M2因子的计算和测量与所采用的坐标系有关, 所以对光斑为非圆对称的光束进行M2因子测量时, 若选取的实验室坐标系不同或者是在非完全相同的实验条件下进行的测量, 测量所得的M2因子并不唯一, 这给实际应用中光束质量的评价带来了不便。为更方便地进行光束质量的评价, 使得不同的实验室坐标系下测量所得M2因子统一, 引入了两个交叉项来表征待测光束光斑主轴与实验室坐标系的位置关系, 定义了M2因子矩阵。同时研究了M2因子矩阵的测量原理和方法, 搭建了M2因子矩阵测试系统, 实验研究了非圆对称光束的束宽以及M2因子随坐标系旋转的变化规律, 测出了M2因子矩阵。

It is inconvenience for the practical application of beam quality assessment because of the uncertainty when test beam quality factor about non-circular symmetry beam is done. The value of M2 will change if the reference frame or other experimental conditions are different because the test for M2 is based on reference frame. To have a unity of different laboratory coordinate systems of the M2, two cross-terms were introduced into present the relationship of beam spot spindle and laboratory coordinates under test. For describing the beam quality convenient, the M2 factor matrix is defined. The principle and method for test is studied, and a system to test the M2 factor matrix has been built. The law of beam width and quality factor M2 vary with the rotation of the coordinates has been studied by using two laser diodes who have the non-circular symmetry beam on the test system. Their M2 factor matrix have been tested and calculated at last.