Objective Shack-Hartmann wavefront sensors (SHWFSs) are widely used in the wavefront measurement of adaptive optics systems. Their detection accuracy directly affects the correction performance of the entire system. The optical path of light waves propagating in the atmosphere changes owing to atmospheric turbulence, resulting in wavefront aberrations. The influence of atmospheric turbulence distorts the laser wavefront, leading to the flicker and drift of the optical signal at the receiving end, which severely interferes with target detection. Atmospheric turbulence shows strong randomness and poor reproducibility. Therefore, it is necessary to conduct a numerical simulation of atmospheric turbulence distortion wavefront to study laser atmospheric transmission and the correction of adaptive optics systems. Second, to study and analyze the design, performance estimation, algorithm optimization, and other aspects of SHWFS, it is necessary to simulate various parts of SHWFS, including the entire process from the useful signal input to output. Our goal is to establish a digital simulation platform for SHWFS that is flexible, easy to adjust, easy for statistical analysis, and convenient to provide data for the optical system. Additionally, the simulation platform can analyze spot positioning and wavefront reconstruction errors under different distorted wavefronts and noises. Furthermore, it can examine and optimize optical system parameters and improve the detection accuracy and performance of the entire system.
Methods Because numerical simulation technology has the advantages of low cost, easy implementation, and repeated experiments, the simulation platform for SHWFS is established using this technology. The simulation platform for SHWFS involves three modules: wavefront generation, SHWFS detection, and wavefront reconstruction. Using the theoretical analysis of each module, the corresponding mathematical model is established to realize the simulation of each module. The Zernike polynomial method is used to generate a distorted wavefront conforming to the Kolmogorov turbulence statistical characteristics. Additionally, the random dynamic, static, and function-modulated wavefronts are generated using the Zernike polynomial method. Different spot location algorithms are used to achieve the position of the spot quickly and accurately under different signal-to-noise ratio conditions. Based on the requirements of the optical system, different wavefront reconstruction algorithms are selected to realize fast and accurate wavefront reconstruction. Finally, the correctness of the simulation platform is verified by comparing the simulation results with the theoretical results.
Results and Discussions The structure of the simulation platform for SHWFS includes the generation of the spot array image, spot positioning, and wavefront reconstruction. The generation of the spot array image includes wavefront generation, noise addition, sensor structure parameters, and light emphasis (Fig. 3). The control interface of the simulation platform for SHWFS is divided into three interfaces: control interface for wavefront simulations, control interface for spot positioning, and control interface for wavefront reconstruction (Fig. 4). Parameters can be set on the control interface as required. The added noise includes Gaussian, Poisson, salt and pepper, and special background noise. A single type of noise can be added or several types of noise can be superimposed based on actual requirements (Fig. 6). Figure 8 shows the verification of the statistical characteristics of the Kolmogorov turbulence. This figure shows that the simulated variance of the turbulent wavefront is consistent with the theoretical variance, which conforms to the statistical law of the Kolmogorov turbulence. The results of the spot positioning and wavefront reconstruction errors obtained using the thresholding center of gravity (T-COG) algorithm for spot positioning and the modal algorithm for wavefront reconstruction confirm the correctness of spot positioning and wavefront reconstruction (Figs. 9 and 10).
Conclusions The proposed simulation platform has the advantage of flexibility and changeability. It can also set and optimize the parameters of each part involved in the SHWFS detection process based on the requirements. The simulation platform contains five parts. The first part involves four types of distortion wavefront simulations. The second part involves the arbitrary selection of the superposition of multiple noises, mainly involving four types of noise: Gaussian, Poisson, salt and pepper, and special background noise. The third part consists of various subaperture structure simulations, which can automatically divide the detection area. The fourth part involves seven types of spot location algorithms commonly used in engineering, i.e., T-COG, thresholding weighted center of gravity, thresholding intensity-weighted centroiding, windowed thresholding center of gravity, windowed thresholding intensity-weighted centroiding, windowed thresholding weighted center of gravity, and cross-correlation. The final part involves the two types of wavefront reconstruction algorithms. When a special situation causes partial subaperture lack of light, the subaperture slope zero reconstruction and subaperture removal reconstruction methods can be adopted to handle this situation. The control interface of the SHWFS simulation platform is mainly divided into three interfaces: wavefront generation, spot positioning, and wavefront reconstruction. The control interface is simple and easy to operate. In this study, the SHWFS digital simulation platform is tested and test results show that the simulation platform can well characterize the statistical characteristics of the turbulent phase. Additionally, it can optimize the spot positioning algorithms and parameters based on the working environment of the adaptive optical system. It can also ensure the correctness of the wavefront reconstruction (the accuracy of the wavefront restoration error is 10 -2) and handle special cases of subaperture lack of light.
