Noise robustness of optical correlation for amplitude or phase modulation of the input image

We analyze the influence of the phase or amplitude coding of the input information in an optical correlator. For binary images, we show that the ratio between the signal-to-noise ratios of both codings is independent of the images when the matched filter is modified in order to have a zero mean value. Moreover these signal-to-noise ratios can be equivalent, but the price is a decrease in the amplitude of the correlation peak in the phase-coding case. With the nonmodified matched filter, characteristics of the phase coding appear to be unattractive.