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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Wiley Series in Pure and Applied Optics
- Sprache: Englisch
Gets you quickly up to speed with the theoretical and practical aspects of free space optical systems engineering design and analysis
One of today's fastest growing system design and analysis disciplines is free space optical systems engineering for communications and remote sensing applications. It is concerned with creating a light signal with certain characteristics, how this signal is affected and changed by the medium it traverses, how these effects can be mitigated both pre- and post-detection, and if after detection, it can be differentiated from noise under a certain standard, e.g., receiver operating characteristic. Free space optical systems engineering is a complex process to design against and analyze. While there are several good introductory texts devoted to key aspects of optics—such as lens design, lasers, detectors, fiber and free space, optical communications, and remote sensing—until now, there were none offering comprehensive coverage of the basics needed for optical systems engineering. If you're an upper-division undergraduate, or first-year graduate student, looking to acquire a practical understanding of electro-optical engineering basics, this book is intended for you. Topics and tools are covered that will prepare you for graduate research and engineering in either an academic or commercial environment. If you are an engineer or scientist considering making the move into the opportunity rich field of optics, this all-in-one guide brings you up to speed with everything you need to know to hit the ground running, leveraging your experience and expertise acquired previously in alternate fields. Following an overview of the mathematical fundamentals, this book provides a concise, yet thorough coverage of, among other crucial topics:
- Maxwell Equations, Geometrical Optics, Fourier Optics, Partial Coherence theory
- Linear algebra, Basic probability theory, Statistics, Detection and Estimation theory, Replacement Model detection theory, LADAR/LIDAR detection theory, optical communications theory
- Critical aspects of atmospheric propagation in real environments, including commonly used models for characterizing beam, and spherical and plane wave propagation through free space, turbulent and particulate channels
- Lasers, blackbodies/graybodies sources and photodetectors (e.g., PIN, ADP, PMT) and their inherent internal noise sources
The book provides clear, detailed discussions of the basics for free space optical systems design and analysis, along with a wealth of worked examples and practice problems—found throughout the book and on a companion website. Their intent is to help you test and hone your skill set and assess your comprehension of this important area. Free Space Optical Systems Engineering is an indispensable introduction for students and professionals alike.
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Veröffentlichungsjahr: 2017
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Table of Contents
Cover
Wiley Series in Pure and Applied Optics
Title Page
Copyright
Preface
About the Companion Website
Chapter 1: Mathematical Preliminaries
1.1 Introduction
1.2 Linear Algebra
1.3 Fourier Series
1.4 Fourier Transforms
1.5 Dirac Delta Function
1.6 Probability Theory
1.7 Decibels
1.8 Problems
References
Chapter 2: Fourier Optics Basics
2.1 Introduction
2.2 The Maxwell Equations
2.3 The Rayleigh–Sommerfeld–Debye Theory of Diffraction
2.4 The Huygens–Fresnel–Kirchhoff Theory of Diffraction
2.5 Fraunhofer Diffraction
2.6 Bringing Fraunhofer Diffraction into the Near Field
2.7 Imperfect Imaging
2.8 The Rayleigh Resolution Criterion
2.9 The Sampling Theorem
Problems
References
Chapter 3: Geometrical Optics
3.1 Introduction
3.2 The Foundations of Geometrical Optics – Eikonal Equation and Fermat Principle
3.3 Refraction and Reflection of Light Rays
3.4 Geometrical Optics Nomenclature
3.5 Imaging System Design Basics
3.6 Optical Invariant
3.7 Another View of Lens Theory
3.8 Apertures and Field Stops
3.9 Problems
References
Chapter 4: Radiometry
4.1 Introduction
4.2 Basic Geometrical Definitions
4.3 Radiometric Parameters
4.4 Lambertian Surfaces and Albedo
4.5 Spectral Radiant Emittance and Power
4.6 Irradiance from a Lambertian Source
4.7 The Radiometry of Images
4.8 Blackbody Radiation Sources
4.9 Problems
References
Chapter 5: Characterizing Optical Imaging Performance
5.1 Introduction
5.2 Linearity and Space Variance of the Optical System or Optical Channel
5.3 Spatial Filter Theory of Image Formation
5.4 Linear Filter Theory of Incoherent Image Formation
5.5 The Modulation Transfer Function
5.6 The Duffieux Formula
5.7 Obscured Aperture OTF
5.8 High-Order Aberration Effects Characterization
5.9 The Strehl Ratio
5.10 Multiple Systems Transfer Function
5.11 Linear Systems Summary
References
Chapter 6: Partial Coherence Theory
6.1 Introduction
6.2 Radiation Fluctuation
6.3 Interference and Temporal Coherence
6.4 Interference and Spatial Coherence
6.5 Coherent Light Propagating Through a Simple Lens System
6.6 Partially Coherent Imaging Through any Optical System
6.7 Van Cittert–Zernike Theorem
6.8 Problems
References
Chapter 7: Optical Channel Effects
7.1 Introduction
7.2 Essential Concepts in Radiative Transfer
7.3 The Radiative Transfer Equation
7.4 Mutual Coherence Function for an Aerosol Atmosphere
7.5 Mutual Coherence Function for a Molecular Atmosphere
