Abstract Absolute phase retrieval is important for three-dimensional (3D) shape measurement in fringe projection technique. Numerous phase unwrapping methods have been proposed for addressing this issue, and gray-level is one such technique employed to determine fringe orders for wrapped phase. However, the codeword detection can fail due to random noise or cameras/projectors defocus. We propose an improved method to determine the codewords in this paper. Specifically, three sinusoidal fringe patterns are used to obtain the wrapped phase and three n-ary gray-level (nGL) patterns are employed to obtain the fringe order. Two opposite masks can be calculated through wrapped phase binarization. The masks and the nGL patterns are roughly used to obtain codewords. After half-period correction, the codeword is accurately reconstructed, and the fringe order is also determined. Simulations and experiments demonstrated the robustness and effectiveness of the proposed algorithm to measure isolated objects with complex surfaces.

中文翻译：

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一种改进的基于半周期校正的绝对相位测量灰度编码方法

摘要 绝对相位反演对于条纹投影技术中的三维（3D）形状测量非常重要。已经提出了许多相位展开方法来解决这个问题，灰度是一种用于确定缠绕相位条纹阶次的技术。然而，由于随机噪声或相机/投影仪散焦，码字检测可能会失败。我们提出了一种改进的方法来确定本文中的码字。具体来说，三个正弦条纹图案用于获得包裹相位，三个 n 元灰度 (nGL) 图案用于获得条纹阶次。可以通过包裹相位二值化计算两个相反的掩码。掩码和 nGL 模式大致用于获得码字。经过半周期校正，码字被准确重构，并且边缘顺序也被确定。仿真和实验证明了所提出的算法在测量具有复杂表面的孤立物体方面的鲁棒性和有效性。