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Spie Press Book

Photonics Rules of Thumb, Third Edition
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Book Description

Updated and expanded, the third edition of Photonics Rules of Thumb represents an evolving, idiosyncratic, and eclectic toolbox intended to allow any engineer, scientist, manager, marketeer, or technician (regardless of specialty) to make rapid and accurate guesses at solutions in a wide range of topics during system design, modeling, or fabrication. This book will help any electro-optics team to make quick assessments, generally requiring no more than a calculator, so that they can quickly find the right solution for a design problem.

This book has been assembled to introduce anyone working in the optics and photonics community to a wide range of critical topics through simple calculations, graphics, equations, and explanations. Useful design principles and rules, simple-to-implement calculations, and numerous graphs and tables of important basic information allow you to rapidly pinpoint trouble spots, ask the right questions at meetings, and are perfect for quick checks of last-minute specifications or performance feature additions. Offering a convenient arrangement according to specialty, this unique reference spans the spectrum of photonics. Eighteen chapters cover optics, atmospherics, radiometry, focal plane arrays, degraded visual environments, economics, and photogrammetry, as well as technologies related to security and surveillance systems, infrared, lasers, electro-optics, phenomenologies, self-driving vehicles, and many others.

Book Details

Date Published: 10 June 2020
Pages: 740
ISBN: 9781510631755
Volume: PM314

Table of Contents
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Table of Contents


1 Astronomy
Blackbody Temperature of the Sun
Number of Stars as a Function of Wavelength
Simple Model of Stellar Populations
Number of Infrared Sources Per Square Degree
Number of Stars above a Given Irradiance
Direct Lunar Radiance
Atmospheric Seeing
Comparison of Resonant Fluorescence and Rayleigh Guide Stars
Number of Actuators in an Adaptive Optic
Bandwidth Requirement for Adaptive Optics
Photon Rate at a Focal Plane
Reduction of Magnitude by Airmass
Night-Sky Exposure Time with a Fixed Camera

2 Atmospherics
Vertical Profiles of Atmospheric Parameters
Visibility Distance for Rayleigh and Mie Scattering
Atmospheric Effects at 10.6 Microns
Cn2 as a Function of Weather
Cn2 Estimates
Impact of Weather on Visibility
Bufton Vertical Profile of Wind Speed
Index of Refraction of Air
Fried Parameter
Horizontal-Path Fried Parameter
Phase Error Estimation
Day vs. Night Scintillation Models for Laser Beams
Resolution Looking Down
Isoplanatic Angle
Strehl Ratio of the Atmosphere
Aperture Averaging
Adaptive Optics Influence Function
Shack–Hartmann Noise
Laser Beam Wander Variance Is Approximately Proportional to About the Cube of the Pathlength
Pulse Stretching in Scattering Environments
Optimal Truncation of a Gaussian Beam Propagating in the Atmosphere
Increased Requirement for Rangefinder SNR to Overcome Atmospheric Effects
Free-Space Link Margins
Summary of Phase Modulators for Adaptive Optics
Telescope Seeing Created by a Dome Floor
Telescope Seeing Due to Still or Ventilated Air

3 Acquisition, Tracking, and Pointing
Correct Measure of Detection Performance
Tracker vs. Detection
Detection Criteria
Signal-to-Noise Ratio Requirements
Psychometric Function
Optical Blur Should Be Oversampled by FPA Pixels (Don't Overdo It!)
Dwell in Cell
Probability of Detection Estimation
Limits of Position Estimation
Multisensor Tracking
Johnson Criteria
Extension of Johnson Criteria to Other than 50 Percent
Identification and Recognition Improvement for Interpolation
Resolution Requirement
Resolution Required to Read a Letter
Detection Nomograph
Correcting for Probability of Chance
National Image Interpretability Rating Scale

