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Generalized fractional Fourier transform in optical systems

Author(s): Yu.M.Kozlovskii

Journal: Ukrainian Journal of Physical Optics
ISSN 1609-1833

Volume: 4;
Issue: 3;
Start page: 135;
Date: 2003;
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Keywords: fractional Fourier transform | fractional correlation | cross shifting | image forming rectangular slit | ambiguity

We investigate the properties of intensity distribution of the two optical signals, which are shifted and modulated by a plane wave and correspond to the generalized fractional Fourier transform (FFT). The results of analytic and numerical calculations show the possibilities for designing new systems for the processing of information. As an example, the correlator based on the generalized FFT is considered. The domains of the generalized FFT in the practicable optical systems are obtained and analyzed. A principal possibility for the formation and recording of the interference pattern is demonstrated for the case when the images of the FFT, starting from the general form of the cascade matrix, are optically superimposed.
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