Shack-Hartmann wavefront sensors calculate the position of focal spot in each sub-aperture from intensity distributions, the noises of the detector itself would have a certain impact on the detecting accuracy and would lead to inaccurate wavefront detections using conventional centroiding method. It has been demonstrated that the correlation algorithms with template matching is able to improve the accuracy. In this paper, several correlation algorithms such as absolute difference function, absolute difference function-squared, square difference function, cross-correlation function and normalized cross-correlation are compared at different signal-to-noise ratios. To further improve the accuracy, interpolation algorithms including equiangular line fitting, parabola interpolation, gauss interpolation and least square method are brought in, which turns out that least square method could minimize the detecting error. Besides, simulations within single aperture and full aperture both illustrate that cross-correlation function is most robust but needs more calculations, so is least square method. Moreover, although absolute difference function would be inaccurate at low signal-to-noise ratios, it still can obtain high detecting accuracy at high signal-to-noise ratios and it minimizes the calculations.
Adaptive optics (AO) systems have been used in many applications, such as ground-based astronomical telescopes for improving the resolution by counteracting the effects of atmospheric turbulence. However, the traditional AO system model is not good at dealing with noise interference in the closed-loop correction. Therefore, our paper proposes a subspace system identification method based on errors-in-variables to build an accurate dynamic model of the AO system from measurement data with closed-loop system identification. Experimental simulation results show that the root mean square of the residual wavefront is smaller than that of the traditional method, whether photon noise and camera readout noise exist or not. We conclude that the identified model has good accuracy and noise disturbance compensation ability to deal with dynamic wavefront correction compared with the traditional method.
Fresnel zone lens (FZL) telescope is attracting increasing attention owing to its small volume and light weight. However, depending on the fabrication method of FZL, the linewidth and etch depth of FZL may deviate from the set value. It must be considered that the performance of the FZL is influenced by aberrations generated during manufacture. We simulate the effect of fabrication errors on optical performance of FZL and find that the linewidth error of FZL structure is the main cause of image degradation. In addition, we provide a method for correcting aberrations of FZL telescope with adaptive optics system (AOS). This method is verified by the experimental system. The results show that the image resolution is successfully improved after AO correction. The full-width, half-maximum value of a far-field image is improved from 0.065 to 0.038λ. The peak value of image energy after correction has increased by 4.23 times.
We propose a projection-based decoupling algorithm for a woofer–tweeter (W–T) adaptive optics system. This algorithm uses the response matrix of woofer deformable mirrors (DM) to construct a slope-based orthogonal basis, which can be used to distribute different spatial frequency aberrations to the dual DMs. At the same time, to restrain the cross coupling between the dual DMs, the command vector of the tweeter will be projected onto the slope-based orthogonal basis, and then the portion of the tweeter’s command vector, which may generate opposite shape with the woofer can be calculated and eliminated accurately. Numerical simulation for this algorithm demonstrates that it can make the woofer and tweeter correct different spatial frequency aberrations simultaneously, and have more practical value compared with the traditional decoupling algorithm. Experimental results for this algorithm are consistent with the simulation results and proved that the cross coupling between the dual DMs can be restrained well for both static and dynamic aberrations.
Slab geometry is a promising architecture for power scaling of solid-state lasers. By propagating the laser beams along zigzag path in the gain medium, the thermal effects can be well compensated. However, in the non-zigzag direction, the thermal effects are not compensated. Among the overall aberrations in the slab lasers, the major contributors are two low-order aberrations: astigmatism and defocus, which can range up to over 100 microns (peak to valley), leading to detracted beam quality. Another problem with slab lasers is that the output beams are generally in a rectangular aperture with high aspect ratio (normally 1:10), where square beams are favorable for many applications. In order to solve these problems, we propose an automatic low-order aberration compensation system. This system is composed of three lenses fixed on a motorized rail, one is a spherical lens and the others are cylindrical lenses. Astigmatism and defocus can be compensated by merely adjusting the distances between the lenses. Two wave-front sensors are employed in this compensation system, one is used for detecting the initial parameters of the beams, and the other one is used for detecting the remaining aberrations after correction. The adjustments of the three lenses are directly calculated based on beam parameters using ray tracing method. The initial size of the beam is 3.2mm by 26mm, and peak to valley(PV) value of the wave-front is 33.07λ(λ=1064nm). After correction, the dimension becomes 40mm by 40mm, and peak to valley (PV) value of the wave-front is less than 2 microns.