4 Backgrounds
Clutter and Signal-to-Clutter Ratio
Clutter Power Spectral Density
Infrared Clutter Behavior
Frame Differencing Gain
Earth's Emission and Reflection
Illuminance at Earth's Surface from Various Sources
Illuminance Changes during Twilight
Emissivity Approximations
Reflectivity of a Wet Surface
Effective Sky Temperature
Sky Irradiance
Zodiacal Light
Backgrounds from Asteroids

5 Cost and Economics
Moore's Law
Metcalfe's Law
Englebart's Law
The Value of Early Investment
Cost Reduction Techniques
Learning Curves
Learning Curves for Optics
Optics Cost
Cost Function of a Lens
Price of a Custom vs. Off-the-Shelf Optic
Telescope Component Costs
Impact of Tolerances on the Cost of Optics
Stahl Segmented Cost Rule
Tolerancing Guidelines for Glass Spherical Optics
Tolerancing Guidelines for Plastic Optics
Cost of Digital Image vs. Film
Small Pixels Reduce Cost
System Percentage Costs
Length of a Job Search
Photolithography Yield

6 Degraded Visual Environments
Basic Attenuation and Visibility: Beer's Law
Atmospheric Attenuation Curves
Atmospheric Visibility Curves
Attenuation vs. Particle Size
Visibility in Smoke
Equations for Empirical Visibility
Penetration vs. Resolution
Mandatory Mitigation for Sensor Blindness
Deep Wells Are Good

7 Focal Plane Arrays
Infrared Detector Characterization
Responsivity and Quantum Efficiency
ROIC Charge Capacity
Low Quantum Efficiency Detectors Are Useful
Silicon Quantum Efficiency
HgCdTe x Concentration
Quantum Dot Fundamentals
Avalanche Photodiode Performance
Responsivity of Avalanche Photodiodes
Peak vs. Cut-Off
CMOS Depletion Scaling
Focal Plane Array Noise Sources
Rule 07
Law 19
Radiative Estimate of Dark Current
Defining Background-Limited Performance for Detectors
The Concepts of D and D*
Ideal D* and View Angle
Dependence on R0A
Shot Noise Rule
Infrared Detector DC Pedestal
Digitizer Sizing
Noise as a Function of Temperature
Noise Bandwidth of Detectors
Noise Equations for CMOS
Specifying 1/f Noise
Nonuniformity Effects on SNR
Correlated Double Sampling

8 Human Vision
Retinal Illumination
Diffraction Effects in the Human Eye
Energy Flow into the Eye
Pupil Size
Quantum Efficiency of Rods and Cones
Rod and Cone Response Models
Cone Density of the Human Eye
Rod Density Peak
Eye Resolution
Optical Fields of View
Contrast Performance
Simplified Optical Transfer Functions for Eye Components
Eye Motion during the Formation of an Image
Visual Performance as a Function of Age
Old-Age Rules
Superposition of Colors
Dyschromatopic Vision
Eye Adaptation Time
Eat Your Vegetables
Stereograph Distance
Assorted Eye Facts
Head-Mounted-Display Latency

9 Lasers
Lidar Basic Equations
Laser Brightness
Laser Beam Quality
Gaussian Beam Radius
On-Axis Intensity of a Beam
Aperture Size for Laser Beams
Laser Beam Divergence
Laser Beam Spread vs. Diffraction
Types of Lidars
Laser Radar Range Equation
Lidar Bidirectional Reflectance Distribution Function
Thermal Focusing in Laser Rods
Cross-Section of a Retroreflector
Air Breakdown

