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Tutorial Texts Series
Optical Engineering Fundamentals, Second Edition, Bruce H. Walker, Vol. TT82Fundamentals of Polarimetric Remote Sensing, John Schott, Vol. TT81Radiation Thermometry: Fundamentals and Applications in the Petrochemical Industry,Peter Saunders,
Vol. TT78
Matrix Methods for Optical Layout, Gerhard Kloos, Vol. TT77Fundamentals of Infrared Detector Materials, Michael A. Kinch, Vol. TT76Practical Applications of Infrared Thermal Sensing and Imaging Equipment, Third Edition, Herbert
Kaplan, Vol. TT75
Bioluminescence for Food and Environmental Microbiological Safety, Lubov Y. Brovko, Vol. TT74Introduction to Image Stabilization, Scott W. Teare, Sergio R. Restaino, Vol. TT73Logic-based Nonlinear Image Processing, Stephen Marshall, Vol. TT72 The Physics and Engineering of Solid State Lasers, Yehoshua Kalisky, Vol. TT71 Thermal Infrared Characterization of Ground Targets and Backgrounds, Second Edition, Pieter A. Jacobs,
Vol. TT70
Introduction to Confocal Fluorescence Microscopy, Michiel Mller, Vol. TT69Artificial Neural Networks: An Introduction, Kevin L. Priddy and Paul E. Keller, Vol. TT68Basics of Code Division Multiple Access (CDMA), Raghuveer Rao and Sohail Dianat, Vol. TT67 Optical Imaging in Projection Microlithography, Alfred Kwok-Kit Wong, Vol. TT66Metrics for High-Quality Specular Surfaces, Lionel R. Baker, Vol. TT65Field Mathematics for Electromagnetics, Photonics, and Materials Science, Bernard Maxum, Vol. TT64High-Fidelity Medical Imaging Displays, Aldo Badano, Michael J. Flynn, and Jerzy Kanicki, Vol. TT63Diffractive OpticsDesign, Fabrication, and Test,Donald C. OShea, Thomas J. Suleski, Alan D.
Kathman, and Dennis W. Prather, Vol. TT62
Fourier-Transform Spectroscopy Instrumentation Engineering, Vidi Saptari, Vol. TT61 The Power- and Energy-Handling Capability of Optical Materials, Components, and Systems,Roger M.
Wood, Vol. TT60
Hands-on Morphological Image Processing,Edward R. Dougherty, Roberto A. Lotufo, Vol. TT59Integrated Optomechanical Analysis,Keith B. Doyle, Victor L. Genberg, Gregory J. Michels,Vol. TT58 Thin-Film Design: Modulated Thickness and Other Stopband Design Methods,Bruce Perilloux, Vol. TT57 Optische Grundlagen fr Infrarotsysteme,Max J. Riedl, Vol. TT56An Engineering Introduction to Biotechnology, J. Patrick Fitch, Vol. TT55Image Performance in CRT Displays, Kenneth Compton, Vol. TT54Introduction to Laser Diode-Pumped Solid State Lasers, Richard Scheps, Vol. TT53Modulation Transfer Function in Optical and Electro-Optical Systems, Glenn D. Boreman, Vol. TT52 Uncooled Thermal Imaging Arrays, Systems, and Applications, Paul W. Kruse, Vol. TT51Fundamentals of Antennas, Christos G. Christodoulou and Parveen Wahid, Vol. TT50Basics of Spectroscopy, David W. Ball, Vol. TT49 Optical Design Fundamentals for Infrared Systems, Second Edition, Max J. Riedl, Vol. TT48Resolution Enhancement Techniques in Optical Lithography, Alfred Kwok-Kit Wong, Vol. TT47 Copper Interconnect Technology, Christoph Steinbrchel and Barry L. Chin, Vol. TT46 Optical Design for Visual Systems, Bruce H. Walker, Vol. TT45Fundamentals of Contamination Control, Alan C. Tribble, Vol. TT44Evolutionary Computation: Principles and Practice for Signal Processing, David Fogel, Vol. TT43Infrared Optics and Zoom Lenses,Allen Mann, Vol. TT42Introduction to Adaptive Optics,Robert K. Tyson, Vol. TT41Fractal and Wavelet Image Compression Techniques,Stephen Welstead, Vol. TT40Analysis of Sampled Imaging Systems,R. H. Vollmerhausen and R. G. Driggers, Vol. TT39
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Tutorial Texts in Optical Engineering
Volume TT83
PRESS
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Library of Congress Cataloging-in-Publication Data
Mann, Allen, 1929-
Infrared optics and zoom lenses / Allen Mann. -- 2nd ed.p. cm. -- (Tutorial texts in optical engineering ; v. TT83)
Includes bibliographical references and index.ISBN 978-0-8194-7667-8
1. Infrared equipment. 2. Zoom lenses. I. Title.
TA1570.M34 2009
621.36'2--dc22
2009010126
Published by
SPIE
P.O. Box 10Bellingham, Washington 98227-0010 USA
Phone: +1 360 676 3290
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Web: http://spie.org
Copyright 2009 Society of Photo-Optical Instrumentation Engineers
All rights reserved. No part of this publication may be reproduced or distributedin any form or by any means without written permission of the publisher.
The content of this book reflects the work and thought of the author(s).
Every effort has been made to publish reliable and accurate information herein,but the publisher is not responsible for the validity of the information or for anyoutcomes resulting from reliance thereon.Printed in the United States of America.
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Introduction to the Series
Since its inception in 1989, the Tutorial Texts (TT) series has grown to more than80 titles covering many diverse fields of science and engineering. The initial idea
for the series was to make material presented in SPIE short courses available to
those who could not attend and to provide a reference text for those who could.
Thus, many of the texts in this series are generated by augmenting course notes
with descriptive text that further illuminates the subject. In this way, the TT
becomes an excellent stand-alone reference that finds a much wider audience
than only short course attendees.
Tutorial Texts have grown in popularity and in the scope of material covered
since 1989. They no longer necessarily stem from short courses; rather, they are
often generated by experts in the field. They are popular because they provide aready reference to those wishing to learn about emerging technologies or the
latest information within their field. The topics within the series have grown from
the initial areas of geometrical optics, optical detectors, and image processing to
include the emerging fields of nanotechnology, biomedical optics, fiber optics,
and laser technologies. Authors contributing to the TT series are instructed to
provide introductory material so that those new to the field may use the book as a
starting point to get a basic grasp of the material. It is hoped that some readers
may develop sufficient interest to take a short course by the author or pursue
further research in more advanced books to delve deeper into the subject.
The books in this series are distinguished from other technical monographsand textbooks in the way in which the material is presented. In keeping with the
tutorial nature of the series, there is an emphasis on the use of graphical and
illustrative material to better elucidate basic and advanced concepts. There is also
heavy use of tabular reference data and numerous examples to further explain the
concepts presented. The publishing time for the books is kept to a minimum so
that the books will be as timely and up-to-date as possible. Furthermore, these
introductory books are competitively priced compared to more traditional books
on the same subject.
When a proposal for a text is received, each proposal is evaluated to
determine the relevance of the proposed topic. This initial reviewing process hasbeen very helpful to authors in identifying, early in the writing process, the need
for additional material or other changes in approach that would serve to
strengthen the text. Once a manuscript is completed, it is peer reviewed to ensure
that chapters communicate accurately the essential ingredients of the science and
technologies under discussion.
It is my goal to maintain the style and quality of books in the series and to
further expand the topic areas to include new emerging fields as they become of
interest to our reading audience.
