Four-pattern, phase-step non-sensitive phase shifting method based on Carré algorithm

•The proposed method obtains the wrapped and absolute phases from only 4 patterns.•The accuracy of the retrieved phase is insensitive to the error of phase step.•The absolute accuracy reaches 0.02 mm and relative accuracy reaches 0.03%.•It is suitable for high speed high precision 3D shape measurement. Carré algorithm is a classic phase shifting measurement method due to its advantage in resisting the error caused by inaccurate phase step. The conventional Carré algorithm only calculates the wrapped phase, so multiple frequencies are used to unwrap the phase so as to obtain the absolute phase, which increases the number of patterns and decreases the measuring speed. We propose a high-accuracy and 4-pattern phase retrieval method based on Carré algorithm. The phase step in Carré algorithm is encoded as a linear variable. With the linear phase step, we obtain both the wrapped phase and absolute phase simultaneously from only 4 patterns. The proposed method is non-sensitive to the errors in phase step, the same as the conventional Carré algorithm. In addition, because only 4 patterns are required for obtaining the wrapped phase and absolute phase, the proposed method is practical in high-speed 3D measurement. Experimental results demonstrate its performance in high accuracy (absolute accuracy is higher than 0.02 mm and relative accuracy is higher than 0.03%), efficiency (requires only 4 patterns) and robustness.