中文摘要：

测量激光光束质量（M~2）因子时一般要求光路准直,同时要求降低噪声对光斑半径测量的影响。光路偏移会导致CCD采集的光斑偏离CCD中心,噪声使偏移光束的光斑半径和M~2因子的测量值存在额外误差。针对含噪声且光路偏移CCD中心的情况,提出了一种测量M~2因子的改进方法,即当光路不准直时,在光路每个位置采集两个不同偏移量的光斑,则可校正得到光斑半径的真实值,从而得到无准直误差的M~2因子。理论推导了激光光束的光斑半径和M~2因子与偏移量的变化关系,通过数值仿真和实验研究了偏移光束的光斑半径和M~2因子随偏移量的变化,二者结果一致,验证了所提方法的可靠性。

英文摘要：

The beam quality （M2） factor measurement requires the collimation of the optical path and the reduction of the influence of noise on the measurement of spot radius. Deviation of the optical path results in the deviation of the captured spot from the center of CCD, and the measurement values of spot radius and M2 factor will have extra error caused by noise. Aiming at the condition of containing noise and optical path deviating from the center of CCD, a modified method for M2 factor measurement is proposed. The proposed method can collect two spots at positions in optical path with different offsets when the optical path is not straight. The true value of spot radius can be obtained correctly, and then the M2 factor without collimation error can be obtained. The relationship among the spot radius of laser beam, the M2 factor and offset is deduced theoretically. Numerical simulation and experiments are carried out to study the relationship among the spot radius, M2 factor and offset. Consistent results are obtained, which proves the reliability of the proposed method.