Research on diffraction effect of primary mirror in segmented telescope

The design of the segmented primary mirror makes an idea of the extremely large aperture telescope a reality. In order to study the imaging performance of the segmented telescope, the effect of the segmented primary mirror configuration, translation error, and tilt error on diffraction effect was precisely analyzed and quantified. Based on the imaging principle of the segmented optical system, the pupil models of the segmented primary mirror were established based on the homogeneous coordinate transformation. And the effect of the segmented primary mirror configuration on the diffraction effect was simulated and analyzed. The analysis results show that for the segmented primary mirrors with different configurations, the diffraction effect is affected by the fill factor and the aperture interval of the segmented primary mirror, the higher the fill factor, the smaller the aperture interval, and the better the system imaging quality. Taking the typical segmented primary mirror configuration as an example, the effect of the translation error and tilt error of the single sub-mirror and the overall translation error and tilt error of the segmented primary mirror on diffraction effect was simulated and analyzed, respectively. The analysis results show that for the single sub-mirror, the effect of the translation error on far-field diffraction is periodic. And for the overall segmented primary mirror, the Strehl ratio is higher than 0.95, when the root mean square of the sub-mirror piston error is less than 0.039λ, or the root mean square of the sub-mirror tip-tilt error is less than 0.036λ. The analysis results provide the basis for the imaging performance analysis of the segmented telescope, the configuration design of the primary mirror, and the detection and adjustment of the translation error and tilt error.