Fresnel transforms and Bragg cell processors

In the analysis of coherently illuminated optical systems we distinguish between space planes and spatial frequency or Fourier planes. Between these two planes exists a continuum of Fresnel transform planes; the Fresnel domain therefore shares, more or less equally according to its position, the properties of the space and frequency domains. Since Fresnel transforms are space-variant operations, generalized results are difficult to obtain. When implemented by Bragg cell processors, however, Fresnel transforms have some interesting and useful spatial/temporal properties. We examine the application of Fresnel transforms to analog signal scrambling techniques. We derive the optimum geometry for obtaining the maximum time spreading for a given signal bandwidth. We derive the system response to impulse, short pulse, and cw signals. We show how a permutation of time samples can be achieved and illustrate some of the key features through simulations.