Abstract It is theoretically shown that the distribution of the average intensity of Gaussian optical vortex in the focal plane of a spherical lens scattered by random phase screen has the form of a ring with non-zero value on the optical axis. The radius of the ring depends on the topological charge of the optical vortex and the scattering power of the diffuser. Therefore the topological charge cannot be determined only by the radius of the formed ring. However, it can be determined by the number of points with phase singularity for which detection Shack–Hartmann sensor is used. It is also shown that when using a linear combination of two optical vortices than the distribution of the average intensity will have local maxima the quantity of which is equal to the difference of their topological charges. The number of these maxima does not depend on the degree of diffusion and can serve as an indicator for identifying an optical vortex. Numerical simulation and experiment confirm the theoretical conclusions.

中文翻译：

---

相位屏上衍射后光学涡旋拓扑性质的稳定性

摘要 理论上表明，随机相位屏散射的球面透镜焦平面内高斯光学涡旋的平均强度分布在光轴上呈非零值的环。环的半径取决于光学涡旋的拓扑电荷和漫射器的散射能力。因此拓扑电荷不能仅由形成的环的半径确定。但是，它可以通过使用检测 Shack-Hartmann 传感器的相位奇异点的数量来确定。还表明，当使用两个光学涡旋的线性组合时，平均强度的分布将具有局部最大值，其数量等于它们的拓扑电荷之差。这些最大值的数量与扩散程度无关，可以作为识别光学涡流的指标。数值模拟和实验证实了理论结论。