Abstract

In fringe projection profilometry (FPP), the luminance nonlinearity generated by the superimposed $\gamma$ effect of the projector and camera can lead to distortion of the intensity of the sinusoidal phase-shift fringe, resulting in a reduction of measurement precision and resolution. Traditional phase error compensation and $\gamma$-correction methods need to focus on the projector’s optimal performance. However, commercial projectors often have huge apertures and are, therefore, unable to project a perfectly focused sinusoidal fringe image. This paper proposes an easy-to-implement active projection error correction method with high precision that is insensitive to projector defocus. After calibrating the projector to establish the nonlinear $\gamma$-response model of the optical measurement system, inverse $\gamma$ compensation is performed. By generating and projecting a set of precorrected sinusoidal fringes, the camera can capture the high-quality sinusoidal fringe image and decrease the phase measurement error caused by the nonlinear $\gamma$ effect of the FPP system. Computer simulations and experiments verify the effectiveness and feasibility of the proposed method for estimating and correcting the nonlinear $\gamma$ distortion of the FPP system. The experimental results show that using the proposed active projection method to compensate for the error of the three-step phase-shift algorithm can achieve a high-precision measurement, and the influence of the system’s nonlinear $\gamma$ effect on the measurement accuracy is significantly suppressed.

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