Online nonlinearity elimination for fringe projection profilometry using slope intensity coding

The nonlinearity effect in the system of fringe projection profilometry can cause the non-sinusoidal deviation of the fringe patterns, inducing ripple-like phase errors and further affecting measurement accuracy. This paper presents an online nonlinearity elimination method based on slope intensity coding. Two sequences of sinusoidal phase-shifting fringe patterns with different frequencies, and one slope intensity pattern with one uniform intensity pattern are projected. The equations for the nonlinearity response are established using the defined mean and modulation parameters, the captured uniform intensity and two extracted background intensities. The nonlinearity response coefficients determined by solving the equations are used for pixel-wise nonlinearity correction on the captured images, which are employed for computing the wrapped phase, and further obtaining continuous phase by the multi-frequency phase unwrapping method. Experimental results demonstrate that the proposed method can eliminate the nonlinearity-induced phase error online by using fewer images and maintain the reliability of phase unwrapping in the measurement of isolated objects with complex surfaces.