Hartmann test with minimum apertures for retrieving the atmospheric primary aberrations

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.