FRACTIONAL FOURIER-TRANSFORM DESCRIPTION WITH USE OF DIFFERENTIAL-OPERATORS

The fractional Fourier transform (FRT) is expressed by means of propag ation and thin-lens phase delay operators, and a large number of optic al systems associated with it are found. At the same time, the output of optical systems is found in terms of the FRT, and the simplicity of the approach is illustrated with two examples. Mathematical definitio ns for the P-order convolution and correlation are proposed as general izations of the classical ones such that, when the P-order FRT is appl ied to them, theorems that generalize the classical convolution and co rrelation are verified. (C) 1997 Optical Society of America.