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.

Carré算法是一种经典的相移测量方法，因为它具有抵抗相位不准确引起的误差的优点。传统的Carré算法仅计算包裹相位，因此使用多个频率来包裹相位，以获得绝对相位，这会增加图案数量并降低测量速度。我们提出了一种基于Carré算法的高精度四模式相位检索方法。Carré算法中的相位步长被编码为线性变量。通过线性相位步长，我们仅从4种模式中同时获得了包裹相位和绝对相位。与传统的Carré算法相同，该方法对相位误差不敏感。另外，由于只需要4种模式即可获得包裹相位和绝对相位，所提出的方法在高速3D测量中很实用。实验结果表明，它具有很高的精度（绝对精度高于0.02 mm，相对精度高于0.03％），效率（仅需要4种图案）和鲁棒性。