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VISION-LIST Digest 1989 08 03
Vision-List Digest Thu Aug 03 10:59:09 PDT 89
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Today's Topics:
Re: defocussing & Fourier domain
Defocusing
Subbarao's address
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Date: Tue, 1 Aug 89 09:44:38 BST
From: alien%VULCAN.ESE.ESSEX.AC.UK@CUNYVM.CUNY.EDU (Adrian F. Clark)
Subject: Re: defocussing & Fourier domain
Christian Ronse asks about the effect of defocus blur on images. This
topic was looked at in detail in the paper
"Blind Deconvolution with Spatially Invariant Image Blurs with Phase"
by T. Michael Cannon, IEEE Trans ASSP vol ASSP-24 no. 1 pp58-63 (1976).
In a nutshell, what you do is form the cepstrum (effectively the
logarithm of the power spectrum) and look for the zero crossings: the
defocus blur adds a Bessel function (actually J1(r)/r for a circular
aperture imaging system) pattern. The same paper also treats linear
motion blur.
There are related papers of the same vintage by Cannon and colleagues
(including ones in Proc IEEE and Applied Optics, if I remember
correctly) which are also worth checking out.
Adrian F. Clark
JANET: alien@uk.ac.essex.ese
ARPA: alien%uk.ac.essex.ese@nsfnet-relay.ac.uk
BITNET: alien%uk.ac.essex.ese@ac.uk
Smail: Dept. of Electronic Systems Engineering, University of Essex,
Wivenhoe Park, Colchester, Essex C04 3SQ, U. K.
Phone: (+44) 206-872432 (direct)
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Date: Tue, 1 Aug 89 11:22:32 PDT
From: GENNERY@jplrob.JPL.NASA.GOV
Subject: Defocusing
This is in reply to the question from Ronse. The point spread function
caused by an out of focus lens is an image of the aperture. For a clear,
circular aperture, this is a uniform circular disk, neglecting lens
distortion, and the Fourier transform of this is a J1(x)/x function,
where J1 is the Bessel function of the first kind. (See, for example,
D. B. Gennery, "Determination of Optical Transfer Function by Inspection
of Frequency-Domain Plot," Journal of the Optical Society of America 63,
pp. 1571-1577 (Dec. 1973).) The actual apertures of cameras usually are
more polygonal than circular (because of the adjustable iris). However,
a high-degree polygon can be approximated by a circle fairly well, so
the J1(x)/x function may be reasonably accurate in many cases. But the
Gaussian function is not a good approximation to this, as can be seen by
the fact that its phase is always 0 and its amplitude decays rapidly,
whereas J1(x)/x oscillates in sign (thus its phase jumps betw
0 and 180 degrees), with the amplitude decaying slowly. Of course, if
the blurring from focus is less than the blurring from other causes,
then what happens at the higher spatial frequencies doesn't matter much,
so almost any function will do. But with a large amount of defocus,
the precise nature of the function is important.
Don Gennery
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Date: Tue, 1 Aug 89 15:20:54 EDT
From: sher@cs.Buffalo.EDU (David Sher)
Subject: Subbarao's address
I just thought that I'd correct a small error in the last posting:
last I heard Subbarao was at SUNY Stonybrook.
-David Sher
[ I apologize for this inadvertant error.
phil... ]
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Date: Wed, 02 Aug 89 15:29:36 PDT
From: Shelly Glaser <GLASER%USCVM.BITNET@CUNYVM.CUNY.EDU>
Subject: Re: Vision-List delayed redistribution
Have you tried any textbook on modern optics? Try, for example, J. W.
Goodman's "Introduction to Fourier Optics" (McGraw, 1968).
If the geometrical-optics approximation would do, the FT of out-of-focus
point is the FT of a circle function; it becomes more complicated as you
add diffraction.
Shelly Glaser
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