Monte-Carlo analysis of centroid detected accuracy for wavefront sensor

By utilizing Monte-Carlo simulation technology, the centroid algorithms have been compared in detail. The factors such as the detected window size, threshold and weighting power factor, which affect the detected accuracy of the wavefront sensor, have been studied and the optimal parameters for each algorithm have been found. The numerical results will be helpful for further improving the measurement accuracy of the wavefront sensor.     

基于优化探测窗口的光斑质心探测方法

 哈特曼-夏克波前传感器进行波前探测时，用子孔径光斑强度的一阶矩来计算光斑质心位置，子孔径窗口作为探测窗口，但探测时子孔径窗口内噪声对一阶矩有很大的影响，会使质心探测精度产生很大的误差。因此在计算质心位置时探测窗口的选取对探测精度有重要影响，必须选取合适的探测窗口来提高光斑质心探测精度。为此，在传统算法的基础上提出优化探测窗口的方法来提高质心探测精度,仿真和实验结果表明新方法提高了质心探测的精度，未经处理的高噪声恢复波前的波前残差峰谷值是2.851 4λ，均方根值是0.606 3λ，优化探测窗口后波前残差的峰谷值是1.636 2 λ，均方根值是0.367 1 λ，重构误差减小了40％。证明了算法的可行性和稳定性。     

基于已知球面波前的Hartmann-Shack传感器结构参量标定

微透镜阵列到CCD的距离是影响Hartmann-Shack波前探测器精度的主要装配误差之一。对该平移装配误差的修正,能够有效减小波前探测误差。理论求解了球面波前通过微透镜引起的子孔径光斑质心移动量与波前探测器结构参数之间的关系,借助该关系能够求出微透镜到CCD之间的实际距离,以其改进波前斜率的计算。实验验证了理论推导的合理性,并对实际装配参数进行标定,得实际距离为24.2 mm。利用标定后的参数重建波前,其相对误差减小20.4%。实验表明该标定方法能够有效提高波前传感器测量准确性。     

Accuracy analysis of centroid calculated by a modified center detection algorithm for Shack-Hartmann wavefront sensor

The accuracy of the Shack-Hartmann wavefront sensor for measuring the wavefront distortion is mainly dependent upon the measuring accuracy of the centroid of each spot. A modified center detection algorithm, which uses some power from the photon events of each pixel instead of photon events themselves, is analyzed theoretically and the computer simulations are given. The results show that photon noise error and sampling error increases as the power value goes up; and to some powers, the readout noise and background noise error decrease. An experiment is described through which the optimum power can be obtained.     

夏克-哈特曼波前传感器的波前相位探测误差

对夏克－哈特曼（Ｓｈａｃｋ－Ｈａｒｔｍａｎｎ）波前传感器的相位探测误差进行了分析,并分析了它的政论相位探测极限,分析结果表明,夏克－哈特曼波前传感器的相位探测精度与探测器的噪声水平,探测目标的亮度有关,还与被探测对象的特性、孔径波前分割有关。给出了它们的关系表达式。     

点光源哈特曼最优阈值估计方法研究

针对夏克-哈特曼波前传感器探测系统中噪声随时间及空间变化频率较快的特点,为了准确估计系统的最优阈值,根据高斯光斑与噪声的分布特性,提出一种以滑动窗口内像素均值及图像信号的局部梯度作为参数,构造关于噪声权重函数的方法,由此获得子孔径阈值的最优估计值,并详细分析了算法的基本原理和实现过程.以典型处理方法获取的阈值与理论最优阈值的误差作为评价标准,仿真和实验结果表明本文提出的阈值估计方法在不同信噪比、不同光斑大小的条件下,均能取得优于典型阈值处理方法获得的结果,且与理论最优阈值的误差小于10%.     

Performance analysis of field-of-view shifted Shack–Hartmann wavefront sensor based on splitter

We report on a field-of-view shifted Shack–Hartmann wavefront sensor based on a splitter designed to measure the wavefront information of object light with strong background. The analysis results indicate that increasing the ratio of the signal beam intensity to the incoming beam intensity and reducing the sampling frequency of CCD₂ (detecting the pure background light) can properly enhance the SNR (signal-to-noise ratio) of the object light. A special noise removing algorithm was presented to enhance the centroid measuring accuracy, and it was proved to be effective against the residual noises caused by the differences between the two beam paths. The experimental results indicate that the field-of-view shifted Shack–Hartmann wavefront sensor based on a splitter can exactly measure the wavefront information from the object with strong background. PACS 42.68.Bz; 47.50.Ef; 42.30.Wb     

