Optimized three-step phase-shifting profilometry using the third harmonic injection

Three-step phase-shifting is an extensively employed method for three-dimensional (3D) shape measurement, especially for high speed 3D image acquisition. However, since only three fringe images are used, the measurement result is susceptible to sensor and environment noise. In this paper, we propose a third harmonic injection technique for three-step phase-shifting profilometry to reduce the error caused by the uncertainty noise. By adding a measure of third harmonic to the sinusoidal waveform, the amplitude of the sinusoidal foundational component can be increased by 15.5%, which results in the reduction of the phase error caused by random noise. The advantages of the proposed technique lie in its simplicity, insensitivity to image defocus, and applicability for high speed 3D imaging by projector defocus. Theoretical analysis, simulations, and experiments are presented to verify the effectiveness of the proposed technique.