Transformation of phase to (x,y,z)-coordinates for the calibration of a fringe projection profilometer

In this work we present a phase to (x,y,z)-coordinates transformation method for the calibration of a fringe projection profilometer. Our technique is divided in two parts: (1) phase to z transformation (for axial calibration) based on the typical polynomial fitting which uses a flat plane placed at several z positions to measure the phase of the projected fringes. (2) Phase to x and y transformation (for transverse calibration) based on the use of a crossed gratings pattern and a Fourier phase measurement method to determine x and y coordinates at several z positions. As will be shown the use of the crossed gratings pattern and the Fourier phase measurement method for transverse calibration is advantageous in several aspects: an unique image can give us x and y information at once. It provides x and y coordinates at each pixel in the image avoiding the use of interpolation methods. We present some experimental results and explain the viability of the proposed technique.