Title: Extended depth-range profilometry using the phase-difference and phase-sum of two close-sensitivity projected fringes,
Abstract: We propose a high signal-to-noise extended depth-range three-dimensional (3D)
profilometer projecting two linear-fringes with close phase-sensitivity. We use
temporal phase-shifting algorithms (PSAs) to phase-demodulate the two close
sensitivity phases. Then we calculate their phase-difference and their
phase-sum. If the sensitivity between the two phases is close enough, their
phase-difference is not-wrapped. The non-wrapped phase-difference as
extended-range profilometry is well known and has been widely used. However as
this paper shows, the closeness between the two demodulated phases makes their
difference quite noisy. On the other hand, as we show, their phase-sum has a
much higher phase-sensitivity and signal-to-noise ratio but it is highly
wrapped. Spatial unwrapping of the phase-sum is precluded for separate or
highly discontinuous objects. However it is possible to unwrap the phase-sum by
using the phase-difference as first approximation and our previously published
2-step temporal phase-unwrapping. Therefore the proposed profilometry technique
allows unwrapping the higher sensitivity phase-sum using the noisier
phase-difference as stepping stone. Due to the non-linear nature of the
extended 2-steps temporal-unwrapper, the harmonics and noise errors in the
phase-difference do not propagate towards the unwrapping phase-sum. To the best
of our knowledge this is the highest signal-to-noise ratio, extended
depth-range, 3D digital profilometry technique reported to this date.