 disperser, 41 displacement damage, 34 distortion, 5 distribution, 99 dithering, 35 diverging beam, 4 documentation, 111 dome flats, 35 doping, 27 double-Gauss, 39 dual-beam exchange, 51 dynamical range, 55

Earth-rotation synthesis, 54 ease of access, 111 Echelle grating, 19, 43 effective area, 60 electronic circuit, 55 electrons, 34 electrical cables, 93 electrical switches, 82 EM-CCD, 31 encoder, 80 entrance, 4 error budget, 98 etalon, 45 etching techniques, 29 exit pupil, 4 exposure time calculator, 101 extended source, 7 external occulter, 64 extinction ratio, 20 extrinsic photoconductor, 27 extrinsic semiconductor, 24 f-number, 4 Fabry–Pérot interferometer, 45 face sheet, 68 far field, 6 far focus, 12 ferro-electric liquid crystal, 52 fiber Bragg gratings, 49 fiber link, 91 fiber optic interferometer, 82 fiber scrambler, 23 fiber spectrographs, 48

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Index field curvature, 5 field lens, 37 field of view, 60 field stop, 4 filter, 13 finesse, 45 finite element model, 78, 83 first order approximation, 54 first-order optical designs, 73 fit model parameters, 61 fixed-slit mask, 48 Fizeau interferometer, 56 flat field, 35, 50 flexure, 78 flexure stage, 80 flux calibration, 50 focal length, 4 focal ratio, 4 focal ratio degradation, 23 focal reducer, 38 focal-plane coronagraph, 62, 64 focus, 5 focusing, 109 fold mirror, 78 force controlled, 88 Foster prism, 21 four-quadrant phase mask (4QPM), 62 Foucault knife-edge test, 108 Fourier plane, 59 Fourier transform, 6 Fourier transform spectrometer, 9, 46 Fowler sampling, 32

frame transfer, 31 Fraunhofer diffraction, 6 free spectral range, 43, 45 freeform surfaces, 107 Fresnel diffraction, 6 Fresnel equations, 1, 74 Fresnel number, 6 Fresnel rhombs, 22 fringe visibility, 57 fringing, 33 Fried parameter, 66 fully polarized light, 2 functional flow block diagram, 96 functional testing, 110 gain, 65 Gantt chart, 103 Gaussian, 99 Gaussian weighting, 61 gear, 81 generation-recombination (G-R) noise, 33 geometrical optics approximation, 74 ghost image, 10, 77 global optimization, 75 grating efficiency, 19 grating equation, 19 gratings, 19 gravity, 81 Greenwood frequency, 66 Gregorian, 36 grism, 18 ground-layer adaptive optics, 71

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Index half-wave plate, 22 handling, 111 heat pipe, 87 heat shield, 84 heterodyne receivers, 24, 30 high gain antenna, 91 high resolution spectroscopy, 30 high throughput, 42 high-resolution imagers, 40 hot electron bolometers, 30 image, 7 image plane, 4 image slicer, 47 image space, 4 immersion grating, 19 index-of-refraction fluctuations, 66 infrared arrays, 32 instrument box, 78 instrument control system, 89 instrumental profile, 41 integral field spectrometer, 47 integral field unit, 47 integration time, 101 interface control document, 97 interface, 111 interference filters, 15 interference pattern, 56 interferogram, 54 internal occulter, 64 internal transmission, 1 internal transmittance, 1

intrinsic photoconductors, 25 intrinsic, 24 inverse sensitivity analysis, 76 ion-assisted deposition, 15 ion beam figuring, 107 ionization, 34 ISO 9001, 106 isoplanatic angle, 66 isostatic mount, 79 Johnson, 33 Jones, 2 Jones matrices, 2 Jones vector, 2 kinematic mount, 79 Kolmogorov turbulence, 66 kTC noise, 33 Lagrangian point, 34 laser guide stars, 65, 70 laser tracker, 109 lasers, 109 latent image, 33 launch telescope, 70 lenslets, 47, 67 lenses, 11 lifetime, 111 light weighting, 83 linear ADC, 40 linear motor, 81 linear polarization, 2 linear retarder, 22 liquid crystal polarimeter, 52

