A novel calibration method for fringe projection profilometry based on phase-to-coordinate mapping model

Abstract Fringe projection profilometry (FPP) has been widely applied in fields such as 3D measurement, industrial inspection, and automotive engineering due to its advantages of high precision, non-contact measurement, and simple structure. The calibration of FPP is a critical step for achieving high-precision measurements, as its accuracy directly affects the reliability of the measurement results. However, existing calibration methods usually require complex experimental setups or operational procedures, and they lack flexibility, making it challenging to adapt to diverse application scenarios. To address these issues, this paper proposes a novel and flexible calibration method for FPP with an auxiliary camera based on a phase-to-coordinate mapping model. Firstly, the phase-to-coordinate mapping model is derived by analysing geometric constraints in imaging and projecting process in FPP. With the aid of the auxiliary camera, the phase and 3D coordinates data are computed based on the stereo triangulation of the binocular vision built by the camera in FPP and the auxiliary camera after the camera calibration. After obtaining the phase and 3D coordinates, a random forest method is applied to remove the outliers of the phase-3D coordinate data, and the coefficients of the mapping model are computed by fitting the phase-to-coordinate mapping model. The proposed method reduces requirements of experimental conditions while improving the efficiency and adaptability of the calibration process. Experimental results demonstrate that the proposed method has advantages in calibration accuracy, stability, and operational convenience. It effectively meets the demands for efficiency and flexibility in practical industrial applications, providing a new solution for advancing fringe projection technology.