光束高阶矩传输特性的矩阵表示

Propagation Characteristics of Beam Higher-Order Moments by Using Matrix Formulae

给出了用维格纳分布函数（WDF）定义的光束高阶矩传输特性的矩阵表达式，其中考虑了大气湍流和光学系统对光束高阶矩传输特性的影响。研究结果表明：光束的四阶矩阵与两个湍流参数Tμ和Tμ′有关，光束的三阶矩阵和二阶矩阵只与一个湍流参数Tμ有关，而光柬的一阶矩阵与湍流无关。该光束高阶矩传输特性的矩阵表达式具有一般性，即光束通过Kolmogorov湍流、非Kolmogorov湍流、光学系统以及自由空间中传输的光束高阶矩传输特性的矩阵表达式均可作为特例得到。这种光束高阶矩传输特性的矩阵表达式形式简洁、物理含义明确，具有重要的理论和实际应用意义。

The matrix formulae of beam higher-order moments through an optical system in atmospheric turbulence are derived by using the Wigner distribution function （WDF）. It is shown that the fourth-order moment matrix depends on two turbulence parameters Tμ and Tμ, the third-order and the second-order moment matrixes depend on only Tμ, and the first-order moment matrix is independent of turbulence. The results obtained in this paper are general, for example, the matrix formulae of beam higher-order moments through Kolmogorov turbulence, non- Kolmogorov turbulence, optical system or free space can be given as special cases. The advantages of matrix formulation are that the expressions for higher-order moments are brief, and the physical meanings of higher-order moments are clear. The results obtained in this paper are of considerable theoretical and practical interest.