10 Materials and Structures
Diameter-to-Thickness (Aspect) Ratio
The Influence of the Mounting Method on Plate Deflection
Self-Weight Deflection of Mounted Mirrors
Mirror Support Criteria
Fundamental Frequency of a Vibrating Plate
Natural Frequency of a Deformable Mirror
Design Guidelines for Pressure Windows
Dome Collapse Pressure
Glass Does Not Flow
Allowable Stress in an Optic
Relationship between Tensile and Compressive Stress
Estimation of Preload Torque
Stress Birefringence Induced by an Applied Load
Maximum Stress on an Optic Due to a Metal Retainer
A Bonded Mirror Is Three Times More Stable in Tension or Compression than Shear
Mechanical Stability Rules
Mass Is Proportional to Element Size Cubed
Deflection of a Mirror at the End of a Beam
Scan Mirror Deflection
Figure Change of Metal Mirrors
Foam Core Mirrors
Spin-Cast Mirrors
Serrurier Truss
Spacecraft Issues Related to Space Optics
Damage Mechanisms Associated with Micrometeoroids
Black Coatings
Index of Refraction Resources
Carbon-Silicon Carbide Coefficient of Thermal Expansion
Properties of Aluminum as a Function of Temperature
Permeability of Gases through Thin Films of Aluminum
Time to Uniform Temperature
Temperature Dependence of the Verdet Constant
Modeling Cryo Multilayer Insulation

11 Miscellaneous
Position of the Sun
Distance to Horizon
Digital Pixel Equivalent of Chemical Film
Common Image and Video Compression Formats
The Power of Dimensional Analysis
Scissor Integration
Number of Seconds in a Year
Solid Angles
Speed of Light
Water Weighs a Ton
Avoid Galling Metal
Failure of Cylinders and Spheres under External Pressure
Defining Screw Threads
Friction-Induced Pointing Error after Rate Reversal
Shipping Environments
Clean Room Classifications
Converting Transmission and Optical Density
Safety Factors for Optics
Use Speckle to Focus
90 Percent of Anything Is Plumbing
Arrhenius Equation
Miller's Rule of Test Failure
Cooling with Liquid or Solid Cryogen
Joule-Thomson Cool-Down Time
Low-Earth-Orbit Thermal Changes
Crickets as Thermometers
Image Intensifier Resolution
Photomultiplier Tube Power Supply Noise
Quantization Error

12 Ocean Optics
Index of Refraction of Seawater
Absorption Coefficient
Absorption of Ice at 532 nm
Absorption Caused by Chlorophyll a
f-stop under Water
Underwater Detection
Underwater Glow
Ocean Reflectance
Wave Slope

13 Optical Design and Analysis
Small-Angle Approximation
Effects from Light Passing Through a Plane Parallel Plate
Beam Deviation Due to a Thin Wedge Prism
Impacts of Optical Element Motion
Defocus for a Telescope Focused at Infinity
Hyperfocal Distance
Focal Length and Field of View
Limit on FOV for Reflective Telescopes
Maximum Useful Pupil Diameter
Minimum f-Number
f-Number for Circular Obscured Apertures
Why Light Won't Refract in a Cube
Aberration Scaling
Spherical Aberration and f-Number
Blur vs. Field-Dependent Aberrations
Reducing Optical Design Sensitivities
Separate the Centers of Curvature
Reduce the Ray Angles of Incidence
Efficient Reflective Triplet Layout for Feasibility Checks
Properties of Visible Glass
Per Pixel Resolution of a Spectrometer
Smith's Modern Optics Design Rules of Thumb
Diffraction Graph
Diffraction Is Proportional to Perimeter
Diffraction Principles Derived from the Uncertainty Principle
Why There Are Spikes Radiating from Only Some Objects Seen in Astronomical Images
Estimating Surface Scatter
Power Spectral Density of Surface Roughness
In-Field Source Contribution to Stray Light in the Focal Plane
Fest's Stray Light Rules of Thumb
Performance Budgeting Using the Hopkins Ratio
Linear Approximation for the Optical Modulation Transfer Function
Telescope Aberrations Not Caused by the Atmosphere
Strehl for Obscured Apertures
Total Error Using the Root-Sum-Square Approach
Optical Performance of a Telescope
Visible Imaging System Resolution
Optimal Telescope Resolution for the Human Eye
Peak-to-Valley Approximates Four Times the Root Mean Square
Ritchey-Chretien Telescope Aberrations
Spectral Bandwidth and Resolution of Acousto-optical Tunable Filters
Circular Variable Filters
Blazed Grating Performance
Fabry-Perot Etalons
Pulse Broadening in a Fabry-Perot Etalon
Hollow Waveguides
Inflated Mirrors
Handheld Binocular Efficiency
Stop Down Two Stops
Anti-reflection Coating Index
Coating Shift with Angle of Incidence
Coating Shift with Temperature
Grating Blockers
Far-Field Model of a Light Source, or the "Rule of 5"
Lambertian Source Illumination of a Detector
Detecting Linear Polarization
Modeling an Optical System Using the Fast Fourier Transform
A Collection of Optical Engineering Rules of Thumb
Use a "Pencil Bounce" to Determine Image Orientation
Thermal Gradients in a Primary Mirror
Thermal Lensing

