Xing Shuo, Guo Hongwei
Opt Express. 2018 Jun 25;26(13):16277-16291. doi: 10.1364/OE.26.016277.
In fringe projection profilometry, the original purpose of projecting multi-frequency fringe patterns is to determine fringe orders automatically, thus unwrapping the measured phase maps. This paper presents that using the same patterns, simultaneously, allows us to correct the effects of projector nonlinearity on the measured results. As is well known, the projector nonlinearity decreases the measurement accuracies by inducing ripple-like artifacts on the measured phase maps; and, theoretical analysis reveals that these artifacts, depending on the number of phase shifts, have multiplied frequencies higher than the fringe frequencies. Based on this fact, we deduce an error function for modeling the phase artifacts and then suggest an algorithm estimating the function coefficients from a couple of phase maps of fringe patterns having different frequencies. As a result, subtracting out the estimated phase errors yields the accurate phase maps with the effects of the projector nonlinearity on them being suppressed significantly. Experiment results demonstrated that this proposed method offers some advantages over others, such as working without a photometric calibration, being applicable when the projector nonlinearity varies over time, and having satisfied efficiency in implementation.
在条纹投影轮廓术中，投影多频条纹图案的最初目的是自动确定条纹级数，从而展开测量的相位图。本文提出，同时使用相同的图案可以校正投影仪非线性对测量结果的影响。众所周知，投影仪非线性会在测量的相位图上产生类似波纹的伪影，从而降低测量精度；而且，理论分析表明，这些伪影取决于相移的数量，其倍频高于条纹频率。基于这一事实，我们推导了一个用于对相位伪影进行建模的误差函数，然后提出一种算法，从具有不同频率的条纹图案的几幅相位图中估计函数系数。结果，减去估计的相位误差可得到准确的相位图，其中投影仪非线性的影响被显著抑制。实验结果表明，该方法相对于其他方法具有一些优势，例如无需光度校准即可工作、适用于投影仪非线性随时间变化的情况，并且在实现上具有令人满意的效率。
