Results and Discussions The method can effectively remove the noise of the spot array image and adapt to the change in light intensity. It does not need to dynamically adjust the parameters of the localization algorithm or train the centroid extraction model of the low-SNR sub-spot in advance according to the fluctuation characteristics of light intensity, which has the advantages of simple implementation, strong adaptability, and good robustness. The centroid localization accuracies and wavefront restoration errors of multiple sub-spot images in a single frame of sub-spot images and different near-field fluctuations (Figs. 5-10) are compared, and experiments confirm that the centroid detection error of the method in this paper is improved by more than 2 times, and the wavefront restoration residual is controlled below 0.045λ (Figs. 14-16).

The Shack-Hartmann wavefront sensor is widely used due to its advantages of simple structure, high utilization rate of light energy, and fast detection speed. In practical application scenarios, affected by factors such as skylight background, atmospheric turbulence intensity, return characteristics of beacon light, detector noise, etc., the spot array images collected by the Shack-Hartmann wavefront sensor often have uneven sub-aperture spot intensity distributions, with low signal-to-noise ratios (SNR). In this case, it is difficult to accurately extract the centroid of a light spot, and the detection accuracy of the wavefront decreases. To solve the localization problem of the sub-spots of spot array images with a low SNR, researchers have proposed several improved methods, such as the thresholding centroid method, weighted centroid method, intensity weighted centroid method, cross-correlation algorithm, frequency domain method, local adaptive threshold method, windowed thresholding centroid method, and windowed thresholding weighted centroid method. However, when the near-field light intensity of the beam to be measured fluctuates dynamically, and the detector noise, image background noise, and other interfering noise signals change dynamically, the effective optical signal and noise signal of a spot array image fluctuate in time and space. When the spot centroid is selected, the algorithm parameters need to be dynamically adjusted to ensure the centroid extraction accuracy of the sub-spot. This algorithm mechanism significantly increases the complexity of the centroid extraction algorithm, and there are also problems with optimal parameter selection and dynamic setting, which will eventually lead to a decrease in the wavefront restoration accuracy of the sensor.The efficient centroid extraction of the sub-spot when the near-field intensity of the incident beam dynamically fluctuates requires a centroid localization method for the low-SNR sub-spot image collected by the Shack-Hartmann wavefront sensor with high adaptability.

When the wavefront sensor collects the sub-spot image, the detector introduces signal photon noise, background photon noise and readout noise, etc., due to factors such as the environment and the quantum characteristics of the photodetector. According to the characteristics of detection noise, photodetector noise is generally represented by a Poisson-Gaussian model. In this model, the signal-related noise introduced by the quantum characteristics of the sensor is modeled by Poisson distribution, and the signal-independent noise is modeled by Gaussian distribution. According to the signal characteristics and noise characteristics of the photodetector, this paper proposes a method to extract the centroid of a sub-spot based on variance-stabilizing transformation (VST). It converts the Poisson-Gaussian noise that varies with the signal into Gaussian noise with a fixed variance. An improved block-matching and 3D filtering (BM3D) method, i.e., noise feedback block-matching and 3D collaborative filtering (NFBM3D), is used to remove the noise of the spot array image, and then sub-spot centroid extraction and wavefront restoration are performed.

Through simulation and experiments, it is confirmed that the method proposed in this paper can effectively extract the light spot signal data in the low-SNR spot array image collected by the Shack-Hartmann wavefront sensor. It can avoid noise interference in the image and fully improve the centroid localization accuracy and stability of the sub-aperture spot. Compared with the traditional adaptive threshold and other methods, this method can improve the centroid extraction and wavefront restoration accuracy by more than 2 times when the peak SNR of the sub-spot image is lower than 6. This algorithm is expected to meet the real-time requirements of the centroid extraction of the adaptive optics system after the accelerated processing of similar and fast search and matching.