The effects of space-invariant blurring in the frequency plane of a coherent optical correlator on the system’s performance are considered. The correlator performance criteria used include loss in output correlation peak amplitude, output signal-to-noise ratio, and variation in the probability of a false alarm for a fixed probability of detection. A statistical approach is used to derive general expressions for the mean m and variance var of the output correlation. Expressions for the three correlator performance criteria are then obtained in terms of m and var. When these results are applied to several specific cases, we find that the performance of a correlator can be described and controlled by a new parameter, the space-blur bandwidth product.
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