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Index liquid crystal variable retarder, 52 liquid helium, 85 liquid nitrogen, 85 Littrow configuration, 43 local oscillator (LO), 30 local optimization, 75 long-pass filters, 13 longest baseline, 61 loop update rate, 69 loss of spatial or spectral resolution, 102 lossless data compression, 91 low-background, 44 low-CTE materials, 78 low-level control, 88 LVDT, 82 Lyot coronagraph, 62 Lyot stop, 62, 64 Maksutov, 37 marginal ray, 74 mean time between failures, 111 mechanism requirements, 80 meniscus corrector, 37 merit function, 75-76 microwave kinetic inductance detectors (MKIDs), 28 microshutter arrays, 48 mirror coating, 12 mirror, 12 mixer, 30

modulation transfer function (MTF), 8 Moffat PSF model, 7 monolithic design, 79 Monte Carlo tolerance analysis, 76 moving fringes, 58 Mueller matrix, 2 multi-mode fiber, 23 multi-object spectrometer, 48 multilayer isolation, 84 multiplexer, 32 multi-conjugate adaptive optics, 71 multi-object adaptive optics, 71 n-type, 27 Nasmyth focus, 42 natural frequency, 83 natural guide stars, 70 natural weighting, 61 near field, 6 near focus, 12 nematic liquid crystals, 52 Newton telescope, 108 noise, 99 non-objective prism spectrograph, 44 nonconformity, 106 nondestructive readout, 32 nonlinear curvature sensing, 67 nonsequential ray tracing, 74

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Index normalized angular frequency, 8 numerical aperture, 4, 23 Nyquist sampled, 102 object space, 4 objective, 44 observatory control system, 89 observing time, 101 occulter, 62 off-axis aberrations, 5 off-axis mirror, 12 offner, 39 OH-suppression spectrograph, 49 on-axis aberrations, 5 open-loop controller, 88 operating modes, 71 optical coating, 107 optical design, 72 optical design requirements, 73 optical encoders, 82 optical fibers, 47, 48 optical path difference (OPD), 5, 6, 55, 74 optical shutter, 80 optical table, 78 optical transfer function (OTF), 8–9 optimal extraction, 50 optimization, 75 optimized design, 73 optical design principles, 72 OTCCDs, 31 outgassing, 87 oversampling, 102

p-polarized light, 1 p-type superconductor, 27 Pancharatnam retarders, 22 partially polarized light, 2 peak transmission, 13 Peltier cooling, 85 penta prism, 109 performance requirements, 95 phase apodizer, 63 phase mask, 62 phase transfer function (PTF), 8 phase-induced amplitude apodization, 63 phase-shifting interferometry, 108 photocell, 82 photoconductive layer, 32 photoconductor, 24 photodiode, 28 photonic integrated circuit, 56 pick-off mirror, 48 PID, 88 piezoelectric motor, 81 plane, 59 plane-parallel window, 10 point-spread function (PSF), 7 Poisson distribution, 99 poke matrix, 69 Polarcor™, 20 polarizer, 20 polarizing cube beamsplitter, 20 position control, 88 pre-disperser, 43

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Index precision glass molding, 107 prime-focus corrector, 37 prisms, 18 processing levels, 92 profilometer, 108 protons, 34 pulldown, 33 pupil, 4 pupil-plane coronagraph, 63 pyramid WFS, 67 quality management system, 106 quality management, 106 quantum detectors, 24 quantum efficiency, 26 quarter-wave plate, 22 quality assurance, 106 quality control, 106 radiation environment, 34 radiation shield, 84 radiative heat transfer, 86 radiator, 87 radius of curvature, 12 RAMS, 105 ray tracing, 74 Rayleigh scattering, 70 rays, 74 readout, 26 reconstructor, 69 reference source, 58 reflection, 1 reflectivity, 1 reflection gratings, 19 reflective coatings, 16 refraction, 1

refractive-index structure constant, 66 reimaging optics, 39 reliability, 111 requirements review, 73 requirements analysis, 95 requirements, 72 resonant scattering, 70 research and development, 104 reset-read-read, 32 retarder, 22 retroflector, 109 reviews, 103 RF chokes, 94 risk assessment matrix, 105 risk management, 105 Ritchey–Chrétien telescope, 36 rogue pixel, 33 rooftop prism WFS, 67 Rose criterion, 100 rotating waveplate polarimeter, 51 RVDT, 82 s-polarized light, 1 safety procedures, 111 sag, 12 sample-up-the-ramp, 32 sampling, 102 Savart plate, 21 Schmidt telescope, 37 Schottky diodes, 30 science verification, 110–111 seeing, 65, 66 self-calibration, 58

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Index selection mechanisms, 80 sensitivity, 101 sensitivity analysis, 76 sequential ray tracing, 74 servomotor, 81 Shack–Hartmann WFS, 67 Shannon Nyquist theorem, 102 shielded cable, 94 shielded housing, 94 shielding, 34 short-pass filter, 13 shot noise, 99 signal-to-noise ratio, 41, 60, 100, 101 simplicity, 111 single-conjugate adaptive optics, 71 single-slit spectrometers, 42 single sampling, 32 single-mode fiber, 23 skew ray, 74 sky flat, 35 slit, 41, 42 slit function, 9 slitless spectrometer, 44 Snell’s law, 1, 74 sodium layer, 70 solar coronagraphs, 64 solenoid, 81 space simulator, 87 space mission, 103 spectra overlap, 44 spectral domain, 102 spectral fringes, 10 spectral modulation polarimeters, 53