14 Optical Manufacture and Test
Progress in Optical Fabrication of High-Quality Mirrors
Caution while Cleaning Optics
Thickness of a Doublet Bond
Sag of an Optic
Scratch-Dig Specifications
Oversizing an Optical Element for Producibility
Mind Your Karow Factor
Cyanoacrylate Usage
Surface Tilt Is Typically the Worst Error
Diamond-Turned Mirror Substrate Design
Diamond-Turned Mirror Figure Error
Accuracy of Figures
Fringe Movement
Approximations for the Foucault Knife-Edge Test
Effect of Surface Irregularity on the Wavefront
Hartmann Test for Pinhole Size
Maximum Size of the Opening for an Integrating Sphere
Choosing an Eyepiece for Star Tests
Collimator Design
Temperature Control Is Critical for Accurate Inhomogeneity Testing
Optical Table Displacement Requirements
Detection of Flatness by the Human Eye
Lesser-Known Lab Tools
Yoder's Rules of Thumb

15 Photogrammetry
Basic Optical Equations
Triangulation vs. Model-Based Pose Estimation
Stereo vs. Triangulation
Basic Triangulation Equations
Two-Camera Triangulation Accuracy
Triangulation Error Tree
Sensor Placement for Triangulation
Maximum Triangulation Range
Triangulation Equations for Cameras
Azimuth Corrections for Euclidean Coordinate Systems
Model-Based Pose Estimation: Number of Points and Spatial Distribution
From What Point in an Optical System Is Range Measured?

16 Radiometry
The Electromagnetic Spectrum
Photons-to-Watts Conversion
Brightness of Common Sources
The Blackbody Equation
Logarithmic Blackbody Functions
Narrow-band Approximation to Planck's Law
Peak Wavelength of Wien's Displacement Law
Choice of Waveband
Lambert's Law
In-Band Solar Irradiance at the Top of the Atmosphere
Rule of 4(f/#)2
Relationship between Minimum Resolvable Temperature and Noise-Equivalent Temperature Difference
Ideal NEΔT Simplification
Cavity Emissivity
Incorrectly Sizing Radiometric Areas
No Ice Cream Cones
Calibrate under User's Conditions for Best Results
Radiometry of a Spherical Cow
Dependence on R0A
Quick Test of NEΔT

17 Systems
Pick Any Two
Divide by the Number of Visits
Dawes Limit
BLIP Limiting Rule
Rayleigh Criterion
Focal Length and Resolution
Diffraction Limit in LWIR
Procedures to Reduce Narcissus Effects
System Off-Axis Optical Rejection
Signal-to-Noise Ratio for Different Targets
Simplified Range Equation
General Image Quality Equation
Mechanical Shock Response
Estimating rms Acceleration Response due to Random Vibrations
Typical Values of Electro-optical System Parameters
Vibration Isolation
Wind Loading

18 Target Phenomenology
Emissivity Approximations
Solar Reflection Always Adds to the Signature
Lambertian vs. Specular
Bidirectional Reflectance Distribution Function
Hagen-Rubens Relationship for the Reflectivity of Metals
Causes of White Pigment's Color
Human Body Signature
Infrared Skin Characteristics
Jet Plume Phenomenology
Plume Thrust Scaling
Rocket Plume Rules
Temperature as a Function of Aerodynamic Heating
Laser Cross-Section
Chlorophyll Absorptance
Normalized Difference Vegetation Index