7.6 Mutual Coherence Function for an Inhomogeneous Turbulent Atmosphere
7.7 Laser Beam Propagation in the Total Atmosphere
7.8 Key Parameters for Analyzing Light Propagation Through Gradient Turbulence
7.9 Two Refractive Index Structure Parameter Models for the Earth's Atmosphere
7.10 Engineering Equations for Light Propagation in the Ocean and Clouds
7.11 Problems
References
Chapter 8: Optical Receivers
8.1 Introduction
8.2 Optical Detectors
8.3 Noise Mechanisms in Optical Receivers
8.4 Performance Measures
Problems
References
Chapter 9: Signal Detection and Estimation Theory
9.1 Introduction
9.2 Classical Statistical Detection Theory
9.3 Testing of Simple Hypotheses Using Multiple Measurements
9.4 Constant False Alarm Rate (CFAR) Detection
9.5 Optical Communications
9.6 Laser Radar (LADAR) and LIDAR
9.7 Resolved Target Detection in Correlated Background Clutter and Common System Noise
9.8 Zero Contrast Target Detection in Background Clutter
9.9 Multispectral Signal-Plus-Noise/Noise-Only Target Detection in Clutter
9.10 Resolved Target Detection in Correlated Dual-Band Multispectral Image Sets
9.11 Image Whitener
9.12 Problems
References
Chapter 10: Laser Sources
10.1 Introduction
10.2 Spontaneous and Stimulated Emission Processes
10.3 Laser Pumping
10.4 Laser Gain and Phase-Shift Coefficients
10.5 Laser Cavity Gains and Losses
10.6 Optical Resonators
10.7 The ABCD Matrix and Resonator Stability
10.8 Stability of a Two-Mirror Resonator
10.9 Problems
References
Appendix A: Stationary Phase and Saddle Point Methods
A.1 Introduction
A.2 The Method of Stationary Phase
A.3 Saddle Point Method
Appendix B: Eye Diagram and its Interpretation
B.1 Introduction
B.2 Eye Diagram Overview
Appendix C: Vector-Space Image Representation
C.1 Introduction
C.2 Basic Formalism
Reference
Appendix D: Paraxial Ray Tracing – Abcd Matrix
D.1 Introduction
D.2 Basic Formalism
References
Index
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Begin Reading
List of Illustrations
Chapter 1: Mathematical Preliminaries
Figure 1.1 Example of a periodic function .
Figure 1.2 Dirichlet examples of (a) and (b) .
Figure 1.3 Plots of (a) , (b) , and (c) as a function of
x
.
Figure 1.4 Plots of polar spirals.
Figure 1.5 Venn diagram of events and .
Chapter 2: Fourier Optics Basics
Figure 2.1 Right-hand rule for electromagnetic waves. Source: Reproduced with permission of Newport Corporation.
Figure 2.2 Wavenumbers for fields
A
and
B
in three space.
Figure 2.3 Wavenumber regimes for real and imaginary arguments.
Figure 2.4 The wave vector in angular coordinates.
Figure 2.5 Spherical wave geometry for Huygens–Fresnel–Kirchhoff theory.
Figure 2.6 Angular interpretation of the spherical wave geometry.
Figure 2.7 Geometry for image formation.
Figure 2.8 Fraunhofer diffraction geometry.
Figure 2.9 Plot of .
Figure 2.10 (a) One-dimensional plot of . (b) Two-dimensional image of .
Figure 2.11 Fractional energy of
L
(
x
) contained in a functional argument
x
= .
Figure 2.12 Plane wave illuminating an object, which is imaged by a simple lens.
Figure 2.13 Oscillatory nature of the (a) cosine function and (b) sine function.
Figure 2.14 Two lens geometry setup.
Figure 2.15 Examples of optical aberrations; barrel distortion, chromatic aberrations (https://en.wikipedia.org/wiki/Chromatic_aberration), and astigmatism (https://en.wikipedia.org/wiki/Astigmatism).
Figure 2.16 Two barely resolved point sources (Rayleigh Criterion).
Figure 2.17 Two barely resolved point sources (Rayleigh Criterion) with three phase differences between said sources.
Figure 2.18 Plot of the Sampling Theorem.
Figure 2.19 Depiction of image undersampling. Source: Pratt, 2007 [14]. Reproduced with permission of Wiley.
Figure 2.20 Example of a (a) perfect image and (b) aliased reconstructed image. Source: Pratt, 2007 [14]. Reproduced with permission of Wiley.
Chapter 3: Geometrical Optics
Figure 3.1 Illustration of eikonal equation scenario.
Figure 3.2 Principle of refraction.
Figure 3.3 Principle of refraction and reflections.
Figure 3.4 Spherical wave fronts incident on (a) a flat aperture and (b) curved aperture; both separating two mediums of different refractive indices.
Figure 3.5 Locations of the key parameters characterizing an optical system.
Figure 3.6 Locations of the nodal point.
Figure 3.7 Locations of the key parameters in imaging system model.
Figure 3.8 Locations of the key parameters in a thin lens.
Figure 3.9 Graph of as a function of .
Figure 3.10 Graph of the image distance as a function of object distance .
Figure 3.11 Seven examples of thin lens image formation.
Figure 3.12 Example of an imaging thin-lens system showing a maximal ray.
Figure 3.13 Imaging geometry of a conventional lens.
Figure 3.14 Depiction of a plano-convex lens.
Figure 3.15 Depiction of an aperture stop.
Figure 3.16 Entrance and Exit Pupil locations in a notional multielement optical system.
Figure 3.17 Key parameters in an example multielement optical imaging system.
Figure 3.18 Key parameters in an example multielement optical imaging system.
Figure 3.19 Entrance and Exit Window locations in a notional multielement optical system.
Figure 3.20 Layout of a single-lens imaging system.
Chapter 4: Radiometry
Figure 4.1 The electromagnetic frequency spectrum. Source: Alkholidi, 2014 [7]. Used under http://www.intechopen.com/books/contemporary-issues-in-wireless-communications/free-space-optical-communications-theory-and-practices.
Figure 4.2 (a) Planar and (b) spherical geometrical view of solid angle.
Figure 4.3 Depiction of projected area.
