Photon statistics in adaptive optics
Photon statistics in adaptive optics
复制标题
自适应光学中的光子统计
作者：
M. Cagigal;V. Canales
大气湍流引起的随机像差决定了地面望远镜的角分辨率。自适应光学系统在探测前补偿波前退化。虽然在波前传感器中具有大量子孔径和在可变形反射镜中具有大量致动器的系统提供最佳结果，但是它们复杂且昂贵。相比之下，更简单的自适应光学系统（每个大气相干直径小于一个致动器），部分补偿波前畸变，具有很大的潜在应用。利用Rician分布描述了部分补偿中像面光强的统计特性。为了更完整地描述这种现象，我们采用Rician分布的泊松变换描述了光子在整个图像平面上的统计特性。当没有补偿时，光子统计遵循玻色-爱因斯坦分布。在部分补偿中，PSF由亮核组成，其中光子统计遵循拉盖尔分布，被具有玻色-爱因斯坦统计的斑点晕包围。一些特殊情况进行了研究，并已推出有用的近似。理论计算结果与模拟值吻合较好。作为补偿的函数的光统计的这种描述可以用于提取关于对象的更多信息。
Random aberrations due to atmospheric turbulence determine the angular resolution of ground-based telescopes. Adaptive optics systems compensate the wavefront degradation before detection. Although systems with a large number of subapertures in the wavefront sensor and of actuators in the deformable mirror provide the best results, they are complicated and expensive. In contrast, simpler adaptive optics systems, (less than one actuator per atmospheric coherence diameter), compensate partially the wavefront distortions, having great potential application. The statistics of the image plane light intensity in partial compensation have been described using the Rician distribution. In order to achieve a more complete description of the phenomena, we describe the photon statistics in the whole image plane using the Poisson transform of the Rician distribution. When there is no compensation, the photon statistics follow a Bose-Einstein distribution. In partial compensation the PSF is composed by a bright core, where the photon statistics follow a Laguerre distribution, surrounded by a speckled halo with Bose- Einstein statistics. Some special cases have been studied and useful approximations have been derived. Theoretical results fit well with simulated values. This description of the light statistics as a function of the compensation may be used to extract more information about the object.