QC 351 A7 no. 41 / A function PvN(ß) exists whose finite Fourier transform over a specified
range of its argument is asymptotic (with N) to an Airy distribution with arbitrary scale compression. Consequently, when the function is applied as a
passive coating to a diffraction -limited lens of fixed aperture,the point amplitude response collapses inward as if the lens were physically replaced by
a diffraction-limited lens of greater aperture.
Investigating the implications of coating PN(ß) to image theory, we find
the following: (1) The scalar wave equation has intrinsically a particlelike
solution. (2) A modification of PN(ß) causes an arbitrarily narrow depth of
focus. (3) An arbitrary point amplitude response may be optically produced.
(Suppose g(x) to be a required, and arbitrary, point response function with
G(ß) its finite Fourier transform. Then pupil PN(ß)G(ß) produces g(x), asymptotic with N.) (4) When applied onto any band -limited pupil G(ß), coating
PN(ß) effectively extrapolates G(ß) arbitrarily beyond the bounds of the aperture.
Some amusing analog devices, based on the extrapolating property (No. 4
above), are next developed. These are an optical analog signal extrapolator,
a picture extrapolator, and an analog method of band -unlimited image processing. We also suggest the existence of a laser "superposition mode" whose out-
put would be arbitrarily directive, and the possibility of using an acoustical pupil NO) to resolve these long wavelengths with near-optical quality.
The ultimate limitations on the practical use and fabrication of pupil PN(ß)
are discussed.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/621635 |
| Date | 01 July 1969 |
| Creators | Frieden, B. Roy |
| Publisher | Optical Sciences Center, University of Arizona (Tucson, Arizona) |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | Technical Report |
| Rights | Copyright © Arizona Board of Regents |
| Relation | Optical Sciences Technical Report 41 |
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