Induced coherence in parametric down-conversion between two coherently pumped nonlinear crystals that share a common idler mode can be used as an imaging technique. Based on the interference between the two signal modes of the crystals, an image can be reconstructed. By obtaining an expression for the interference pattern that is valid in both the low- and the high-gain regimes of parametric down-conversion, we show how the coherence of the light emitted by the two crystals can be controlled. With our comprehensive analysis we provide deeper insight into recent discussions about the application of induced coherence to imaging in different regimes. Moreover, we propose a scheme for optimizing the visibility of the interference pattern so that it directly corresponds to the degree of coherence of the light generated in the two crystals. We find that this scheme leads in the high-gain regime to a visibility arbitrarily close to unity.
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