Tables of Numerical, Physical, and Material Properties (or Other Information)
Properties of Infrared Materials
Thermal and Structural Properties of Materials
CIE Chromaticity Diagram
Basic Equations
Blackbody Nomograph
Nomoscope of Telescope Performance
Azimuth and Elevation Conventions
Photonic Noise Sources
Guidelines for Writing SI Units
Derivation of the Third Equation in the Rule "The Relation of Ideal D* to View Angle"



The evolution of the photonic sciences parallels, and feeds from, developments in a number of somewhat unrelated fields, including astronomy, satellite and remote sensing technology, materials science, electronics, biomedical sciences, optical communications, military developments, and many others. The common thread of all of this effort, which was defined in the 1950s, is that scientists and engineers have been able to combine highly successful electronic technologies with the more ancient concepts and methods of optics and electromagnetic wave propagation. The merging of these fields has provided an unprecedented capability for instruments to "see" targets and communicate with them in a wide range of wavelengths for the benefit of security systems, science, defense, and (more recently) consumers. In the future, we see the rise of autonomous systems as a sea change that will drive a significant increase in the need for sensing systems to allow the autonomous system to sense and understand its environment.

Major departments at universities are now devoted to producing new graduates with specialties in this field. There is no end in sight for the advancement of these technologies, especially with the continued development of electronics and computing as increasingly integral parts of photonic instrumentation. One of the disturbing trends in this technology is the constant narrowing of the role of engineers. As the technology matures, it becomes more difficult for anyone working in an area of photonics to understand all that is being done in the related sciences and engineering. This book has been assembled to make a first, small step to expose anyone working in the optics and photonics community to a wide range of critical topics through simple calculations and explanations.

There is no intent to compete with classic texts or the many journals or conferences devoted to the photonics field, all of which provide considerable detail in every area. Rather, this book is intended to allow any engineer or scientist, regardless of specialty, to make rapid and accurate guesses at solutions in a wide range of topics that might be encountered in system design, modeling, or fabrication, as well as to provide a guide for choosing which details to consider more diligently. This book will help any electro-optics (EO) team to make quick assessments, generally requiring no more than a calculator, so that they quickly find the right solution for a design problem.

The book is also useful for managers, marketeers, and other semi-technical folks who are new to the optics industry (or are on its periphery) to develop a feel for the difference between the chimerical and the real. Students may find the same type of quick-calculation approach valuable, particularly in the case of oral exams in which the professor is pressuring the student to do a complex problem quickly. Using these assembled rules, you can keep your wits about you and provide an immediate and nearly correct answer, which usually will save the day. But after the day is saved, you should go back to the question and perform a rigorous analysis. These rules are useful for quick sanity checks and basic relationships. Being familiar with the rules allows one to rapidly pinpoint trouble areas or ask probing questions in meetings. They aid in thinking on your feet and in developing a sense of what will work and what won't. Another potential application of the contents is to provide a checklist for reviewers asked to assess the completeness of a design or resolve trade studies early in the development of a system. But they are not, and never will be, the last word.

Dear reader, it is fully recognized that errors may still be present, and for that we apologize in advance to you and to those from whom the material was derived. We try to the best of our abilities to remove errors we inherit from the references we used and in new material we created. To assist us in this endeavor, we have solicited the cooperation of as many experts as would agree to help. Their input gives us a wide variety of experience from many different technical points of view. Alas, technology advances, and all of us wonder how we can possibly keep up. Hopefully, this book will not only provide some specific ideas related to photonics technology, it will also suggest some ways of thinking about things that will lead to a whole new generation of such rules and ideas.

As we discovered with the previous editions of this book, not everyone has the same thing in mind when considering "a rule of thumb." To qualify for our definition of a rule of thumb, a rule should be useful to a practitioner and possess at least most of the following attributes:

  • * It should be easy to implement.
  • * It should provide roughly the correct answer.
  • * The main points should be easy to remember.
  • * It should be simple to express.
  • * It should highlight the important variables and diminish the role of generally unimportant variables.
  • It should provide useful insight to the workings of the subject matter.