Figure 4.4 Example of the (a) keystone effect and (b) its correction. Source: https://en.wikipedia.org/wiki/File:Vertical-keystone.jpg.
Figure 4.5 Integration geometry for a circular cone.
Figure 4.6 Coordinate systems for setting the direction vector .
Figure 4.7 Energy transfer from point to point .
Figure 4.8 Power transfer from object space to image space via a simple lens.
Figure 4.9 Geometry of a Lambertian source emitting into a hemisphere.
Figure 4.10 Elemental are illuminating a point
x
0
.
Figure 4.11 Schematic of the relationship between the exit pupil and the image plane.
Figure 4.12 Cosine to the fourth as a function of angle.
Figure 4.13 Comparison of reflector's angular response and the cosine to the fourth law.
Figure 4.14 Example of an aplanatic optical systems setup.
Figure 4.15 Scene radiance mapping into image irradiance.
Figure 4.16 Example optical systems setup.
Figure 4.17 Comparison of exo- and endo-atmospheric solar spectral irradiance and blackbody (the shaded areas indicate atmospheric absorption by the molecular constituents noted) [12].
Figure 4.18 Comparison among Planck's law, Wien's law, and the Rayleigh–Jeans law irradiance distributions as a function of wavelengths.
Chapter 5: Characterizing Optical Imaging Performance
Figure 5.1 Example output images created by a linear, space-variant system using input functions that comprised (a) shifted delta functions and (b) shifted arbitrary functions.
Figure 5.2 Example output images created by a nonlinear processing an input functions where (a) high, (b) low, and (c) high and low intensities are zeroed.
Figure 5.3 (a) Lens layout and (b) telecentric lens layout for filtering an incoherent and coherent image.
Figure 5.4 Image of the USAF 1951 Resolution Test Chart.
Figure 5.5 (a) Spatial and (b) radiance distribution of an arbitrary bar series.
Figure 5.6 Effect on imaged edge by the point spread function of the optics.
Figure 5.7 Blurring effect on an imaged square wave.
Figure 5.8 Plot of modulation as function of line pairs per millimeter for (a) one system and (b) two systems.
Figure 5.9 Plot of (a) and (b) 1 +.
Figure 5.10 Plot of for a specific MTF and .
Figure 5.11 Image contrast for a chirped spatial intensity waveform [8]. Source: Schowengerdt [8]. Reproduced with permission from Professor Emeritus Robert A. Schowengerdt, University of Arizona.
Figure 5.12 Graphical depiction of the overlap between two circles of diameter
D
and center positions and .
Figure 5.13 Picture showing the area of overlap of two displaced rectangles centered on the -axis.
Figure 5.14 Graphs of the OTF for a square aperture in (a) one dimension and (b) two dimensions.
Figure 5.15 Graphical depiction of the overlap between two circles of diameter
D
and center positions and .
Figure 5.16 (a) Pictures showing the area of overlap of two displaced circles and (b) the geometry for calculations specific fraction of that area.
Figure 5.17 Graphs of the OTF for a circular aperture in (a) one dimension and (b) two dimensions.
Figure 5.18 Geometry for (a) a centrally obscured circular lens and (b) the image plane.
Figure 5.19 Geometrical interpretation of given in Eq. (5.92).
Figure 5.20 Plot of the centrally obscured circular Lens OTF for various obscuration levels.
Figure 5.21 Wave aberration function at the exit pupil of an optical imaging system.
Figure 5.22 Cross section of the square aperture OTF with a focusing error.
Figure 5.23 Defocused image of a starburst pattern [3, p. 151].
Figure 5.24 Propagation geometry for Zernike polynomials.
Figure 5.25 Depictions of the first 10 Zernike polynomial modes.
Figure 5.26 Linear system summary.
Figure P5.1
Chapter 6: Partial Coherence Theory
Figure 6.1 Spatial example of (a) an amplitude spectrum and (b) its wave train.
Figure 6.2 Temporal example of (a) an amplitude spectrum and (b) its wave train.
Figure 6.3 Interference experimental setup.
Figure 6.4 Normalized intensity as a function.
Figure 6.5 Interference from a source and a mirror.
Figure 6.6 Depiction of the fringe pattern for large applied to Eq. (6.74).
Figure 6.7 Depictions of the fringe pattern for (a) and (b) as applied to Eq. (6.66).
Figure 6.8 Geometry for image formation.
Figure 6.9 Geometry of a two slit experiment.
Figure 6.10 Another geometry for a two slit experiment.
Chapter 7: Optical Channel Effects
Figure 7.1 Key concepts in radiative transfer: (a) Beer's law and (b) volume scattering function .
Figure 7.2 Percent transmittance of various atmospheric constituents [5, p. 129].
Figure 7.3 MODTRAN atmospheric transmission model example.
Figure 7.4 Extinction coefficient as a function of altitude for the various models for the (a) Spring–Summer and (b) Fall–Winter Seasons [6, pp. 4–47].
Figure 7.5 Transmissivity of the atmosphere [5, p. 132].
Figure 7.6 Volume extinction, absorption and scattering coefficients as a function of wavelength for (a) urban and (b) maritime aerosols for a moderately clear atmosphere (23 km visibility) [6, pp. 4–47].
Figure 7.7 Typical volume scattering function of seawater off Santa Catalina Island taken on June 19, 1975 [8].
Figure 7.8 Depth profiles of radiance for different Zenith angles in the plane of the Sun on a clear day [9, Figure 23].
Figure 7.9 Example images of image contrast [10, p. 432].
Figure 7.10 Example images of image contrast [10, p. 433].
Figure 7.11 Visibility map of the United States [11].
Figure 7.12 Geometry for propagation through an aerosol environment.
Figure 7.13 Geometry for propagation through a turbulent environment.
