The aim of this paper is to describe and demonstrate what should be done to the measured Zernike coefficients when conjugating the pupil and wavefront sensor planes with a ${4}f$ system. I provide theoretical and experimental evidence. The experimental setup consisted of two ${4}f$ systems of magnifications 1 and 1/3 with their corresponding wavefront sensors at their ends. Spherical and cylindrical trial lenses were measured. In addition, I measured a phase plate with high-order aberrations. I show that the Zernike coefficients of the wavefront expansion at two planes conjugated by a ${4}f$ system are related independently of the magnification of the ${4}f$ system by the following equation: ${b_i} = {(- 1)^{n}}{a_i}$, with $n$ being the order of the radial Zernike polynomial.

中文翻译：

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使用4 f系统将光瞳和波前传感器平面共轭时，应对测得的Zernike系数进行哪些处理：讨论

本文的目的是描述和演示在使用$ {4} f $系统将光瞳和波前传感器平面共轭时，对测得的Zernike系数应采取的措施。我提供理论和实验证据。实验装置由两个放大率分别为1和1/3的$ {4} f $系统组成，两端分别具有相应的波前传感器。测量了球形和圆柱形试验镜片。另外，我测量了具有高阶像差的相位板。我表明，在由一个共轭的两个平面波前膨胀Zernike系数$ {4} F $系统独立的倍率的有关$ {4} F $系统由下面的等式：$ {b_i} = {（ -1）^ {n}} {a_i} $，其中$ n $是径向Zernike多项式的阶数。