Research On The Co-Phasing Technologies Of Segmented Mirror Telescope

Since its birth,the telescope has helped mankind make a significant contribution to the exploration of the unknown Universe.With the increasing demand for deep space and/or dim target detection,the need for large-aperture telescopes by scientific community becomes more and more urgent.Traditionally,the monolithic primary mirrors are utilized to construct the large-aperture optical telescopes,however,its development is seriously limited by various practical factors,such as,mirror processing,detection,loading,transportation,cost,and et.al.At present,the largest single-mirror telescope is at 8m level.Since the concept of segmented mirror was put forward in 1980 s,the segmented telescope has been favored by astronomers,and has become a promising choice for the construction of the next generation large optical telescopes.Up to now,there have been many segmented telescopes operating stably in the world.In order to achieve the same imaging power as that for the equivalent large aperture mirror,the coplanar error of each sub-mirror must be corrected.Compared with the tip/tilt error,it is more difficult to measure the piston error.Therefore,the measurement technology of piston error becomes the key to the development of the segmented telescope.This thesis focuses on the co-phasing technology of segmented telescope.Aiming at the co-phasing technology based on the broadband far-field distribution rooting from two-segment aperture with piston-error modulation,the research works are carried out and listed as follows:Firstly,based on the theory of mathematical statistics,the statistical laws of the mean value and variance of the segmented wavefront with piston error or tip/tilt error are calculated analytically for the first time.The results show that the mean value of the segmented wavefront with only piston error obeys Gaussian distribution,and the variance obeys the Gamma distribution;at the same time,the mean value of the segmented wavefront with only tip/tilt error is identically equal to zero,and the variance also obeys the Gamma distribution.Meanwhile,the statistical characteristics of the center of gravity for the far-field distribution corresponding to these two cases are analyzed analytically.On the basis of obtained statistical characteristics of the segmented wavefront and with Maréchal approximation,the ensemble-average characteristics of Strehl ratio for these two kinds of misalignment errors are also obtained.Especially for tip/tilt error,its result is with extended applicable range and stronger universality.Secondly,the non-iterative orthogonalization process is generalized to segmented pupil,with which the orthogonal polynomials defined on the segmented pupil could be derived.Taking two segmented pupils,Keck-type and GMT-type,as examples,the corresponding orthogonal polynomials are calculated analytically.Considering the active correction ability of each sub-aperture in segmented pupil,the ability of compensating global aberration modes with active motions of sub-aperture is also analyzed.The results show that the global piston and tip/tilt aberrations could be fully compensated by the active rigid motions of sub-aperture.And this result provides the theoretical basis for analyzing the segmented wavefront.Then,through the theoretical and simulation analysis,the broadband/narrow-band co-phasing algorithm is studied.The optical transfer function for incomplete circular pupil,which is a kind of special aperture appearing in the broadband/narrow-band algorithm,is analytically calculated.Based on the derived analytical expressions,two elegent properties,including the finite supported set region and the peak position for sidelobe as a function of gap ratio,are studied.The evolution rule of far-field pattern for equivalent aperture with physical gap and decenter error in narrow-band algorithm is analyzed by simulation experiment.The possibility of narrow-band co-phasing by taking the far-field patterns stemming from the ideal circular pupil without gap and decenter error as the templates is also analyzed.The results show that when the gap ratio and decenter ratio are not greater than 0.3,the co-phasing could be realized by directly ultilizing the ideal template to correlate the far-field subimage in question corresponding to the non-ideal circular pupil.In addition,a merit-function-based broadband co-phasing algorithm via piston sweep is proposed.The algorithm makes full use of the active actuation ability of the sub-mirror,and within the effective stroke range,the merit function value for corresponding far-field pattern for each scanning step is evaluted,then the piston error can be obtained by processing the merit-functionvalue data.There is no need for the operations relevant to the template as that in the traditional realization,so it is much simpler and of great convenience.Moreover,it exhibits high measurement accuracy.Finally,the dispersed fringe sensor is studied.A visibility enhancement method is proposed to improve the visibility of dispersed fringe pattern.The results show that the visibility of dispersed fringe patterns corresponding to different piston errors in the whole capture range can be dramatically increased to 1.In view of the shortcomings of traditional methods of extracting piston errors from dispersed fringe pattern,a coarse co-phasing method based on the global average slope of dispersion fringes is proposed.The results show that the method can effectively sense the piston errors,and after active correction,the residual piston is well within the fine co-phasing capture range,and it exhibits strong robustness to noise.To overcome the limitation that the traditional dispersed fringe sensor is merely suitable for point target,the research of extendedscene-based dispersed fringe sensor on the foundation of the proposed slope-based coarse co-phasing method is carried out.A merit-function-based co-phasing sensing method based on active scanning is introduced to solve the problem of low signal-tonoise ratio of dispersed fringe pattern.The results show that the method shows strong noise robustness.In order to solve the problem of spatially overlapping fringes in the traditional dispersed fringe sensor,a digital dispersed fringe sensor based on a tunable optical filter is proposed.In this scheme,which is easy to operate and convenient to realize,the dispersed fringes are generated mainly by the algorithm to avoid the use of specialized dispersed element array.The above research can provide theoretical and practical guidance for the further development of segmented mirror technology.