Multi-frequency inverse-phase fringe projection profilometry for nonlinear phase error compensation

•A multi-frequency inverse-phase method is proposed to compensate nonlinear phase errors in fringe projection profilometry.•The nonlinear phase error inverses its sign and can be compensated by an addition operation of the unwrapped phases before and after a phase-offset.•Simulations and experiments verify the feasibility and applicability of the proposed method.

A new multi-frequency inverse-phase method was proposed to compensate for nonlinear phase errors in fringe projection profilometry and to measure the three-dimensional shape of discontinuous objects. After introducing a phase offset of π/4 into the multi-frequency four-step phase-shifting method the corresponding nonlinear phase error reversed its sign, which allowed the addition of unwrapped phases before and after the phase-offset operation to compensate for the error. For the four-step phase-shifting method, simulation analysis showed that the nonlinear phase error had quadrupled the fringe frequency. Moreover, experimental results verified the feasibility and applicability of the proposed method.