Optical feedback for iterative processing

Iterative processing techniques can often provide useful solutions to problems, especially problems of inversion, when deterministic solutions are impracticable or too costly. These iterative techniques usually require a feedback path so some measure of the output can affect an input of the system in order to guide it towards the correct solution. This feedback path often needs to be a sophisticated manipulation of the output state, such as linear transformation of a vector. However, when the processing can be properly designed, the necessary dynamic range of this feedback path doesn't need to be as high as the desired precision of the solution. Such feedback operations can be performed quite well by analog multichannel optical processing systems. We show how we have used optical systems in a simulated-annealing inversion algorithm to invert a system of linear equations, such as deconvolution for recovering an intensity distribution from an image formed by an aberrated or indirect imaging system. We show that we can significantly increase the execution speed over the digital processor, but we do not sacrifice the ultimate precision of the solution by using the analog optical system.