A unified approach for least-squares surface fitting

This paper presents a novel approach for least-squares fitting of complex surface to measured 3D coordinate points by adjusting its location and/or shape. For a point expressed in the machine reference frame and a deformable smooth surface represented in its own model frame, a signed point-to-surface distance function is defined, and its increment with respect to the differential motion and differential deformation of the surface is derived. On this basis, localization, surface reconstruction and geometric variation characterization are formulated as a unified nonlinear least-squares problem defined on the product space SE(3) × R ^m . By using Levenberg-Marquardt method, a sequential approximation surface fitting algorithm is developed. It has the advantages of implementational simplicity, computational efficiency and robustness. Applications confirm the validity of the proposed approach.     

最小二乘拟合计算有机薄膜晶体管迁移率的研究

本文通过制备了一个基于并五笨为有源层的顶栅底接触OTFT器件获取电流电压实验数据,并运用电流电压特性曲线理论拟合计算方法计算其场效应迁移率.研究发现,采用不同的拟合方法得到的场效应迁移率值有较大的差异.若选取转移特性曲线线性区距中心1/2范围内测试点进行最小二乘拟合计算出的场效应迁移率能减少采用其他拟合方法的固有不准确性,而且与其他方法得到的场效应迁移率最接近. 关键词： 最小二乘拟合 场效应迁移率 有机薄膜晶体管     

Using higher steps phase-shifting algorithms and linear least-squares fitting in white-light scanning interferometry

White-light scanning interferometry (WLSI) has been a well-established tool for measuring the profile of objects. Since the white-light source is continuous in spectrum, the phase ambiguity problem can be avoided. Specimens with discontinuous profile can therefore be possibly measured by WLSI. In this paper, using higher steps, i.e. nine and eleven steps, phase-shifting algorithms (PSAs) based on local linear conditions of envelope function were proposed. The actual zero optical path difference position was retrieved by extracting the phase value and phase compensation. Maximum intensity peak positions at five points were used to calculate the center wavelength of the light source by both phase unwrapping and linear least-squares fitting. Both simulated and experimental results showed that the proposed nine- and eleven-step PSAs have good linearity and robustness to accurately measure the profile and center wavelength of the light source.     

Zernike多项式拟合曲面中拟合精度与采样点数目研究

为了研究采样点数目对由Zernike多项式所拟合的曲面的拟合精度的影响,采用不完全归纳法,取得了采样点与拟合精度之间的数据关系。结果表明:不同的测试函数遵循相同的规律,即采样点数目达到一定数目后,拟合精度随采样点的变化很小。并且,通过计算得到了在较高拟合精度时,采样点数目与Zernike多项式的项数之间的变化规律,实际例子证明了该变化规律的正确性,其对于Zernike多项式拟合曲面具有很好的指导意义。     

数字剪切散班干涉术中的刚体位移补偿的新方法

给出一个数字剪切散斑干涉术中的刚体位移补偿的新方法。当刚体位移大于一个像素时，加载前后的散斑图将会由于位置的变化导致失相关。重新安排每一个像素将会克服此失相关。散斑平均、条纹重构以及迭代方法用来改善条纹质量，消除散斑噪声，最后得到可取结果。     

近柱面中频面形检测中曲面拟合法精度问题研究

研究了曲面拟合法对特定抛物和双曲近柱面检测中波前像差的处理过程，结果表明，对振幅为01λ的中频正弦型面形，由曲面拟合法得到的结果与该正弦型面形之差的RMS值分别可以达到0015λ（825nm）和0013λ（715nm）.通过分析拟合阶数对精度的影响，确认存在一个特殊的阶数n_o、它使曲面拟合法的精度达到最高；讨 论了估计n_o值的方法，得到了和n_o真实值完全符合的估计值，表明这些方 法是行之有效的. 关键词： 光学检测 近柱面 曲面拟合     

反演与拟合相结合处理核磁共振弛豫数据的方法

讨论非负最小二乘（NNLS）法和非线性拟合在分析处理核磁共振（NMR）弛豫数据中的应用.同时将二者结合，提出用NNLS的反演结果来设定非线性拟合初值的方法，并用计算机模拟和实验证明了该方法在分析处理NMR弛豫数据中的有效性. 关键词： 非负最小二乘法 非线性拟合 核磁共振 弛豫时间     

