Phase encoding and phase-shift profilometry are two commonly used 3D measurement techniques. However, the acquired phases in the techniques are subject to jump errors due to phase ambiguity and phase errors caused by multiple heterodyne. The phase-shifting profilometry also makes the selection of fringe period difficult. To overcome this problem and achieve high-precision measurement, a phase unwrapping method that combines dual-frequency heterodyne with double complementary phase encoding is proposed. First, two wrapped phases are obtained by two groups of sinusoidal fringes; the heterodyne phase is obtained after heterodyne processing, and the high-frequency phase is expanded by heterodyne phase. Second, the fringe levels are obtained using the complementary phase encoding fringes that are shifted by half an order, and then the absolute phase is obtained by selecting different phase coding levels according to different regions for the first phase unwrapping; Finally, the phase noise is removed by exploiting the difference between the phase slopes of adjacent pixels. Experimental results show that a system with the proposed method achieves an RMS error of 0.015 mm. In addition, the period of dual-frequency heterodyne synthesis does not need to cover the whole field of view, which breaks the limitation of frequency selection of the traditional dual-frequency heterodyne method and triple frequency heterodyne method, enabling high-precision measurement with higher frequency fringes. This method overcomes the limitations of the phase principal value error when using higher frequency fringes for high-precision measurement, improves the measurement effect of reflective objects, and effectively avoids the error caused by phase jump.

中文翻译：

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双频外差与双互补相位编码相结合的相位展开方法

相位编码和相移轮廓测量法是两种常用的 3D 测量技术。然而，由于相位模糊和多外差引起的相位误差，这些技术中获得的相位会受到跳跃误差的影响。相移轮廓测量法也使条纹周期的选择变得困难。为克服这一问题，实现高精度测量，提出了一种将双频外差与双互补相位编码相结合的相位展开方法。首先，通过两组正弦条纹得到两个包裹相位；外差处理后得到外差相位，高频相位由外差相位扩展。其次，使用偏移半个阶的互补相位编码条纹获得条纹电平，然后根据不同的区域选择不同的相位编码级别，得到绝对相位，进行第一次相位解缠；最后，利用相邻像素的相位斜率之间的差异去除相位噪声。实验结果表明，采用所提出方法的系统实现了 0.015 mm 的 RMS 误差。另外，双频外差合成周期不需要覆盖整个视场，打破了传统双频外差法和三频外差法的选频限制，实现了高精度测量，更高频率条纹。该方法克服了使用较高频率条纹进行高精度测量时相位主值误差的限制，