James A. HarringtonRutgers University
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Contents
Preface ................................................................................................................. xi
1. System Considerations ................................................................................... 1
1.1 Radiometry .................................................................................................. 11.1.1 Blackbody radiation .............................................................................. 11.1.2 Planck's equation ................................................................................. 11.1.3 Stefan-Boltzmann law .......................................................................... 21.1.4 Wien displacement law ........................................................................ 2
1.2 Atmospheric Transmission .......................................................................... 31.2.1 Scattering ............................................................................................. 31.2.2 Absorption ............................................................................................ 41.2.3 Infrared windows .................................................................................. 41.2.4 Computer calculation ........................................................................... 4
1.3 Lens Transmission ...................................................................................... 51.3.1 Transmittance ...................................................................................... 51.3.2 Reflectance .......................................................................................... 51.4 Coatings ...................................................................................................... 71.4.1 Single-layer coatings ............................................................................ 71.4.2 Multilayer coatings ............................................................................... 8
1.5 Infrared Detectors ....................................................................................... 91.5.1 Basic relations ...................................................................................... 91.5.2 Types ................................................................................................... 91.5.3 Arrays ................................................................................................. 111.5.4 Matching the detector with the optics ................................................ 11
1.6 References ................................................................................................ 122. Optics Fundamentals .................................................................................... 13
2.1 Lens Equation ........................................................................................... 132.2 Stops and Pupils ....................................................................................... 132.3 Optical Formulas ....................................................................................... 152.4 Optical Performance Criteria ..................................................................... 162.5 Telescopes ................................................................................................ 172.6 Primary Aberrations .................................................................................. 19
2.6.1 Definition of the Seidel aberrations .................................................... 192.6.2 Variation of primary aberrations with aperture and field height ......... 192.6.3 Stop shift equations ........................................................................... 20
2.7 Achromatism ............................................................................................. 212.7.1 Primary achromatism ......................................................................... 212.7.2 Secondary spectrum .......................................................................... 22
2 8 Principal Planes 22
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2.9 Problems ................................................................................................... 242.10 References .............................................................................................. 24
3. Unique Features of the Infrared Region ...................................................... 253.1 Optical Materials ....................................................................................... 25
3.1.1 Materials for the infrared .................................................................... 253.1.2 Calculation of index of refraction ....................................................... 27
3.2 Thermal Compensation ............................................................................. 283.2.1 Focus shift with temperature .............................................................. 283.2.2 Athermalization .................................................................................. 283.2.3 Athermalization methods ................................................................... 29
3.3 Cold Stop and Cold Shield ........................................................................ 303.4 Narcissus .................................................................................................. 30
3.4.1 Types of retroreflections .................................................................... 303.4.2 Reduction techniques ........................................................................ 30
3.5 Glass Substitution ..................................................................................... 313.6 References ................................................................................................ 32
4. Optical Design Techniques .......................................................................... 35
4.1 Optical Design Starting Point .................................................................... 354.2 Scaling ...................................................................................................... 354.3 Optical Materials Selection ....................................................................... 374.4 Techniques for Compactness ................................................................... 374.5 Symmetry Principle ................................................................................... 374.6 Bending ..................................................................................................... 384.7 Aplanatic Condition ................................................................................... 384.8 Adding an Element .................................................................................... 394.9 Field Lens Utilization ................................................................................. 394.10 Conics and Aspheres .............................................................................. 404.11 Diffractive Surfaces ................................................................................. 414.12 Aperture Stop Location ........................................................................... 414.13 Computer Optimization ........................................................................... 414.14 Global Search ......................................................................................... 424.15 Tolerances .............................................................................................. 444.16 References .............................................................................................. 44
5. Zoom Lenses ................................................................................................. 45
5.1 Types of Zoom Lenses.............................................................................. 455.1.1 Optically compensated zoom lens ..................................................... 455.1.2 Mechanically compensated zoom lens .............................................. 48
5.2 Infrared Zoom Lens Specifications ........................................................... 505.2.1 Spectral region ................................................................................... 515.2.2 Optical system performance .............................................................. 515.2.3 Aperture ............................................................................................. 515.2.4 Effective focal length .......................................................................... 515.2.5 Magnification range ............................................................................ 515.2.6 Size constraints .................................................................................. 515.2.7 Operating environment ...................................................................... 515.2.8 Distortion ............................................................................................ 52
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5.2.9 Transmission ...................................................................................... 525.2.10 Narcissus ......................................................................................... 525.2.11 Vignetting ......................................................................................... 52
5.3 Extenders .................................................................................................. 525.4 References ................................................................................................ 53
6. Refractive Infrared Zoom Lenses ................................................................ 55
6.1 Target Simulators ...................................................................................... 556.1.1 CI Systems ......................................................................................... 556.1.2 Hughes Aircraft Company .................................................................. 566.1.3 Lockheed Martin ................................................................................ 606.1.4 Optics 1 .............................................................................................. 63
6.2 Scanning Systems .................................................................................... 656.2.1 Barr & Stroud ..................................................................................... 656.2.2 Pilkington P.E. .................................................................................... 676.2.3 Optics 1 .............................................................................................. 706.2.4 Precision-Optical Engineering ........................................................... 716.2.5 Zhejiang University, Department of Optical Engineering ................... 736.2.6 Electrooptical Industries, Ltd. ............................................................. 746.2.7 Scotoptix ............................................................................................ 76
6.2.7.1 Boresighted zoom lens ............................................................... 766.2.7.2 Athermalized zoom lens ............................................................. 766.2.7.3 Optically compensated zoom lens .............................................. 81
6.2.8 Optimum Optical Systems ................................................................. 816.2.9Royal Institute of Technology ............................................................ 836.2.10Fuji Photo Optical Company ............................................................ 836.2.11 Carl Zeiss ......................................................................................... 84
6.3 Charge-Coupled Device Imaging Systems ............................................... 846.3.1 Angenieux .......................................................................................... 846.3.2 University of Alabama, Huntsville ...................................................... 876.3.3 National First University of Science and Technology ........................ 876.3.4 Industrial Technology Research Institute ........................................... 88
6.4 Laser Beam Expanders ............................................................................. 886.4.1 Carl Zeiss ........................................................................................... 886.4.2 University of Twente .......................................................................... 89
6.5 Diffractive Optics ....................................................................................... 936.5.1 Optics 1 .............................................................................................. 946.5.2 Optical E.T.C., Inc. and Teledyne Brown ........................................... 956.5.3 Wescam ............................................................................................. 996.5.4 Texas Instruments ........................................................................... 1016.5.5 Raytheon .......................................................................................... 1026.5.6 Raytheon .......................................................................................... 104
