Nonlinear error self-correction for fringe projection profilometry with minimum phase probability variance

Nonlinear intensity responses of used devices, resulting in negative effects on the measurement accuracy, are a well-known problem in fringe projection profilometry (FPP). Previous studies have concentrated on estimating the global response parameters of the system through tedious calibration or auxiliary fringe patterns, which weaken the generalization capability and reduce measurement efficiency, respectively. To this end, we introduce a flexible nonlinear error self-correction method based on the minimum phase probability variance without prior calibration or extra projection. First, based on the nonlinear response expression of the system, we derive a pixel-independent parameter estimation model, which reveals that the resulting inverse-wrapped phase can correct nonlinear errors to some extent. Subsequently, an iterative averaging scheme is further developed to maximize the error correction and finalize the optimal phase. In particular, a new phase quality metric, called the phase probability variance, is proposed to guide the iteration process and evaluate the acquired average phases. The proposed method does not require tedious calibration or extra projection while being insensitive to unwrapping schemes, time-varying nonlinear systems, and fringe frequencies, thus greatly improving measurement efficiency and facilitating generalization capabilities. Moreover, the pointwise correction is able to effectively protect the edges and details of the measured object. The results of the simulations and experiments confirm that the proposed method is capable of significantly reducing the phase errors induced by the system’s nonlinearity and improving the measurement accuracy.