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dc.contributor.authorFrieden, B. Roy
dc.date.accessioned2016-12-14T18:09:30Z
dc.date.available2016-12-14T18:09:30Z
dc.date.issued1969-07-01
dc.identifier.urihttp://hdl.handle.net/10150/621635
dc.descriptionQC 351 A7 no. 41en
dc.description.abstractA 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.
dc.language.isoen_USen
dc.publisherOptical Sciences Center, University of Arizona (Tucson, Arizona)en
dc.relation.ispartofseriesOptical Sciences Technical Report 41en
dc.rightsCopyright © Arizona Board of Regents
dc.subjectOptics.en
dc.titleTHE EXTRAPOLATING PUPIL, IMAGE SYNTHESIS, AND APPLICATIONS FOR THE FUTUREen_US
dc.typeTechnical Reporten
dc.description.collectioninformationThis title from the Optical Sciences Technical Reports collection is made available by the College of Optical Sciences and the University Libraries, The University of Arizona. If you have questions about titles in this collection, please contact repository@u.library.arizona.edu.
refterms.dateFOA2018-06-17T05:22:18Z
html.description.abstractA 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.


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