Signal Detection Theory models are developed which yield comparisons of optical and digital Fourier transform techniques in terms of detectability of power peaks obtained in their Fourier domains. A stochastic model is first given describing the quantization noise introduced by the finite register size in digital transform computers. The signal detection models are then developed describing the detectability of a transformed signal among this kind of noise, with models given for fixed-point and floating-point machines and for signal-known-exactly and signal-unknown detection problems. Signal Detection Theory provides a number of useful results here including the optimum detection statistic to be used, decision criteria for choosing cut-off points, the performance curve of the detector, and detection indexes which summarize detector performance. Once the digital transform computer and the type of detection has been specified, the resulting signal detectability can be used to specify requisite signal-to-noise ratios which the optical processor must achieve to obtain performance in optical Fourier domain equivalent to the digital processor. Alternately, the digital machine can be specified as to fixed-point or floating-point number representation, truncation or rounding of results, and register length to match the detection performance of a given optical processor. Results are given demonstrating these comparisons in which register length, array size, number-representation, and type of detection are the major independent variables.