Optical fractional correlation: experimental results

Abstract

Recently a new mathematical tool, the fractional Fourier transform (FRT) was introduced into the optical field [ J. Opt. Soc. Am. A10, 1875 and 2521 ( 1993)]. So far, theoretical investigations have been done in order to prove the potential of the FRT operations. On the basis of the FRT operation, the conventional correlator has been generalized through definition of the fractional correlation (FC) operation. We demonstrate the experimental evaluation of the FC operation. Because of the shift-variance property of the FRT, FC makes shift-variant object recognition possible. The laboratory experiments are supplemented by computer simulations, and a reasonable agreement between the results is demonstrated.