## Abstract

Fractional correlation was introduced recently. We generalize
the architecture of a joint (Fourier) transform correlator
(JTC) to achieve the joint fractional (Fourier) transform
correlator (JFrTC) such that fractional correlation can be
obtained. Here the Fourier transform in the JTC is replaced by the
fractional Fourier transform, and four different JFrTC architectures
can be implemented. The mathematical derivations for these JFrTC
architectures are given, together with the simulation
verifications. The JFrTC can provide a correlation signal similar
to a delta function but with a small discrimination ratio, such that it
is insensitive to additive noise. In a conventional JTC the
distance between the two desired correlation signals at the output
plane is fixed and depends on the distance between the input and the
reference signals. However, with a given fractional order and an
additional phase mask the separation distance between the two
correlation signals at the output plane of a JFrTC can be larger or
smaller than that of a JTC. This property is useful for the
applications of real-time target tracking. Unlike in a previous
approach [Appl. Opt. **36**, 7402 (1997)], we need only
two fractional Fourier transformations instead of three to achieve
fractional correlation.

© 1998 Optical Society of America

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