Coherent and noncoherent methods of correlation and convolution

Abstract

Correlation and convolution are based on the idea of getting the response of one function to another. When the data is available in two dimensional transparency form it is convenient to use optical systems. Different techniques of performing the correlation and convolution operations in coherent and noncoherent light are described. Their applications in optics are mentioned. A random-dots code is presented. This was used for coding dilute and continuous-tone pictures. The coded pictures were decoded by correlating them with the code. Coherent and non­ coherent correlation methods were employed. In the coherent method a complex filter was used and the coded pictures were decoded by coherent optical filtering. The noncoherent method is based on the idea of reversing the rays involved in the coding process. The two methods are compared, the effect of the decoding on dilute and continuous-tone objects is illustrated, noise analysis is given and the decoded images resolution is considered. Theories of formation of Fourier images are discussed. A confusion is shown to exist between Fourier images derived from related objects. Coherent and noncoherent correlation experiments are reported. Their results serve to confirm the possibility of confusion. Finally a new method of noncoherent spatial filtering, using blocking filters, is presented.