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Electro-Optical System Analysis and Design: A Radiometry Perspective
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Book Description

The field of radiometry can be dangerous territory to the uninitiated, faced with the risk of errors and pitfalls. The concepts and tools explored in this book empower readers to comprehensively analyze, design, and optimize real-world systems. This book builds on the foundation of solid theoretical understanding, and strives to provide insight into hidden subtleties in radiometric analysis. Atmospheric effects provide opportunity for a particularly rich set of intriguing observations.

The term 'radiometry' is used in its wider context to specifically cover the calculation of flux. This wider definition is commonly used by practitioners in the field to cover all forms of manipulation, including creation, measurement, calculation, modeling, and simulation of optical flux.

Two concurrent themes frame the discussion: fragmenting a complex problem into simple building blocks and then designing complex systems from smaller elements. Analysis and design, as a creative synthesis of something new, cannot be easily taught other than by example; for this purpose, several case studies are presented. This book also provides a number of problems, some with solutions demonstrated in Matlab® and the Python pyradi toolkit.

Book Details

Date Published: 29 April 2013
Pages: 528
ISBN: 9780819495693
Volume: PM236

Table of Contents
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Chapter 1 Electro-Optical System Design
1.1 Introduction
1.2 The Principles of Systems Design
     1.2.1 Definitions
     1.2.2 The design process
     1.2.3 Prerequisites for design
     1.2.4 Product development approaches
     1.2.5 Lifecycle phases
     1.2.6 Parallel activities during development
     1.2.7 Specifications
     1.2.8 Performance measures and figures of merit
     1.2.9 Value systems and design choices
     1.2.10 Assumptions during design
     1.2.11 The design process revisited
1.3 Electro-Optical Systems and System Design
     1.3.1 Definition of an electro-optical system
     1.3.2 Designing at the electro-optical-system level
     1.3.3 Electro-optical systems modeling and simulation
1.4 Conclusion

Chapter 2 Introduction to Radiometry
2.1 Notation
2.2 Introduction
2.3 Radiometry Nomenclature
     2.3.1 Definition of quantities
     2.3.2 Nature of radiometric quantities
     2.3.3 Spectral quantities
     2.3.4 Material properties
2.4 Linear Angle
2.5 Solid Angle
     2.5.1 Geometric and projected solid angle
     2.5.2 Geometric solid angle of a cone
     2.5.3 Projected solid angle of a cone
     2.5.4 Geometric solid angle of a flat rectangular surface
     2.5.5 Projected solid angle of a flat rectangular surface
     2.5.6 Approximation of solid angle
     2.5.7 Projected area of a sphere
     2.5.8 Projected solid angle of a sphere
2.6 Radiance and Flux Transfer
     2.6.1 Conservation of radiance
     2.6.2 Flux transfer through a lossless medium
     2.6.3 Flux transfer through a lossy medium
     2.6.4 Sources and receivers of arbitrary shape
     2.6.5 Multi-spectral flux transfer
2.7 Lambertian Radiators and the Projected Solid Angle
2.8 Spatial View Factor or Configuration Factor
2.9 Shape of the Radiator
     2.9.1 A disk
     2.9.2 A sphere
2.10 Photometry and Color
     2.10.1 Photometry units
     2.10.2 Eye spectral response
     2.10.3 Conversion to photometric units
     2.10.4 Brief introduction to color coordinates
     2.10.5 Color-coordinate sensitivity to source spectrum

Chapter 3 Sources
3.1 Planck Radiators
     3.1.1 Planck's radiation law
     3.1.2 Wien's displacement law
     3.1.3 Stefan-Boltzmann law
     3.1.4 Summation approximation of Planck's law
     3.1.5 Summary of Planck's law
     3.1.6 Thermal radiation fromcommon objects
3.2 Emissivity
     3.2.1 Kirchhoff's law
     3.2.2 Flux transfer between a source and receiver
     3.2.3 Grey bodies and selective radiators
     3.2.4 Radiation from low-emissivity surfaces
     3.2.5 Emissivity of cavities
3.3 Aperture Plate in front of a Blackbody
3.4 Directional Surface Reflectance
     3.4.1 Roughness and scale
     3.4.2 Reflection geometry
     3.4.3 Reflection from optically smooth surfaces
     3.4.4 Fresnel reflectance
     3.4.5 Bidirectional reflection distribution function
3.5 Directional Emissivity
3.6 Directional Reflectance and Emissivity in Nature
3.7 The Sun

