Electro-Optical System Analysis and Design A Radiometry Perspective Cornelius J Willers SPIE PRESS Bellingham, Washington USA
Nomenclature xvii Preface xxiii 1 Electro-Optical System Design 1 11 Introduction 1 12 The Principles of Systems Design 2 121 Definitions 2 122 The design process 123 Prerequisites for design 3 124 Product development approaches 4 125 Lifecycle phases 4 126 Parallel activities during development 7 127 Specifications 8 128 Performance measures and figures of merit 10 129 Value systems and design choices 11 1210 Assumptions during design 11 1211 The design process revisited 12 13 Electro-Optical Systems and System Design 14 131 Definition of an electro-optical system 14 132 Designing at the electro-optical-system level 15 133 Electro-optical systems modeling and simulation 16 14 Conclusion 17 17 2 Introduction to Radiometry 19 21 Notation 19 22 Introduction 20 23 Radiometry 231 Definition of quantities 23 Nomenclature 23 232 Nature of radiometric quantities 25 233 Spectral quantities 25 234 Material properties 27 24 Linear Angle 27 2 vii
25 Solid Angle 28 251 Geometric and projected solid angle 28 252 Geometric solid angle of a cone 29 253 Projected solid angle of a cone 31 254 Geometric solid angle of a flat rectangular surface 255 Projected solid angle of a flat rectangular surface 32 32 256 Approximation of solid angle 33 257 Projected area of a sphere 34 258 Projected solid angle of a sphere 35 26 Radiance and Flux Transfer 35 261 Conservation of radiance 35 262 Flux transfer through a lossless medium 37 medium 38 41 263 Flux transfer through a lossy 264 Sources and receivers of arbitrary shape 38 265 Multi-spectral flux transfer 39 27 Lambertian Radiators and the Projected Solid Angle 28 Spatial View Factor or Configuration Factor 43 29 Shape of the Radiator 44 291 A disk 44 292 A sphere 45 210 Photometry and Color 45 2101 Photometry units 45 2102 Eye spectral response 2103 Conversion to photometric units 47 2104 Brief introduction to color coordinates 48 2105 Color-coordinate sensitivity to source spectrum 46 49 51 Problems 53 3 Sources 57 31 Planck Radiators 57 311 Planck's radiation law 60 312 Wien's displacement law 62 313 Stefan-Boltzmann law 63 314 Summation approximation of Planck's law 64 315 Summary of Planck's law 65 316 Thermal radiation from common objects 65 32 Emissivity 65 321 Kirchhoff's law 69 322 Flux transfer between a source and receiver 70 323 Grey bodies and selective radiators 71 324 Radiation from low-emissivity 325 Emissivity surfaces 73 of cavities 74
ix 33 Aperture Plate in front of a Blackbody 75 34 Directional Surface Reflectance 75 341 Roughness and scale 76 342 Reflection geometry 77 343 Reflection from optically smooth surfaces 77 344 Fresnel reflectance 78 345 Bidirectional reflection distribution function 80 35 Directional Emissivity 83 36 Directional Reflectance and Emissivity in Nature 85 37 The Sun 86 87 Problems 91 4 Optical Media 97 41 Overview 97 42 Optical Mediums 98 421 Lossy mediums 98 422 Path radiance 99 423 General law of contrast reduction 102 424 Optical thickness 103 425 Gas radiator sources 103 43 Inhomogeneous Media and Discrete Ordinates 104 44 Effective Transmittance 105 45 Transmittance as Function of Range 108 46 The Atmosphere as Medium 108 461 Atmospheric composition and attenuation 108 462 Atmospheric molecular absorption Ill 463 Atmospheric aerosols and scattering 112 464 Atmospheric transmittance windows 116 465 Atmospheric path radiance 118 466 Practical consequences of path radiance 120 467 Looking up at and looking 468 Atmospheric water-vapor down on the earth 121 content 121 469 Contrast transmittance in the atmosphere 124 4610 Meteorological range and aerosol scattering 127 47 Atmospheric Radiative Transfer Codes 129 471 Overview 129 472 Modtran 129 130 Problems 133 5 Optical Detectors 135 51 Historical Overview 135