6.6 Focal Plane Arrays .................................................................................. 1046.6.1 Agency for Defence Development ................................................... 1046.6.2 Royal Institute of Technology .......................................................... 1066.6.3 Royal Institute of Technology .......................................................... 106
6.7 References .............................................................................................. 108
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7. Reflective Infrared Zoom Systems ............................................................ 111
7.1 Obscured Systems .................................................................................. 1117.1.1 Korea Advanced Institute of Science and Technology .................... 111
7.1.2 Center for Applied Optics, University of Alabama, Huntsville .......... 112
7.2 Unobscured Systems .............................................................................. 1137.2.1 Hughes Aircraft Company ................................................................ 1137.2.2 Optical E.T.C., Inc. ........................................................................... 1137.2.3 Beijing Institute of Technology ......................................................... 1167.2.4 Contraves Brashear ......................................................................... 117
7.3 Special Systems ...................................................................................... 1177.3.1 Lockheed Martin .............................................................................. 1197.3.2 Industrial Research, Ltd. .................................................................. 1197.3.3 Optical Research Associates ........................................................... 120
7.4 References .............................................................................................. 1218. Future Trends .............................................................................................. 123
8.1 Athermalization ....................................................................................... 1238.2 Diffractive Optical Elements .................................................................... 1238.3 Conics and Aspherics ............................................................................. 1238.4 Materials .................................................................................................. 1238.5 Detector Technology ............................................................................... 1248.6 Simulators ............................................................................................... 1248.7 Mirror Systems ........................................................................................ 1248.8 Wavelength Region ................................................................................. 1258.9 Optomechanical Considerations ............................................................. 1258.10 Computer Optimization ......................................................................... 1258.11 References ............................................................................................ 125
9. Summary of Applications ........................................................................... 127
9.1 Scene Projection and Simulation ............................................................ 1279.2Wide and Narrow Field of View Scanning Telescopes for Target Search
and Recognition ....................................................................................... 1279.3WFOV and NFOV FPA or CCD Surveillance, Tracking, and Target
Recognition .............................................................................................. 1279.4 Battlefield Detection of Enemy Soldiers and Armaments ....................... 1279.5 Search and Rescue Operations .............................................................. 1289.6Mineral Resource Surveys and Forest Fire Detection ............................ 1289.7 Laser Scanning Systems ........................................................................ 1289.8Cutting Sheet Metal with High-Power Lasers ......................................... 1289.9Observation of Solar Regions ................................................................. 1289.10 Camera Cell Phones ............................................................................. 128
Appendix A. Miscellaneous Patents .............................................................. 129
Appendix B. Computer Analysis of Selected Patents ................................. 155
Appendix C. Answers to Problems from Chapter 2 ..................................... 159
Index ................................................................................................................. 161
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Preface
This tutorial is an outgrowth of my SPIE short course entitled Infrared Optics
and Zoom Lenses. The title was selected to reflect the scope of the subject
matter, and this has been carried over to the tutorial. The first three chapters
present an introduction to the principles of optics and the unique aspects of theinfrared region of the wavelength spectrum. This foundation makes it possible for
those readers who are not optical engineers to acquire the background
information needed for a treatise on infrared zoom lenses.Chapter 1 presents overall system considerations involved in establishing the
requirements for an application that includes an optical system as one of its
elements. Chapter 2 sets forth the basic fundamentals of optics involved in thedesign and analysis of optical systems. Chapter 3 presents the optics features that
are unique to the infrared region of the spectrum. Chapter 4 discusses some of the
optical design techniques that may be utilized in the optical design of infrared
systems. These four chapters could serve as an introduction to any treatise on
infrared optical systems. Further discussion of these topics may be found in thetutorial text on this subject by Max J. Riedl.
1
Chapters 5 through 8 present the subject matter that is unique to thesubject of zoom lenses in the infrared. Chapter 5 sets forth the basic types of
zoom lenses and the establishing of specifications to meet the requirements of a
particular application. Chapters 6 and 7 present numerous examples of refractive
and reflective infrared zoom systems; the optical design techniques from Chapter
4 are employed in designing these representative infrared (IR) zoom lenses to
illustrate the utilization of these techniques. Companies identified in Chapters 6
and 7 are the names in existence at the time the reference papers were published;
some of them have since merged with other companies and lost their separate
identity. Chapter 8 presents a brief discussion of future trends in this subject area.
Chapter 9 presents a summary of infrared zoom lens applications.Appendix A contains three landmark IR zoom lens patents in their entirety as
published. This appendix is included not only for the insights contained therein,
but also to provide lens prescription data to serve as potential starting points for
future design activity. Appendix B presents computer analysis that I have
performed on these patents and on one additional patent described in Sec. 7.2.1.
A definition of the analysis categories is to be found in Chapter 2. Appendix C
gives the answers to self-test problems presented in Sec. 2.9.
The infrared zoom lens literature consists primarily of patents and of papers
presented at conferences or published in journals and proceedings. In 1993 SPIE
published in its Milestone Series of Selected Reprints a volume on zoom lenseswhich included a number of infrared papers and patents.2 To my knowledge, this
t t i l i th fi t bli ti t b d t d l i l t IR l It
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xii Preface
should serve as an introduction to the subject for the uninitiated and as an aid to
the engineer who has an infrared zoom lens application to pursue. It is not
intended to be a step-by-step instruction manual for this complex optical design
activity.
Additions to Infrared Optics and Zoom Lenses are included in the second
edition of this tutorial. The additions are based on an expanded short course that I
recently presented. There are substantive additions to the topics in the table of
contents. They are discussed below. Also, 18 new refractive and reflective
systems have been added to the 23 zoom systems in the first edition, bringing the
total to 41 optical systems. The 18 new systems were published in the reference
literature since publication of the first edition, in the time interval from the year
2000 to 2007. These additional systems are in part the result of adding a new
categoryfocal plane arraysto the chapter on refractive infrared zoom lenses.
In part these additions are a result of including dual field-of-view infrared opticalsystems in this tutorial. The 18 new zoom systems are intended to bring the
technology and the list of refractive and reflective zoom infrared systems up to
date. There are 24 additional references.
One of the themes that will be presented is the gradual shift in recent years
from the 8- to 12-micrometer (m) region to the 3- to 5-m region of thewavelength spectrum. This shift is discussed in Secs. 2.7, 3.1, 3.2, 6.5, and 6.6.
The rationale for the substantive additions is presented below:
2.8Principal planes: The location of the principal planes is important in order to
calculate accurately the separation between lens elements when going from athin-lens solution to a thick-lens solution. The location also affects the overall
length of the zoom system.
2.9 Self-test problems: A problem set is included in order to ensure a clear
understanding of optics fundamentals before discussing the infrared spectrum
and infrared zoom systems.
3.5 Glass substitution: Glass substitution is a powerful technique for performing
computer optimization and athermalization simultaneously by passive
substitution of infrared optical materials. I have done this glass substitution
successfully, and I present a detailed example with a reference to the paper Iwrote on this subject.
4.14 Global search: Global search has been demonstrated in recent years to be a
viable computer optimization tool. An example is presented of designing zoom
lenses by means of global search without designer intervention. The computer
program flowchart of the decision-making process is included in this discussion.
5.3 Extenders: Extenders are a practical means of extending the focal length
range of zoom lens systems. It is important to understand the optical limitations
of extenders.
6.6 Focal plane arrays: The use of focal plane arrays (FPA) to eliminatescanning is an important development in infrared optical systems. Techniques for
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Infrared Optics and Zoom Lenses xiii
overcoming the limitations of resolution of FPAs at higher spatial frequencies are
discussed in this section.
7.3 Special reflective systems: Due to the increase in the number of reflectiveinfrared zoom systems, it is important to understand techniques for dual-channel
detector arrays and for designing compact reflective systems through the use of
folding mirrors and the Mangin mirror.
Chapter 9 Summary of applications: It is useful to summarize the scope and
variety of infrared zoom lens applications. The discussion includes a reference to
each of the zoom systems presented in this tutorial. This overview makes this
chapter a fitting conclusion.
I would like to thank the reviewers for their helpful comments and
suggestions. Acknowledgment is also due to Gwen Weerts of SPIE for her
editorial assistance in the publication of this second edition ofInfrared Opticsand Zoom Lenses.
Allen Mann
January 2009
1. Riedl, M. J., Optical Design Fundamentals for Infrared Systems, Second
Edition, SPIE Press, Bellingham, WA (2001).
2. Mann, A., Ed., Selected Papers on Zoom Lenses, SPIE Press, Bellingham,
WA (1993).
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1
Chapter 1
System Considerations
1.1 Radiometry
1.1.1 Blackbody radiation
Blackbody radiation is the emission of radiant energy which takes place from a
blackbody at a fixed temperature.1 A blackbody is an ideal body which absorbs
all incident radiation and reflects none. Its radiating and absorbing efficiency,
called its emissivity factor, is unity. A graybody is an object with an emissivity
factor less than unity. Although an ideal radiator, a blackbody should not be
considered a meaningless abstraction. On a cosmological level, cosmic
background radiation which came into being shortly after the creation of the
universe has been observed to fit a blackbody curve with a high degree of
precision. In the context of electro-optical system design, the ideal assumption of
a blackbody is extremely useful because it represents a limiting case or may be
an approximation to a real set of conditions, as for example in the calculation ofstray radiation from an internal baffle. Blackbodies are used as calibrated sources
in simulation and spectrometer applications.
