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The ``pairing function'' concept applied to digital area correlation is described. One standard and three synthesized correlation functions are expressed in terms of the pairing functions Nij. The Nij are also random variables with easily calculated expected values Nij. The Nij are used to calculate ``background levels'' and detection thresholds, and using signal-to-noise ratios as the criteria, the three synthesized correlation functions yield better results than the standard one.