ABSTRACT The present study aimed to evaluate the ability of the 4- and 8-aperture Hartmann method to calculate atmospheric primary aberrations. In the 4-aperture Hartmann screen, the holes can be located at the entrance pupil of a telescope in two configurations such as cross shape and X shape. The results of simulation indicate that the atmospheric defocus aberration can be measured correctly for both cross and X configurations, due to the intrinsic symmetry of defocus aberration. On the other hand, the astigmatism aberration is calculated correctly in the cross configuration, although it is associated with a high error in X configuration. The X configuration provides the astigmatism aberration with a good degree of accuracy while the cross configuration fails to measure the astigmatism . Matching aperture locations with the wavefront shape of these aberrations is regarded as one of the reasons for the errors in measuring astigmatism aberrations with two states of 4-apertures arrangement. The astigmatism aberration in the cross configuration places the apertures at the highest point of phase deviation. In addition, this mode is observed for astigmatism in X configuration. Based on the results, an optimal design of the mask with the appropriate place for apertures is required to measure two astigmatisms correctly. The combination of two 4-aperture cross and X configurations results the eight-aperture configuration, which has the most overlap with the deviation of two astigmatism phases. The results of simulation were evaluated experimentally at the site of the Iranian National Observatory, in which the compatibility of experimental results confirmed the accuracy of simulations.

中文翻译：

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用于检索大气主要像差的最小孔径哈特曼测试

摘要 本研究旨在评估 4 孔和 8 孔哈特曼方法计算大气初级像差的能力。在4孔径哈特曼屏幕中，孔可以以十字形和X形两种配置位于望远镜的入瞳处。模拟结果表明，由于散焦像差的内在对称性，可以正确测量十字和 X 配置的大气散焦像差。另一方面，像散像差在交叉配置中计算正确，尽管它与 X 配置中的高误差相关。X 配置提供具有良好精度的散光像差，而交叉配置无法测量散光。将孔径位置与这些像差的波前形状相匹配，被认为是两种4孔径排列状态的散光像差测量误差的原因之一。交叉配置中的像散像差将孔径置于相位偏差的最高点。此外，在 X 配置中观察到这种模式的散光。根据结果​​，需要对具有适当孔径位置的掩模进行优化设计，以正确测量两个散光。两个 4 孔交叉和 X 配置的组合产生了八孔配置，其与两个散光相位的偏差重叠最大。模拟结果在伊朗国家天文台现场进行了实验评估，