Figure 7.14 Growth in beam diameter as a function of distance from the laser source.
Figure 7.15 Plot of normalized wavefront curvature radius versus normalized range.
Figure 7.16 Normalized resolving power for long-exposure imaging as a function of .
Figure 7.17 Spot size profile after laser beam propagation through a turbulent environment.
Figure 7.18 Heterodyne efficiency as a function of .
Figure 7.19 Observed scintillation versus predicted scintillation.
Figure 7.20 Idealistic example of turbulent scatter.
Figure 7.21 The AO-corrected PSF after turbulence degradation as compared to a perfect PSF.
Figure 7.22 Comparison of exact Strehl ratio calculation for turbulence with Andrews and Phillips' approximate equation.
Figure 7.23 Vertical distribution of atmospheric turbulence for the HV model.
Figure 7.24 Multiples of HV 5/7 model compared to Korean turbulence statistics.
Figure 7.25 Comparison of HV and Bufton wind speed profiles as a function of altitude.
Figure 7.26 Comparison of Hufnagel–Valley (HV) and Hufnagel–Andrews–Phillips (HAP) models.
Figure 7.27 Various light beam effects from particulate scattering process.
Figure 7.28 Angular distribution of the apparent radiance produced by a uniform, spherical underwater lamp at distance of 7.5, 17.5, 29, and 39 ft [9, Figure 15].
Figure 7.29 Total irradiance produced as a function of distance by a uniform, spherical underwater lamp [9, Figure 16].
Figure 7.30 In-water radiance distributions in the plane of the Sun obtained experimental data [9, Figure 26].
Figure 7.31 Normalized in-water radiance distributions for the data shown in Figure 7.27 [9, Figure 27].
Figure 7.32 Diffuse attenuation coefficient for the waters of the world (Jerlov water types) [1].
Figure 7.33 Water reflectivity as a function of wavelength for the Jerlov water types [1].
Figure 7.34 Comparison of normalized receiver field-of-view loss with experimental data [1].
Figure 7.35 Comparison of Monte Carlo-based radiance model with experimental data [41].
Figure 7.36 Graphs of (a) channel transmittance and (b) normalized spatial spread as a function of optical and diffusion thickness, respectively.
Figure 7.37 Graphs of (a) the normalized transmittance of absorptive clouds as function of optical thickness for two single scatter albedos and (b) the RMS pulse spreading in absorptive clouds as function of optical thickness for various single scatter albedos[1].
Chapter 8: Optical Receivers
Figure 8.1 Photoelectric effect for (a) a metal and (b) an intrinsic semiconductor.
Figure 8.2 Plots of (a) typical spectral response curves, with 0080 lime-glass window for silver–oxygen–cesium (Ag–O–Cs), cesium-antimony (), and multialkali or trialkali () and (b) for various photocathodes useful in scintillation counting applications. (The variation in (b) of the cutoff at the low end is due to the use of different envelope materials).
Figure 8.3 (a) Schematic and (b) equivalent circuit layout for a phototube.
Figure 8.4 Electron multiplication in a photomultiplier tube (PMT) with a semitransparent photocathode operated in the transmission mode.
Figure 8.5 Optical absorption coefficient for selected semiconductors versus wavelength.
Figure 8.6 Pictures of (a) p–n-junction diode structure and (b) its diffusion forces and electric field.
Figure 8.7 Schematics of zero-biased circuits using (a) a p–n-junction structure and (b) the electronic component symbol.
Figure 8.8 The energy-band diagram for the p–n junction in thermal equilibrium.
Figure 8.9 Electric potential through the space charge region of a uniformly doped p–n junction.
Figure 8.10 Schematics of reverse-biased circuits using (a) a p–n-junction structure and (b) the electronic component symbol, and (c) its open-circuit condition.
Figure 8.11 The revised energy-band diagram for the p–n junction under reversed bias conditions.
Figure 8.12 Schematics of forward-biased circuits using (a) a p–n-junction structure and (b) the electronic component symbol, and (c) its short-circuit condition.
Figure 8.13 The revised energy-band diagram for the p–n junction under forward bias conditions.
Figure 8.14 Current versus voltage (
I–V
) characteristics of (a) ideal and (b) Zener p–n-junction diodes.
Figure 8.15 Pictures of (a) p–n-junction diode structure and (b) its electronic symbol.
Figure 8.16 Example plots of (a) penetration depth () of light into silicon substrate for various wavelengths and (b) spectral responsivity of several different types of planar diffused photodiodes.
Figure 8.17 Equivalent circuit for the junction photodiode.
Figure 8.18 Characteristic
I–V
curves of a junction photodiode for photoconductive and photovoltaic modes of operation. , , 2, 3, etc., indicate different incoming light power levels.
Figure 8.19 Schematic drawing of a PIN photodiode.
Figure 8.20 An example of the basic layout for an optical receiver system.
Figure 8.21 Basic RIN measurement setup.
Figure 8.22 Schematic of a PIN-based optical receiver.
Figure 8.23 Noise powers and signal-to-noise ratio for an erbium-doped fiber preamplifier system as a function of amplifier gain.
Figure 8.24 Fiber-coupling efficiency as a function of the number of speckles, , over the receiver aperture. The coupling geometry parameter equals 1.12 in this curve. The circles in this graph represent the coupling efficiency for optimized values of derived for six specific number of speckles .
Figure 8.25 Spatial coherence radius of a collimated Gaussian-beam wave, scaled by the plane wave coherence radius and plotted as a function of the Fresnel ratio .
Figure 8.26 The binary signal is encoded using rectangular pulse amplitude modulation with (a) polar return-to-zero code and (b) polar non-return-to-zero code.
