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本节通过实验来比较上述不同自校正算法的有效性。测量系统如图2所示,包括了一个DLP投影机(PHILIPS PPX4010, 854 pixel×480 pixel),和一个CCD摄像机(AVT Stingray F-125B)。采用3步相移算法计算位相,利用多频条纹投射方法以时域位相解包裹算法求解绝对位相。图8(a)为一幅条纹图,大小为512 pixel×512 pixel,其测量位相在去除载波成分后如图8(b)所示。从中可见波纹状的位相误差,且频率为对应条纹的3倍,是典型的投影机非线性误差。
分别使用了上述的自校正方法,对位相图进行非线性误差校正,并将其结果转化为深度图。对应的深度图如图9所示。其中,图9(a)显示的是未经非线性校正的深度图,图9(b)显示的是采用光度标定主动补偿投影机非线性后的测量结果,图9(c)显示第2.1节所述强度非线性曲线迭代拟合算法所得结果,图9(d)为第2.2节所述基于单幅位相图位相误差估计的自校正方法测量结果,图9(e)为利用第2.3.2节所述基于统计学的自校正方法从双频位相图中重建的深度图,图8(f)则是利用第2.3.1节所述最小二乘迭代自校正方法从双频位相图中重建的深度图。由图中可见,主动补偿方法及各种自校正方法均可有效地抑制投影机非线性的影响。相比较而言,主动补偿方式和统计学自校正方法计算所得深度图中尚残留较多谐波误差。
Figure 9. Depth maps of different correcting methods for projector nonlinearities. (a) Projector nonlinearity not corrected; (b) Photometric calibration;(c) Self-correcting methods based on iterative fitting of intensity curve[41]; (d) Phase error estimation from a single phase map[42]; (e) Self-correcting method based on statistics[45]; (f) Iterative least squares fitting method based on two-frequency phase maps[44]
为了评估前述自校正方法的精度与效率,图10比较了各种方法的均方根(RMS)误差及计算时间。图中的均方根误差由被测物体背景平板上的竖直截面深度测量数值求得。从图10中可见,各类校正方法在不同程度上均可有效地抑制投影机非线性的影响。其中,采用光度标定方法,因其无需在数据处理阶段校正位相误差,耗时较少。但是,在测量之前,标定投影机非线性曲线却需要耗费大量时间。在各类自标定方法中,基于迭代光强拟合的自校正算法的数据处理效率相对较低,这是因为该方法涉及迭代计算条纹的位相、背景与调制度,耗时较多。最小二乘迭代拟合的双频位相图自校正方法具有相对较高的精度,但其数据处理仍涉及迭代拟合操作,也需要一定的计算时间。基于统计学的双频位相图自校正方法计算效率很高,但其只能估计并抑制最低一项谐波的影响,精度较其他自校正方法为低。表1中以传统的基于标定的非线性补偿方法和相移算法为参照,对文中所介绍的各种自校正方法的主要性能进行了比较。其中,关于计算复杂性,各种方法的计算时间严重依赖于计算机系统的性能。随着计算硬件水平的提升,计算时间已逐渐不再是一个制约自校正算法应用的主要因素。
Figure 10. Comparison among different compensating methods with the methods in (a)-(f) corresponding to those in Fig. 9(a)-(f)
Methods Prior calibration required Number of the required fringe patterns Computational complexity Insensitivity to time-variance of the projector nonlinearity Expected accuracy Calibration-based methods (e.g. LUT and
phase-error function)Yes Small Low High Middle Increasing the number of phase shifts with phase-shifting technique No Large Low Low High Iterative least squares fitting to the intensity curve based on single-frequency fringe patterns[41] No Small High Low High Phase error estimation from a calculated
phase map[42]No Small Middle Low High Phase error estimation from two-frequency phase maps using iterative least squares fitting method[44] No Small Middle Low High Phase error estimation from two-frequency phase maps using fringe statistics[45] No Small Low Low Low Table 1. Performance comparisons of projector nonlinearity correcting methods
Progress in self-correcting methods of projector nonlinearity for fringe projection profilometry
doi: 10.3788/IRLA202049.0303009
- Received Date: 2019-11-02
- Rev Recd Date: 2019-12-26
- Publish Date: 2020-03-24
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Key words:
- projector nonlinearity /
- fringe projection /
- phase measurement
Abstract: In fringe projection profilometry, the luminance nonlinearity of the projector has been recognized as one of the most crucial factors decreasing the measurement accuracy. It induces the ripple-like artifacts on the measured phase map. The self-adaptive correcting algorithms, i.e., self-correcting algorithms, allow us to suppress the effect of the projector nonlinearity without a prior calibration for the projector intensities or phase errors. This paper introduces the research progress in the self-correcting algorithms. Among them, the first algorithm is to determine a nonlinear curve representing the projector nonlinearity, directly from the captured fringe patterns, thus correcting the phase errors using this curve. The second one is to recognize and remove the nonlinearity-induced errors, directly from a calculated phase map. With the last one, error function coefficients are estimated from a couple of phase maps having different frequencies. Measurement results demonstrate these self-correcting algorithms to be effective in suppressing influences of the projector nonlinearity in the absence of any calibration information.