spectral resolution, 18–19, 41–42, 44, 46 spectral transfer function (STF), 9 spectrograph, 9, 41 spectrometer, 108 spherical surface, 107 spot diagram, 74 stage gate process, 103 stakeholders, 95 standard deviation, 99 star earthing, 94 starshade, 64 statistical significance, 100 stepper motor, 81, 88 STF, 9 stop, 4 Stokes I, 2 Stokes Q, 2 Stokes U, 2 Stokes V, 2 Stokes vector, 2 straylight, 77 stress, 27 struts, 78 Strehl ratio, 65 subaperture, 67 superconductor–insulator– superconductor junctions super-achromatic retarder, 22 surface imperfections, 108 system of constraints, 80 system parameters, 75

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Index TDRSS, 91 technical requirements definition process, 95 technology development, 104 technology readiness levels, 104 telecentric beam, 4 telescope aperture, 101 telescope control system, 89 telescopes, 36 temperature fluctuations, 66 temperature, 15 temperature cycling, 87 temperature sensors, 82 temporal domain, 102 theodolite, 109 thermal detectors, 24 thermal excitation, 27 thermal model, 86 thermal radiation, 86 thermal simulation software, 86 thermometer, 29 thermal properties, 86 thick-lens equation, 11 third-order (Seidel) aberrations, 5 throughput, 41 three-mirror anastigmat, 36 time stability, 35 tolerance analysis, 76 tolerance balancing, 76 tolerances, 98 tolerancing, 73

top level requirements, 110 total integrated scatter, 107 total internal reflection, 3 transition edge sensor (TES), 28 transmission grating, 19 transmission, 1 true zero-order retarder, 22 tuning, 88 twilight flats, 35 uncertainty propagation, 98 undersampling, 102 uniform weighting, 61 unpolarized light, 2 vacuum tank, 84 valence band, 25 Van Allen radiation belt, 34 vanes, 77 variable parameters, 75 variable retarders, 22 velocity control, 88 vibrations during launch, 78 view factor, 86 vignetting, 4 visibility, 60 voice coil linear motor, 81 voltage limits, 93 volume phase hologram, 19 vortex coronagraph, 62

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Index wavefront, 65 wavefront error variance, 69 wavefront sensor, 65, 67 wavefront variance, 65–66 wavelength calibration, 50 waveplate, 22 white-light fringe, 57 wide-angle lens, 11 wind, 66

window material, 10 windows, 10 wire materials, 93 wire-grid polarizer, 20 Wollaston prism, 21 Woods anomaly, 19 work breakdown structure, 103 Zernike polynomials, 5

Field Guide to Astronomical Instrumentation

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Christoph U. Keller is a Professor of Experimental Astrophysics at Leiden University in the Netherlands. He develops instruments for the direct imaging of circumstellar matter and exoplanets, space- and ground-based remote sensing instruments to measure aerosol, and instruments for the life sciences based on astronomical technologies. He received an MSc degree in Physics and a PhD in Astrophysics from ETH Zurich, Switzerland. Ramon Navarro manages the NOVA optical & infrared astronomical instrumentation division at ASTRON, located in Dwingeloo, the Netherlands. He develops imagers, spectrographs, interferometers, and polarimeters for the ESO VLT, ESO E-ELT, the James Webb Space Telescope, and other telescopes. He received an MSc degree in Applied Physics from the Eindhoven University of Technology, the Netherlands. He has experience in developing lithography equipment for the semiconductor industry at ASML. Bernhard R. Brandl is a Professor of Infrared Astronomy at Leiden University in the Netherlands. He develops near- and mid-infrared instruments for ground- and space-based facilities, including Palomar Observatory, the Spitzer and James Webb Space Telescopes, and ESO’s E-ELT. His scientific interest focuses on starburst galaxies. He received a PhD in Physics from the Ludwig-MaximiliansUniversität, München, Germany.

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Astronomical Instrumentation Christoph U. Keller Ramon Navarro Bernhard R. Brandl This Field Guide is a concise, organized reference that explains the functions and configurations of astronomical instrumentation. It provides an overview of aspects of astronomical instrumentation from principles of general optics and optical design to optical manufacturing and systems engineering. Practitioners will also gain valuable insight from information on polarimeters, interferometers, coronagraphs, cryogenics, software, and more.

SPIE Field Guides The aim of each SPIE Field Guide is to distill a major field of optical science or technology into a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena. Written for you—the practicing engineer or scientist— each field guide includes the key definitions, equations, illustrations, application examples, design considerations, methods, and tips that you need in the lab and in the field.

John E. Greivenkamp Series Editor

P.O. Box 10 Bellingham, WA 98227-0010 ISBN: 9781628411775 SPIE Vol. No.: FG32

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