With the development of ground-based telescope systems, adaptive optics has become the necessary method to improve the resolution of telescopes by correcting the effects of atmospheric turbulence actively. An adaptive optical system can detect the distortion of the wavefront phase with real-time, and make relative compensations to it to improve the imaging quality. As the most widely used sensor in the field of wavefront detection, a Shack-Hartmann sensor uses a micro-lens array to sample the wavefront and calculate the slope of the local wavefront. Then, the purpose of wavefront detection and wavefront reconstruction can be achieved. Spot centroiding and offset estimation is the primary step of slope calculation, and its performance determines the accuracy of wavefront detection.
However, the estimation of the centroid offset is degraded by random noise of the detection device and discrete sampling inevitably, reducing the accuracy of the slope measurement.The application of sodium laser guide star technology poses a big challenge for the centroid estimation for its very low signal-to-noise ratio (SNR). Therefore, the purpose of this thesis is to find a suitable centroiding algorithm for point source spots of Shack-Hartmann sensor at low SNR condition.
This thesis starts with the digital image detection devices, and analyzes the noise model and signal model of Shack-Hartmann sensor spots, which is necessary for the simulation of centroiding algorithms. As the centroid estimation error increases with the decreasing of signal intensity as well as the increasing of noise level, this thesis proposes a SNR estimation theory of point source spots, in order to describe the relationship between centroid estimation error and SNR. Both methods of theoretical SNR calculation and SNR estimation of real spots are analyzed.
Secondly, this thesis presents a comprehensive review of multiple centroiding algorithms. These algorithms are divided into three categories, i.e. center-of-gravity based methods, registration based methods and Taylor-expansion based methods. The principles of these methods are introduced one by one, as well as their robustness, linearity and dynamic range. This paper analyzes the influence of threshold selection on traditional center-of-gravity method, and proposes a locally adaptive threshold segmentation method based on statistical ranking, which can eliminate the differences among sub-apertures and segment the spot more effectively.
Then, this thesis demonstrates a study on the spatial registration algorithm, which is less sensitive to uniform background. The influence of the reference spot’s amplitude and equivalent Gaussian width(EGW) on the performance of the four main criterion functions (including absolute difference function, square of absolute difference function, minimum mean square error function and cross-correlation function) are compared and analyzed firstly. It is found that the cross-correlation function is the most optimal criterion function for point source spots, which has good stability and anti-noise performance, suitable for low SNR centroid estimation. Secondly, this thesis compares several interpolation methods of sub-pixel obtaining, including the Equal-angular Line Fitting method, the parabolic interpolation method and the Gaussian interpolation method. We found that different criterion function has its own optimal interpolation method. For CCF, Gaussian interpolation method improves the accuracy of centroiding at high SNR conditions, but not at low SNR conditions where parabolic interpolation is a better choice. Considering the single peak of CCF, this thesis proposes combing fast search algorithms with CCF, which can decrease its calculation cost effectively. Fast search algorithms such as three step search, two-dimensional logarithm search, cross search and orthogonal search, can reduce more than 80% of the pixel level offset computational cost. This thesis also verifies the effectiveness of fast search strategy under low SNR condition through simulation experiments.
Finally, this thesis designed an experiment of aberration measurement, in order to verify the performances of algorithms. As the laser light source is strong, we adjust the intensity of spots collected by Hartmann by adjusting the power of laser source, changing the exposure time of the camera and adding attenuation tablets in the light path, in order to obtain spots under high SNR, middle level SNR and low SNR. Through the analysis of experiment data, this thesis firstly verifies the distribution and the statistical properties of digital noise. Then the performance of proposed local adaptive threshold selection method is verified. Considering the real-time performance, the anti-noise performance and the dynamic range of centroiding algorithms, we found that intensity weighted centre-of-gravity(IWC) method and cross-correlation method are more suitable for low SNR point source spots. therefore, these two methods are further tested under real experiments.
The experimental result shows that, the IWC method can effectively increase the accuracy of centroid estimation, comparing with traditional CoG method. However, with the decrease of SNR, the boundary between spots and their back noise is gradually blurred, and the optimal threshold selection becomes more difficult. And the accuracy of CoG based methods depends on the selection of optimal threshold. In contrast, the cross-correlation function method is not sensitive with the uniform background, depending less on the selection of optimal threshold.