Hartmann－Shack波前传感器的Fourier光学分析

Ｈａｒｔｍａｎｎ－Ｓｈａｃｋ波前传感器是自适应光学中几种重要的波前传感器之一。本文利用Ｆｏｕｒｉｅｒ光学方法分析研究了Ｈａｒｔｍａｎｎ－Ｓｈａｃｋ波前传感器的原理，导出了辐照度分布质心与子孔径波前倾斜的解析表达式，说明了辐照度分布质心及其算法的物理意义，总结了该传感器的若干重要特点。     

点源信标相关哈特曼-夏克波前传感器光斑偏移测量误差分析

在基于哈特曼-夏克波前传感器(SH-WFS)的自适应光学系统中,通常采用质心算法探测点源信标的子孔径光斑偏移量.然而质心算法探测精度受到诸如减阈值等因素的影响,在低信噪比(SNR )时不能准确估计光斑质心位置,而相关哈特曼算法不需要减阈值,具有更好的鲁棒性.本文在介绍相关SH-WFS基本原理的基础上,通过建立基于点源信标探测的相关SH-WFS算法的随机噪声模型,推导了光斑偏移测量误差表达式,系统分析了光子噪声、CCD读出噪声、背景光子噪声等因素对相关SH-WFS测量误差的影响.并进行了数值仿真及实验,仿真 关键词： 相关哈特曼-夏克波前传感器 相关哈特曼算法 质心算法 测量误差     

光强非均匀分布对波前曲率传感器的影响

为了将波前曲率传感器用于涉及激光波前的领域,理论分析了非均匀光强入射条件下的曲率传感器测量信号。用菲涅耳衍射公式,数值计算了相位分布为前10阶泽尼克多项式,光强为高斯分布和正态随机分布闪烁的曲率传感器信号,并和相同相位分布,光强均匀情况下的传感器信号比较。分析表明光强非均匀分布给波前曲率传感器测量信号带来了一定的误差。光强高斯分布对散焦相差的曲率信号影响较大,信号百分比误差达到25%,对其他相差的曲率信号影响很小;对于有正态随机分布闪烁的光强分布,信号百分比误差与正态随机分布的均方差成线性关系。在一定条件下,波前曲率传感器也能够用于光强非均匀分布的领域。     

基于相干波面光强分布的静态干涉图的数字分析

提出了基于相干波面光强分布的静态干涉图数字处理的新方法 ,即在CQG Ⅱ型激光数字波面干涉仪上通过分别微调参考镜和被测镜的倾斜量 ,在CCD探测器上获得形成静态干涉图的两幅相干波面光强分布图 ,利用这两幅光强分布图与它们所形成的干涉图 ,可高精度地完成静态干涉图的数字分析。利用相干原理 ,给出了实现该方法的基本过程 ,并编程实现了该数字分析 ,获得了实验测量结果。通过与相移测量结果相比较 ,验证该方法对口径为 60mm的平面有望达到的测量精度。     

基于电子倍增电荷耦合器件的哈特曼-夏克波前传感器质心探测误差分析

哈特曼-夏克(Hartmann-Shack,H-S)波前传感器的探测误差是自适应光学系统中的一个主要误差源.本文分析了电子倍增电荷耦合器件(electron multiplying charge-coupled devices,EMCCD)的各种噪声源对H-S波前传感器质心探测误差的影响,推导了基于EMCCD的H-S波前传感器的质心探测误差的数学表达式,并进行了数值仿真和实验研究.结果表明,基于EMCCD的H-S波前传感器的质心探测误差与增益直接相关,在增益小于P_max/(Q·N_mean)时质心探测误差随着增益的增大而减小,在增益大于P_max/(Q·N_mean)时质心探测误差随着增益的增大而增大,其中P_max是EMCCD的峰值电荷,Q是量子效率,N_mean是平均入射光强. 关键词： 自适应光学 电子倍增电荷耦合器件 波前传感器 质心探测误差     

Wavefront sensing based on phase contrast theory and coherent optical processing

A novel wavefront sensing method based on phase contrast theory and coherent optical processing is proposed. The wavefront gradient field in the object plane is modulated into intensity distribution in a gang of patterns, making highdensity detection available. By applying the method, we have also designed a wavefront sensor. It consists of a classical coherent optical processing system, a CCD detector array, two pieces of orthogonal composite sinusoidal gratings, and a mechanical structure that can perform real-time linear positioning. The simulation results prove and demonstrate the validity of the method and the sensor in high-precision measurement of the wavefront gradient field.     

