At present, optical-axis component of nodal surface displacement to the original surface is fitted by Zernike polynomials, which is not accurate. Some algorithms of surface corrected displacement are described and compared.
针对目前常用轴向位移作为拟合量描述拟合面形的不足，给出了几种常用的表面位移校正方法并说明了其优缺点。
Experimental results indicate that the Zernike polynomial fitting realized wavefront detection and reconstruction. The method of fitting sample points selection was studied based on the least average error of laser energy intensity testing precision.
采用Zernike多项式对波前进行拟合和重构，讨论了拟合采样点的布设方法，并用激光能量密度测试精度平均误差较小的同心放射状采样点布局方案。
The experimental results show that the improved Zernike moment has better invariant poperties and can be used as region-based shape descriptor.
试验结果证明，和改进前的Zernike矩相比，改进后的Zernike矩具有更好的不变特征，可用作基于区域的形状描述算子。
By studying ZOM theory in details, the curve model of ZOM edge detection algorithm is deduced.
根据图象边缘的灰度阶跃模型推导了Zernike正交矩亚象素边缘检测理论，证明了ZOM的一些有用的性质，给出了直线边缘模型ZOM边缘检测模板权值的计算公式及检测图象边缘的算法。
Firstly the face image convolves Gabor filter bank to obtain Gabor feature.
首先对 Gabor 滤波噪组提出来的人脸特征进行组合构造 Gabor 特征图像，然后利用正交伪 Zernike 矩获得不变性特征，并进一步用线性判别分析方法进行特征选择，最后采用最近邻分类方法进行识别。
The adjustment of the given mode of the aberration could be realized in the optics through the precise control of the surface of the deformable mirror if necessary.
眼像差以Zernike多项式表示，通过对可变形镜的精确控制，可在光路中生成特定模式和幅值的像差。
When the ratio of central obscuration is small, the circular polynomial with 9 terms could take place of the annular polynomial to solve the SEIDEL coefficients in some special situations.
在某些特殊情况下，对于中心遮拦很小的环孔径波面，可以采用9项Zernike圆多项式来代替环多项式进行拟合求取SEIDEL系数。
The basic principle of the stitching method was introduced, and the reasonable mathematical model and effective splicing algorithm were established based on least squares method and Zernike polynomial fitting. Meanwhile the computer simulation experiment was carried on, the PV and RMS of the full aperture phase distribution residual error are 0.0079λ and 0.0027λ, respectively. The results show that this splicing model and algorithm are accurate and feasible, and it can provide another quantitive measurement for testing aspheric surfaces besides null compensation, especially for large aperture asphere.
介绍了该技术的基本原理，并基于最小二乘法和Zernike多项式拟合建立了合理的数学模型，同时对其进行了计算机模拟实验，拼接前后全孔径相位分布残差的PV值和RMS值分别为0.0079λ和0.0027λ，说明该拼接模型和算法是准确可行的，从而提供了除零位补偿外又一种定量测试非球面尤其是大口径非球面的途径。
Considering the statistical weight factors of different Zernike model aberrations caused by atmospheric turbulence, and the different arrangements of mirror positioning, the optimization of the bimorph deformable mirror is analyzed.
考虑到由大气湍流造成的光学波前畸变中各泽尼克基元模式的统计权重分布，以及变形镜的实际装夹定位方式，对双压电变形反射镜的优化设计进行了分析。
In this paper, a new model is developed named Zernike-facet model, which is used to fit local image intensity. And coefficients of the model are solved by the Total Least Squares method, which performance in resisting noise is better than the Least Squares method.
发展了一种新的图像局部灰度拟合模型，即Zernike-facet模型，模型参数的求解采用比最小二乘抗噪能力更强的总体最小二乘算法。
Using Zernike- moment invariants as features of a pattern, an automatic recognition scheme is designed, and is examined by test software, and so is performable.
