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
CONTENTS Preface xiii 1 INTRODUCTION 1.1 The Scheme of This Text 4 1.2 The Future 5 1.3 References and Bibliography 6 2 OPTICS OVERVIEW 2.1 Photons, Waves, and Rays 7 2.2 The Detection of Radiation 7 2.3 Interference 8 2.4 Wavefronts, Normals, Beams, and Rays 8 2.5 Refractive Index 9 2.6 The Laws of Reflection and Refraction 9 2.7 Total Internal Reflection 10 2.8 Diffraction 11 2.9 Geometric Optics and Optical Design 12 2.10 The Idealized Thin Lens 12 2.11 The Lens Maker's Equation 12 2.12 Aberrations 13 2.13 Bending the Lens 15 3 RADIOMETRY REVIEW 3.1 Definitions of Important Radiometric Quantities 17 3.2 Radiative Transfer 19 3.3 Solid Angle and Speed 20 3.4 Stops and Pupils 21 4 SPECTROMETER SPECIFICATIONS 4.1 Spectral Variables 23 4.2 Resolution 23 4.3 Resolving Power 24 Vll
5 IMAGING INTRODUCTION 5.1 The Field of View 27 5.2 Scanners 28 5.3 Strip Mappers 30 5.4 Pushbroom Scanners 31 5.5 Whiskbroom Scanners 32 6 DETECTOR DESCRIPTIONS 6.1 Descriptors 33 6.2 Properties of Elemental Detectors 34 6.3 Properties of Detector Arrays 34 6.4 Fundamental Limits 35 7 SYSTEM SENSITIVITY 7.1 Specification 37 7.2 Charge-Collecting Detectors 39 7.3 Summary of Figures of Merit 39 8 FILTER PHENOMENA 8.1 Types of Filters 41 8.2 One-Layer Filters 42 8.3 Multilayer Filters 43 8.4 Circular and Linear Variable Filters 44 8.5 Fabry-Perot Filters 45 8.6 Acousto-Optical Filters 46 9 PRISM SPECTROMETERS 9.1 Prism Deviation 50 9.2 Minimum Deviation 51 9.3 Geometric Layout 51 9.4 Resolution and Resolving Power 52 9.5 Throughput 52 9.6 An Example 53 10 GRATING SPECTROMETERS 10.1 Diffraction Theory 55 10.2 Geometric Layout 57 10.3 Resolution and Resolving Power 57 10.4 Throughput 58 10.5 Blazing Rulings 58 10.6 Operation 58 Vlll
11 MICHELSON INTERFEROMETER SPECTROMETERS 11.1 Two-Beam Interference 60 11.2 Interference in the Michelson Interferometer 61 11.3 The Twyman-Green Interferometer 62 11.4 The Fourier Transform Spectrometer 62 11.5 Throughput and Sensitivity 65 12 AN IMAGING FOURIER TRANSFORM SPECTROMETER 12.1 Monochromatic Operation 66 12.2 Field Operation 68 13 FABRY-PEROT INTERFEROMETER SPECTROMETERS 13.1 Description 70 13.2 Spectral Transmission 70 13.3 Resolving Power, Throughput, and Free Spectral Range 71 13.4 The Fabry-Perot Imaging Spectrometer 72 14 A CHALLENGING APPLICATION 14.1 Requirements 74 14.2 The (Up)Front-Filter Approach 75 14.3 The Rear (FPA) Filter Approach 76 14.4 The Multiple-Lens Filter Approach 77 14.5 The Acousto-Optic Filter 77 14.6 The Grating Approach 79 14.7 The FTS Approach 79 14.8 Sensitivity Calculations 79 15 A SATELLITE SPECTROMETER 15.1 Requirements 84 15.2 Analysis 86 15.3 Another Way to Calculate 87 16 A MARS ROVER EXPERIMENT 16.1 Requirements Definitions 90 16.2 The Martian Environment 91 16.3 Optical Properties of (Martian?) Minerals 91 16.4 The Candidate Imaging Spectrometers 95 16.4.1 Candidates using linear arrays 95 16.4.2 Sensitivity 96 16.4.3 The filter "wheel" 97 16.4.4 The FTS system 97 16.5 Two-Dimensional Array Systems 98 16.6 Possible Improvements 99 ix
17 «SOME TRADE-OFFS 17.1 General Considerations 103 17.2 Optical Efficiency 103 17.3 Bandwidth 103 17.4 Sensitivity 104 17.5 Examples 104 18» OTHER EXAMPLES 18.1 The Westinghouse AOTF System 108 18.2 HYDICE»108 18.3 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
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