Introduction to Imaging Spectrometers

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1 Introduction to Imaging Spectrometers William L. Wolfe Professor Emeritus, Optical Sciences Center, University of Arizona Tutorial Texts in Optical Engineering Volume TT25 Donald С O'Shea, Series Editor Georgia Institute of Technology SPIE O P T I C A L E N G I N E E R I N G P R E S S A Publication of SPIE The International Society for Optical Engineering Bellingham, Washington USA

2 CONTENTS Preface xiii 1 INTRODUCTION 1.1 The Scheme of This Text The Future References and Bibliography 6 2 OPTICS OVERVIEW 2.1 Photons, Waves, and Rays The Detection of Radiation Interference Wavefronts, Normals, Beams, and Rays Refractive Index The Laws of Reflection and Refraction Total Internal Reflection Diffraction Geometric Optics and Optical Design The Idealized Thin Lens The Lens Maker's Equation Aberrations Bending the Lens 15 3 RADIOMETRY REVIEW 3.1 Definitions of Important Radiometric Quantities Radiative Transfer Solid Angle and Speed Stops and Pupils 21 4 SPECTROMETER SPECIFICATIONS 4.1 Spectral Variables Resolution Resolving Power 24 Vll

3 5 IMAGING INTRODUCTION 5.1 The Field of View Scanners Strip Mappers Pushbroom Scanners Whiskbroom Scanners 32 6 DETECTOR DESCRIPTIONS 6.1 Descriptors Properties of Elemental Detectors Properties of Detector Arrays Fundamental Limits 35 7 SYSTEM SENSITIVITY 7.1 Specification Charge-Collecting Detectors Summary of Figures of Merit 39 8 FILTER PHENOMENA 8.1 Types of Filters One-Layer Filters Multilayer Filters Circular and Linear Variable Filters Fabry-Perot Filters Acousto-Optical Filters 46 9 PRISM SPECTROMETERS 9.1 Prism Deviation Minimum Deviation Geometric Layout Resolution and Resolving Power Throughput An Example GRATING SPECTROMETERS 10.1 Diffraction Theory Geometric Layout Resolution and Resolving Power Throughput Blazing Rulings Operation 58 Vlll

4 11 MICHELSON INTERFEROMETER SPECTROMETERS 11.1 Two-Beam Interference Interference in the Michelson Interferometer The Twyman-Green Interferometer The Fourier Transform Spectrometer Throughput and Sensitivity AN IMAGING FOURIER TRANSFORM SPECTROMETER 12.1 Monochromatic Operation Field Operation FABRY-PEROT INTERFEROMETER SPECTROMETERS 13.1 Description Spectral Transmission Resolving Power, Throughput, and Free Spectral Range The Fabry-Perot Imaging Spectrometer A CHALLENGING APPLICATION 14.1 Requirements The (Up)Front-Filter Approach The Rear (FPA) Filter Approach The Multiple-Lens Filter Approach The Acousto-Optic Filter The Grating Approach The FTS Approach Sensitivity Calculations A SATELLITE SPECTROMETER 15.1 Requirements Analysis Another Way to Calculate A MARS ROVER EXPERIMENT 16.1 Requirements Definitions The Martian Environment Optical Properties of (Martian?) Minerals The Candidate Imaging Spectrometers Candidates using linear arrays Sensitivity The filter "wheel" The FTS system Two-Dimensional Array Systems Possible Improvements 99 ix

5 17 «SOME TRADE-OFFS 17.1 General Considerations Optical Efficiency Bandwidth Sensitivity Examples » OTHER EXAMPLES 18.1 The Westinghouse AOTF System HYDICE» TRW Devices «110 Appendix to Chapter 2 OPTICS OPERATIONS A2.1 Derivation of the Wave Equation from Maxwell's Equations»111 A2.2 Representation of Fields «112 A2.3 The Poynting Vector «113 A2.4 Derivation of Snell's Law»115 A2.5 Interference «116 A2.6 Diffraction «116 A2.7 The Thin Lens 120 A2.8 Refraction at a Spherical Surface 121 A2.9 The Aberrations 123 A2.9.1 Spherical aberration 123 A2.9.2 Comatic aberration 124 A2.9.3 Astigmatism 124 A2.9.4 Curvature of field 125 A2.9.5 Distortion 125 A2.9.6 Chromatic aberrations 126 A2.10 Bending the Lens 126 Appendix to Chapter 6 DETECTORS A6.1 The Signal 128 A6.2 The Noise 128 A6.3 The Noises 129 A6.4 Expressions for the Limiting Specific Detectivities 130 Appendix to Chapter 9 PRISMS A9.1 Throughput 132 A9.2 Slit Sizes and Resolution 133 A9.3 Deviation 133 A9.4 Dispersion 135 A9.5 Some Mounting Arrangements 135 x

6 Appendix to Chapter 10 GRATINGS A 10.1 The Grating Diffraction Pattern 137 Al0.2 The Grating Equation 138 Al 0.3 Resolving Power 138 A 10.4 Free Spectral Range 139 Al 0.5 Some Mounting Arrangements 139 Appendix to Chapter 12 FTS FOUNDATIONS Al 2.1 Resolution 141 Al 2.2 Resolving Power 142 Al 2.3 Sensitivity 142 Al 2.4 Apodization 142 Bibliography 144 Index 147

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