IOE OpenIR  > 光电技术研究所博硕士论文
低信噪比下点源目标哈特曼传感器的子光斑定位算法研究
李旭旭1,2
学位类型博士
导师李新阳研究员 ; 李梅研究员
2018-06
学位授予单位中国科学院研究生院
学位授予地点北京
学位专业信号与信息处理
关键词夏克—哈特曼传感器 点源光斑 低信噪比 光斑定位 互相关算法
其他摘要

随着地基天文望远镜系统的发展,采用自适应光学原理主动校正大气湍流带来的影响,已经成为提高望远镜分辨率的必要手段。自适应光学系统通过实时探测畸变的波前相位,并对其施加一定的补偿来提高成像质量。哈特曼传感器作为波前探测领域应用最为广泛的传感器,采用微透镜阵列对波面进行采样,计算局部波前斜率,从而实现波面重建,达到波前探测的目的。光斑质心提取或偏移量的估计是斜率计算的首要步骤,其性能直接影响着波前探测的准确性。

然而,探测器件的随机噪声和离散采样,不可避免地会对光斑偏移估计带来误差,降低斜率测量的准确度。例如基于钠信标的波前探测情况下图像的信噪比极低,带来极大技术挑战。因此,本文的研究目的就是寻求适合低信噪比下点源目标哈特曼传感器的子光斑定位算法。

本文首先从探测器件入手,分析了哈特曼传感器光斑的噪声模型和信号模型,为算法的性能仿真提供了必要条件。由于偏移量估计误差会随着信号的减弱或噪声的增大而增大,为了便于描述估计误差与信噪比的关系,本文建立了一套子孔径内点源目标的信噪比估计理论,并从理论信噪比和实际估计信噪比两方面进行了阐述。

 

其次,本文对现有的多种光斑定位算法进行了较为全面的梳理,从原理上将算法分为三大类,分别为:基于传统重心法的改进算法、基于配准的算法和基于泰勒微分展开的算法。并且逐一进行了原理性介绍和性能分析,包括其稳定性、线性度和动态范围等。分析了阈值选取对于传统质心法的影响,提出了在低信噪比下阈值应取得相对保守的观点。并提出了一种基于统计排序的局部自适应阈值分割方法,能够消除子孔径间差异,从而更加有效地分割出光斑。

接着,本文开展了对空域配准算法的研究。首先,从参考选取的角度,对比分析了参考光斑的幅度和等效高斯宽度对四种主流准则函数(包括绝对差分函数、绝对差分平方函数、最小均方误差函数和互相关函数)性能的影响。发现,互相关函数对于点源目标来说是性能最优的准则函数,其稳定性和抗噪性均较好,更加适合用于低信噪比下的子光斑定位。其次,本文对比了几种亚像素插值方法在不同信噪比下的表现,包括等角线插值、抛物线插值和高斯插值。发现,不同的准则函数有各自适合的亚像素插值方法。对于互相关函数来说,高斯插值法对高信噪比的光斑定位精度有较大改善,而在低信噪比下,高斯插值法的优势并不明显,抛物线插值是更好的选择。鉴于互相关函数较好的单峰特性,本文还提出了结合快速搜索的互相关函数法,可以有效降低传统互相关函数法的运算量。诸如三步搜索、二维对数搜索、交叉搜索和正交搜索等快速搜索策略,通过事先设计的搜索步骤,可以将求取像素级偏移量的运算量降低80%以上。本文还通过仿真实验,验证了极低信噪比下快速搜索策略的有效性。

 

最后,本文设计了一套哈特曼传感器相差测量实验,用于算法性能的验证。实验中通过调节光源的光功率、相机的曝光时间和在光路中添加衰减片三种途径调节哈特曼传感器采集到的光斑强度,同时获得了高信噪比、中等信噪比和低信噪比下的光斑图。通过对实验数据的分析,本文首先验证了靶面上的噪声分布情况及噪声统计特性,接着本文验证了局部自适应阈值选取方法的效果。综合实时性、抗噪性及动态范围,本文发现灰度加权质心法和互相关算法较适合低信噪比下点源光斑的定位,因此在实验中对两者进行了性能验证。

实验结果表明,灰度加权质心法比传统质心法的精度有较大改善。然而随着信噪比的降低,光斑与噪声的界限逐渐模糊,最佳阈值的选取也得变得更加困难,而基于重心法改进的算法对最佳阈值的选取较为敏感。相比之下,互相关函数法对均匀背景较不敏感,对阈值的要求不严格。

 

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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.

 

学科领域图象处理
语种中文
文献类型学位论文
条目标识符http://ir.ioe.ac.cn/handle/181551/8300
专题光电技术研究所博硕士论文
作者单位1.中国科学院大学
2.中国科学院光电技术研究所自适应光学重点实验室
推荐引用方式
GB/T 7714
李旭旭. 低信噪比下点源目标哈特曼传感器的子光斑定位算法研究[D]. 北京. 中国科学院研究生院,2018.
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