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中文摘要：
在相位测量轮廓术（PMP）系统中，由光路可逆原理将投影仪当成另一台摄像机看待。研究了空间点在摄像机和投影仪上投影关系，得到投影仪无畸变时PMP系统的相位-高度影射关系；再将它展开成多项式，使参数标定变得方便．进一步研究了投影仪存在镜头畸变时，相位畸变量与相位的关系；最后得到考虑镜头畸变的PMP系统相位-高度映射算法及其多项式表达式．通过计算机仿真表明，在通常的镜头畸变情况下采用4阶多项式表达的新算法最大绝对误差达到士1．0369×10^-3mm，标准偏差达到7．832×10^-4mm．最后在实际系统中进行了验证，实验中虽然由于测量误差的影响，测量标准偏差仍然可以达到0．0425mm．
英文摘要：
The projector can be regarded as another camera in Phase Measurement Profilometry （PMP） system according to the principle of reversibility of light path. The phase-height mapping equation without projector distortion was obtained by studying the projecting relationships of space points on camera and projector. And then, the equation was expanded to polynomial for the convenience of calibration. Finally, the phase-height mapping algorithm with projector distortion and its polynomial expression were acquired by means of investigating the relationship between distortion value and phase. Under condition of general lens distortion, the absolute error of new algorithm expressed as quartic polynomial reached ±1.0369×10^-3mm and the standard residual reached 7.832×10^-4mm in computer simulation. In experiment, the standard deviation of measurement reached 0.0425mm even though the result was affected by measurement error.
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