Figure 8.27 Measured DPSK transceiver and OAGC BER baselines as a function of received optical power into the OAGC with a 100 GHz drop filter. Note: These measurements include the input losses into the OAGC.
Figure 8.28 Eye Diagrams for ORCA NRZ–OOK system with, and without, the OAGC.
Figure 8.29 Example of received power dynamics and operation of first-generation OAGC during ORCA flight tests.
Chapter 9: Signal Detection and Estimation Theory
Figure 9.1 (a) Probability density functions (PDFs) for Hypotheses
H
0
and
H
1
, pinpointing mean levels, and , respectively, and (b) same PDFs with threshold .
Figure 9.2 Plot of the Bayes and minimax risks.
Figure 9.3 Example of a receiver operator characteristic (ROC) curve.
Figure 9.4 Decision regions for a two measurement data set.
Figure 9.5 (a) Example of a gate for calculating local image statistics and (b) an illustration of the two windows used the RX algorithm.
Figure 9.6 Depiction of (a) NRZ-OOK and (b) RZ-OOK.
Figure 9.7 Depiction of DPSK.
Figure 9.8 Conception of a OOK determination of bit transmitted.
Figure 9.9 Maximum likelihood ratio as a function of the normalized photocurrent for various Rytov log-amplitude standard deviations.
Figure 9.10 Example probability of bit error as a function of the normalized threshold for and .
Figure 9.11 Normalized threshold for maximum-likelihood symbol-by-symbol detection versus the log-amplitude standard deviation of the turbulence for selected values of AWGN.
Figure 9.12 Examples of DTED.
Figure 9.13 Block schematics of (a) bistatic and (b) monostatic LADAR/LIDAR systems.
Figure 9.14 Range accuracy versus resolution.
Figure 9.15 Coherent detection intensity processor block diagram.
Figure 9.16 Spatial orientation of carrier and oscillator signals for (a) a collimated optical receiver and (b) a focusing optical receiver.
Figure 9.17 Continuous direct detection intensity processor block diagram.
Figure 9.18 Photo-counting direct detection intensity processor block diagram.
Figure 9.19 Concept of operation for LIDAR system.
Figure 9.20 Backscatter cross section comparison.
Figure 9.21 Examples of LIDAR phenomena, types and application.
Figure 9.22 (a) Calibration targets from the photo resolution range, Edwards Air Force Base and (b) Tri-bar array at Eglin Air Force Base, Florida.
Figure 9.23 Matched filter response using the resolved target test statistic.
Figure 9.24 Probability of false alarm versus threshold for (a) and (b) , as a function of pixel observations
K
.
Figure 9.25 CFAR probability of detection versus GSNR for (a) and (b) , as a function of spectral bands
M
, as compared to that of a perfect matched filter.
Figure 9.26 CFAR probability of detection versus GSNR for (a) and (b) , as a function of pixel observations
K
, as compared to that of a perfect matched filter.
Figure 9.27 The incremental improvement in SNR provided by adding clutter and target reference bands collected by TIMS.
Figure 9.28 The incremental improvement in SNR provided by adding clutter and target reference bands collected by SMIFTS.
Figure 9.29 Vector projections of the components of .
Figure 9.30 Scatter plot of two infrared images with system noise taken captured sequentially (a) before and (b) after whitening.
Chapter 10: Laser Sources
Figure 10.1 Bohr model representation of (a) absorption, (b) spontaneous emission, and (c) stimulated emission.
Figure 10.2 Quantized energy state representation of (a) absorption, (b) spontaneous emission, and (c) stimulated emission.
Figure 10.3 Insides of a helium–neon gas laser showing the isotropic spontaneous emissions and the directional stimulated emissions within the laser cavity.
Figure 10.4 Graphs of energy versus energy state population following a Boltzmann distribution (a) with and (b) without absorption and stimulated energy diagrams.
Figure 10.5 (a) Energy state diagram depicting pump and laser transition, as well as spontaneous emission between the three-energy states and (b) histogram of energy versus population density highlighting key decay times.
Figure 10.6 (a) Energy state diagram depicting pump and laser transition, as well as spontaneous emission between the four-energy states and (b) histogram of energy versus population density highlighting key decay times.
Figure 10.7 Illustration of atomic energy states “0,” “1,” and “2,” and decay times.
Figure 10.8 Plot of as a function of .
Figure 10.9 Illustration of photon flux density entering and exiting a cylinder of length .
Figure 10.10 Spectral plots of (a) gain and (b) phase-shift coefficients for an optical amplifier with a Lorentzian line-shape function.
Figure 10.11 Basic laser layout.
Figure 10.12 Depiction of the complex amplitude signal within a flat mirror resonator.
Figure 10.13 (a) Example resonator frequency spectrum and (b) an expanded view of its first three frequencies.
Figure 10.14 Mode spectrum for a lossy resonator.
Figure 10.15 Effect on several longitudinal mode laser output by gain coefficient of the laser medium.
Figure 10.16 The irradiance distribution for the four lowest transverse modes (same ) of the optical resonator. The subscripts and are identified as the number of nodes along two orthogonal axes perpendicular to the axis of the optical cavity.
Figure 10.17 Example irradiance distribution for the transverse mode (same ) of the optical resonator.
Figure 10.18 Example configurations of (a) stable and (b) unstable resonators.
Figure 10.19 Relationship between laser pump region and cavity mode structure.
Figure 10.20 (a) Optical cavity formed by two spherical mirrors and (b) two lens system.
Figure 10.21 Plot of versus showing regions of stability and instability with example resonator structures.
Appendix A: Stationary Phase and Saddle Point Methods
Figure A.1 Oscillatory nature of the (a) Cosine function and (b) Sine function.
Figure A.2 Notional plot of .
