Large-scale wave-front reconstruction for adaptive optics systems by use of a recursive filtering algorithm

We propose a new recursive filtering algorithm for wave-front reconstruction in a large-scale adaptive optics system. An embedding step is used in this recursive filtering algorithm to permit fast methods to be used for wave-front reconstruction on an annular aperture. This embedding step can be used alone with a direct residual error updating procedure or used with the preconditioned conjugate-gradient method as a preconditioning step. We derive the Hudgin and Fried filters for spectral-domain filtering, using the eigenvalue decomposition method. Using Monte Carlo simulations, we compare the performance of discrete Fourier transform domain filtering, discrete cosine transform domain filtering, multigrid, and alternative-direction-implicit methods in the embedding step of the recursive filtering algorithm. We also simulate the performance of this recursive filtering in a closed-loop adaptive optics system

Fast wave-front reconstruction by solving the Sylvester equation with the alternating direction implicit method

Large degree-of-freedom real-time adaptive optics (AO) control requires reconstruction algorithms that are computationally efficient and readily parallelized for hardware implementation. In particular, we find the wave-front reconstruction for the Hudgin and Fried geometry can be cast into a form of the well-known Sylvester equation using the Kronecker product properties of matrices. We derive the filters and inverse filtering formulas for wave-front reconstruction in two-dimensional (2-D) Discrete Cosine Transform (DCT) domain for these two geometries using the Hadamard product concept of matrices and the principle of separable variables. We introduce a recursive filtering (RF) method for the wave-front reconstruction on an annular aperture, in which, an imbedding step is used to convert an annular-aperture wave-front reconstruction into a squareaperture wave-front reconstruction, and then solving the Hudgin geometry problem on the square aperture. We apply the Alternating Direction Implicit (ADI) method to this imbedding step of the RF algorithm, to efficiently solve the annular-aperture wave-front reconstruction problem at cost of order of the number of degrees of freedom, O(n). Moreover, the ADI method is better suited for parallel implementation and we describe a practical real-time implementation for AO systems of order 3,000 actuators

Long-period ground motion effect in Shaanxi Province of Changning Ms6.0 earthquake

At 22:55 on June 17, 2019, an earthquake of magnitude 6.0 occurred in Shuanghe Town, Changning County, Yibin City, Sichuan Province. In Shaanxi Province, the obvious earthquake sense appeared in some places which are 600 km to 800 km away from the epicenter. Based on the collection, collation and analysis of the data about Weihe Basin, Hanzhong Basin and Ankang Basin in Shaanxi Province, and the analysis of representative seismic network records and seismic wave propagation distance in each basin, the mechanism of the long-period disaster induced by the Changning Ms6.0 earthquake in Shaanxi Province is revealed. This study has a positive significance for the seismic fortification of long-period structures in this area, the scientific popularization of long-term ground motion effect, and the avoidance of earthquake panic