针对相位法光学测量交叉光轴系统中普遍存在的投影光栅在参考平面非线性变化引起的非线性误差的问题,提出了将非线性问题转换为线性问题的基本逻辑.通过光路的几何关系分别在3种交叉光轴系统条件下推导出光栅相位分布表达式,消除了非线性误差项对解算物点空间坐标的影响,从而使该类问题在理论上得到根本的解决.这对于提高系统测量精度、简化系统标定和后期处理具有重要的意义,使得条纹投影法测量三维物体轮廓更加简便和有效.%For the wide existing nonlinear error caused by nonlinear variation of projected grating on reference plane in crossed optical axes geometry of phase measuring profilometry,a basic logic of the nonlinear problem into a linear problem was proposed.The formula of grating phase distribution were deduced through the geometric relationships to eliminate the nonlinear error in three crossed axes systems respectively.This formula can calibrate the phase modulation item in calculating the coordinates of objects,so as to solve this kind of problems fundamentally in theory.It has important meaning for improving accuracy of measurement,simplifing system calibration and post processing.Therefore,it makes fringe projection profilometry flexible and universal in measuring three-dimensional objects.
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