Appendix B: Eye Diagram and its Interpretation
Figure B.1 Illustration of an eye diagram and its interpretation.
Figure B.2 Example of an eye diagram from (a) single trigger of recovered 10 Gbps eye, 600 ms persistence and (b) long persistence of recovered 10 Gbps eye.
Appendix C: Vector-Space Image Representation
Figure C.1 Illustrative optical surveillance and reconnaissance geometry.
Appendix D: Paraxial Ray Tracing – Abcd Matrix
Figure D.1 Example of a paraxial ray making a small angle with the optical axis.
Figure D.2 Propagation in a homogeneous medium of length
d
.
Figure D.3 Propagation into a curved mirror.
Figure D.4 Propagation into a refractive index interface.
Figure D.5 Simple lens system.
Figure D.6 Multielement optical system.
List of Tables
Chapter 1: Mathematical Preliminaries
Table 1.1 Probabilities for Possible Outcomes from Flipping a Coin
Table 1.2 Equivalent Power Ratios
Chapter 3: Geometrical Optics
Table 3.1 Key Parameters for Thin Lens Images in Figure 3.11
Chapter 4: Radiometry
Table 4.1 List of Fundamental Radiometric Quantities and Their Standard Notation
Chapter 5: Characterizing Optical Imaging Performance
Table 5.1 Selected orthonormal Zernike circle polynomials and associated aberrations
Chapter 8: Optical Receivers
Table 8.1 List of Work Functions and Richardson's Constants for a Set of Specific Materials
Table 8.2 List of Photodetector Semiconductors Materials, and Their Bandgaps and Wavelengths at 300 K
Wiley Series in Pure and Applied Optics
The Wiley Series in Pure and Applied Optics publishes authoritative treatments of foundational areas central to optics as well as research monographs in hot-topic emerging technology areas. Existing volumes in the series are such well known books as Gaskill's Linear Systems, Fourier Transforms, and Optics, Goodman's Statistical Optic, and Saleh & Teich's Fundamentals of Optics, among others.
A complete list of titles in this series appears at the end of the volume.
FREE SPACE OPTICAL SYSTEMS ENGINEERING
Design and Analysis
LARRY B. STOTTS
Copyright © 2017 by John Wiley & Sons, Inc. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
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Library of Congress Cataloging-in-Publication Data
Names: Stotts, Larry B., author.
Title: Free space optical systems engineering : design and analysis / Larry B. Stotts.
Description: Hoboken, New Jersey : John Wiley & Sons, Inc., [2017] | Series: Wiley series in pure and applied optics | Includes bibliographical references and index.
Identifiers: LCCN 2016043633 (print) | LCCN 2016053936 (ebook) | ISBN 9781119279020 (cloth) | ISBN 9781119279037 (pdf) | ISBN 9781119279044 (epub)
Subjects: LCSH: Optical engineering. | Optical communications.
Classification: LCC TA1520 .S76 2017 (print) | LCC TA1520 (ebook) | DDC 621.36–dc23
LC record available at https://lccn.loc.gov/20160436330
Cover Image Credit: Courtesy of the author
Cover Design: Wiley
Preface
Just before graduating from the college, I took a job at a Navy Laboratory because there were not any research grants to help pay for my future graduate school work. As it turned out, it was a very rewarding experience, allowing me to work on many fascinating projects during my time there. They ranged from fiber optic communications, integrated optics in II–VI compounds, optical signal processing, data storage in electro-optical crystals, laser communications, and atmospheric and space remote sensing. Although I had a very good education in undergraduate applied physics from UCSD, many of these projects involved new optical technologies, as well as engineering concepts, that I had not been exposed to previously. My first two years in graduate school concentrated on graduate physics, which also did not cover these areas. Consequently, I had to spend a large amount of time in the library reading books and papers in order to come up to speed in these areas. I often wished that UCSD offered undergraduate and graduate classes in optical system engineering with an accompanying textbook(s) covering the breadth of the engineering basics necessary to tackle these various engineering areas. As it turned out, the mathematical foundations of each area were common, but many times the definitions and concept descriptions of one area masked its commonality with other topics in optics. In addition, the details were often absent and/or hard to find. In the absence of classes, it would have been nice to have an introductory reference to use to review the basic foundation concepts in optics and to find some of the original key references with the derivations of important equations at the time. This would have made it easier to move among a plethora of ever changing engineering projects.
Since then, several comprehensive books on optics have been written, for example, Fundamentals of Photonics by Saleh and Teich, the SPIE Encyclopedia of Optics, Electro-Optics Handbook by Waynant and Ediger. Although excellent in their content, these are written for a conversant researcher who has done graduate work, and/or been working, in optics for several years in order to fill in the blanks or to understand the nuances contained within the text. Unfortunately, this leaves junior, senior, and first/second year graduate students behind the power curve, requiring additional time, work, and consultation with their advisor or seasoned colleague, to understand what is written. Even with the Internet, this can be a formidable task. Thus, it appears that they are in the same situation as I was at the beginning of my career. In looking across the literature, there also are introductory textbooks focused on certain aspects of optics such as lens design, lasers, detectors, optical communications, and remote sensing, but none of which seem to encompass the breadth of free space optical systems engineering at a more basic level.
This textbook is an attempt to fulfill this need. It is intended to be the reference book for the engineer changing fields, and at the same time, to be an introduction to the field of electro-optics for upper division undergraduates and/or graduate students. Many of the original papers for the field are referenced, and an (comprehensive) introduction and overview of the topic has been attempted. Presentation and integration of physical (quantum mechanical), mathematical, and technological concepts, where possible, hopefully assists in the students' understanding.