1.1.2 Plancks equation
Blackbody radiation has a spectral energy distribution as a function of
temperature which is described by Plancks equation (see Fig. 1.1):
( )( )
23 1
5
2 1W m sr ,
exp 1
hcL
hc kT
=
(1.1)
where
L is spectral radianceh is Plancks constant, 6.6262 10-34 Joule (J)
c is the velocity of light, 2.9979 108 m/s
is the wavelength in meters
kis the Boltzmanns constant, 1.3806 10-23 J/K
Tis absolute temperature in degrees K.
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2 Chapter 1
Figure 1.1 Blackbody radiation.
1.1.3 Stefan-Boltzmann law
The total power radiated per unit area of a blackbody is obtained by integrating
Plancks radiation law over all wavelengths and is known as the Stefan-
Boltzmann law. Blackbody radiation takes place at a rate expressed by the
Stefan-Boltzmann law as:
( )4 2W m total power radiated per unit area,M T= = (1.2)
where
is the emissivity factor and is Stefan-Boltzmann constant, 5.66961 10-8 (W m2 K4 ).
1.1.4 Wien displacement law
The wavelength at which maximum radiation occurs for a given temperature is
described by the Wien displacement law:
(max) = const/T= 2898/T(m) . (1.3)
This wavelength is significant for calibration purposes. It is desirable to use
relatively hot blackbody calibration sources. However, this calibration ideal is
often difficult to follow because of the problem of operating and maintaining
high-temperature blackbodies (that is, blackbodies that operate above 1000 C,where the materials begin to glow red hot and suffer oxidation). Also, such high-
temperature blackbody sources tend to overdrive or saturate sensitive electro-
optical sensors.1
The radiant emittance of a blackbody as a function of temperature and
wavelength is shown in Fig. 1.2.2
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System Considerations 3
Figure 1.2 Blackbody curves as a function of temperature.2
1.2 Atmospheric Transmission
1.2.1 Scattering
Atmospheric attenuation of infrared radiation is caused by scattering and
absorption. There are two types of scattering, Rayleigh and Mie. With Rayleigh
scattering, the scattering particle diameter is smaller than the wavelength of
transmission. Rayleigh scattering is wavelength dependent. With Mie scattering,
the particle diameter is equal to or greater than the wavelength of transmission.
Mie scattering is independent of wavelength and predominates in the infrared
region of the spectrum. Since water droplets in clouds and fog have sizesbetween 5 and 100 m, Mie scattering in haze or fog is just as bad in the infrared
as it is in the visible. The attenuation s resulting from scattering by particles
suspended in the atmosphere may be calculated according to
s = ex, (1.4)
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4 Chapter 1
where x is the path length and is a function of wavelength, concentration of
particles and their diameters, refractive index, and absorption coefficient.
1.2.2 Absorption
Absorption in the atmosphere is influenced primarily by the amount of ozone and
absorbing gases present, in particular water vapor, and by the wavelength of
transmission, which helps determine whether infrared radiation will encounter
absorbing gases or go through a window in the atmosphere. Atmospheric
transmission due to absorption as a function of wavelength is shown in Fig. 1.3.2
1.2.3 Infrared windows
The most important windows for infrared zoom lens systems are the 3- to 5-m
and 8- to 12-m regions because of the relatively low amount of atmospheric
absorption in those regions. The choice of the particular window to be used isdetermined by the temperature of the source and by the spectral sensitivity of the
detector. Atmospheric transmission a attenuated by absorption can be expressed
as
a = ex , (1.5)
where x is the path length and is the absorption coefficient. When both
absorption and scattering are present, the effective transmittance can be
expressed by the product( ) .xeff a s e
+ = = (1.6)
1.2.4 Computer calculation
Detailed computer models exist for the calculation of transmission through the
atmosphere. The best known of these models is the LOWTRAN from the
Geophysics Directorate at Hanscom Air Force Base in Massachusetts.3
Figure 1.3 Atmospheric transmission due to absorption as a function of wavelengththrough 1.8 km at sea level.
2
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System Considerations 5
1.3 Lens Transmission
Lens transmission can be expressed by
r+ t+ a = 1, (1.7)
where
r= reflectance r= 1 for an ideal reflector,
t= transmittance t= 1 for an ideal transmitter,
a = absorptance a = 1 for an ideal absorber (blackbody).
Additionally, according to conservation of energy, if no energy is lost through
absorption,
r+ t= 1. (1.8)
1.3.1 Transmittance
The transmission Ta through an optical element after absorption losses is
expressed by
Ta = ex, (1.9)
where
= absorption coefficient and
x = distance traveled through optical element.
1.3.2 Reflectance
The uncoated reflection loss per surface r(see Fig. 1.4) is expressed by
( )
( )
2
2
1,
1
nr
n
=
+(1.10)
Figure 1.4 Uncoated reflection loss per surface.
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6 Chapter 1
where
r= uncoated reflection loss per surface and
n = index of refraction of optical material.
Table 1.1 shows the uncoated reflection loss per surface as a function of index of
refraction.
The total transmission Tr through an optical system after reflection losses is
Tr = (1 r)m, (1.11)
where m = number of surfaces. Figure 1.5 shows the uncoated transmittance of
common IR materials.2
Table 1.1 Uncoated reflection loss per surface in air as a function of index of refraction.
Index of
refraction n
Reflection loss per
surface (uncoated)
1.5 4%
2.0 11%
2.5 18%
3.0 25%
3.5 31%
4.0 36%
Figure 1.5 Transmittance of common IR materials (uncoated).2
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System Considerations 7
Figure 1.6 Snells law of refraction.
1.4 Coatings
1.4.1 Single-layer coatings
As an introduction to a discussion of coatings, Snells law is the law of refractionat an interface between two media, such as air-glass (shown in Fig. 1.6) or glass-
air. It can be stated as
sin ' sin ',n i n i = (1.12)
where n and n are the two media, i is the angle of incidence, and i is the angle of
refraction.
Antireflection coatings play a significant role in increasing the throughput of
an optical system. This is particularly true in the infrared region where high index
materials like germanium and silicon are so commonly used. As noted in the
previous section, reflection losses increase dramatically with higher index
materials. Also, zoom lens systems may require additional elements in order to
minimize the aberration residuals, which also increases the transmission losses
through the optical system. According to coating theory, the index of refraction
for a thin-film single-layer coating should be equal to the square root of the index
of refraction of the substrate at one particular wavelength.According to the principle of the interactions at surface boundaries, there is a
half-wave phase change when light travels through a low-index medium and is
reflected from a high-index medium. There is no phase change when light travels
through a high-index medium and is reflected from a low-index medium. When
the thin-film layer thickness is a quarter wave, reflection losses are minimized
and transmission is maximized.
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8 Chapter 1
Figure 1.7 Infrared multilayer antireflection coating.4
1.4.2 Multilayer coatings
For broad spectral bands such as from 3 to 5 and from 8 to 12 m, a single layer
is not sufficient and a multilayer coating must be used. Most infrared materials
can be antireflection coated to reflectivities of 0.5% or less. An example of an
infrared multilayer antireflection coating is shown in Fig. 1.7.4 A layer of zinc
sulfide is used as an antireflection coating for a germanium substrate. However,
zinc sulfide has a relatively bad adhesion to the substrate. Thus, there is a
potential problem in that the layer of zinc sulfide could be easily stripped and
removed. This is solved by having a layer of silicon dioxide formed contiguously
to the germanium substrate. Silicon dioxide has good adherence to the substrate,
but will absorb a certain percentage of infrared light in the 3- to 5-m range.
