Research On Sparse Resconstruction Of Atmospheric Turbulence Distorted Wavefront Signals

In order to overcome the interference of atmospheric turbulence,avoid the degradation of astronomical images observed by Ground-based telescopes and improve the observation resolution of telescopes,large ground-based astronomical telescopes are gradually equipped with adaptive optical systems in astronomical imaging observation.As an indispensable part of adaptive optical system,wavefront sensor can measure the dynamic errors of atmospheric turbulence wavefront in real time and it is one of the key components of adaptive optical system.Shack-Hartmann wavefront sensor?SHWFS?is a commonly used wavefront sensor.It can measure the distortion wavefront signals of atmospheric turbulence by measuring the phase gradient change of atmospheric turbulence with an array of small lenses in real time.Therefore,the measurement and reconstruction of wavefront phase gradient signals have important theoretical and practical significance.In the traditional measurement and processing framework of atmospheric turbulence distorted wavefront signals,the signals will not be destroyed in the transmission process when the sampling frequency of the signals satisfies the Nyquist sampling theorem,and then the acquisition,transmission,storage and recovery of the signals can be completed.With the increase of the aperture of astronomical optical telescope and the improvement of imaging resolution,higher requirements are put forward for atmospheric turbulence wavefront measurement system.Therefore,compressed sensing technology is applied to measurement and reconstruction of atmospheric turbulence wavefront phases.Compressed sensing technology used in atmospheric turbulence wavefront gradient measurement can greatly reduce the number of wavefront gradient measurements,while reducing the hardware pressure of the wavefront measurement system.Compared with the existing methods of wavefront gradient measurement,the method of compressed sensing wavefront measurement increases the reconstruction process from sparse measurement value of wavefront gradient to wavefront gradient signal.In order to meet the requirements of real-time measurement of wavefront signals,the fast and high-precision wavefront gradient reconstruction algorithms is needed firstly when compressed sensing technology is applied to wavefront measurement.Smoothed l₀ Norm?SL0?algorithm is an optimal iterative reconstruction algorithm with approximate l₀ norm estimation.It is more in line with the requirements of phase gradient reconstruction of atmospheric turbulence wavefront because it does not need to know the sparsity of the signal in advance,it has low computational complexity and high reconstruction accuracy.Based on the SL0 algorithm,this paper implements a regional parallel algorithm-Block-Smoothed l₀ Norm?B-SL0?algorithm which measures the wavefront gradient signals in a subarea and parallel operations.The theoretical analysis and simulation results show that B-SL0 is superior to other existing reconstruction algorithms in computing time and accuracy,and prove the feasibility of applying compressed sensing technology to atmospheric turbulence wavefront measurement preliminarily.SL0 algorithm is a one-dimensional reconstruction algorithm,and the atmospheric turbulence wavefront gradient signal is a two-dimensional signal.When reconstructing a two-dimensional signal,the two-dimensional signal is usually converted into a one-dimensional signal,which will not only destroy the internal structure of the signal,but also increase the computational complexity and storage space.In this paper,two-dimensional reconstruction of two-dimensional signals is realized directly,and the Two-dimensional Newton Smoothed l₀ Norm?2D-NSL0?algorithm is proposed.In this algorithm,the hyperbolic tangent function is used to approximate the l₀ norm and the modified Newton direction is used as the search direction,which improves the reconstruction accuracy of the algorithm and reduces the running time and the use of memory.Compared to the one-dimensional reconstruction algorithms,the speed and accuracy of 2D-NSL0 algorithm are improved under the same conditions.