Allen Mann-Infrared Optics and Zoom Lenses, Second Edition (SPIE Tutorial Text Vol. TT83) (Tutorial Texts in Optical Engineering)-SPIE Publications(2009)

7/27/2019 Allen Mann-Infrared Optics and Zoom Lenses, Second Edition (SPIE Tutorial Text Vol. TT83) (Tutorial Texts in Optical

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Tutorial Texts Series

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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,

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Fourier-Transform Spectroscopy Instrumentation Engineering, Vidi Saptari, Vol. TT61 The Power- and Energy-Handling Capability of Optical Materials, Components, and Systems,Roger M.

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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


3/173Bellingham, Washington USA

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

Fax: +1 360 647 1445Email: [email protected]

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

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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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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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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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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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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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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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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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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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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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Documents

Allen Mann-Infrared Optics and Zoom Lenses, Second Edition (SPIE Tutorial Text Vol. TT83) (Tutorial Texts in Optical Engineering)-SPIE Publications(2009)