Thermal Imaging Systems pp 68-116 | Cite as

# Linear Filter Theory

## Abstract

There is frequent need in thermal imaging practice to describe the responses of a system to various signals, to predict spatial resolution, and to devise image enhancement schemes. A tool which is useful for this purpose is linear filter theory^{1,2}, a branch of Fourier transform analysis used for analyzing the signal response of the class of linear, invariant, stable systems. Linear filter theory is applicable to optical, electro-optical, mechanical, and electronic devices. It originated in the description of electrical networks and servomechanisms and was extended to optical systems. Linear filter theory forms an indispensible part of image analysis and is necessary to every thermal imaging system design evaluation.

### Keywords

Attenuation Recombination Coherence Assure Autocorrelation## Preview

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### References

- 1.J.W. Goodman,
*Introduction to Fourier Optics*, McGraw-Hill, 1968.Google Scholar - 2.E.L. O’Neill,
*Introduction to Statistical Optics*, Addison-Wesley, 1963.Google Scholar - 3.R.N. Bracewell,
*The Fourier Transform and its Applications*, McGraw-Hill, 1965.Google Scholar - 4.P.M. Duffieux,
*L’Integrale de Fourier et Ses Applications a L’Optique*, Societe Anonyme des Imprimeries Oberthur, 1946.Google Scholar - 5.O.H. Schade, “Electro-Optical Characteristics of Television Systems”, RCA Review, 9, in four parts: pp 5–37, March 1948; pp 245-286, June 1948; pp 490-530, September 1948; pp 653-686, December 1948.Google Scholar
- 6.E.W.H. Selwyn, “The Photographic and Visual Resolving Power of Lenses”, Photographic Journal, Section B,
*88*, in two parts: pp 6-12, and pp 46–57.Google Scholar - 7.M. Françon,
*Modern Applications of Physical Optics*, Wiley, 1963.Google Scholar - 8.E.H. Linfoot,
*Fourier Methods in Optical Image Evaluation*, Focal Press, 1964.Google Scholar - 9.H.H. Hopkins, “On the Diffraction Theory of Optical Images”, Proc. Roy. Soc.,
*217A*, pp 408–432, 1953; “The Frequency Response of a Defocussed Optical System”, Proc. Roy. Soc,*231*, pp 91-103, July 1955.MathSciNetADSGoogle Scholar - 10.H.H. Hopkins, “The Frequency Response of Optical Systems”, Proc. Phys. Soc, Section B,
*69*, pp 562–576, May 1956; “Application of Frequency Response Techniques in Optics”,*79*, pp 889-919, May 1962.MathSciNetADSMATHCrossRefGoogle Scholar - 11.M. De, “The Influence of Astigmatism on the Response Function of an Optical System”, Proc. Roy. Soc,
*233A*, pp 91–104, 1955.ADSGoogle Scholar - 12.E.L. O’Neill, “Transfer Function for an Annular Aperture”, JOSA,
*46*, pp 285–288, April 1956.ADSCrossRefGoogle Scholar - 13.G. Black and E.H. Linfoot, “Spherical Aberration and the Information Content of Optical Images”, Proc Roy. Soc,
*239A*, pp 522–540, 1957.ADSGoogle Scholar - 14.A.M. Goodbody, “The Influence of Spherical Aberration on the Response Function of an Optical System”, Proc Phys. Soc.,
*72*, pp 411–422, September 1958.ADSCrossRefGoogle Scholar - 15.R. Barakat and M.V. Morello, “Computation of the Transfer Function of an Optical System from the Design Data for Rotationally Symmetric Aberrations”, JOSA
*52*, in two parts, pp 985-991 and pp 992–997, September 1962.ADSCrossRefGoogle Scholar - 16.B.P. Hildebrand, “Bounds on the Modulation Transfer Function of Optical Systems in Incoherent Illumination”, JOSA,
*56*, pp 12–13, January 1966.ADSCrossRefGoogle Scholar - 17.J.B. De Velis and G. B. Parrent, Jr., “Transfer Function for Cascaded Optical Systems”, JOSA,
*57*, pp 1486–1490, December 1967.ADSCrossRefGoogle Scholar - 18.J.W. Coltman, “The Specification of Imaging Properties in Response to a Sine Wave Input”, JOSA,