Chapter 4 Optical Media
4.1 Overview
4.2 Optical Mediums
     4.2.1 Lossy mediums
     4.2.2 Path radiance
     4.2.3 General law of contrast reduction
     4.2.4 Optical thickness
     4.2.5 Gas radiator sources
4.3 Inhomogeneous Media and Discrete Ordinates
4.4 Effective Transmittance
4.5 Transmittance as Function of Range
4.6 The Atmosphere as Medium
     4.6.1 Atmospheric composition and attenuation
     4.6.2 Atmospheric molecular absorption
     4.6.3 Atmospheric aerosols and scattering
     4.6.4 Atmospheric transmittance windows
     4.6.5 Atmospheric path radiance
     4.6.6 Practical consequences of path radiance
     4.6.7 Looking up at and looking down on the earth
     4.6.8 Atmospheric water-vapor content
     4.6.9 Contrast transmittance in the atmosphere
     4.6.10 Meteorological range and aerosol scattering
4.7 Atmospheric Radiative Transfer Codes
     4.7.1 Overview
     4.7.2 Modtran

Chapter 5 Optical Detectors
5.1 Historical Overview
5.2 Overviewof the Detection Process
     5.2.1 Thermal detectors
     5.2.2 Photon detectors
     5.2.3 Normalizing responsivity
     5.2.4 Detector configurations
5.3 Noise
     5.3.1 Noise power spectral density
     5.3.2 Johnson noise
     5.3.3 Shot noise
     5.3.4 Generation-recombination noise
     5.3.5 1/f noise
     5.3.6 Temperature-fluctuation noise
     5.3.7 Interface electronics noise
     5.3.8 Noise considerations in imaging systems
     5.3.9 Signal flux fluctuation noise
     5.3.10 Background flux fluctuation noise
     5.3.11 Detector noise equivalent power and detectivity
     5.3.12 Combining power spectral densities
     5.3.13 Noise equivalent bandwidth
     5.3.14 Time-bandwidth product
5.4 Thermal Detectors
     5.4.1 Principle of operation
     5.4.2 Thermal detector responsivity
     5.4.3 Resistive bolometer
     5.4.4 Pyroelectric detector
     5.4.5 Thermoelectric detector
     5.4.6 Photon-noise-limited operation
     5.4.7 Temperature-fluctuation-noise-limited operation
5.5 Properties of Crystalline Materials
     5.5.1 Crystalline structure
     5.5.2 Occupation of electrons in energy bands
     5.5.3 Electron density in energy bands
     5.5.4 Semiconductor band structure
     5.5.5 Conductors, semiconductors, and insulators
     5.5.6 Intrinsic and extrinsic semiconductor materials
     5.5.7 Photon-electron interactions
     5.5.8 Light absorption in semiconductors
     5.5.9 Physical parameters for important semiconductors
5.6 Overview of the Photon Detection Process
     5.6.1 Photon detector operation
     5.6.2 Carriers and current flow in semiconductor material
     5.6.3 Photon absorption and majority/minority carriers
     5.6.4 Quantum efficiency
5.7 Detector Cooling
5.8 Photoconductive Detectors
     5.8.1 Introduction
     5.8.2 Photoconductive detector signal
     5.8.3 Bias circuits for photoconductive detectors
     5.8.4 Frequency response of photoconductive detectors
     5.8.5 Noise in photoconductive detectors
5.9 Photovoltaic Detectors
     5.9.1 Photovoltaic detector operation
     5.9.2 Diode current-voltage relationship
     5.9.3 Bias configurations for photovoltaic detectors
     5.9.4 Frequency response of a photovoltaic detector
     5.9.5 Noise in photovoltaic detectors
     5.9.6 Detector performance modeling
5.10 Impact of Detector Technology on Infrared Systems

