基于CCD探测器的点目标成像平均半径误差分析及最优阈值选择
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摘要
在反射式望远镜系统误差校正过程中,常以点目标的清晰度函数作为成像质量的评价指标。通过优化算法对存在误差的参量进行校正,使清晰度函数达到极值。平均半径作为点目标成像的清晰度函数由于具有适用范围大、动态特性好的特点而得到广泛的应用。然而,在实际工作过程中,由于探测器噪声等因素的影响,平均半径计算值与理论值存在一定的偏差,从而对校正过程产生影响。对噪声下平均半径的计算误差以及阈值对误差的影响进行了理论和仿真分析,结果表明存在最优阈值使计算误差达到最小,并对不同噪声强度下仿真的最优阈值数据进行拟合,给出了最优阈值拟合公式,分析表明该公式能够较准确的计算最优阈值。
In the process of error correction based on reflecting telescope system, definition function of spot target is usually used as performance metric of imaging quality. The definition function will reach extremum by using optimization algorithm to correct parameter error. Mean radius as definition function of spot diagram is widely used for its large-scale and good dynamic property in correction. While the value of mean radius of calculation is different from the value of theory because of the noise of detector, thus the correction process is affected. The calculation error of mean radius because of noise and the influence of threshold is analyzed through theory and simulation.The result indicates that there exists an optimal threshold to make the error minimum. A fitting formula is proposed by the simulating optimal thresholds in different noise intensities.The formula can accurately calculate optimal thresholds.
In the process of error correction based on reflecting telescope system, definition function of spot target is usually used as performance metric of imaging quality. The definition function will reach extremum by using optimization algorithm to correct parameter error. Mean radius as definition function of spot diagram is widely used for its large-scale and good dynamic property in correction. While the value of mean radius of calculation is different from the value of theory because of the noise of detector, thus the correction process is affected. The calculation error of mean radius because of noise and the influence of threshold is analyzed through theory and simulation.The result indicates that there exists an optimal threshold to make the error minimum. A fitting formula is proposed by the simulating optimal thresholds in different noise intensities.The formula can accurately calculate optimal thresholds.
引文
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3 Wang Sanhong,Liang Yonghui,Ma Haotong,et al..Beam cleanup experiments for master oscillator power amplifier laser system by adaptive optics based on stochastic parallel gradient descent algorithm[J].Chinese J Lasers,2009,36(10):2763-2768.王三宏,梁永辉,马浩统,等.随机并行梯度下降自适应光学对主振荡功率放大器激光系统的光束净化实验[J].中国激光,2009,36(10):2763-2768.
4 Liang Yonghui,Wang Sanhong,Long Xuejun,et al..Experimental explorations of the laser beam cleanup system based on stochastic parallel-gradient-descent algorithm[J].Acta Optica Sinica,2008,28(4):613-618.梁永辉,王三宏,龙学军,等.随机并行梯度下降光束净化实验研究[J].光学学报,2008,28(4):613-618.
5 Yang Huizhen,Li Xinyang,Jiang Wenhan.Comparison of several stochastic parallel optimization control algorithms for adaptive optics system[J].High Power Laser and Particle Beams,2008,20(1):11-16.杨慧珍,李新阳,姜文汉.自适应光学系统几种随机并行优化控制算法比较[J].强激光与粒子束,2008,20(1):11-16.
6 Genrui Cao,Xin Yu.Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object[J].Opt Eng,1994,33(7):2331-2335.
7 Jiang Wenhan,Xian Hao,Shen Feng.Detecting error of Shack-Hartmann wavefront sensor[J].Chinese Journal of Quantum Electronics,1998,15(2):218-227.姜文汉,鲜浩,沈锋.夏克-哈特曼波前传感器的探测误差[J].量子电子学报,1998,15(2):218-227.
8 Xiaoyu Ma,Changhui Rao,Hanqing Zheng.Error analysis of CCD-based point source centroid computation under the background light[J].Opt Express,2009,17(10):8525-8541.
9 Yuanxing He,Xinyang Li.Error analysis of laser beam quality measured with CCD sensor and choice of the optimal threshold[J].Optics&Laser Technology,2013,45:671-677.
10 Zhou Zhicheng.On the subject of Gauss approximation of poisson distribution[J].Acta Scientiarum Naturalium Universitatis Pekinensis,1988,24(5):605-619.周志成,关于泊松分布的高斯近似问题[J].北京大学学报(自然科学版),1988,24(5):605-619.
11 Fei Yetai.Error Theory and Data Processing[M].Beijing:China Machine Press,2004:58-60.费业泰.误差理论与数据处理[M].北京:机械工业出版社,2004:58-60.