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

S P I E 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

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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

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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

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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

A p p e n d i x t o C h a p t e r 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

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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 A l 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 A l 2.4 Apodization • 142

Bibliography • 144 Index • 147