Solomon C J, Loos G C, Rios S
School of Physical Sciences, University of Kent, Canterbury, UK.
J Opt Soc Am A Opt Image Sci Vis. 2001 Jul;18(7):1519-22. doi: 10.1364/josaa.18.001519.
Common wave-front sensors such as the Hartmann or curvature sensor provide measurements of the local gradient or Laplacian of the wave front. The expression of wave fronts in terms of a set of orthogonal basis functions thus generally leads to a linear wave-front-estimation problem in which modal cross coupling occurs. Auxiliary vector functions may be derived that effectively restore the orthogonality of the problem and enable the modes of a wave front to be independently and directly projected from slope measurements. By using variational methods, we derive the necessary and sufficient condition for these auxiliary vector functions to have minimum-error norm. For the specific case of a slope-based sensor and a basis set comprising the Zernike circular polynomials, these functions are precisely the Gavrielides functions.
常见的波前传感器，如哈特曼传感器或曲率传感器，可测量波前的局部梯度或拉普拉斯算子。因此，用一组正交基函数来表示波前通常会导致一个线性波前估计问题，其中会出现模态交叉耦合。可以推导出辅助向量函数，这些函数能有效地恢复问题的正交性，并能从斜率测量中独立且直接地投影出波前的模式。通过使用变分方法，我们推导出这些辅助向量函数具有最小误差范数的充要条件。对于基于斜率的传感器和包含泽尼克圆多项式的基集的特定情况，这些函数正是加夫列利德斯函数。
