基于双相位编码光学联合变换相关技术提出了一种测量透镜中心偏差的方法以确定偏差方向并提高测量精度。在经典联合变换相关原理基础之上，使用两个相位函数分别对参考图像和联合功率谱进行编码，并选用合适的滤波器消除旁瓣干扰，得到单个互相关峰的输出。利用该双相位编码后的联合变换相关技术探测不同目标图像相对于参考图像的位移矢量，并拟合圆。此拟合圆圆心到圆上点的矢量即为经自准直光学系统放大后的偏心矢量，从而同时确定了中心偏差的大小和方向。实验结果表明，通过双相位编码后的相关输出仅保留一个尖锐的相关峰，实现了位移矢量的亚像元探测; 使用联合变换相关技术准确地测量了透镜的中心偏差，其测量结果的实验标准差为0.1 μm,误差绝对值最大为0.3 μm, 满足一般透镜中心偏差测量的要求。

A measurement method for the lens centering error based on double phase-encoding optical Joint Transform Correlator(JTC) was proposed for improving the measuring accuracy and determining the orientation of the centering error. On the basis of the principle of traditional JTC, two phase functions were utilized to code the reference image and the joint power spectrum, and proper filters were chosen to eliminate the effect of the sidelobe and to obtain an output with one cross-correlation peak. Then, this JTC technique after double phase-encoding was used to detect the displacement vectors between target images and reference image and to fit a circle using the displacement vectors. The vector between the center of the fitting circle and a certain point on the fitting circle is the magnified centering vector of corresponding angle, which means that the size and orientation of the centering error have been determined simultaneously. The experimental results show that the outputs keep only one speculate cross-correlation peak after double phase-encoding, which implements the displacement measurement with sub-pixel accuracy. This technology is used to measure the centering error of a lens accurately, the experimental standard deviation is 0.1 μm, and the biggest absolute error is 0.3 μm, which meets the requirement of centering error measurement.