Signal spatial filtering for co-phasing in seeing-limited conditions

We present the results of the co-phasing closed loop performed with a pyramid wavefront sensor for what we believe to be the first time in the presence of emulated atmospheric disturbance. The performance of the co-phasing loop is significantly improved by applying two spatial filters in the sensor signal space. The first is a zonal filter applied to the interaction matrix before the computation of the reconstructor; the second is a modal filter applied to the sensor signals before the correction command computation. The presented laboratory results demonstrate that, applying both filters, the time requested to average out the atmospheric disturbance in each loop step is reduced by 2 orders of magnitude, improving the loop stability and accuracy.     

Hartmann－Shack传感器结构参量的自基准标定

提出一种标定Hartmann Shack波前传感器结构参量的新方法,通过基于Zernike多项式的模式复原算法推导出公式,结合实验手段获得相应数据,处理后得到微透镜阵列到CCD之间的距离.该方法有效改善了以微透镜焦距代替实际参量计算斜率引入较大误差的状况,在降低传感器装配准确度要求的同时,提高了Hartmann Shack波前传感器的探测准确度.经实验验证该方法在一般实验条件下即可获得满意效果.     

哈特曼-夏克波前传感器子孔径合并的理论研究

在大气湍流条件较好而被探测信标光信号极弱的工作条件下,自适应光学系统在实际的应用中需要采用子孔径合并的部分校正方式。本文针对云南天文台1.2m高分辨率自适应光学系统中的哈特曼－夏克（Hartmann-Shack ）波前传感器结构,从光子起伏噪声和CCD像素读出噪声对子孔径内哈特曼光斑质心探测精度的影响的角度,对子也径软件合并和硬件合并两种方案进行了理论分析和计算,导出了有实际应用意义的结论。     

一种提高HWS采样率的透镜式微扫描方法

为改善传统哈特曼-夏克波前传感器对待测波前采样不足的缺点,对哈特曼-夏克波前传感器和微扫描进行了分析,提出一种提高哈特曼-夏克波前传感器采样率的透镜式微扫描方法。通过在微透镜阵列之前加入由PZT驱动的透镜扫描装置,对CCD采集的光斑分布情况进行高分辨率微扫描图像重建,通过对重建后的光斑分布进行波前重构,提高了哈特曼波前传感器对待测波前的采样率。通过对比实验验证,波前复原精度提高了41%,可以有效提高哈特曼传感器对波前探测的精度。     

一种适于自适应光学的旋转软刀口波面传感器的研究

利用傅里叶光学理论,证明了一种新型波面传感器——旋转软刀口波面传感器的概念.在经典刀口法的刀口区,以渐变透过率代替突变透过率函数,在光瞳象面上可获得反映光瞳面位置待测波面位相梯度及位相梯度方向的调制信号.文中给出了实验结果和讨论.     

Influence of the size,geometry and temporal response of the finite piezoelectric sensor on the photoacoustic signal: the case of the point-like source

Most photoacoustic (PA) work assumes a point-like detection of generated pressure waves; this assumption results in important differences between predicted and experimental signals, as shown in this paper. We used the geometry of a real sensor in the theoretical signal generation through the discretization of the sensing surface, considering each element as a point-like sensor. We modeled the interaction between the wavefront and the real sensor, starting from a well-known PA pressure relation for a point-like source and punctual detection. We obtained the electrical response of the real sensor experimentally and modeled it as a summation of Gaussian functions. The impulse response was convolved with the total PA pressure to obtain the theoretical PA signal. We analyzed the dependence of the source-sensor distance on the discretization size. Then the predicted signal and experimental data were compared for two different frequency response transducers. We found differences in shape and temporal width of simulated PA signals for point-like-source/punctual-detection model and for point-like-source/finite-sensor model.     

A modified phase diversity diffraction wavefront sensor with a grating

The phase diversity wavefront sensor is one of the tools used to estimate wavefront aberration, and it is often used as a wavefront sensor in adaptive optics systems. However, the performance of the traditional phase diversity wavefront sensor is limited by the accuracy and dynamic ranges of the intensity distribution at the focus and defocus positions of the CCD camera. In this paper, a modified phase diversity wavefront sensor based on a diffraction grating is proposed to improve the ability to measure the wavefront aberration with larger amplitude and higher spatial frequency. The basic principle and the optics construction of the proposed method are also described in detail. The noise propagation property of the proposed method is also analysed by using the numerical simulation method, and comparison between the diffraction grating phase diversity wavefront sensor and the traditional phase diversity wavefront sensor is also made. The simulation results show that the diffraction grating phase diversity wavefront sensor can obviously improve the ability to measure the wavefront aberration, especially the wavefront aberration with larger amplitude and higher spatial frequency.