1 January 1998 Fractional correlations based on the modified fractional order Fourier transform
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Optical Engineering, 37(1), (1998). doi:10.1117/1.601845
Abstract
Based on the modified fractional order Fourier transform (MFROFT), we introduce a modified fractional correlation operation (MFCO). We propose two systems to implement the MFCO experimentally. These are analyzed theoretically to conclude that the MFCO of two objects equals the conventional correlation between the two objects modified by multiplying each by a quadratic phase factor that contains the parameter that determines the fractional order. The MFCO is applied to a rectangular slit analytically, numerically, and experimentally. We show that the MFCO results in superior correlation peaks compared to those of the conventional correlation operation.
Ahmed M. Al-Manasreh, Mustafa A. G. Abushagur, "Fractional correlations based on the modified fractional order Fourier transform," Optical Engineering 37(1), (1 January 1998). http://dx.doi.org/10.1117/1.601845
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KEYWORDS
Fourier transforms

Optical correlators

Convolution

Fractional fourier transform

Optical engineering

Spatial light modulators

Phase only filters

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