Co-phasing Of The Segmented Telescope And Image Retrieval Based On Phase Diversity Algorithm

In order to pursuit the higher resolving power and observation ability, the telescopes have been developing toward systems with long focal length, large diameter in recent years. The current large telescopes can be divided into two categories: single primary mirror telescope and segmented primary mirror telescope. For now, more than 30 telescopes with a diameter larger than 4 meters have been built. However, there are great challenges in the mirror materials preparation, processing and testing, the support structure, transport emission or cost to build single primary mirror telescopes with ten meters or even tens of meters diameter by using the existing technologies. The appearance of segmented telescope greatly reduces the quality of the primary mirror, processing costs and manufacturing cycle. All the sub-mirrors can be transmitted to the designated orbit, then assembly or expand on-orbit which greatly reduce the cost and difficulty of transport and emission. However, utilizing smaller sub-mirrors to form a large diameter telescope still faces a series of technical challenges. The most difficult problem is the co-phasing of all the sub-mirrors. Researchers believe that the total RMS error on the phase of segmented mirror must be less than 30 nm for the segmented primary mirror to achieve the same optical performance equivalent to those of a monolithic mirror. The traditional mechanical alignment method cannot provide high enough precision, so it is necessary to build active optics system and applied to the co-phasing of the segmented large-diameter telescope. Based on the needs of building segmented large-diameter telescope, this paper is carried around the key issues of co-phasing the segmented mirror and image recovery, the main research work are summarized as below:1. Study on the main mission of the active optics system for segmented large-diameter telescope, system configuration, wavefront sensing process and key technologies. For the segmented telescopes to reach the diffraction limit imaging quality, active optics system needs to be established rather than relying on traditional mechanical alignment. Active optical system contains a wavefront sensing system, pose solver system and pose adjustment system. The process of wavefront sensing includes crude confocal, segment identification and search, coarse and fine co-phase.2. Research and comparison of a variety of wavefront detection technology, and ultimately determine using the phase diversity algorithm as the fine co-phase correction method. To achieve large-scale, high-precision wavefront detection, wavefront sensing system uses a hierarchical detection, gradual convergence strategy. It first utilizes such as Shack-Hartmann sensor and the dispersive fringe sensing to process coarse co-phase correction. Since the phase diversity method has many advantages such as high accuracy, applicable to both point source and extended scenes and can detect both the continuous wavefront aberration and discontinuous phase errors, the optical path is also very simple, it is used as the fine co-phase correction method.3. Utilize Matlab to complete the establishment of segmented optical telescope model. Compare different numerical optimization algorithms during solving the co-phase errors based on phase diversity method, such as genetic algorithm, conjugate gradient method, and limited memory BFGS algorithm. Due to good numerical performance and fast convergence characteristics, BFGS algorithm is chose for solving co-phase error coefficients.4. The conventional BFGS method has a good global convergence for convex functions; however, when the cost function is non-convex, the solution will fall into local minimums, which leads to the failure of reconstructing the wavefront. Aimed at this problem, a modified BFGS method which has fine global convergences for both convex and non-convex functions is presented, guarantees that the solutions will converge to the global minimum, corresponding to the actual wavefront coefficients.5. As phase diversity algorithm is a wavefront detection method based on detected images, which are inevitably contaminated by photon noise and CCD readout noise, it will lead to the decline of wavefront detection accuracy and image recovery quality. Aimed at this problem, an effective regularization parameter estimate strategy is proposed to improve the noise tolerance of the algorithm.6. Analyze the errors that may encounter during practical applications of wavefront detection based on phase diversity method, including focal plane position error, uncertainty of defocus amount, image alignment error, exposure delay and image noise, etc. Methods to eliminate these impacts through modifying the phase diversity algorithm are presented, which can vastly improve the wavefront detection accuracy without other auxiliary correction strategies and can provide important technology support for the usage of phase diversity wavefront detection technology in practical engineering.7. Aimed at the high computational complexity and possible convergence to local optima of the classic phase diversity, a real-time wavefront detection algorithm is proposed. It utilizes the iterative linearization of OTFs in at least two diversity planes to establish a direct linear relationship between the collected images and unknown wavefront aberration, and then solve the wavefront aberration by using the LS estimator to achieve high accuracy real-time wavefront correction.8. Design viable experiment protocols and build optical test platform to verify the feasibility and correctness of the algorithm based on the specific condition of the progress of the project.