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We have calculated the total critical current as a function of applied magnetic flux for a superconducting interferometer consisting of many Josephson junctions in parallel. An enhancement and narrowing of the periodic principal maxima in the critical current versus flux characteristic is predicted as the number of junctions in parallel increases, even when the effects of finite self‐ and mutual inductances and nonuniformity of the junction critical currents are included in the calculations. The possible application of the superconducting quantum interference grating, or SQUIG, for the detection of magnetic flux is discussed.