The existence problem of optical correlation based pattern recognition, namely its range of validity and its limitation, is discussed in this paper conjointly with the function approximation theory of neural networks. The conclusion is that only if the sets to be recognized are linearly separable (which is rare) or the subsets, in which a segmental sample of the targets is involved, are linearly separable, can the classical 4f optical correlation system carry out the task of recognition inerrably. The recognition principle of a joint transform correlator is the same as that of a 4f system, and so is its range of validities. Based on the demonstration of the existence problem of optical correlation based pattern recognition an evaluation on some important problems that were studied in this field over the past 40 years is presented explicitly.