中文摘要：

在相位测量轮廓术（PMP）中，探测器的非线性响应是导致测量误差的重要因素．对该误差进行了理论分析和计算机模拟，比较了几种相移算法对这一误差的抑制能力，模拟结果与理论分析的结果一致．提出一种存在非线性误差时光强函数的几何描述方法，采用帕斯卡蜗线描述二阶非线性光强函数，这是一种用角度射线与帕斯卡蜗线交点在横轴上的投影长来表示相对光强的几何模型，形象地表示了探测光强与光栅移动角度的关系，以及非线性误差存在和不存在时的光强变化．同样，文中采用准卡西尼卵形线蜗线描述三阶非线性光强函数，用同样的方法形象地表示了在存在三阶非线性时探测光强与光栅移动角度的关系，以及非线性误差存在和不存在时的光强变化，可为实际应用中合理地选择算法和直观的评估非线性导致的光强变化提供帮助．

英文摘要：

Phase-shifting technique is commonly applied in surface measurement of three-dimensional object in recent years. In phase measuring profilometry detector nonlinearity is the main factor introducing the errors of the measurement . This paper gives the theoretical analysis and the computer simulation of this kind of error , and compares the ability of tolerance with the second and the third order nonlinearity of detector for N - frame phase shifting algorithms. Also,this paper gives several geometry diagram to show intensity of ray when there is the nonlinearty error. The results of numerical simulation and theoretical analysis are consistent and it offers a theoretical basis of selection of algorithms.