  The multi-frequency temporal phase unwrapping (MF-TPU) method, as a classical
phase unwrapping algorithm for fringe projection profilometry (FPP), is capable
of eliminating the phase ambiguities even in the presence of surface
discontinuities or spatially isolated objects. For the simplest and most
efficient case, two sets of 3-step phase-shifting fringe patterns are used: the
high-frequency one is for 3D measurement and the unit-frequency one is for
unwrapping the phase obtained from the high-frequency pattern set. The final
measurement precision or sensitivity is determined by the number of fringes
used within the high-frequency pattern, under the precondition that the phase
can be successfully unwrapped without triggering the fringe order error.
Consequently, in order to guarantee a reasonable unwrapping success rate, the
fringe number (or period number) of the high-frequency fringe patterns is
generally restricted to about 16, resulting in limited measurement accuracy. On
the other hand, using additional intermediate sets of fringe patterns can
unwrap the phase with higher frequency, but at the expense of a prolonged
pattern sequence. Inspired by recent successes of deep learning techniques for
computer vision and computational imaging, in this work, we report that the
deep neural networks can learn to perform TPU after appropriate training, as
called deep-learning based temporal phase unwrapping (DL-TPU), which can
substantially improve the unwrapping reliability compared with MF-TPU even in
the presence of different types of error sources, e.g., intensity noise, low
fringe modulation, and projector nonlinearity. We further experimentally
demonstrate for the first time, to our knowledge, that the high-frequency phase
obtained from 64-period 3-step phase-shifting fringe patterns can be directly
and reliably unwrapped from one unit-frequency phase using DL-TPU.
