In the paraxial approximation a partially coherent beam can be characterized by its intensity moments. In the most general case a 3D beam has 10 second order moments, which describe the beam radii, far field divergences, radii of curvature, orientations in the near field and the far field, etc. The 10 second order moments can be written in a 4 $MUL 4 symmetric matrix, called the variance matrix. In first order optical systems the variance matrix obeys a simple propagation law. The unknown parameters of the second order moments are the twist parameters, which describe the rotation of the beam during propagation. The twist is directly related to the z-component of the intrinsic angular momentum flux of the field. The ten second order moments can be experimentally determined by measuring the intensity of the beam in a reasonable number of positions around the focal region and measuring the beam twist.
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机译：在近似近似下，部分相干的光束可以特征在于其强度时刻。在最常规的情况下，3D光束具有10秒的阶段，它描述了光束半径，远场分歧，曲率的曲率半径，近场和远场的方向等。10秒钟可以写入10秒的瞬间4 $ MUL 4对称矩阵，称为方差矩阵。在一阶光学系统中，方差矩阵遵守一个简单的传播法。二阶矩的未知参数是扭曲参数，其描述了传播期间光束的旋转。扭曲直接与该领域内在角动量通量的Z组分相关。通过在焦点区域周围的合理数量的位置测量光束的强度并测量光束扭转，可以通过测量梁的强度来实验确定十个阶矩。
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