A Method for Suppressing Saturation-Induced Errors in Fringe Projection Profilometry by Fringe Restoration Assisted via Euler Formula-Based Method and Intersection Points

Fringe projection profilometry (FPP) is a widely utilized technique in 3-D measurement for its high accuracy, speed, and non-contact capabilities. However, it faces significant challenges when measuring objects with varying reflectance due to the camera’s limited dynamic range, resulting in saturation-induced errors. Existing methods to address these issues, such as multiexposure techniques, adaptive projection methods, and hardware assistance approaches, each have their limitations, including cumbersome measurement steps and reduced measurement efficiency. This article proposes a novel method for suppressing saturation-induced errors through fringe restoration assisted by the Euler formula-based method and the lower intersection points of adjacent fringes. This method avoids the need for complex logical discussions during the solution process using fringe combinations in previous methods. By expanding effective information and utilizing constraint relationships for solving, the accuracy of fringe restoration is significantly enhanced. Moreover, it can be applied to any number of phase shift steps. This method enhances the adaptability to saturation and improves dynamic range without requiring additional equipment or auxiliary patterns. The feasibility, robustness, and superiority of the proposed method are validated through simulations and experiments, demonstrating improvements in measurement accuracy and efficiency for high-dynamic-range scenes.