Chapter 6 Sensors
6.1 Overview
6.2 Anatomy of a Sensor
6.3 Introduction to Optics
     6.3.1 Optical elements
     6.3.2 First-order ray tracing
     6.3.3 Pupils, apertures, stops, and f-number
     6.3.4 Optical sensor spatial angles
     6.3.5 Extendedand point target objects
     6.3.6 Optical aberrations
     6.3.7 Optical point spread function
     6.3.8 Optical systems
     6.3.9 Aspheric lenses
     6.3.10 Radiometry of a collimator
6.4 Spectral Filters
6.5 A Simple Sensor Model
6.6 Sensor Signal Calculations
     6.6.1 Detector signal
     6.6.2 Source area variations
     6.6.3 Complex sources
6.7 Signal Noise Reference Planes
6.8 Sensor Optical Throughput

Chapter 7 Radiometry Techniques
7.1 Performance Measures
     7.1.1 Role of performance measures
     7.1.2 General definitions
     7.1.3 Commonly used performance measures
7.2 Normalization
     7.2.1 Solid angle spatial normalization
     7.2.2 Effective value normalization
     7.2.3 Peak normalization
     7.2.4 Weighted mapping
7.3 Spectral Mismatch
7.4 Spectral Convolution
7.5 The Range Equation
7.6 Pixel Irradiance in an Image
7.7 Difference Contrast
7.8 Pulse Detection and False Alarm Rate
7.9 Validation Techniques

Chapter 8 Optical Signatures
8.1 Model for Optical Signatures
8.2 General Notes on Signatures
8.3 Reflection Signatures
8.4 Modeling Thermal Radiators
     8.4.1 Emissivity estimation
     8.4.2 Area estimation
     8.4.3 Temperature estimation
8.5 Measurement Data Analysis
8.6 Case Study: High-Temperature Flame Measurement
8.7 Case Study: Low-Emissivity Surface Measurement
8.8 Case Study: Cloud Modeling
     8.8.1 Measurements
     8.8.2 Model
     8.8.3 Relative contributions to the cloud signature
8.9 Case Study: Contrast Inversion/Temperature Cross-Over
8.10 Case Study: Thermally Transparent Paints
8.11 Case Study: Sun-Glint

Chapter 9 Electro-Optical System Analysis
9.1 Case Study: Flame Sensor
9.2 Case Study: Object Appearance in an Image
9.3 Case Study: Solar Cell Analysis
     9.3.1 Observations
     9.3.2 Analysis
9.4 Case Study: Laser Rangefinder Range Equation
     9.4.1 Noise equivalent irradiance
     9.4.2 Signal irradiance
     9.4.3 Lambertian target reflectance
     9.4.4 Lambertian targets against the sky
     9.4.5 Lambertian targets against terrain
     9.4.6 Detection range
     9.4.7 Example calculation
     9.4.8 Specular reflective surfaces
9.5 Case Study: Thermal Imaging Sensor Model
     9.5.1 Electronic parameters
     9.5.2 Noise expressed as D*
     9.5.3 Noise in the entrance aperture
     9.5.4 Noise in the object plane
     9.5.5 Example calculation
9.6 Case Study: Atmosphere and Thermal Camera Sensitivity
9.7 Case Study: Infrared Sensor Radiometry
     9.7.1 Flux on the detector
     9.7.2 Focused optics
     9.7.3 Out-of-focus optics
9.8 Case Study: Bunsen Burner Flame Characterization
     9.8.1 Data analysis workflow
     9.8.2 Instrument calibration
     9.8.3 Measurements
     9.8.4 Imaging-camera radiance results
     9.8.5 Imaging-camera flame-area results
     9.8.6 Flame dynamics
     9.8.7 Thermocouple flame temperature results

Chapter 10 Golden Rules
10.1 Best Practices in Radiometric Calculation
10.2 Start from First Principles
10.3 Understand Radiance, Area, and Solid Angle
10.4 Build Mathematical Models
10.5 Work in Base SI Units
10.6 Perform Dimensional Analysis
10.7 Draw Pictures
10.8 Understand the Role of π
10.9 Simplify Spatial Integrals
10.10 Graphically Plot Intermediate Results
10.11 Follow Proper Coding Practices
10.12 Verify and Validate
10.13 Do It Right - the First Time!