However, in this case the predetermined thickness of the silicon dioxide layer isso slight that its absorption is negligible. Referring to Fig. 1.7, the first layer is
made of fluoride, the second layer of zinc sulfide, the third of germanium, and
from the fourth layer, zinc sulfide and germanium layers are formed alternately.
The (n1) layer is made of germanium, and the nth layer is made of silicon
dioxide.
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System Considerations 9
1.5 Infrared Detectors
1.5.1 Basic relations
The signal-to-noise ratio (SNR) is a useful means of measuring the performance
of a complete system. In its simplest form the signal-to-noise ratio is stated by
,NEP
PSNR = (1.13)
where P is the collected radiant power in watts received by the detector, and NEP
is the noise-equivalent power (the radiant power that produces a signal-to-noise
ratio of one at the output of the detector).
The NEP is a function of the detector size d, the electrical bandwidth f
used in the measurement, and the detector figure of merit D*. D* is a relativesensitivity parameter used to compare performance of different detector types.
D* is the signal-to-noise ratio at a particular electrical frequency and in a 1-Hz
bandwidth when 1 W of radiant power is incident on a 1-cm2 active area detector.
The higher theD*, the better the detector.
( )( )
( )
1 22
* 1 2 1
1 2
active area cmcm Hz W .
NEP W HzD
=
(1.14)
Responsitivity is the detector photocurrent output per unit incident radiant
power at a particular wavelength.
1.5.2 Types
An infrared detector is a converter that absorbs infrared energy and converts it
into an electrical signal. There are two principal types of infrared detectors.
Thermal detectors measure the rate at which energy is absorbed; their response is
independent of wavelength. They tend to have a slow response time. The mostcommon types of thermal detectors are thermocouple, thermopile, bolometer, and
pyroelectric. The most important type of detector for infrared zoom lens
applications, however, is the photon detector. Photon detectors respond only to
incident photons that possess more than a certain minimum energy; their
response at any wavelength is proportional to the rate at which photons of that
wavelength are absorbed. All photon detectors are composed of semiconductormaterial. They have a fast response time but require cooling for optimum
sensitivity. Typically, liquid nitrogen is used in a Joule-Thomson cooler to
achieve an operating temperature of 77 K. A detector dewar assembly diagram is
shown in Fig. 1.8. HgCdTe is a photoconductor detector with a spectral range
from 2 to 25 m. InSb is a photovoltaic detector with a spectral range from 1 to
5.5 m.
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10 Chapter 1
Figure 1.8 Detector dewar assembly diagram.
A charge-coupled device (CCD) may be used in the near-infrared region
from 0.65 to 1.05 m for imaging applications. A CCD chip is an array of
photoelectric detectors built on a silicon base using layers of electrical
components printed on the surface. This structure divides the base into a grid of
separate compartments, called pixels, that hold electrical charges; the size of a
pixel may vary from about 6 to 25 m. The CCD chip provides a 2D array that
converts incoming photons into electrical signals. These signals are then sent to a
display where they are reconverted into an image or to a storage device for future
reconversion. Sensitivity of the CCD array may be improved by cooling using
either circulating water, liquid gases, or by means of a thermoelectric cooler thatcan be integrated into the CCD camera package. The idealized relative spatial
response of a CCD to long-wavelength photons is shown in Fig. 1.9. 5
Figure 1.9 Idealized relative spatial response of a CCD to long-wavelength photons.5
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System Considerations 11
Figure 1.10 Linear-detector arrays, large-square rectangular arrays, and staring arrays.2
1.5.3 Arrays
Infrared systems have evolved over the years through the development of linear-
detector arrays, large-square rectangular arrays, and staring arrays. They are
defined below and illustrated in Fig. 1.10.2
(1) Serial scan: A small detector array with only a few elements is scannedin a serial form. Two scan mirrors are required, one for azimuth and the
other for elevation.
(2) Parallel scan: A long detector array covering the full extent of the fieldof view (FOV) in one dimension is swept out across the object space,
creating the full format image. Only a single-scan mirror is required.(3) Staring array: No moving parts are required, and a full-format image is
created directly. The advent of staring arrays has eliminated scanning
and the corresponding need for pupil control.
1.5.4 Matching the detector with the opticsIn an imaging system, the optics, detector, electronics, and display all have
inherent resolutions (Fig. 1.11). The overall system resolution is a composite of
these subsystem resolutions. Generally, in well-designed systems, the electronics
and display do not adversely affect the perceived image quality; therefore, it has
become commonplace to infer image quality from the optics and detector
performance.
System resolution depends on the optical blur diameter and the detector size.
When the system is detector limited, small changes in the blur diameter have
little effect on the system resolution. The detector size limits the smallest size
that can be discerned. With a large blur diameter, the resolution is limited by the
optics; most infrared imaging systems fall into this category.
A commonly used measure of optical resolution is the Airy disk size. It is thebright center of the diffraction pattern produced by an ideal optical system. In the
focal plane of the lens, the Airy disk diameter is
= 2.44 F, (1.15)
where is the wavelength andFis the lensf/#.
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12 Chapter 1
Figure 1.11 Imaging system.
Detector arrays are specified by the detector size and the number of pixels.
Again, the smallest target that can be discerned is limited by the detector size.
For example, a 256 256 one-half-inch detector array would have a pixel width
of 50 m. The optical designer can select both the aperture size D and the focal
lengthf(i.e., thef/#, whereF=f/D). As the detector size decreases, the f/# mustalso decrease to match the detector. For a system with a pixel width of 40 m
operating at a central wavelength of 10 m, the system will be optics limited
above an f/# of 1.64.6 The lower the f/# for a diffraction-limited system, the
higher the resolution and the smaller the optical blur diameter. The challenge for
the optical designer is to minimize image aberrations while decreasing thef/#.
CCD arrays operate in the visual and near-infrared regions of the wavelength
spectrum. A typical one-half-inch CCD array may have pixels that are about 10
m in size. For most CCD camera applications, the camera will be operating in
the detector-limited region when the f/# is less than about 6 due primarily to the
relatively short operating wavelength. Refer to Sec. 6.3 for an example of an
infrared zoom lens using a CCD camera.
1.6 References
1. Wyatt, C.L.,Radiometric System Design, Macmillan Co., New York (1987).
2. Fischer, R.E., Lens design for the infrared, in Infrared Optical Design andFabrication, R. Hartmann and W. J. Smith, Eds., SPIE Press, Bellingham,
WA (1991).
3. Riedl, M.J., Optical Design Fundamentals for Infrared Systems, SPIE Press,Bellingham, WA (1995).
4. Hatano, T., Antireflection coating for infrared light, U.S. Patent No.5,243,458, (September 1993).
5. Holst, G.C., CCD Arrays, Cameras, and Displays, 2nd Ed., SPIE Press,Bellingham, WA (1998).
6. Holst, G.C., Image quality: does your detector match your optics?Photonics Spectra33(1), 144146 (1999).
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13
Chapter 2
Optics Fundamentals
2.1 Lens Equation
The basic lens equation is illustrated in Fig. 2.1 and can be stated as
1 1 1 ,l l
= (2.1)
where fis the effective focal length, lis the object distance, and l is the image
distance. In Fig. 2.1, lis negative and l is positive, in accordance with the sign
convention. The focal length f = 1/P, where P is the power of the lens. For
example, ifl= 1 and l = +1, thenP= 2 andf= 0.5.
