Mafusire Cosmas, Krüger Tjaart P J
Appl Opt. 2017 Mar 10;56(8):2336-2345. doi: 10.1364/AO.56.002336.
The concept of orthonormal polynomials is revisited by developing a Zernike-based orthonormal set for a non-circular pupil that is transmitting an aberrated, non-uniform field. We refer to this pupil as a general pupil. The process is achieved by using the matrix form of the Gram-Schmidt procedure on Zernike circle polynomials and is interpreted as a process of balancing each Zernike circle polynomial by adding those of lower order in the general pupil, a procedure which was previously performed using classical aberrations. We numerically demonstrate this concept by comparing the representation of phase in a square-Gaussian pupil using the Zernike-Gauss square and Zernike circle polynomials. As expected, using the Strehl ratio, we show that only specific lower-order aberrations can be used to balance specific aberrations, for example, tilt cannot be used to balance spherical aberration. In the process, we present a possible definition of the Maréchal criterion for the analysis of the tolerance of systems with apodized pupils.
通过为传输像差非均匀场的非圆形光瞳开发一种基于泽尼克的正交归一化集合，重新审视了正交归一化多项式的概念。我们将此光瞳称为一般光瞳。该过程通过对泽尼克圆多项式使用格拉姆 - 施密特过程的矩阵形式来实现，并被解释为通过在一般光瞳中添加低阶多项式来平衡每个泽尼克圆多项式的过程，该过程以前是使用经典像差来执行的。我们通过比较使用泽尼克 - 高斯方形和泽尼克圆多项式在方形 - 高斯光瞳中相位的表示来数值演示这一概念。正如预期的那样，使用斯特列尔比，我们表明只有特定的低阶像差可用于平衡特定像差，例如，倾斜不能用于平衡球差。在此过程中，我们提出了一种可能的马雷夏尔判据定义，用于分析具有变迹光瞳的系统的容限。
