Sparse Representataion Of Atmospheric Turbulence Distortion Wavefront And Its Application

During the observation of the astronomical telescope,the disturbance of the atmospheric turbulence and noise will obscure the observed image and reduce the resolution of the image.For this reason,most of the existing large-scale ground-based telescopes are equipped with adaptive optics,in which the wavefront sensor measures the distortion wavefront caused by atmospheric turbulence in real time.As the aperture of the telescope increases,the hardware requirements for the wavefront sensor are also increasing.Using compressed sensing technology to compress and measure the atmospheric turbulence distortion wavefront can greatly reduce the amount of measurement data,effectively reduce the data transmission and storage pressure,facilitate the real-time measurement of atmospheric turbulence distortion wavefront,and alleviate the hardware of the wavefront sensor.The primary condition for the measurement of atmospheric turbulence distortion wavefront compression is that the atmospheric turbulence distortion wavefront signal is sparse or can be expressed sparsely in a transform domain.Therefore,the sparse representation of the wavefront signal has important research significance and is the precondition for the measurement of atmospheric turbulence distortion wavefrontcompression.According to the atmospheric turbulence power spectrum,the distortion wavefront power spectrum has the characteristics of low-frequency components,which is consistent with the requirements of signal sparse representation.In the adaptive optics system,the gradient of the distorted wavefront is measured using a Hartmann wavefront sensor,and the distortion wavefront can be recovered by the gradient.According to the physical characteristics of atmospheric turbulence,the wavefront gradient of atmospheric turbulence distortion is sparsely decomposed.Through the golden section method,the frequency sampling interval increases with the increase of frequency,and a non-uniform frequency point is obtained.The wavefront sparse dictionary is established by using frequency points to realize the sparse representation of the distortion wavefront slope at low sparsity.In this thesis,the power spectrum inversion method is used to simulate the atmospheric turbulence,the wavefront distortion is consistent with the theory.The distorted wavefront gradient in the X,Y direction is sparsely represented.The simulation results show that the sparse dictionary built in this paper can achieve better sparse representation of distortion wavefront gradient at low sparseness than Fourier dictionary,discrete cosine dictionary and Zernike dictionary.Sparse dictionary establishment is a priori condition for implementing distortion wavefront gradient compression sampling.The Gaussian random matrix samples and compresses the distortion wavefront gradient,and the reconstructed wavefront gradient obtained by iterative weight least squares method through the compressed gradient data.Simulation experiments show that under low sampling conditions,the sparse dictionary obtained by the golden section method is closer to the original data than the other sparse dictionary,and the reconstruction performance is good.In order to verify the universality of the sparse dictionary,the scale and turbulence intensity of the distortion wavefront were changed and the experimental results were consistent with the theoretical analysis.Image restoration technology based on wavefront sensing is a post-image correction method.The reconstructed image is obtained by deconvolution method by measuring the atmospheric turbulence distortion wavefront and the degraded image disturbed by the turbulence in real time.In this paper,the data of the wavefront is compressed and measured toreduce the amount of data for transmission,and the distortion wavefront is obtained later.Then,the point spread function corresponding to the distorted wavefront is used to realize the fuzzy image restoration by the method of deconvolution from wavefront sensing,which provides a method for the post-event recovery technology of the image.