Lü Fuxing, Xing Shuo, Guo Hongwei
Appl Opt. 2017 Sep 1;56(25):7204-7216. doi: 10.1364/AO.56.007204.
In phase-shifting fringe projection profilometry, the luminance nonlinearity of the used projector has been recognized as one of the most crucial factors decreasing the measurement accuracy. To solve this problem, this paper presents a self-correcting technique that allows us to suppress the effect of the projector nonlinearity in the absence of any calibration data regarding the projector intensities or regarding the phase errors. In its first step, the standard phase-shifting algorithm is used to recover the phases, as well as the background intensities and the modulations. Using these results enables normalizing the fringe patterns, for ridding them of the effects of the background and modulations. Second, we smooth the calculated phase map by use of a low-pass filter in order to remove the ripple-like phase errors induced by the projector nonlinearity. Third, we determine a polynomial representing the projector nonlinearity by fitting the curve of the normalized fringe intensities against the cosine values of the smoothed phases. Finally, we correct the phase errors using the curve just obtained. Doing these steps in an iterative way eventually results in a phase map and, further, a 3D shape with their artifacts induced by the projector nonlinearity suppressed significantly. Experimental results demonstrate that this technique offers some advantages over others. It does not require a prior calibration of the projector, thus being suitable for dealing with a time-variant nonlinearity; its pointwise operation protects the edges and details of the measurement results from being blurred; and it works well with very few fringe patterns and is efficient in image capturing.
在相移条纹投影轮廓术中，所用投影仪的亮度非线性已被认为是降低测量精度的最关键因素之一。为了解决这个问题，本文提出了一种自校正技术，该技术使我们能够在没有任何关于投影仪强度或相位误差的校准数据的情况下抑制投影仪非线性的影响。第一步，使用标准相移算法来恢复相位，以及背景强度和调制。利用这些结果可以对条纹图案进行归一化，以消除背景和调制的影响。其次，我们使用低通滤波器对计算出的相位图进行平滑处理，以去除由投影仪非线性引起的波纹状相位误差。第三，通过将归一化条纹强度曲线与平滑相位的余弦值进行拟合，确定表示投影仪非线性的多项式。最后，我们使用刚刚得到的曲线校正相位误差。以迭代方式执行这些步骤最终会得到一个相位图，进而得到一个三维形状，其由投影仪非线性引起的伪像被显著抑制。实验结果表明，该技术比其他技术具有一些优势。它不需要对投影仪进行预先校准，因此适用于处理时变非线性；其逐点操作可保护测量结果的边缘和细节不被模糊；并且它在条纹图案很少的情况下也能很好地工作，并且在图像采集方面效率很高。
