一种具有宽松约束的相位—高度映射算法

为了提升PMP测量系统的测量精度以及放宽该系统搭建的约束条件,提出一种新的具有宽松约束的相位测量轮廓术相位—高度映射算法.这种算法既不要求投影装置光心和成像装置光心的连线平行于参考平面,也不要求投影装置的光轴与成像装置的光轴共面,只要保证成像装置光轴垂直于参考平面,即可实现相位—高度映射.本文详细推导了该算法的数学模型,发现当投影装置光心与成像装置光心的连线不平行于参考平面时,相位—高度映射不仅与三维测量系统的结构参数有关,还与参考面的相位分布有关.由于在实际测量中难以保证投影装置光心与成像装置光心的连线严格平行于参考平面,因此所采用的新的相位—高度映射算法是实际测量系统的真实反映,也使系统更易于搭建.实验结果表明:本文所提算法进行测量的平均绝对误差和均方根误差最大不超过0.031 mm和0.040 mm.该算法拓宽了搭建测量系统时的约束条件,使得光路更易于实现.实验验证了该算法的有效性,表明所提算法的精确性和可重复性均优于传统算法.

Phase-to-height mapping algorithm with loose constraints

A new phase-to-height mapping algorithm with loose constraints based on phase measuring profilometry is proposed to improve the measurement accuracy of PMP and relax the constraints of its system. The algorithm requires neither the linking line between the optic centers of the projection system and the imaging system to be parallel to the reference plane, nor the projecting optic axis and the imaging optic axis to be on the same plane. Just by making sure that the imaging optic axis is vertical to the reference plane can the phase-to-height mapping be successfully realized. The mathematic model of the algorithm was deduced in detail, and it was found that the phase-to-height mapping was not only related to the structure parameters of the 3D measurement system but also to the phase distribution of reference plane. In actual measurement, it is difficult to guarantee that the linking line between the optical centers of the projection system and the imaging system is parallel to the reference plane, but the new phase-to-height mapping algorithm avoids this challenge, thus providing a true reflection of the actual measurement system. It also makes the experimental system easier to build. Experimental results show that the mean absolute errors and the root mean square errors of the proposed method were no more than 0.031mm and 0.040 mm, respectively. The algorithm could relax the constraints when building the measurement system and make the beam path easier to realize. The effectiveness of the proposed algorithm was verified by the experiment, indicating that the proposed algorithm is superior to the traditional algorithm in terms of accuracy and repeatability.