采用Zernike 矩不变量作为模式的特征拟定自动识别方案，并通过试验软件进行了实算分析，说明本文所拟定的识别方案是可行的
Rotation, scaling and translation attacks can desynchronize watermark detection, thus making many watermarking systems fail. In this paper, an image adaptive RST invariant watermark is proposed by using the rotation invariant property of pseudo-Zernike moments and odd-even quantization.
针对旋转、缩放和平移等几何攻击能够破坏水印检测的同步性，容易使常规水印算法检测失败的问题，利用图像伪Zernike矩的幅度具有旋转不变的性质，结合奇偶量化，提出了一种图像自适应旋转、缩放和平移不变水印算法。
The results indicate that, the correction capability of bimorph deformable mirror is greatly dependent on the statistic weight function of the corrected Zernike model wave aberrations induced by atmospheric air turbulence, so far as to the optimization design of mirror.
结果表明：变形镜的校正能力随被校正的各项泽尼克模式像差在大气湍流造成的波前畸变中所占统计权重的不同而有很大的差别，其优化设计结果也随之而变；变形镜的定位方式对其校正能力有一定的影响，但影响不大。
METHODS: Monochromatic aberrations of the whole eye were measured with a COAS Shack-Hartmann wavefront analyzer before and after wearing SCL for myopia correction with a natural pupil. The fitted Zernike coefficients were calculated for each eye including 47 myopic eyes with fixed optical zones of 6.0 mm.
使用依据Hartmann-Shack原理设计的COAS波前像差仪对47只单纯性近视眼分别测量角膜接触镜矫正低阶离焦像差前后的高阶像差，提取瞳孔直径为6 mm时高阶像差的均方根值进行分析。
Firstly the image corners are obtained by using some type of image corners detection method, and then the more important corners are selected by using Zernike moments and neural networks..
其主要思路是首先利用角点检测方法提取图像中的角点之后，然后再通过Zernike矩和神经网络对它们进行筛选，从而达到自提取特征角点的目的。
Subpixel algorithm is an effective method to improve the error of edge location under assured hardware condition. Aiming at the circle parameters detection of small size parts in industry, a novel algorithm for subpixel location of circle parameters was proposed based on Zernike moments, quadratic polynomial interpolation and leastsquares method.
亚像素软件处理技术可以在一定程度上补偿图像测量系统由硬件限制引起的边缘定位误差，针对工业中的小尺寸圆形零件参数检测，提出了一种基于Zernike矩、二次多项式插值和最小二乘法拟合的圆参数亚像素定位算法。
In the research procedure for these questions, we use two siganl transforms which are respectively called Zernike transform and Gabor transform.
在论文的研究过程中，我们使用了两类新的信号变换技术，即：图象的Zernike变换和信号的Gabor变换。
Noll. From the irradiance distribution in two defocal planes, one in front of focal plane and the other behind, with a given detector array the elements of response matrix for each normalized term of Zernike polynomials can be obtained. For an incoming atmospheric disturbed random wavefront, with its irradiance distribution detected in two defocal planes and the response matrix, it is easy to solve the corresponding Zernike term coefficients of incoming wavefront and reconstruct the detected one.
Noll建议的Zernike多项式表征经大气扰动的入瞳处的光学波前畸变；求出由两个离焦面上的光强分布决定的归一化Zernike项在特定形状的探测器上的响应矩阵；由响应矩阵和入瞳处的波前在两个离焦面上的光强分布，求出其Zernike项的系数，从而实现波前的探测和重构。
The Southwell zonal wavefront reconstruction model was applied to some terms of Zernike polynomials by numeric simulation, and the error caused by data precision of wavefront-reconstruction-matrix is studied.
采用Southwell区域法波前重构模型对泽尼克多项式的前几项进行了波前重构的数值模拟，研究了由重构矩阵存储精度原因而引起的波前重构误差。
A relatively small set of pseudo-Zernike moments can characterize the global shape of a pattern effectively.
实验结果证明，该改进后的伪 Zernike矩较改进前的伪 Zernike矩，具有更好的旋转和比例不变性。