位相叠加效应对连续位相板束匀滑特性的影响

在大型激光系统的运行过程中，为了对相位畸变导致的焦斑分布不均匀进行改善，在光路通常会使用连续位相板(CPP) 来进行远场束匀滑。根据CPP 面型的随机特性，利用统计的方法对位相板与畸变波前相位的叠加特性进行了计算，系统研究了连续位相板对光束波前分布实现控制的机理。从CPP面形的概率密度与远场直方图之间的关系出发，推导了畸变波前通过CPP 后远场光强分布的表达式，从理论上解释了这种束匀滑器件的工作原理及特性。通过数值模拟计算了不同畸变光束经过CPP后的远场直方图，对结果进行比较并分析了不同面型特性对最终束匀滑效果的影响。结果证明:位相板能在焦斑光强上起到卷积滤波的作用，从而实现光束匀滑效果。从原理上解释了CPP 在具有小相关长度时具有更高匀滑效果这一特性，为实际面型设计和优化提供理论基础。另外，应用统计几何光学方法进行分析，可有效降低波前叠加分析的难度。

Influence of phase additive effect on beam smoothing character of continuous phase plate

During the operational process of high power laser system, the uniformity of focal spot will impact the experiment and application seriously. To improve the focal spot quality, a continuous phase plate (CPP) should be used in the light path for far field beam smoothing. As a phase element CPP has different functions, such as decoherece and beam shaping. In this paper the smoothing performance of CPP was concerned. Good performance of beam smoothing depended on a reasonable surface figure distribution. According to the random characteristic of phase plate surface, the statistical method was employed to study the beam smoothing mechanism. According to the relationship between the probability density and far field histogram of the surface of CPP, the expression of the superposition intensity envelope of distorted beam and CPP surface figure was deduced. The formula proved that the function of a CPP for focal spot was just a convolution filtering. So the mathematical explanation on the beam smoothing mechanism was achieved. Furthermore, using this analysis model the reason that the CPP with short correlation length will have the capability of better beam smoothing was explained theoretically. Numerical simulations were done to show the beam smoothing performance of CPP. The far field histograms with different distorted beams are calculated and compared. The results show that after the phase additive of the distorted beam and CPP a new wavefront was generated. If the law of large numbers is satisfied, when the correlation length and the gradient of the wavefront is small, the light focus spot distribution is smooth and uniform. The statistical geometrical optical method used in this paper can reduce the analysis difficulty on the phase additive effectively.