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The Fourier-transform relation between the spatial electric field-vector distribu-tion in a quasi-spherical unfocused wavefront, and the focused field near its center, was recognized at least as early as the begin-ning 1900's by A.A.Michelson (see e.g. refer-ences in G.W.Stroke,"Diffraction Gratings" pp. 426-754 in Vol. 29, Handbuch der Physik, Springer Verlag, Heidelberg 1967), and con-temporary operational image-formation rela-tions were used by him in his famous text "Studies in Optics" before 1927! Recently revived, thanks in particular to the work of Duffieux (1946), D.Gabor (1949), Peter Elias, D.Grey and D.Z.Robinson(1952),AiMarechal, E. L.O'Neill and others, Fourier-transform des-criptions of optical image formation and processing have become particularly powerful with their introduction into holography [Gabor(1949),Cutrona, Leith, Palermo and Porcello,(1960), B.J.Thompson and others(1964), etc.] especially since the introduction of the "lensless Fourier-transform hologram" by Stroke(1964,1965), who showed that such a hologram, formed by interference of the field scattered by the "object" and a reference field originating from a reference "point" situated near the object, had an intrinsic resolution gain which may exceed by more than three orders of magnitude the film-limited resolution capability of single-side band, "off-axis" Fresnel holograms. Among the several extensions and applications of the "lensless Fourier-transform hologram "arran-gement" is that recently exploited by J.Goodman for remote object holography,where the traversal by the point-source reference beam of an air path similar to that of the object beam permits to surmount atmospheric turbulence and path-difference variation effects. In addition to these and other 3-D imaging applications, the author (in part with D. Gabor) has proposed and demonstrated several operational image-processing and computing applications, among which the multiply-expos-ed holograms used for image-synthesis. interferometry and computer-generated holograms, and, most recently, and new type of "holographic Fourier-tranform division" [Stroke and Zech, Physics Lett. 25A, 89(1967)] which has now permitted to restore into sharp focus images from ordinary blurred photographs of three-dimensional objects, photographed in ordinary white light [Stroke et. ali., Physics Lett. 25A, 443(25 March 1968).
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