Method for performing complex-valued linear operations on complex-valued data using incoherent light.

Under normal circumstances, the operations achievable by means of an incoherent optical data processing system are limited to superposition integrals (or, as a special case, convolution integrals) involving real, nonnegative impulse responses and real, nonnegative input data. This restriction arises due to the linearity of such systems in intensity, rather than in complex amplitude. The class of achievable operations can be broadened to include real bipolar spread functions if the results of two nonnegative operations are subtracted, or if a phase switching interferometer is employed. Recently, Lohmann has described a method whereby complex-valued impulse responses can be applied to complex-valued input data, yet the system is still incoherent. We wish to describe here an alternative approach which also allows complex-valued spread functions to be applied to complex-valued input data with an incoherent optical system. The operation to be performed is described mathematically by