It has been suggested that this material is too advanced for upper division undergraduate students. I think not for two reasons. First, today's students have been exposed to advanced subjects since middle/junior high school, for example, calculus and differential equations. They are used to being challenged. Second, and more importantly, the book provides the details of complex calculations in the many examples and discussions, so the students can become comfortable with complex mathematical manipulations. I never thought the concepts and calculations described by professors as “obvious to the most casual observer” were, and my fellow students and I struggled because of our lack of confidence, experience, and familiarity in figuring complex things out. Professors Booker and Lohmann independently taught me that if I understood the mathematical details, it would be easier to understand experimental results and to invent and explain complex concepts. This has helped me greatly over my career. However, getting this understanding sooner over a broader range of subjects in optics would have benefited me a lot and I hope to achieve that for readers of this book. I also believe students will be better prepared for graduate school and jobs by seeing complex subjects with this foundation. This book breaks down as follows:
Chapter 1
provides the background mathematics for the rest of the book. Specific topics include linear algebra, Fourier series, Fourier transforms, Dirac Delta function, and probability theory.
In
Chapter 2
, we discuss Fourier Optics, which includes sections on (1) Maxwell Equations, (2) Rayleigh–Sommerfeld–Debye Theory of Diffraction, (3) The Huygens–Fresnel–Kirchhoff Theory of Diffraction, (4) Fresnel Diffraction, and (5) Fraunhofer Diffraction. The Huygens–Fresnel–Kirchhoff formalism is the workhorse of laser propagation analysis, as the reader will soon find out. Examples and comments are also provided, so the reader gets insights on the application of Fourier Optics in typical engineering problems.
Geometrical Optics uses the concept of rays, which have direction and position but no phase information, to model the way light travels through space or an optical system. This is the subject of
Chapter 3
. In this chapter, we focus on imaging systems, which cover a broad class of engineering applications. We begin by summarizing the first-order lens design approaches. Key concept and definitions are explained, so the student can understand the key aspects of lens design. We also discuss the basic elements in an optical system such as windows, stops, baffles, and pupils that are sometimes confusing to the new optical engineer.
In
Chapter 4
, we outline the field of Radiometry, which is the characterization of the distribution of the optical power or energy in space. It is distinct from the quantum processes such as photon counting because this theory uses “ray tracing” as its means for depicting optical radiation transfer from one point to another. It ignores the dual nature of light.
Chapter 5
deals with the convolutional theory of image formation. Specifically, the reader will find that convolution process can characterize the effects of an imperfect optical system or those of an optical channel such as the optical scatter channel or turbulent channel on an input distribution. Most of the engineering analyses one finds in the literature exploit this mathematical theory.
Chapter 6
focuses on partial coherence theory. It covers the situation where the resulting light interference is barely visible, exhibiting only low contrast effects. Partial coherence theory is considered the most difficult subject in optics. Much is written on this subject; sometimes successfully, sometimes not. This chapter looks at this theory from the most basic level, clarifying the definitions and concepts with examples, so the reader will better understand the theory, compared to others, after completing this chapter.
In
Chapter 7
, we address the characterization of optical channel effects. We begin a discussion of radiative transfer through particulate media, then move to the development of the mutual coherence function (MCF) for aerosols and molecules, and then turbulence. Finally, we provide a set of engineering equations useful in understanding and characterizing light propagation in those same channels.
In
Chapter 8
, we provide a first-order overview of the various optical detector mechanisms and devices. We next look at the possible noise sources in an optical receiver that influence the quality of signal reception. When these detector and noise mechanisms are combined with the received signal, we obtain the arguably key parameter in detection theory, the electrical signal-to-noise ratio (SNR). The construction of this particular metric connects it with RF engineering, so the synergism between the two areas can be easily exploited. Finally, we discuss the various forms of SNR and include some detection sensor/receiver examples to illustrate their variation.
Chapter 9
reviews the classical statistical detection theory and then shows its applicability to optical communications and remote sensing. This is not found in many introductory optics books and discusses two of the key detection concepts: the probabilities of detection and false alarm. Both the signal-plus-additive-noise and replacement model hypothesis testing approaches are discussed. Examples of the theory's application to communications and remote sensing system are given.
In the early chapters, we emphasized blackbody sources, which are based on the concept of the spontaneous emission of light from materials such as gases and solids. An alternative source concept was proposed in 1917 by Albert Einstein. It is called the simulated emission of light. Although it was almost 60 years before it became a reality, the laser, which is an acronym for Light Amplification by Stimulated Emission of Radiation, has revolutionized optical system design. The final chapter of this textbook,
Chapter 10
, provides an overview of the fundamentals of laser theory, the key source for all optical communications and remote sensing applications.
During my career, I have had the great fortune to have worked under the guidance of some key leaders in Electrical Engineering and Optics. Alphabetically, they were H.G. Booker (RF propagation), S.Q. Duntley (Visibility/Underwater Optics), R.M. Gagliardi, (Optical Communications), C.W. Helstrom (RF and Optical Detection and Estimation theory), S. Karp (Optical Communications), A.W. Lohmann (Optical Signal Processing), and I.S. Reed (RF/Optical Remote Sensing and Communications, and Forward Error Correction). These minds have served as both inspiration and mentors in my studies and projects, and I am forever grateful to have passed through their lives.
In addition, I would like to thank my many colleagues who helped me over the years succeed in my optical systems projects and gain the insights I discuss in this book. They also have influenced me greatly. In writing this book, I want to acknowledge Larry Andrews, Guy Beaghler, David Buck, Ralph Burnham, Barry Hunt, Skip Hoff, Juan Juarez, Ron Phillips, H. Alan Pike, Gary Roloson, and Ed Winter for their help and assistance.