Appendix A: Reference Information

Appendix B: Infrared Scene Simulation
B.1 Overview
B.2 Simulation as Knowledge-Management Tool
B.3 Simulation Validation Framework
B.4 Optical Signature Rendering
     B.4.1 Image rendering
     B.4.2 Rendering equation
B.5 The Effects of Super-Sampling and Aliasing
B.6 Solar Reflection, Sky Background, and Color Ratio

Appendix C: Multidimensional Ray Tracing

Appendix D: Techniques for Numerical Solution
D.1 Introduction
D.2 The Requirement
D.3 Matlab® and Python as Calculators
     D.3.1 Matlab®
     D.3.2 Numpy and Scipy
     D.3.3 Matlab® and Python for radiometry calculations
     D.3.4 The pyradi toolkit
D.4 Helper Functions
     D.4.1 Planck exitance functions
     D.4.2 Spectral filter function
     D.4.3 Spectral detector function
D.5 Fully Worked Examples
     D.5.1 Flame sensor in Matlab®
     D.5.2 Flame detector in Python
     D.5.3 Object appearance in an image in Python
     D.5.4 Color-coordinate calculations in Python
     D.5.5 Flame-area calculation in Matlab®
     D.5.6 The range equation solved in Python
     D.5.7 Pulse detection and false alarm rate calculation
     D.5.8 Spatial integral of a flat plate in Matlab®

Appendix E: Solutions to Selected Problems
E.1 Solid Angle Definition
E.2 Solid Angle Approximation
E.3 Solid Angle Application (Problem 2.4)
E.4 Flux Transfer Application
E.5 Simple Detector System (Problem 6.2)
E.6 InSb Detector Observing a Cloud (Problem 8.2)
E.7 Sensor Optimization (Problem 9.1)

Appendix F: Additional Reading and Credits
F.1 Additional Reading
F.2 Credits


On Sharing

Teachers cross our paths in life. Some teachers have names, others leave their marks anonymously. Among my teachers at the Optical Sciences Center at the University of Arizona were James Palmer, Eustace Dereniak, and Jack Gaskill. They freely shared their knowledge with their students. Some teachers teach through the pages of their books, and here I have to thank Bill Wolfe, George Zissis, and many more. Many years ago, R. Barry Johnson presented a short course which influenced my career most decisively.

The intent with this book is to now share some of my experience, accumulated through years of practical radiometry: design, measurements, modeling, and simulation of electro-optical systems. The material presented here builds upon the foundation laid at the Optical Sciences Center. I had the opportunity to share this material in an academic environment at graduate level in an engineering school, thereby clarifying key concepts. Beyond the mathematics and dry theory lies a rich world full of subtle insights, which I try to elucidate. May this book help you, the reader, grow in insight and share with others.

Reductionism, Synthesis, and Design

The reductionist approach holds the view that an arbitrarily complex system can be understood by reducing the system to many, smaller systems that can be understood. This view is based on the premise that the complex system is considered to be the sum of its parts, and that by understanding the parts, the sum can be understood. While the reductionist approach certainly has weaknesses, this approach works well for the class of problems considered in this book. The methodology followed here is to develop the theory concisely for simple cases, developing a toolset and a clear understanding of the fundamentals.

The real world does not comprise loose parts and simple systems. Once the preliminaries are out the way, we proceed to consider more complex concepts such as sensors, signatures, and simple systems comprising sources, a medium, and a receiver. Using these concepts and the tools developed in this book, the reader should be able to design a system of any complexity. Two concurrent themes appear throughout the book: fragmenting a complex problem into simple building blocks, and synthesizing (designing) complex systems from smaller elements. In any design process, these two actions take place interactively, mutually supporting each other. In this whirlpool of analysis and synthesis, uncontrolled external factors (e.g., the atmosphere, noise) influence the final outcome. This is where the academic theory finds engineering application in the real world. This book aims to demonstrate how to proceed along this road.

Toward the end of the book, the focus shifts from a component-level view to an integrated-system view, where the 'system' comprises a (simple or composite) source, an intervening medium, and a sensor. Many real-world electro-optical applications require analysis and design at this integrated-system level. Analysis and design, as a creative synthesis of something new, cannot be easily taught other than by example. For this purpose several case studies are presented. The case studies are brief and only focus on single aspects of the various designs. Any real design process would require a much more detailed process, beyond the scope of this book.

