We propose a high signal-to-noise extended depth-range three-dimensional (3D)profilometer projecting two linear-fringes with close phase-sensitivity. We usetemporal phase-shifting algorithms (PSAs) to phase-demodulate the two closesensitivity phases. Then we calculate their phase-difference and theirphase-sum. If the sensitivity between the two phases is close enough, theirphase-difference is not-wrapped. The non-wrapped phase-difference asextended-range profilometry is well known and has been widely used. However asthis paper shows, the closeness between the two demodulated phases makes theirdifference quite noisy. On the other hand, as we show, their phase-sum has amuch higher phase-sensitivity and signal-to-noise ratio but it is highlywrapped. Spatial unwrapping of the phase-sum is precluded for separate orhighly discontinuous objects. However it is possible to unwrap the phase-sum byusing the phase-difference as first approximation and our previously published2-step temporal phase-unwrapping. Therefore the proposed profilometry techniqueallows unwrapping the higher sensitivity phase-sum using the noisierphase-difference as stepping stone. Due to the non-linear nature of theextended 2-steps temporal-unwrapper, the harmonics and noise errors in thephase-difference do not propagate towards the unwrapping phase-sum. To the bestof our knowledge this is the highest signal-to-noise ratio, extendeddepth-range, 3D digital profilometry technique reported to this date.
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