Fractional correlations based on the modified fractional order Fourier transform
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.