Gamma correction in simultaneously dual fringe projection moiré profilometry

Abstract

Fringe projection profilometry (FPP) is a well-established and noncontact optical method for tridimensional shape measurement. As an FPP technology, simultaneously dual fringe projection moiré profilometry (SDFPMP) increases twice the measurement sensitivity by taking advantage of two illumination directions (projectors) and the phase demodulation of the moiré patterns. In general, the SDFPMP technique is simple and low-cost; however, the projector-camera system usually has a nonlinear intensity response; hence, it distorts the acquired fringe patterns. This intensity alteration, namely gamma distortion, is translated into the appearance of undesired high-order harmonics, so they can impede reaching high accuracy measurements while not removing them adequately. In this manuscript, we study the purely temporal phase demodulation in SDFPMP to cope with the gamma distortion via harmonic rejection. Our analysis depicts that the optimal phase demodulation requires 3(𝐾 + 2) fringe patterns being 𝐾 the highest-order, distorting harmonic. Moreover, we show that when the system's gamma is around 2.0, we can effectively reduce the gamma error amplitude to 0.001 radians by selecting 𝐾 = 2. Numerical experiments demonstrate the approach's feasibility in overcoming gamma distortion.