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Phase reconstruction from undersampled intensity pattern(s): underdetection

We analyze the problem of recording and detection of high density fringe patterns with finite pixel size. Two detrimental consequences of the pixalation are identified, both increasing the difficulty of phase reconstruction. First, the intensity information is undersampled for the large pixel center-to-center separation. Second, the intensity distribution, averaged over a pixel of about the same size or larger than the fringe width, significantly decreases the detected fringe visibility. In the limiting case that the pixel width is equal to that of a fringe and with a proper registration, no phase information is recorded: a condition we call the moire limit. Neither the intensity, nor contrast, nor phase reversal effects are seen in the simulations. We show that the high-density fringe detection may not be characterized with the modulation transfer function.