Comparing between zonal reconstruction algorithms and modal reconstruction algorithms in adaptive optics system

In this paper, the compensation effects of sub-aperture gradients of Hartmann-Shack wavefront sensor in an adaptive optics (AO) system with four different reconstruction algorithms were analyzed. A kind of optimal-gradient reconstruction algorithm was deduced from least-square (LS) reconstruction algorithm by consider the statistical characteristics of atmospheric turbulence and measurement noise. A kind of sensor-eigen (SE) modal reconstruction algorithm was deduced from LS reconstruction algorithm by orthogonalizing the statistical correlation matrix of drive voltages by means of singular value decomposition (SVD) method. Two kinds of zonal reconstruction algorithms, the LS reconstruction algorithm and the optimal-gradient reconstruction algorithm, along with two modal reconstruction algorithms, the Zernike modal reconstruction algorithm and the SE modal reconstruction algorithm, were compared together on a 61-element AO system working in atmospheric turbulence. Performances of the four reconstruction algorithms were calculated and analyzed in different work conditions. It is showed that zonal reconstruction algorithms can achieve better compensation, but the modal reconstruction algorithms can achieve better stability. Zonal reconstruction algorithms are suitable in general condition, but the modal reconstruction algorithm with ability of partial compensation will be better in lower signal-to-noise ratio (SNR) condition.