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Spie Press Book

Modulation Transfer Function in Optical and Electro-Optical Systems, Second Edition
Author(s): Glenn D. Boreman
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Book Description

This second edition introduces the theory and applications of the modulation transfer function (MTF), used to specify the image quality achieved by an imaging system. It starts with the relationship between impulse response and transfer function, and the implications of a convolutional representation of the imaging process. Optical systems are considered first, including effects of diffraction and aberrations on the image, with attention to aperture and field dependences. Then electro-optical systems with focal-plane arrays are considered, with an expanded discussion of image-quality aspects unique to these systems, including finite sensor size, shift invariance, sampling MTF, aliasing artifacts, crosstalk and electronics noise. Various test configurations are then compared in detail, considering the advantages and disadvantages of point-response, line-response and edge-response measurements. The impact of finite source size on the measurement data, and its correction, are discussed. An expanded discussion of the practical aspects of the tilted-knife-edge test is presented. New chapters are included on speckle-based and transparency-based noise targets, and square-wave and bar-target measurements. A range of practical measurement issues are then considered, including mitigation of source coherence, combining MTF measurements of separate subsystems, quality requirements of auxiliary optics, and low-frequency normalization. Some generic measurement-instrument designs are compared, and the book closes with a brief consideration of MTF impacts of motion, vibration, turbulence, and aerosol scattering.

Book Details

Date Published: 25 January 2021
Pages: 156
ISBN: 9781510639379
Volume: TT121

Table of Contents
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Table of Contents

Preface to the Second Edition
Preface to the First Edition

1 MTF in Optical Systems
1.1 Impulse Response
1.2 Spatial Frequency
1.3 Transfer Function
      1.3.1 Modulation transfer function
      1.3.2 Phase transfer function
1.4 MTF and Resolution
1.5 Diffraction MTF
      1.5.1 Calculation of diffraction MTF
      1.5.2 Diffraction MTFs for obscured systems
1.6 Effect of Aberrations on MTF
      1.6.1 MTF and Strehl ratio
      1.6.2 Effect of defocus on MTF
      1.6.3 Effects of other aberrations on MTF
      1.6.4 Minimum modulation curve
      1.6.5 Visualizing other MTF dependences
1.7 Conclusion
References and Further Reading

2 MTF in Electro-optical Systems
2.1 Detector Footprint MFT
2.2 Sampling
      2.2.1 Aliasing
      2.2.2 Sampling MTF
2.3 Crosstalk
2.4 Electronic Network MTF
2.5 Conclusion

3 Point-, Line-, and Edge-Spread Function Measurement of MTF
3.1 Point-Spread Function (PSF)
3.2 Line-Spread Function (LSF)
3.3 Edge-Spread Function (ESF)
3.4 Comparison of PSF, LSF, and ESF
3.5 Increasing SNR in PSF, LSF, and ESF Tests
      3.5.1 Object- and image-plane equivalence
      3.5.2 Averaging in pixelated detector arrays
3.6 Correcting for Finite Source Size
3.7 Correcting for Image-Receiver MTF
      3.7.1 Finite pixel width
      3.7.2 Finite sampling interval
3.8 Oversampled Knife-Edge Test
3.9 Conclusion

4 Square-Wave and Bar-Target Measurement of MTF
4.1 Square-Wave Targets
4.2 Bar Targets
4.3 Conclusion

5 Noise-Target Measurement of MTF
5.1 Laser-Speckle MTF Test
5.2 Random-Transparency MTF Test
5.3 Conclusion

6 Practical Measurement Issues
6.1 Measurement of PSF
6.2 Cascade Properties of MTF
6.3 Quality of Auxiliary Optics
6.4 Source Coherence
6.5 Low-Frequency Normalization
6.6 MTF Testing Observations
6.7 Use of Computers in MTF Measurements
6.8 Representative Instrument Designs
      6.8.1 Example system #1: visible edge response
      6.8.2 Example system #2: infrared line response
      6.8.3 Example system #3: visible square-wave response
      6.8.4 Example system #4: bar-target response
6.9 Conclusion
References and Further Reading

7 Other MTF Contributions
7.1 Motion MTF
7.2 Vibration MTF
7.3 Turbulence MTF
7.4 Aerosol-Scattering MTF
7.5 Conclusion
References and Further Reading


Preface to Second Edition

It had been 19 years since the first edition of this book, when the extended quarantine period of 2020 afforded me the rare opportunity of quiet time away from my usual administrative and research activities. I have significantly expanded the treatment of several topics, including bar-target measurements, noise-target measurements, effects of aberrations, and slant-edge measurements. I have been gratified by the recent industrial and government-lab interest in the speckle techniques, which, after all, comprised a good portion of my dissertation at University of Arizona some 36 years ago. All other topics in the book were reviewed and updated, with recent references added. I have kept my original emphasis on practical issues and measurement techniques.

I acknowledge with pleasure discussions about MTF with colleagues and their students here at UNC Charlotte, among whom are Profs. Angela Allen, Chris Evans, and Thomas Suleski. During the writing process, I appreciated receiving daily encouragement by telephone from Dot Graudons, daily encouragement via WhatsApp from Prof. Mike Sundheimer of the Universidade Federal Rural de Pernambuco in Recife Brazil, and weekly encouragement via Zoom from Skye Engel. I am grateful for the permissions granted for reproductions of some of the figures from their original sources, to the two anonymous reviewers for their insightful and helpful comments, and to Dara Burrows of SPIE Press for her expert copyediting.

Last but surely not least, I want to thank Maggie Boreman—my wife of 30 years, my main encourager, and technical editor. You have graciously taken time from your equestrian pleasures to struggle, once again, with turning my writing into something approaching standard English. Thanks.

Glenn D. Boreman
Emerald Rose Farm
1 November 2020

Preface to First Edition

I first became aware that there was such a thing as MTF as an undergraduate at Rochester, scurrying around the Bausch and Lomb building. There was, in one of the stairwells, a large poster of the Air Force bar target set. I saw that poster every day, and I remember thinking…gee, that’s pretty neat. Well, more than 25 years later, I still think so. I have had great fun making MTF measurements on focal-plane arrays, SPRITE detectors, scanning cameras, IR scene projectors, telescopes, collimators, and infrared antennas. This book is an outgrowth of a short course that I have presented for SPIE since 1987. In it, I emphasize some practical things I have learned about making MTF measurements.

I am grateful for initial discussions on this subject at Arizona with Jack Gaskill and Stace Dereniak. Since then, I have had the good fortune here at Central Florida to work with a number of colleagues and graduate students on MTF issues. I fondly recall discussions of MTF with Arnold Daniels, Jim Harvey, Didi Dogariu, Karen MacDougall, Marty Sensiper, Ken Barnard, Al Ducharme, Ofer Hadar, Ric Schildwachter, Barry Anderson, Al Plogstedt, Christophe Fumeaux, Per Fredin, and Frank Effenberger. I want to thank Dan Jones of the UCF English Department for his support, as well as Rick Hermann, Eric Pepper, and Marshall Weathersby of SPIE for their assistance and enthusiasm for this project. I also appreciate the permissions granted for reproductions of some of the figures from their original sources.

Last but surely not least, I want to thank Maggie Boreman—my wife, main encourager, and technical editor. Once again, Meg, you have wrestled with my occasionally tedious expository and transformed it, if not into poetry, then at least into prose. Thanks.

Cocoa Beach
15 March 2001

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