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1 March 1974 Fourier Transform Properties Of Polar Formatted Data
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One of the basic reasons for using optical processing is the sim-plicity of using a spherical lens to take a 2-dimensional Fourier transform (FT) of input data. Intrinsically, the 2-dimensional FT is best understood in rectangular coordinates (Ref. 1). Most FT techniques take advantage of rectangular formatted data. However, a polar format is often the most natural form for data obtained with a technique where rotation is inherent in the data taking process. Such cases exist in radio astronomy of rotating planets (Ref. 2) and other stellar objects where the earth's rotation is used to advantage (Ref. 3), and in processing image projections (Ref. 4). In addition, the concept of recording data on a rotating disk for near real time optical processing is also very attractive (Ref. 5). All these areas of interest might take advantage of optical data processing. However, a major stumbling block is that the FT of many of the simplest polar forms, e.g. a pie shaped wedge (Ref. 6) do not lend themselves to closed form expressions that can be easily under-stood. Hence, whatever advantages a polar formatted optical processing system might have are not readily evident.
© (1974) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Carl C . Aleksoff "Fourier Transform Properties Of Polar Formatted Data", Proc. SPIE 0052, Coherent Optical Processing, (1 March 1974);


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