Error Analysis Of Segmented Primary Mirror And Research On Co-phasing Measurement

Large aperture telescope is great significance for astronomical research. To meet the needs of astronomical research, telescopes are required to have higher resolution and better detection capability. So effective diameter of the telescope has to be increased in order to have a clearer and further observation. However, the diameter cannot be infinitely increased due to the limits of glass materials, gravity deformation, manufacture, testing, research factors et al. Segmented primary mirror is the most effective method to increase the effective diameter. And it is also the trend of development of giant telescope. In this method, the primary mirror is composed of a series of hexagonal off-axis parabolic mirrors, which can be controled and adjusted separately Compared to monoliphic primary mirror telescope system, segmented primary mirror telescope has unique optical properties as the defocus errors and co-phasing errors are produced, and it is different in the design, manufacture, alignment, testing and other aspects. It has unique optical properties. So it is need to in-depth research of the relation between the errors of segmented mirrors and the near-field characters and the far-field characters of the segmented telescope, and determine the error tolerance of the segmented mirror, which provides the basis for the designing of segmented telescope. In this paper, aiming at 10 m diameters segmented telescope’s optical systems we do the researches as the following, the asphericity of segmented mirror with hexagon shape, the optical characteristics of the segmented telescope systems and the effect of various errors induced by segmented primary mirror, the detection of co-phasing error of segmented mirror etc.. The main contents are as as following:1. Numerical simulation model of segmented primary mirror was established, a detecting method of calculating the asphericity of segmented mirror with hexagon shape was proposed. Using the feature points combined with lagrange condition extreme, the asphericity calculation of the asymmetrical hexagon off-axis parabolic mirror in different central points is solved. Using this method, the nonlinearity problem is avoid when calculate the aspericity with least square method. This calculation method is reliable and high precision.2. The theoretical analytic expression of segmented mirror telescope was derived from the optical diffraction theory. In-depth research on the far-field optical characteristics of principal focus, the impact of piston error, tip-tilt error and gaps of segmented mirror on optical system was analyzed. We get it, the combined of piston error and tip-tilt error is the product of results with separately errors.3. According to the principle of geometrical optics, ray tracing mode of segmented primary mirror optical system was done. With this model the wave front aberration, point spread function, optical transfer function, Strehl ratio and other related information of system was obtained. The far-field optical characteristics of segmented telescope can been analysis with this model. This model is tested by simulation a monoliphic primary mirror telescope systems compare Zemax software.4. Numerical simulation experimental study was carried out on 10 m diameter segmented telescope. Combing theoretical analytic expression and ray-tracing simulation model, far-field characteristics of segmented primary mirror system was fully and extensively analyzed. In order to keep the Strehl ratio of segmented telescope optical systems large than 0.9(SR>90%), the piston error of segmented primary mirror is ? /40 ~ /30?P? ?? ? and the tip-tilt of segmented primary mirror is better in one times resolution of telescope( ?/ D). Some experiment about segmented telescope optical systems was carried on, the experimental results is consistent to theoretical calculation.5. Proposed a self-calibrating phase measurement method of segmented mirror. Based on the diffraction optical theory, the rectangular aperture with arbitrary position of entrance pupil would image at optical axis with symmetrical diffraction shape, and the image is symmetrical about optical axis,so the center of image can be calibrated as reference center. The relationship between interference peak value and phase error of adjacent segmented mirrors was derived. By measuring interference image peak position, the piston error and tilt error of segmented mirrors can be quickly measured with high accuracy. The theoretical equations have been proved by numerical simulation and their results are consisten.Theoretical analysis and experimental numerical simulation on large-diameter segmented telescope system were presented in the paper. The work provides a theoretical basis and data support for large-diameter segmented telescope system in our country. It also gives instructive suggestions on the design, manufacture, testing, and alignment of the telescope system.