Research On The Correlation Algorithm For Extracting Wavefront Error Of The Extended Target

It is usually use correlating Shack-Hartmann wave-front sensor to detect the phase aberration of extended targets in solar adaptive optics system.The correlating ShackHartmann wave-front sensor is one of the most important components of adaptive optics system,and its detection capability affects the performance of adaptive optics system.Therefore,the performance,accuracy and applicability of the wave-front slope algorithm directly affect the performance of the adaptive optics system.In this dissertation,we focus on the research of the correlation algorithm for extracting the wave-front error of extended target.The main contents of this paper include the introduction and physical meaning of correlation algorithms,theoretical derivation and experimental results of measurement error of cross-correlation algorithm,performance comparison and experimental results of difference correlation algorithms,research and exploration of general interpolation method,performance comparison and experimental results of correlation algorithm and optimal threshold centroid algorithm and so on.Firstly,the measurement error of cross-correlation algorithm is analyzed by using the thresholding centroid algorithm.Different from the existing theoretical error model in some other literatures,the theoretical error model of displacement measurement error we build not only related to the SNR of reference image,the contrast of reference image,the size of reference image,the half width at half maximum of cross-correlation function and the image sampling condition,but also realted to the threshold value used in the thresholding centroid algorithm.By using the actual acquisition of different contrast extended target,the theroethical results were calculated and compared with the actual measurement results.The results show that the theoretical results obtained by the theoretical model are in good agreement with the actual results,and are applicable to any image sampling conditions and any contrast extended targets(include the high contrast target,like sunspot),the theoretical model is more general than the model in the literature.Secondly,we giving theoretical deduction and analysis of accuracy of measurement based on parabolic interpolation and then using mean squared error to evaluate the solar granule images collected from real scene to validate the two difference algorithms(Absolute Difference Function and Absolute Difference Function-Squared).The results show that correlation function of absolute difference function-squared better accord with parabolic distribution than absolute difference function.At the same time,a more general interpolation curve method is proposed by using the polynomial interpolation curve method,and then we have discussed the theoretical formula,the physical meaning,the approximate formula and the application scene of this method in detail,which could effectively improve the measurement accuracy of correlation algorithms.By using the general interpolation curve method,the results show that the absolute difference algorithm and the absolute difference square algorithm can all achieve higher measurement accuracy when selecting the optimal interpolation curve method.Thirdly,the comparsion of cross-correlation algorithm,square difference algorithm,absolute difference algorithm and absolute difference-squared algorithm with different sub-pixel interpolation methods were compared and analyzed based on different resampling images.The results show that the accuracy of the correlation algorithm is affected by the sub-pixel interpolation curve method and the size of reference image.At the same time,the measurement accuracy of Shack-Hartmann wavefront sensor with different resolutions are also compared with different contrast targets.The results show that for different contrast extended targets,we can choose an appropriate resolution wave-front sensor to get better measurement accuracy.Finally,the measurement error of correlation algorithm and optimal thresholding centroid algorithm are deduced and analyzed based on the Gaussian spot model.The measurement accuracy of the two algorithms are verified with the actual spot(the Full width at half maximum is greater than 20pixels).The final analysis and experimental results show that when the spot energy is high(high signal to noise ratio),the correlation algorithm and optimal thresholding centroid algorithm have the same measurement accuracy,when the spot energy is low(low signal to noise ratio),the correlation algorithm is superior to the optimal thresholding centroid algorithm.In summary,the correlation algorithms are widely used in solar adaptive optics,its accuracy directly affects the accuracy of wavefront sensor.The discussion of the correlation algorithms not only helps us to improve the measurement accuracy of wavefront sensor,but also helps to improve the correction effect of adaptive optics.