An important special case of the lens equation is illustrated in Fig. 2.2. This
is when the object is assumed to be at infinity, as is the case in most infrared
zoom lens applications. In accordance with Eq. (2.1), 1/l= 0,f= l, and the image
plane lies in the focal plane of the lens. In the above example,f= l = 0.5.
2.2 Stops and Pupils
The aperture stop is the limiting aperture of the optical system. The aperture stop
for a simple lens is shown in Fig. 2.3.1 The entrance pupil is the image of the
aperture stop in object space and is coincident with it. The exit pupil is the image
of the aperture stop in image space and is also coincident with the aperture stop
in the figure.1 The field stop limits the size of the detector at the image plane.
Figure 2.1 Basic lens equation.
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14 Chapter 2
Figure 2.2 Lens equation with object at infinity.
The chief ray is the central ray of an off-axis bundle of rays. Figure 2.4 1
illustrates the entrance and exit pupils and chief ray of an optical system. The
entrance pupil is located where the projection of the chief ray at the first lens
surface crosses the optical axis. The aperture stop is located where the chief ray
crosses the optical axis. If the aperture stop is in front of the optical system, it is
coincident with the entrance pupil; if it is behind the optical system, it is
coincident with the exit pupil.
The location of the aperture stop has a strong influence on such first-order
properties as pupil location, lens diameters, chromatic aberration, and
illumination at the image plane. Achieving the desired solution for all of these
properties is further complicated in a zoom lens system because the relationships
that relate to the aperture stop location have to hold for all magnifications all the
way from one end of the zoom range to the other. Placement of the aperture stop
has particular importance for infrared systems.
Figure 2.3 Aperture stop for a simple lens.1
(From Wyatt, Radiometric System Design,Macmillan, 1987, with permission of The McGraw-Hill Co.)
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Optics Fundamentals 15
Figure 2.4 Entrance and exit pupils and chief ray of an optical system.1
(From Wyatt,Radiometric System Design, Macmillan, 1987, with permission of The McGraw-Hill Co.)
2.3 Optical Formulas
The following are some basic formulas used in the design and analysis of optical
systems; the nomenclature definitions follow. These equations are utilized in
formulating the first-order parameters and in analyzing the theoretical and actual
performance of the optical system (refer to Figs. 2.3 and 2.4).
sin ,NA n u= (2.2)
( ) ( )/ 1/ 2 sin 1/ 2 ,F f D n u NA= = = (2.3)
Vo = 2NA / (mm), (2.4)
= 2.44 /D, (2.5)
= spot size /f, (2.6)
IFOV = d /f, (2.7)
tan = (d/2) /f, (2.8)
depth of focus (Rayleigh limit) = 4F2 , (2.9)
Strehl ratio ( )
22
2221 e
(2.10)
and = 2.44F, (2.11)
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16 Chapter 2
where
= wavelength
= rms wave errorF=f/#
f= effective focal length
D = entrance pupil diameter
u = half-angle of the limiting axial ray
= half-angle field of view in image space
d = pixel width
d= image diameter
IFOV = instantaneous field of view
n = index of refraction
NA = numerical aperture
= limiting angular resolution (diffraction)
= angular resolution (geometrical)Vo = diffraction limit (line pairs/mm)
= diffraction limited blur size (Airy disk).
2.4 Optical Performance Criteria
The following are various performance criteria utilized in evaluating the image
quality of an optical system:
Angular resolution: image spot size divided by the lens focal length.
Modulation transfer function (MTF): percent reduction in object contrast in the
image at a given spatial frequency.
Strehl definition: the ratio of the light intensity at the peak of the diffraction
pattern of an aberrated image to that at the peak of an aberration-freeimage.
Seidel aberrations: the five terms in the fourth degree in the expansion of the
wavefront aberration in the image plane.2 They can be expressed for each
surface and can be summed up for the entire optical system. Examples
can be found in Appendix B.
Zernike polynomials: mathematical decomposition of the aberrations present in
an optical system, which provides an evaluation of the effects of each
order of the aberration set on the image. This set of terms provides a
useful method for determining the most appropriate balance for the
various Seidel aberrations against higher-order residuals.3
Rayleigh limit: An optical system is considered essentially perfect if the
wavefront can be included between two concentric spherical surfaces /4apart. If the peak-to-valley optical path difference is /4, the system just
meets the Rayleigh criterion. For the 3- to 5-m and 8- to 12-m spectral
bands, the longitudinal depth of focus that meets the Rayleigh criterion is
shown in Table 2.1. This is a very useful value for infrared zoom lens
systems because it indicates the extent to which the image plane may
vary longitudinally from one end of the zoom range to the other.
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Optics Fundamentals 17
Table 2.1 Longitudinal depth of focus at 4 m and 10 m.
f/# 4 m (in mm) 10 m (in mm)1 0.016 0.04
2 0.064 0.16
3 0.144 0.36
4 0.256 0.64
5 0.400 1.00
2.5 Telescopes
The basic formulas for telescope magnification m and overall length L are
expressed as
tan.
tano o
e e
f Dm
f D
= = =
(2.12)
.o e
L f f= + (2.13)
There are two types of telescopes, astronomical and Galilean (refer to Fig. 2.5).4
For each case, the object and the image are at infinity. In the astronomical
telescope, both the objective and the eyepiece have positive focal lengths.
Therefore, the overall length is the sum of the two focal lengths. An intermediate
image is formed at the common focal point of the objective and eyepiece. In the
Galilean telescope, the objective is positive and the eyepiece is negative. The
image point of the object and the object point of the eyepiece are coincident.
Therefore, applying the above formula, the overall length between the objectiveand the eyepiece is the difference between the absolute focal lengths. For
example, iffo= 100 andfe = 10,L = 110; but, iffo= 100 andfe= 10, thenL = 90.
Figure 2.5 (a) Astronomical telescope and (b) Galilean telescopes.4
(Reproduced fromW. J. Smith, Modern Optical Engineering, 2
ndEd. with permission of The McGraw-Hill
Companies, Inc.)
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18 Chapter 2
Figure 2.6 Primary aberrations: spherical, coma, distortion, astigmatism, and chromatic.4
(a) A simple converging lens with undercorrected spherical aberration; (b) graphicalrepresentation of spherical aberration: longitudinal spherical aberration (LA) is plottedagainst ray height (Y), and transverse aberration, in which the ray intercept height (H) atthe paraxial reference plane is plotted against the final ray slope (TAN H); (c) coma,where the rays through the outer portions of the lens focus at a different height than therays through the center of the lens; (d) the coma patch, where the image of a point sourceis spread out into a comet-shaped flare; (e) distortion, where dotted lines denote theundistorted image; (f) astigmatism; (g) the primary astigmatism of a simple lens, where thetangential image is three times as far from the Petzval surface as the sagittal image; (h)undercorrected longitudinal chromatic aberration of a simple lens due to blue raysundergoing greater refraction than red rays; and (i) lateral color, which results in differentsized images for different wavelengths. (Adapted from W. Smith, Modern OpticalEngineering, 2
ndEd., with permission of The McGraw-Hill Co.)
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Optics Fundamentals 19
These are important considerations in the design of infrared zoom lenses. In
some applications, a zoom telescope serves as an afocal attachment in front of a
fixed imager; if it is of the Galilean type, it tends to have a shorter overall lengththan would otherwise be the case (for an example, refer to Fig. 6.16).
2.6 Primary Aberrations
2.6.1 Definition of the Seidel aberrations
The primary aberrations, also known as the Seidel or third-order aberrations, are
shown in Fig. 2.6.4 Strictly speaking, the Seidels do not include longitudinal and
lateral chromatic aberration. They may be defined as follows:
(1) Spherical aberration: the variation of focus with aperture.(2) Coma: the variation of magnification with aperture.(3)Astigmatism: tangential and sagittal images from a point source do not
coincide. The tangential image is three times as far from the Petzval
surface as the sagittal image.
