By Henry Stark
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9-1). Thus S > , v)=\ S(& η)Ηπ(η -ξ,ν-η)άξ άη. 9-2) J — oo J — οο The weight given to S(£, η) at ξ = u is zero, which is quite the opposite of what a typical aperture—which would normally give a maximum weight at ξ = u—would do. The significant averaging over frequency extends over the two lobes on either side of ξ = u, which furnish a null-to-null width in frequency of 4L" *. For an ordinary rectangular aperture of the same width, the significant FIG. 9-3. (a) Diffraction pattern of a square aperture, (b) Same as part (a) but with the π-phase step in place.
Riverside Res. , New York.  M. G. Jenkins and D. G. Watts (1968). " HoldenDay, San Francisco, California.  N. I. Achieser (1956). " Ungar, New York.  A. Papoulis (1973). IEEE Trans. Inf. Theory IT-19, 9-12.  H. Stark and B. Dimitriadis (1975). J. Opt. Soc. Am. 65, 425-431.  A. Papoulis (1972). J. Opt. Soc. Am. 62, 1423-1429.  P. Jacquinot and B. Roizen-Dossier (1964). In "Progress in Optics" (E. ), Vol. Ill, p. 31. North-Holland, Amsterdam.  H. Stark, D. Lee, and B. Dimitriadis (1975).
22] H. Stark and G. Shao (1977). Appl. Opt. 10, 1670-1674. APPLICATIONS OF OPTICAL FOURIER TRANSFORMS Chapter 2 Pattern Recognition via Complex Spatial Filtering SILVERIO P. ALMEIDA and GUY INDEBETOUW DEPARTMENT OF PHYSICS VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY BLACKSBURG, VIRGINIA INTRODUCTION The concept of spatial filtering, that is, the manipulation of spatial frequencies in order to alter the properties of an image, has been known for over 100 years as a result of the work of Abbe.
Application of Optical Fourier Transforms by Henry Stark