Rotation-invariant optical processing

The use of optical processors to realize certain two-dimensional linear filtering operations in polar coordinates is studied. When a filtering operation is rotation invariant, an angular cyclic convolution appears in the corresponding polar-superposition integral. Cyclic convolution is reviewed and compared with the standard linear convolution in both space and frequency domains. It is shown that the cyclic convolution of two periodic functions may be obtained from the linear convolution of a single period of one function with three periods of the other. Coherent optical methods for performing cyclic convolution are proposed and practical aspects discussed. Experimental results are presented for one optical realization.