As in earlier editions of books in this series, we found it valuable to create a detailed standard form and stick to it as closely as possible. We did in this edition as well. References are provided whenever possible. In addition, reference material is mentioned that can be considered as recommended reading for the reader with a desire for more detail than could be presented in the "rule" and "discussion." The reader should note that each rule "stands on its own," so the abbreviations and terminology may not be entirely consistent throughout. This is intentional; we use the notation of the reference whenever we can so that if you read the original material you will recognize what that author defined. Some rules are derived from the laws of physics, and some represent existing technology trends. Many derive from observations made by researchers in the field, augmented by curve fitting that results in polynomial approximations.

The authors of the previous versions of this book arrived at the same place by very different paths. John (now retired, but busy consulting) spent some of his career in infrared astronomy before joining the aerospace industry to work on infrared sensors for space surveillance. He later worked on tactical sensors for search-and-rescue, self-driving cars, active imaging and enhanced vision systems. Ed (now retired, but very busy teaching) spent most of his career working on remote sensing technologies applied to Earth, its atmosphere and oceans, and, more recently, astronomical instruments and advanced pointing systems. John and Ed met in Denver in 1985, both working for a major government contractor on exotic electro-optical systems.

Those were halcyon days, with money flowing like water, and contractors winning billions of dollars for some concepts that were overly optimistic or barely possible at best. In the center of the whole fray were bureaucrats, politicians, and managers who were demanding that we design systems that would be capable of the impossible. We saw many requirements and goals being levied on our systems that were far from realistic, often resulting from confusing (and poorly understood) interpretations of the capabilities of optical and electro-optical systems and the properties of targets or backgrounds. We found a common ground when managers discovered that many co-workers, in an attempt to outdo the competition, were promising to perform sensor demonstrations that violated many rules of engineering, if not physics. On one multibillion-dollar program, after some consistent exposure to neophytes proposing all sorts of undoable things, we decided to try to educate everyone by creating a half-serious, half-humorous posting for the local bulletin board (this was before websites were ubiquitous) called "Dr. Photon’s Rules of Thumb." It was a list of basic rules that apply when optics or electro-optics are used. Figure 1 shows the first version that we found all across the company, and even among competitors.

For the current version, John and Ed invited (maybe some would say tricked) three other younger authors to modernize, enhance, and yield a new perspective. These luminaries are Jack Sanders-Reed,Brian McComas, and Katie Schwertz, whose bios appear in the back matter of this book.

Katie is a hybrid optical and optomechanical designer, drawing from her time at both the University of Rochester and University of Arizona optics programs. She primarily works on commercial and industrial optical subsystems. Her time spent under the tutelage of Jim Burge in Arizona taught her the value of a good estimation, which she didn’t fully appreciate until her time spent in industry. Her Master’s work involved optomechanics "rules of thumb." Jack has 40 years of experience ranging from medical imaging, to surface science, to pilot vision systems and atmospheric phenomenology, to target detection, tracking, and photogrammetry and covering the electromagnetic spectrum from hard x-ray through visible and infrared to millimeter-wave with both passive and active imaging. Brian has over 30 years of experience working on EO systems for military, astronomical, remote sensing, and industrial use. His Ph.D. was developed under the direction of Ed Friedman.

To summarize, this collection of rules and concepts represents an evolving, idiosyncratic, and eclectic toolbox. The rules, like tools, are neither good nor bad; they can be used to facilitate the transition of whimsical concepts to mature hardware or to immediately identify a technological path worth pursuing. Conversely, misused, they can obfuscate the truth and, if improperly applied, derive incorrect answers. Our job was to refine complex ideas to simplified concepts and present these rules to you with appropriate cautions. However, it is your responsibility to use them correctly. Remember, it is a poor worker who blames their tools and we hope you will find these tools useful.

John L. Miller
Edward Friedman
Jack Sanders-Reed
Katie Schwertz
Brian McComas
March 2020

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