Smoothed-Truncated-Sine (STS) Pattern for Accuracy Improvement in Sinusoidal Fringe Projection Profilometry

Sinusoidal patterns are widely employed in fringe projection profilometry (FPP) for high-accuracy measurements. However, in practice, random factors, such as camera noise, will seriously affect the accuracy of sinusoidal patterns. This article presents a smoothed-truncated-sine (STS) pattern design method that can achieve higher accuracy than sinusoidal patterns under the same noise. By insensitive harmonic modulation, the STS pattern can achieve a higher signal-to-noise ratio (SNR) to reduce the random error and maintain the amplitude of sensitive harmonics low to restrain the systematic error. First, the error mechanism is analyzed, and the error model is established for the phase-shifting algorithm, taking into account the resistance of the phase-shifting algorithm to part of high-order harmonic errors. Second, an STS pattern is proposed and optimized based on the error model. The parameters of the STS pattern are optimized to achieve a high SNR and a small phase error, resulting in improved performance of the multiple-step phase-shifting algorithm, especially when the number of steps is large. Simulations and experiments demonstrate that the proposed method achieves higher accuracy than sinusoidal patterns and that the maximum error reduction ratio exceeds 20% if the number of steps is sufficiently large in sinusoidal FPP.