Calibration of a Fringe Projection 3D Measurement System Using an Equi-Phase Coordinate Method Based on Two-Reference-Plane

Calibration is to transform the 2D phase information to the world coordinates in a fringe projection 3D measurement system. For the phase-to-height conversion, an equi-phase coordinate method based on two-reference-plane is proposed in this paper. The surface height is calculated by a linear interpolation using the coordinates where have the identical phase value of the object and the two reference planes. The conventional method, called equi-coordinate phase method in this paper, builds the function of the absolute phase and height by using the absolute phase obtained by subtracting the phase of object from that of the reference plane in the same coordinate. The proposed method can handle phase-to-height conversion and non-sinusoidal error caused by nonlinear response of the fringe projection system in one go. Theoretical and experimental analysis is given to prove the validity of the proposed method. Result indicates that the RMS error produced by equi-phase coordinate method is less half of equi-coordinate phase method when the primary error source is from the non-sinusoidal fringe patterns