X 52 Overview of the Detection Process 136 521 Thermal detectors 136 522 Photon detectors 138 523 Normalizing responsivity 140 524 Detector configurations 140 53 Noise 140 531 Noise power spectral density 141 532 Johnson noise 142 533 Shot noise 143 534 Generation-recombination noise 144 535 1//noise 145 536 Temperature-fluctuation noise 145 537 Interface electronics noise 146 538 Noise considerations in imaging systems 146 539 Signal flux fluctuation noise 146 5310 Background flux fluctuation noise 147 5311 Detector noise equivalent power and detectivity 147 5312 Combining power spectral densities 149 5313 Noise equivalent bandwidth 149 5314 Time-bandwidth product 150 54 Thermal Detectors 151 541 Principle of operation 151 542 Thermal detector responsivity 152 543 Resistive bolometer 155 544 Pyroelectric detector 157 545 Thermoelectric detector 159 546 Photon-noise-limited operation 161 547 Temperature-fluctuation-noise-limited operation 55 Properties of Crystalline 163 Materials 163 551 Crystalline structure 164 552 Occupation of electrons in energy 553 Electron density in energy bands 165 bands 166 554 Semiconductor band structure 169 555 Conductors, semiconductors, and insulators 170 556 Intrinsic and extrinsic semiconductor materials 171 557 Photon-electron interactions 174 558 Light absorption in semiconductors 176 179 559 Physical parameters for important semiconductors 56 Overview of the Photon Detection Process 179 561 Photon detector operation 179 562 Carriers and current flow in semiconductor material 179 563 Photon absorption and majority/minority carriers 180
xi 564 Quantum efficiency 181 57 Detector Cooling 183 58 Photoconductive Detectors 187 581 Introduction 187 582 Photoconductive detector signal 187 583 Bias circuits for photoconductive detectors 189 584 Frequency response of photoconductive detectors 190 585 Noise in photoconductive detectors 191 59 Photovoltaic Detectors 193 591 Photovoltaic detector operation 193 592 Diode current-voltage relationship 196 593 Bias configurations for photovoltaic detectors 594 Frequency response of a photovoltaic detector 197 202 210 595 Noise in photovoltaic detectors 203 596 Detector performance modeling 207 510 Impact of Detector Technology on Infrared Systems 212 Problems 218 6 Sensors 221 61 Overview 221 62 Anatomy of a Sensor 221 63 Introduction to Optics 223 631 Optical elements 223 632 First-order ray tracing 225 633 Pupils, apertures, stops, and/-number 226 634 Optical sensor spatial angles 230 635 Extended and point target objects 232 636 Optical 637 Optical point spread aberrations 232 function 235 638 Optical systems 236 639 Aspheric 6310 Radiometry 64 Spectral 65 A Simple lenses 237 of a collimator 238 Filters 240 Sensor Model 240 66 Sensor Signal Calculations 242 661 Detector signal 242 662 Source area variations 244 663 Complex sources 245 67 Signal Noise Reference Planes 245 68 Sensor Optical Throughput 248 250 Problems 250
7 Radiometry Techniques 71 Performance Measures 255 711 Role of performance measures 255 712 General definitions 256 713 Commonly used performance 72 Normalization 261 255 measures 257 721 Solid angle spatial normalization 261 722 Effective value normalization 261 723 Peak normalization 262 724 Weighted mapping 73 Spectral Mismatch 264 74 Spectral Convolution 265 75 The Range Equation 76 Pixel Irradiance in an Image 268 77 Difference Contrast 271 78 Pulse Detection and False Alarm Rate 272 79 Validation Techniques 275 Problems 276 8 Optical Signatures 279 81 Model for Optical Signatures 279 82 General Notes on Signatures 283 83 Reflection Signatures 284 84 Modeling 841 Emissivity estimation 287 263 267 275 Thermal Radiators 285 842 Area estimation 288 843 Temperature estimation 290 85 Measurement Data Analysis 292 86 Case Study: High-Temperature 87 Case Study: Low-Emissivity Flame Measurement Surface Measurement 295 295 88 Case Study: Cloud Modeling 297 881 Measurements 297 882 Model 298 883 Relative contributions to the cloud signature 300 89 Case Study: Contrast Inversion/Temperature Cross-Over 300 810 Case Study: Thermally Transparent Paints 301 811 Case Study: Sun-Glint 302 303 Problems 304 9 Electro-Optical System Analysis 309 91 Case Study: Flame Sensor 309
