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.