基于健壮中国剩余定理的频率选择准则及其在相位解包裹中的应用

高质量相位解包裹是相位轮廓术的重要问题。分析了亮度噪声对相位主值的影响，将相位解包裹问题转化为同余问题，基于健壮中国剩余定理推导出频率选择的上限准则，利用该准则指导多频相位展开算法中参数的设置，并利用健壮中国剩余定理的封闭解确定对应性。实验结果表明，健壮中国剩余定理与传统中国剩余定理相比具有强抗干扰特性，在满足频率上限准则时可实现接近100%正确率的解包裹；反之，相位展开效果则会恶化。

Frequency Selection Rule based on Robust Chinese Remainder Theorem and Its Application in Phase Unwrapping

Phase unwrapping is an essential problem in phase measuring profilometry. In this paper, phase unwrapping is modeled as a congruence problem. Based on robust Chinese remainder theorem, the frequency selection rule is proved by analyzing the uncertainty of wrapped phase because of the intensity noise. Then, this rule is adopted to design the frequency unwrapping algorithm and the parameters are determined with high confidence probability. After that, the closed-form algorithm of robust Chinese remainder theorem is employed to determine the correspondence. Finally, the quantitative comparisons are implemented in our developed structured light measurement system. The experimental results show that the frequency selection rule is valid, and robust Chinese remainder theorem is less sensitive to the phase noise than the traditional Chinese remainder theorem. If the frequency selection rule is satisfied, the accuracy of the unwrapped phase can achieve nearly 100%, otherwise, the performance is deteriorated.