Fractional correlator with real-time control of the space-invariance property.

In pattern recognition, it happens that the amount of space variance should be controlled. This may be achieved by use of a partially space-variant correlator. We present a novel configuration for achieving a partially controlled space-variant correlator. In this configuration the lenses are fixed in their focal lengths and locations. The filter function is also fixed. To change the amount of space variance, we need change only the longitudinal location of the filter without reencoding it. It is also shown that this type of correlator provides improved correlation peaks according to correlation-sharpness criteria.

[1]  V. Namias.  The Fractional Order Fourier Transform and its Application to Quantum Mechanics , 1980 .

[2]  K. Wolf.  The Un,1 and IUn Representation Matrix Elements , 1972 .

[3]  D A Gregory,et al.  Nonconventional joint-transform correlator. , 1989, Optics letters.

[4]  A. Lohmann.  Image rotation, Wigner rotation, and the fractional Fourier transform , 1993 .

[5]  T. Seligman,et al.  Canonical Transformations and the Radial Oscillator and Coulomb Problems , 1972 .

[6]  Luís B. Almeida,et al.  The fractional Fourier transform and time-frequency representations , 1994, IEEE Trans. Signal Process..

[7]  B. Kumar,et al.  Performance measures for correlation filters. , 1990, Applied optics.

[8]  O. Soares,et al.  Fractional Fourier transforms and optical systems , 1994 .

[9]  H. Ozaktas,et al.  Fractional Fourier transforms and their optical implementation. II , 1993 .

[10]  Levent Onural,et al.  Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms , 1994 .

[11]  A W Lohmann,et al.  Binary fraunhofer holograms, generated by computer. , 1967, Applied optics.

[12]  A. B. Vander Lugt,et al.  Signal detection by complex spatial filtering , 1964, IEEE Trans. Inf. Theory.

[13]  D M Cottrell,et al.  Space-variant Fresnel transform optical correlator. , 1992, Applied optics.

[14]  A. Lohmann,et al.  Chirp filtering in the fractional Fourier domain. , 1994, Applied optics.

[15]  Zeev Zalevsky,et al.  Synthesis of pattern recognition filters for fractional Fourier processing , 1996 .