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分析了光学系统的波像差与对应的光束质量β因子间的关系,推导了光束质量β因子的近似计算公式。用数值计算方法建立了各种泽尼克多项式的波像差均方根值(RMS)与β因子间的拟合关系式。在此基础上,分析了科尔莫哥诺夫大气湍流引起的波像差与对应光束质量β因子间的关系。数值计算结果验证了推导的近似计算公式在相当大的像差范围内是准确的。
The relationship between the wavefront aberration and the corresponding β factor of the beam quality is analyzed, and the approximate formula of the β factor of the beam quality is deduced. The fitting relationship between wave root mean square (RMS) and β factor of various Zernike polynomials is established by numerical method. Based on this, the relationship between the wavefront aberration and the β factor of the corresponding beam quality caused by the Kolmogorov atmospheric turbulence is analyzed. The numerical results verify that the derived approximate calculation formula is accurate over a large range of aberrations.