I also want to thank Mr. Jim Meni, Science and Technology Associates (STA), for his friendship and for his support of my little project. He kindly let me use an office and his staff at STA to facilitate this textbook's development. It would have been much harder without his strong support.
Finally, I want to recognize the biggest contributors to this book, my partner Debra, who has shown both understanding and patience during the preparation of this manuscript. Anyone who has imbedded themselves in an all-consuming goal knows the importance of receiving those facets from loved ones.
Although I stand upon the shoulders of all of these individuals, any deficiencies in this textbook are attributable to me alone. I request your feedback regarding all improvements that might help this text, both in content, style, and perhaps most importantly, in its ability to serve as the desired introduction to upper division undergraduate students. Please pass along any and all suggestions to attain this goal.
Larry B. StottsArlington, VirginiaSeptember 2016
About the Companion Website
This book is accompanied by a companion website:
www.wiley.com/go/stotts/free_space_optical_systems_engineering
The website includes:
Solutions Manual
Chapter 1Mathematical Preliminaries
1.1 Introduction
Free space optical systems engineering addresses how light energy is created, manipulated, transferred, changed, processed, or any combination of these entities, for use in atmospheric and space remote sensing and communications applications. To understand the material in this book, some basic mathematical concepts and relationships are needed. Because our audience is envisioned to be junior and senior undergraduates, it is not possible to require the readers to have had exposure to these topics at this stage of their education. Normally, they will have a working knowledge of algebra, geometry, and differential and integral calculus by now, but little else.
In this chapter, we provide a concise, but informative, summary of the additional mathematical concepts and relationships needed to perform optical systems engineering. The vision is to form a strong foundation for understanding what follows in subsequent chapters.
The intent is to establish the lexicon and mathematical basis of the various topics, and what they really mean in very simple, straightforward means, establishing that envisioned foundation.
1.2 Linear Algebra
Imaging sensors create pictures stored as two-dimensional, discrete element arrays, that is, matrices. It is often convenient to convert these image arrays into a vector form by column (or row) scanning the matrix, and then stringing the elements together in a long vector; that is, a lexicographic form [1]. This is called “vectorization.” This means that the optical engineers need to be adept in linear algebra to take on problems in optical signal processing and target detection. This section reviews the notational conventions and basics of linear algebra following Bar-Shalom and Fortmann, Appendix A [2]. A more extensive review can be found in books on linear algebra.
1.2.1 Matrices and Vectors
A matrix, , is a two-dimensional array that can be mathematically written as
The first index in the matrix element indicates the row number and the second index, the column number. The dimensions of the matrix are . The transpose of the above matrix is written as
A square matrix is said to be symmetric, which means that
which means that .
A vector is a one-dimensional matrix array, which is written as
The column vector has dimension in this case. By convention, we assume all vectors are column vectors. The transpose of a column vector is a row vector and the transpose of Eq. (1.4) can be written as
Comparing Eqs. (1.4) and (1.5), it is clear that
1.2.2 Linear Operations
The addition of matrices and multiplication of a matrix by a scalar are given by the following equation:
where
for. Obviously, all three matrices have the same dimensions.
The product of two matrices is written in general as
where
for . Here, is a matrix, is a matrix, and is a matrix. In general, matrix products are not commutative, that is, .
The transpose of a product is
Equation (1.10) implies that if the matrix–vector product is written as
where is a matrix, is a vector, and is a vector, then its transpose is equal to
with being a (row) vector, being a vector, and still being a matrix.
1.2.3 Traces, Determinants, and Inverses
The trace of a matrix is defined as
which implies that
The determinant of a matrix is defined as
where
The parameter set are called the cofactors of and is the matrix formed by deleting the ith row and jth column from . The determinant of a scalar is defined as the scalar itself since essentially is a matrix. This implies that the determinant of a matrix multiplied by a scalar is given by
and the determinant of a product of two matrices is written as
Example 1.1
The determinant of a 2 × 2 matrix is given by
The determinant of a 3 × 3 matrix is given by
Example 1.2
Let us now look at the solution for Eq. (1.12), where matrix is a matrix. Multiplying Eq. (1.12) out, we have three simultaneous equations:
The solutions to these equations are:
and
assuming the determinant of matrix is not zero.
The inverse of a matrix (if it exists) can be expressed as
In Eq. (1.20), the matrix is called the identity matrix, which has 1's down the diagonal and 0's everywhere else. The inverse is given by the equation
where are the cofactors of . The matrix is called the adjugate of . A matrix is considered invertible or nonsingular if and only if its determinant is nonzero; otherwise, it is said to be singular. Let us discuss these points a little more.
The inverse of a matrix exists if and only if the columns of the matrix (or its rows) are linearly independent. This means that
where is the zero vector.
A general matrix can be inverted using methods such as the Cayley–Hamilton (CH) method, Gauss–Jordan elimination, Gaussian elimination, or LU decomposition.
Example 1.3
The cofactor equation given in Eq. (1.17) gives the following expression for the inverse of a 2 × 2 matrix:
The CH method gives the solution
Example 1.4
The inverse of a matrix is given by
where
The CH method gives the solution
Example 1.5
With increasing dimensions, expressions for becomes complicated. However, for , the CH method yields
Example 1.6
The inverse of a (nonsingular) partitioned matrix also can be shown to be given by
where is a matrix, is a matrix, is a matrix, is a matrix, and . In the above,
and
If , , and , then the following matrix equation
can be rewritten as
The above is known as matrix inversion formula.
It is easy to show that
1.2.4 Inner Products, Norms, and Orthogonality
The inner product of two arbitrary vectors of the same dimension is given by
If , then we write
Equation (1.44) is called the squared norm of the vector . The Schwartz inequality states that
Two vectors are defined to be orthogonal if
The orthogonal projection of the vector onto is