xiii 92 Case Study: Object Appearance in an Image 311 93 Case Study: Solar Cell Analysis 315 931 Observations 315 932 Analysis 316 94 Case Study: Laser Rangefinder Range Equation 321 941 Noise equivalent irradiance 321 942 Signal irradiance 322 943 Lambertian target reflectance 323 944 Lambertian targets against the sky 324 945 Lambertian targets against terrain 325 946 Detection range 326 947 Example calculation 326 948 Specular reflective surfaces 327 95 Case Study: Thermal Imaging Sensor Model 330 951 Electronic parameters 330 952 Noise expressed as D* 331 953 Noise in the entrance aperture 331 954 Noise in the object plane 332 955 Example calculation 333 96 Case Study: Atmosphere and Thermal Camera Sensitivity 334 97 Case Study: Infrared Sensor Radiometry 337 971 Flux on the detector 337 972 Focused optics 339 973 Out-of-focus optics 342 98 Case Study: Bunsen Burner Flame Characterization 344 981 Data analysis workflow 345 982 Instrument calibration 346 983 Measurements 348 984 Imaging-camera 985 Imaging-camera radiance results 350 flame-area results 352 986 Flame dynamics 353 987 Thermocouple flame temperature results 354 355 Problems 356 10 Golden Rules 365 101 Best Practices in Radiometric Calculation 365 102 Start from First Principles 365 103 Understand Radiance, Area, and Solid Angle 366 104 Build Mathematical Models 366 105 Work in Base SI Units 367 106 Perform Dimensional Analysis 367 107 Draw Pictures 368
the xjv 108 Understand the Role of n 371 109 Simplify Spatial Integrals 371 1010 Graphically Plot Intermediate Results 372 1011 Follow Proper Coding Practices 372 1012 Verify and Validate 372 1013 Do It Right First Time! 373 373 A Reference Information 375 B Infrared Scene Simulation 385 Bl Overview 385 B2 Simulation as Knowledge-Management Tool 386 B3 Simulation Validation Framework 386 B4 Optical Signature Rendering 387 B41 Image rendering 391 B42 Rendering equation 393 B5 The Effects of Super-Sampling and Aliasing 396 B6 Solar Reflection, Sky Background, and Color Ratio 398 401 C Multidimensional Ray Tracing 403 383 D Techniques for Numerical Solution 407 Dl Introduction 407 D2 The Requirement 407 D3 Matlab and Python as Calculators 409 D31 Matlab 410 D32 Numpy and Scipy 410 D33 Matlab and Python for radiometry calculations 410 D34 The pyradi toolkit 411 D4 Helper Functions 411 D41 Planck exitance functions 412 D42 Spectral filter function 413 D43 Spectral detector function 415 D5 Fully Worked Examples 417 D51 Flame sensor in Matlab 417 D52 Flame detector in Python 421 D53 Object appearance in an image in Python 424 D54 Color-coordinate calculations in Python 430 D55 Flame-area calculation in Matlab 434 D56 The range equation solved in Python 435
xv D57 Pulse detection and false alarm rate calculation 436 D58 Spatial integral of a flat plate in Matlab 437 440 E Solutions to Selected Problems 441 El Solid Angle Definition 441 E2 Solid Angle Approximation 441 E3 Solid Angle Application (Problem 24) 448 E4 Flux Transfer Application 448 E5 Simple Detector System (Problem 62) 450 E6 InSb Detector Observing a Cloud (Problem 82) 451 E 7 Sensor Optimization (Problem 91) 459 F Additional Reading and Credits 471 F l Additional Reading 471 F2 Credits 471 472 Index 477