(4)Field curvature: image is formed on the Petzval surface in the absence ofastigmatism, or the variation of magnification with field angle.
(5)Distortion: displacement of an off-axis image point from the paraxialimage position. An increase in the FOV produces pincushion distortion;
a decrease in FOV results in barrel distortion.(6)Longitudinal color: variation of focus with wavelength.(7)Lateral color: variation of image height with wavelength.
2.6.2 Variation of primary aberrations with aperture and field height
Table 2.2 shows how the primary aberrations vary as a function of aperture and
field height.4 For example, since longitudinal spherical aberration varies with y2,
a 1.5 increase in aperture will cause this aberration to be 2.25 as large.
Table 2.2 Variation of primary aberrations as a function of aperture and field height.
Aberration
Versus
semiaperture
Versus field
height
Spherical (longitudinal) y2 --
Spherical (transverse) y3 --
Coma y2 h
Astigmatism -- h2
Astigmatic line length y2 h
Field curvature -- h2
Distortion (linear) -- h3
Distortion (percentage) -- h2
Chromatic (longitudinal) -- --
Chromatic (lateral) -- h
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20 Chapter 2
2.6.3 Stop shift equations
Thin-lens approximations provide a useful tool for calculating the third-orderaberrations of an optical system.4 For a lens element not at the stop, theaberration contributions may be determined from the following formulas:
spherical SC* = SC, (2.14)
coma CC* = CC+ SC.Q uk, (2.15)
astigmatism * 22 ,
k
QAC AC CC SC Q
u= + +
(2.16)
Petzval sum PC* =PC, (2.17)
distortion * 3( 3 ) 3 2 .k kDC PC AC Q u CC Q SC Q u= + + + (2.18)
These stop shift equations may be applied to the surface contributions to
determine the third-order aberrations for a different stop position by setting
*
,p p
y yQ
y
= (2.19)
where
y is the axial paraxial marginal ray height at a surface,
yp is the principal paraxial ray height at a surface,
*
py is the principal paraxial ray height at a surface after the stop isshifted,
and
ku is the angular slope of the axial paraxial marginal ray in image space.
Since Q is an invariant, the values fory, yp, and*
py may be taken at any
convenient surface. When the equations are used in this way, the unstarred terms
refer to the aberrations with the stop in the original position, and the starred terms
refer to the aberrations with the stop in the new position. Another consequence of
the invariant nature of this definition ofQ is the fact that the stop shift may be
applied either to the individual surface contributions or to the sum of thecontributions of the entire system.
Some obvious conclusions can be drawn from an examination of the above
formulas. Third-order spherical aberration and the Petzval sum, also known as
the field curvature, are unaffected by a shift of the aperture stop to a newlocation. If third-order spherical aberration is zero, coma is unaffected by a shift
of the aperture stop. Additionally, if third-order spherical and coma are both zero,
which is the aplanatic condition, astigmatism is unaffected by a stop shift. It
should be kept in mind that the effect on higher-order aberrations due to a shift of
the aperture stop cannot be determined from these formulas.
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Optics Fundamentals 21
2.7 Achromatism
Since achromatism is a first-order property, achromatic balance can bedetermined through the application of thin-lens equations.
2.7.1 Primary achromatism
For a series of thin lenses in close contact, the longitudinal chromatic aberration
is given by
2 1 2
1 2
l fV V
= +
(2.20)
for a thin-lens doublet where
( )
( )
1,
M
S L
nV
n n
=
(2.21)
= 1 /f, (2.22)
and nM, nS, and nLare the mid-, short-, and long-wavelength indices of refraction.
For a thin-lens achromatic doublet, two wavelengths will come to focus when
a ba
a
V Vf f
V
=
and
.b abb
V Vf
V
=
(2.23)
To make a positive achromat, combine a positive low-dispersion element with a
negative high-dispersion element:
3 to 5 m: silicon is low dispersion (V= 250)
germanium is high dispersion (V= 107)
f= 100:fa= 57.2,fb= 133.6
8 to 12 m: germanium is low dispersion (V= 1073)
zinc selenide is high dispersion (V= 58)
f= 100:fa= 94.6,f
b= 1750.
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22 Chapter 2
2.7.2 Secondary spectrum
The secondary spectrum is the variation in focus of the third wavelength withrespect to the other two wavelengths:
( )
( )1 2
1 2
s
P Pl f
V V
=
, (2.24)
where
( )
( ).
s M
S L
n nP
n n
=
(2.25)
2.8 Principal Planes
In a thin-lens first-order solution the principal planes are located coincident with
the thin lens. In the basic lens imaging Eq. (2.1), land l are measured from the
principal planes. In a thick-lens starting point solution the optical train object-to-
image distance is set according to the location and separation of the principal
planes of each lens element. A complex lens system has only two principal
planes which move about as the lens system is zoomed.
In Fig. 2.7(a), diverging rays from the primary focal point Femerge parallel
to the axis. In 2.7(b), parallel incident rays are brought to a focus at the secondary
focal pointF". In each case the incident and refracted rays have been extended to
their point of intersection between the surfaces. Transverse planes through these
intersections constitute primary and secondary principal planes. The ray heighton the first principal plane is the same on the second principal plane, i.e., unit
lateral magnification.
Figure 2.7 Ray diagrams showing the primary and secondary principal planes of a thicklens.
5(Reproduced from Jenkins and White, Fundamentals of Optics, copyright of The
McGraw-Hill Co., Inc.)
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Optics Fundamentals 23
Figure 2.8 Illustrating the significance of the nodal points and nodal planes of a thicklens.
5(Reproduced from Jenkins and White, Fundamentals of Optics, copyright of The
McGraw-Hill Co., Inc.)
Of all the rays that pass through a lens from an off-axis object point to its
corresponding image point, there will always be one ray for which the direction
of the ray in the image space is the same as in the object space, i.e., the segments
of the ray before reaching the lens and after leaving it are parallel. The two points
at which these segments, if projected, intersect the axis are called the nodal
points. This third pair of points and their associated planes are shown in Fig. 2.8,
which also shows the optical center of the lens at C. Since the incident and
emergent rays make equal angles with the axis, the nodal points are called
conjugate points of unit angular magnification. This concept is discussed further
in Ref. 6.
In general, the focal points and principal points are not symmetrically located
with respect to the lens but are at different distances from the vertices. The
positions of the principal planes for a given lens focal length can be changed by
bending the lens shape, as shown in Fig. 2.9. Moving the principal planes to the
right decreases the overall object-to-image distance. This can be a useful
technique in designing compact zoom lens systems. Moving the principal planes
to the left increases the overall object-to-image distance.
Figure 2.9 Illustrating the variation of the positions of the primary and secondary principalplanes as a thick lens of fixed focal length is subject to bending.
5(Reproduced from
Jenkins and White, Fundamentals of Optics, copyright of The McGraw-Hill Co., Inc.)
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24 Chapter 2
2.9 Problems
1. An f/2.5 zoom lens system is to be used in the 8- to 12-m wavelengthregion. What is the Rayleigh limit at the central wavelength?
2. A Galilean telescope has a positive thin lens with 120-mm focal length and anegative thin lens with 12-mm focal length.
(a) What is the magnification?(b) What is the overall length?(c) If the exit pupil diameter is 10 mm, what is the entrance pupil diameter?
3. A 150-mm focal length doublet consists of two singlets with Vvalues of 200and 100, respectively.
(a) Which singlet has the higher dispersion, the one with the higher or lower
Vvalue?(b) What is the focal length of each singlet in an achromatic doublet?
4. An f/2 singlet has a clear aperture of 50 mm with a refractive index of 3.5and dn/dt = 0.000150 per degree C. The operating temperature range is
40 C. The wavelength region is from 8 to 12 m.
(a) What is the change in focal length with temperature?(b) Is this change within the depth of focus for this wavelength region?
