McDonald Observatory, University of Texas at Austin, 1 University Station C1402, Austin, Texas 78712, USA.
Opt Lett. 2010 Jul 1;35(13):2173-5. doi: 10.1364/OL.35.002173.
An efficient way of estimating orthonormal aberration coefficients on variable noncircular pupils is proposed. The method is based on the fact that all necessary pieces of information for constructing orthonormal polynomials (via the Gram-Schmidt process) can be numerically obtained during a routine least-squares fit of Zernike polynomials to wavefront data. This allows the method to use the usual Zernike polynomial fitting with an additional procedure that swiftly estimates the desired orthonormal aberration coefficients without having to use the functional forms of orthonormal polynomials. It is also shown that the method naturally accounts for the pixelation effect of pupil geometries, intrinsic to recording wavefront data on imaging sensors (e.g., CCDs), making the coefficient estimate optimal over a given pixelated pupil geometry. With these features, the method can be ideal for real-time wavefront analysis over dynamically changing pupils, such as in the Hobby-Eberly Telescope (HET), which is otherwise inefficient with analytic methods used in past studies.
提出了一种在可变非圆形光瞳上估计正交像差系数的有效方法。该方法基于这样一个事实，即在通过 Gram-Schmidt 过程构建正交多项式的过程中，可以在对波前数据进行常规的 Zernike 多项式拟合的同时，通过数值方法获得构建正交多项式所需的所有信息。这使得该方法可以使用通常的 Zernike 多项式拟合，并结合一个额外的过程，该过程可以快速估计所需的正交像差系数，而无需使用正交多项式的函数形式。还表明，该方法自然考虑了成像传感器（例如 CCD）上记录波前数据时固有的光瞳几何图形的像素化效应，从而使系数估计在给定的像素化光瞳几何图形上是最优的。利用这些特性，该方法可以非常适合在动态变化的光瞳上进行实时波前分析，例如在 Hobby-Eberly 望远镜（HET）中，而过去研究中使用的分析方法在这方面效率低下。