*44*, pp 468–471, June 1954.ADSCrossRefGoogle Scholar - 19.P. Elias, D.S. Grey, and D.Z. Robinson, “Fourier Treatment of Optical Processes”, JOSA,
*42*, pp 127–134, February 1952.ADSCrossRefGoogle Scholar - 20.R.V. Shack, “Characteristics of an Image-Forming System”, Journal of Research of the National Bureau of Standards,
*56*, pp 245–260, May 1956.MathSciNetMATHCrossRefGoogle Scholar - 21.R.L. Lamberts, “Relationship between the Sine-Wave Response and the Distribution of Energy in the Optical Image of a Line”, JOSA,
*48*, pp 490–495, July 1958.ADSCrossRefGoogle Scholar - 22.R.L. Lamberts, “Application of Sine-Wave Techniques to Image-Forming Systems” JSMPTE,
*71*, pp 635–640, September, 1962.CrossRefGoogle Scholar - 23.R.L. Lamberts, G.C. Higgens, and R.N. Wolfe, “Measurement and Analysis of the Distribution of Energy in Optical Images”, JOSA,
*48*, pp 487–490, July 1958.ADSCrossRefGoogle Scholar - 24.F.H. Perrin, “Methods of Appraising Photographic Systems” JSMPTE,
*69*, in two parts: pp 151–156, March 1960, and pp 239-249, April 1960.CrossRefGoogle Scholar - 25.F.D. Smith, “Optical Image Evaluation and the Transfer Function”, Appl. Opt., 2, pp 335–350, April 1963.ADSCrossRefGoogle Scholar
- 26.O.H. Schade, “Modern Image Evaluation and Television (the Influence of Electronic Television on the Methods of Image Evaluation)”, Appl. Opt.,
*3*. pp 17–21, January 1964.ADSCrossRefGoogle Scholar - 27.G.C. Higgins, “Methods for Engineering Photographic Systems”, Appl. Opt.
*3*, pp 1–10, January 1964.ADSCrossRefGoogle Scholar - 28.D.H. Kelly, “Spatial Frequency, Bandwidth, and Resolution”, Appl. Opt.,
*4*, pp 435–437, April 1965.ADSCrossRefGoogle Scholar - 29.R.M. Scott, et al., a series of papers entitled “The Practical Applications of Modulation Transfer Functions”, Phot. Sci. and Eng.,
*9*, pp 235–263, 1965.Google Scholar - 30.J.R. Jenness, Jr., and J.A. Ake, “The Averaging-Aperture Model of an Electro-Optical Scanning System”, JSMPTE, pp 717-720, July 1968.Google Scholar
- 31.L.M. Biberman and S. Nudelman, editors,
*Photoelectronic Imaging Devices*, 2 Volumes, Plenum, 1971.Google Scholar - 32.H.E. Brown, F.A. Collins, and J.A. Hawkins, “Analysis of Optical and Electro-Optical Imaging Systems Using Modulation Transfer Functions”, Memorandum DRL-TR-68-13, Defense Research Laboratory, the University of Texas at Austin, March 1968.Google Scholar
- 33.N. Jensen,
*Optical and Photographic Reconnaissance Systems*, Wiley, 1968.Google Scholar - 34.O.H. Schade, “A Method of Measuring the Optical Sine-Wave Spatial Spectrum of Television Image Display Devices”, JSMPTE,
*67*, pp 561–566, 1958.CrossRefGoogle Scholar - 35.J.R. Jenness, Jr., W.A. Eliot, and J.A. Ake, “Intensity Ripple in a Raster Generated by a Gaussian Scanning Spot”, JSMPTE, 76, pp 549–550, June 1967.CrossRefGoogle Scholar
- 36.L.E. White, “Comparison of Various Types of Resolution Measurement”, Westinghouse Product Engineering Memo ETD-6402, Westinghouse Electric Corporation, Electronic Tube Division, Elmira, New York, September 1964.Google Scholar
- 37.M. Beran and G.B. Parrent, Jr.,
*The Theory of Partial Coherence*, Prentice Hall, 1964.Google Scholar - 38.V.K. Viswana than, personal communication, Honey well Radiation Center, Lexington, Massachusetts.Google Scholar
- 39.M.V. Klein,
*Optics*, Wiley, 1970.Google Scholar - 40.W.J.
*Smith, Modern Optical Engineering*, McGraw-Hill, 1966.Google Scholar - 41.R. Barakat, Chapter 15 of
*Handbook of Military Infrared Technology*, W.L. Wolfe, editor, USGPO, 1965.Google Scholar - 42.R.L. Sendall, personal communications, Xerox Electro-Optical Systems, Pasadena, Cal.Google Scholar
- 43.A. Papoulis,
*Systems and Transforms with Applications in Optics*, McGraw-Hill, 1968.Google Scholar