5. A 1 to 5 zoom lens is to be used as part of a forward-looking infrared(FLIR) scanning system. It will operate at f/2 in the 8- to 12-m wavelength
region. It has a 12-mm exit pupil and an eyepiece focal length of 20 mm.
(a) What is the entrance pupil diameter at each end of the zoom range?(b) What is the objective lens focal length at each end of the zoom range?
2.10 References
1. Wyatt, C.L.,Radiometric System Design, Macmillan Co., New York (1987).
2. Welford, W.T., Aberrations of the Symmetrical Optical System, AcademicPress (1974).
3. Kim, C.J. and Shannon, R.R., Catalog of Zernike Polynomials, in AppliedOptics and Optical Engineering, Vol. X, R.R. Shannon and J. Wyant, Eds., pp.
193221, Academic Press, New York (1987).
4. Smith, W.J., Modern Optical Engineering, Second Ed., McGraw-Hill, New
York (1990).5. Jenkins, F.A. and White, H.E, Fundamentals of Optics, McGraw-Hill, New
York (1957).
6. Johnson, R.B., Correctly making panoramic imagery and the meaning ofoptical center,Proc. SPIE, 7060, 70600F (2008).
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25
Chapter 3
Unique Features of the InfraredRegion
3.1 Optical Materials
3.1.1 Materials for the infrared
A large number of optical materials transmit in the infrared region of the
spectrum. However, the list of materials is quite limited when one considers
physical characteristics, workability, and cost. Table 3.11 indicates the materialsmost commonly used in infrared zoom-lens systems for the 3- to 5-m and 8- to
12-m regions. It is apparent that indices of refraction are higher than they are
for optical materials in the visible spectrum. This is an advantage in the
correction of third-order and higher-order aberrations. For example, with a lens
shaped for minimum spherical aberration, the angular spherical aberration SPHfor an object at infinity can be expressed by
( )( ) ( )( )
2 3
4 1,
128 1 2SPH
n n
n n F
=
+ (3.1)
where
n = index of refraction and
focal length, or .
diameter
fF
d
=
The variation with a refractive index can readily be seen by tabulating for anf/1
lens as an example in Table 3.1. The advantage of using a high-index material
like silicon or germanium is quite apparent from these calculations.
Table 3.1 Variation of spherical aberration with a refractive index.
f/# n
1.0 4.0 0.008681
1.0 3.0 0.012891
1.0 2.0 0.027344
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26 Chapter 3
Figure 3.1 V value versus index of refraction for several of the more commonly usedinfrared materials.
2
Also, infrared materials tend to have low dispersion, which corresponds to ahigh Vnumber. Figure 3.1 presents the Vvalue versus the index of refraction for
several of the more commonly used infrared materials.2 The hatched area
indicates the more limited range ofVvalues and refractive indices as compared
with visible materials. However, one should keep in mind that the Schott catalog
alone contains some 200 optical glasses within the hatched area;3 in fact, the
number of available glasses in the visual region is more than one order of
magnitude greater than in the infrared.
Germanium is less expensive than zinc selenide or zinc sulfide. Since silicon
has become an order of magnitude less expensive than germanium, its use in
infrared zoom lens systems has greatly increased in recent years. This
development, in turn, has helped caused a shift from the 8- to 12-m to the 3- to
5-m region. Another factor is the availability of detectors such as InSb whichwork well in the 3- to 5-m waveband.
In Table 3.2, Vis defined as:
4 m 10 m
3 5 m 8 12 m
3 m 5 m 8 m 12 m
.n n
V Vn n n n
1 1= , =
(3.2)
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Unique Features of the Infrared Region 27
Table 3.2 Refractive index data for infrared materials.
Material Zinc sulfide Zinc selenide Silicon Germanium Calcium fluoride3 m 2.2570 2.4376 3.4320 4.0452 1.4179
4 m 2.2520 2.4331 3.4255 4.0243 1.4097
5 m 2.2460 2.4295 3.4223 4.0161 1.3990
V 114 177 250 107 22
8 m 2.2229 2.4173 3.4184 4.0051 --
10 m 2.2005 2.4065 3.4179 4.0032 --
12 m 2.1704 2.3930 3.4157 4.0023 --
V 23 58 896 1073 --
dn/dt 0.000043 0.000060 0.00015 0.000396 0.000011density 4.09 5.27 2.33 5.33 3.18
Since many infrared components require aspheric or diffractive surfaces,
diamond turning is often the method of choice for the fabrication of these
surfaces that are so difficult to fabricate by traditional methods. Among other
methods, reactive ion etching has been successfully utilized to transfer a binary
optic diffractive pattern into the substrate.4
3.1.2 Calculation of index of refraction
The calculation of refractive index data may be accomplished through the use of
general polynomials to provide interpolation at infrared wavelengths of interest
for purposes of optical design and analysis. Several forms of general polynomials
are available for use with infrared materials.
For their optical glasses Schott uses:
n2 =A0 +A12 +A2
2 +A34 +A4
6 +A58, (3.3)
which provides a worst-case fit of the refractive index to within 0.000005. For
infrared materials, Barr & Stroud5 used a modified version of the Schott formula.
The data for infrared materials require additional positive terms. The full
expansion is:
n2 = C88 + C
66 + C
44 + C
22 + C
0+ C
22 + C
44 + C
66. (3.4)
A least-squares technique is applied to form a set of linear equations to solve
to obtain the required coefficients. The least-squares fit process allows an
estimation of error by computing the fit error. This process is dependent on using
more data points than polynomial coefficients. The rms refractive index error
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28 Chapter 3
ranges from 0.00008 for germanium in the 8- to 13-m range to 0.00002 for zinc
sulfide.
Another commonly used formula in the infrared is the Sellmeier equation,
( )
22
2 21
1m
k
k k
An
B=
=
. (3.5)
For example, the Optical Research Associates CODE V optics program uses
this equation in its special materials catalog for infrared materials. The number of
terms varies from two to five, depending on the material. Most materials use
three terms.6 The acceptable level of fit accuracy for inclusion in the CODE V
special catalog is based on the optical path difference (OPD) errors that can be
expected due to departures from measured data. The criterion chosen is that the
induced chromatic effect, OPD, be less than /10 for af/1.5 singlet of 200-mmdiameter in any one of three spectral bands: 8 to 12, 3 to 5, and 0.4 to 0.7 m.
The result of imposing these criteria is that in certain cases, the same material is
fitted for two spectral ranges and both fits are included in the special catalog
using different names.7 Some infrared zoom lens applications may require tighter
criteria. For example, the Pilkington "Dezir" compact infrared zoom telescope
has an entrance lens that has a diameter somewhat in excess of 200 mm and
operates at approximatelyf/1.0.8
3.2 Thermal Compensation
3.2.1 Focus shift with temperature
Focus shift with temperature is a significant problem in the infrared region. Thechange in refractive index with temperature, dn/dt, is presented in Table 3.1 for
the listed materials. Germanium, in particular, has a very high dn/dt. For a thin
lens the change in focal length with temperature can be expressed as1
( ).
1
f dndf dt
n dt
=
(3.6)
For a system with a 100-mm focal length and a 40o C temperature range, the focal
shift is 0.527 mm for germanium. This would exceed the Rayleigh limit for
acceptable performance of 0.400 mm for anf/5 system in the 3- to 5-m spectral
region and of 0.490 forf/3.5 systems in the 8- to 12-m region.
3.2.2 Athermalization
Athermalization is the correction of this effect of focus shift with temperature.
There are several mechanical and optical methods, active and passive, available
to accomplish athermalization. It is possible to solve for achromatism and
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