Noise performance of a white-light optical signal processor I Temporally partially coherent illumination

White-light optical processors are known to perform better under noisy conditions as compared with their monochromatic counterparts. Here we give an analysis of their performance under temporally incoherent illumination and obtain quantitative results to support the claim. The output signal-to-noise ratio (SNR) for the proposed white-light optical processor is evaluated as a measure of performance. We study the behavior of the system when the noise is presented at the input or at the Fourier plane. We show that, except for the case when the amplitude noise is present at the input plane, the resulting output SNR improves considerably with the increasing bandwidth of the light source employed.