Abstract Binary defocusing technique has been widely used in fringe projection profilometry for high-speed measurement. This technique projects designed binary patterns with a defocused projector to generate fringes for wrapped phase calculation, and n-ary simple codes (nSC) or n-ary gray codes (nGC) for phase unwrapping. The unwrapped phase reflecting the object surface profile is calculated by a phase-shifting algorithm with nSC/nGC phase unwrapping. However, it remains unclear which phase unwrapping method, nSC or nGC, is more appropriate for high-accuracy and high-speed measurement. This paper comprehensively compares nSC and nGC with the consideration of various factors, including the strategies for error removal, the base n, the step heights and invalid regions on the measured objects, defocusing level and noise level of the system. From simulations and experiments, we conclude that, (i) in general, nSC with a proposed identification and binary classification (IBC) method has a similar result as nGC; (ii) when accuracy is critical, binary simple code (nSC with n = 2) and binary gray code (nGC with n = 2) methods are recommended; (iii) when speed is critical, quaternary simple code (nSC with n = 4) method with continuity/geometry constraints is recommended.

中文翻译：

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高速条纹投影轮廓测量中n元简码和n元格雷码相位展开的比较

摘要 二元散焦技术已广泛应用于条纹投影轮廓仪的高速测量。该技术使用散焦投影仪投影设计的二进制图案以生成用于缠绕相位计算的条纹，以及用于相位展开的 n 元简单码 (nSC) 或 n 元格雷码 (nGC)。反映物体表面轮廓的展开相位是通过具有 nSC / nGC 相位展开的相移算法计算出来的。然而，目前尚不清楚哪种相位展开方法，nSC 或 nGC，更适合高精度和高速测量。本文综合比较了nSC和nGC，考虑了各种因素，包括误差去除策略、基数n、被测物体上的台阶高度和无效区域、系统的散焦水平和噪声水平。从模拟和实验中，我们得出结论：（i）一般而言，采用提议的识别和二元分类（IBC）方法的 nSC 与 nGC 具有相似的结果；(ii) 当精度至关重要时，推荐使用二进制简单码（nSC，n = 2）和二进制格雷码（nGC，n = 2）方法；(iii) 当速度很关键时，推荐使用具有连续性/几何约束的四元简码（nSC，n = 4）方法。