Analysis of coherent optical filter and correlator systems using pixellated spatial light modulators

The authors analyse the optical performance of 4f coherent optical filtering systems using pixellated spatial light modulator devices for the input and filter planes. The performance of such systems is frequently analysed using oversampling fast Fourier transform (FFT) techniques which we show to require large oversampling factors (and hence complexity) to fully take into account the optical field distribution across each individual pixel of the filter plane and thus provide improved accuracy. The authors proposed two methods by which they obtain a piecewise series expansion of the optical field across each pixel using FFT techniques and demonstrate that these methods show faster convergence with increasing complexity and require less memory storage to compute than the oversampling FFT techniques usually used. If the output plane intensity is only required at a few points, such as when optimisation techniques are being used to design the filter, the authors present a third method which also results in improved accuracy but with no penalty in speed.