General Comments

The purpose with this book is to enable the reader to find solutions to real-world problems. The focus is on the application of radiometry in various analysis and design scenarios. It is essential, however, to build on the foundation of solid theoretical understanding, and gain insight beyond graphs, tables and equations. Therefore, this book does not attempt to provide an extensive set of ready-to-use equations and data, but rather strives to provide insight into hidden subtleties in the field. The atmosphere provides opportunity for a particularly rich set of intriguing observations.

The strict dictionary definition of 'radiometry' is the measurement of optical flux. In this book, the term 'radiometry' is used in its wider context to specifically cover the calculation of flux as well. This wider definition is commonly used by practitioners in the field to cover all forms of manipulation, including creation, measurement, calculation, modeling, and simulation of optical flux. The focus of this book is not on radiometric measurement but on the analysis and modeling of measured data, and the design of electro-optical systems.

Antoine de Saint-Exupèry once wrote, "You know you've achieved perfection in design, not when you have nothing more to add, but when you have nothing more to take away." The painful aspect of writing a book is to decide what not to include. This book could contain more content on radiometric measurement, emissivity measurement, properties of different types of infrared detectors, or reference information on optical material properties; however, these topics are already well covered by other excellent books, much better than can be achieved in the limited scope of this book.

The book provides a number of problems, some with worked solutions. The scope of problems in the early chapters tend to be smaller, whereas the problems in later chapters tend to be wider in scope. The more-advanced problems require numerical solutions. Although it is certainly possible to read the book without doing the advanced problems, the reader is urged to spend time mastering the skills to do these calculations. This investment will pay off handsomely in the future. Some of the problems require data not readily found in book format. The data packages are identified (e.g., DP01) and are obtainable from the pyradi website (see Section D.3.4).

To the uninitiated, the broader field of radiometry is dangerous territory, with high potential for errors and not-so-obvious pitfalls. Our work in the design labs, on field measurement trials, and in the academic environment led to the development of a set of best practices, called the 'Golden Rules,' which strives to minimize the risk error. Some of these principles come from James Palmer's class, while most were stripes hard earned in battle. The readers are urged to study, use, and expand these best practices in their daily work. Any feedback, on the golden rules or any other aspect of the book, would be appreciated.

A book is seldom the work of one mind only; it is the result of a road traveled with companions. Along this road are many contributors, both direct and inadvertent. My sincere thanks to all who made their precious time and resources available in this endeavor. My sincere thanks goes to Riana Willers for patience and support, as co-worker on our many projects -- her light footprints fall densely on every single page in this book: advising, scrutinizing every detail, debating symbols and sentences, editing text and graphics, compiling the nomenclature and index, and finally, acting as chapter contributor. Riana is indeed the ghost writer of this book! Fiona Ewan Rowett for permission to use her exquisite "Karoo Summer" on the front cover. The painting beautifully expresses not only the hot, semi-arid Karoo plateau in South Africa, but also expresses radiated light and vibrant thermal energy, the subject of this book. My teachers at the Optical Sciences Center who laid the early foundation for this work. Ricardo Santos and Fábio Alves for contributing to the chapter on infrared detector theory and modeling. The pyradi team for contributing their time toward building a toolkit of immense value to readers of this book. Derek Griffith for the visual and near-infrared reflectance measurements. Hannes Calitz for the spectral measurements, and Azwitamisi Mudau for the imaging infrared measurements. Dr Munir Eldesouki from KACST for permission to use the Bunsen flame measured data in the book. The many colleagues, co-workers, and students at Kentron (now Denel Dynamics), the CSIR, KACST, and the University of Pretoria for influencing some aspect of the book. Scott McNeill and Tim Lamkins for patience and guiding me through the publication process. Scott's untiring patience in detailed correction deserves special mention. Eustace Dereniak for encouraging me to submit the book for publication. Barbara Grant, Eustace Dereniak and an anonymous reviewer for greatly influencing the book in its final form. Finally, Dirk Bezuidenhout, and the CSIR for supporting the project so generously in the final crucial months before publication.

Mark Twain wrote that he did not allow his schooling to get in the way of his education. It is my wish that you, my esteemed reader, will delve beyond these written words into the deeper insights. Someone else said that the art of teaching is the art of assisting in discovery. May you discover many rich insights through these pages.

Nelis Willers
March 2013

1) The pyradi library source files for use with the book are at
2) The PyPI distribution of the library is at
3) The online library documentation for the library is at
4) Some examples and tutorials are at

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