子孔径拼接技术在大口径高陡度非球面检测中的应用

为了能够精确地完成对大口径高陡度非球面在细磨和抛光过程中的测量,提出了一种将子孔径拼接技术和补偿技术相结合的检测方法。介绍了该方法的基本原理,建立了合理的数学模型,编制了拼接计算软件。利用该方法对一外形尺寸为400 mm×300 mm的高次离轴非球面进行了测试,通过最小二乘法拟合消去各子孔径相对基准子孔径的调整误差以及整个系统的装调定位误差,得到了准确的全孔径面形分布。对实验精度和误差来源进行了分析,并将拼接面形与全孔径测量面形相对比,二者是一致的。     

Spectral reflectance characteristics of different snow and snow-covered land surface objects and mixed spectrum fitting

The field spectroradiometer was used to measure spectra of different snow and snow-covered land surface objects in Beijing area.The result showed that for a pure snow spectrum,the snow reflectance peaks appeared from visible to 800 nm band locations;there was an obvious absorption valley of snow spectrum near 1 030 nm wavelength.Compared with fresh snow,the reflection peaks of the old snow and melting snow showed different degrees of decline in the ranges of 300～1 300,1 700～1 800 and 2 200～2 300 nm,the lowe...     

基于插值法波面拟合的球面光学元件检测

为了实现在线自动化检测球面光学镜片的面形偏差,在已有的光学检测系统基础上,对光学检测系统采集的干涉图样进行图像处理和波面拟合算法研究。首先对干涉图样预处理,再根据球面光学镜片大多是圆形孔径,对预处理后的干涉条纹通过最小二乘法拟合出干涉图样的圆边界,确定数据取值边界点的中心和半径值;然后采用Multi-quadric函数插值法拟合出波面的面形轮廓,计算波面的峰谷偏差EPV值及均方根偏差ERMS值;最后用上述方法对Zygo干涉仪采集的干涉图的处理结果与Zygo干涉仪测试结果进行比较分析。结果表明:通过边界处理可有效提高波面拟合精度,采用multi-quadric函数插值法拟合可以理想的还原出波面,且测量误差与国标相比能够控制在0.2的误差范围内,与Zygo干涉仪检测结果相比可以控制在0.03误差范围内,都能够满足球面光学镜片在线检测的精度要求。     

A quasi random search technique for functional fitting of detector responses

The problem of nonlinear optimization is encountered while fitting the observed response of certain radiation detectors. In this paper the development of an optimizing technique based on quasi random search is described. The performance of this technique is compared with other existing methods of gradient search and linear Taylor differential correction technique in the case of fitting the photopeak responses of Nal(Tl) detectors. Our results are favourable especially when the observed data are associated with poor statistics.     

光点定位中的曲面拟合迭代算法

在光电检测系统中,需要对光点信号的位置实现亚像素定位。光纤从一端照明,由光纤另一端出射光点,由面阵CCD摄像机获取光点的灰度分布。基于最小二乘法,采用高斯曲面拟合算法拟合其分布,用高斯拟合函数的极值点作为光点的定位点。实验结果表明,采用多次迭代算法可以提高定位精度;拟合算法的稳定性(标准差)为0.7μm.高斯曲面拟合算法具有重复精度高、稳定性好的特点。     

A unified approach to quantum and classical TTW systems based on factorizations

A unifying method based on factorization properties is introduced for finding symmetries of quantum and classical superintegrable systems using the example of the Tremblay–Turbiner–Winternitz (TTW) model. It is shown that the symmetries of the quantum system can be implemented in a natural way to its classical version. Besides, by this procedure we get also other type of constants of motion depending explicitly on time that allow to find directly the motion of the system whose corresponding trajectories coincide with those obtained previously by using its symmetries.     

基于图像的三维刚体运动估计算法比较

基于图像特征点对应估计三维刚体运动是计算机视觉的一个基本问题。对四种常用的运动估计算法,包括基于三维特征点的奇异值分解法、正交分解法、单位四元数法和基于二维特征点的"8点算法",通过大量仿真实验和一个机载目标运动光测系统进行了精度,稳定性和效率的比较。结论表明,基于三维特征的算法比基于二维特征的算法精度高、稳定性好,效率高。其中在基于三维特征的算法中,奇异值分解法效率更高,单位四元数法稳定性更好,在基于二维特征的算法中采用非线性优化是必须的,而增加特征点数和降低噪声水平对四种算法都能提高精度。讨论了这些结论对解决实际问题的作用。     

对平面运动刚体加速度瞬心问题的进一步讨论

讨论了与加速度瞬心相关的几个问题,进一步深化了对加速度瞬心概念的理解．     

测量物体位移的数字白光散斑照相术

给出了一测量物体刚体位移的数字白光散斑照相术。数字傅里叶变换从双曝光字白光散斑图用来产生杨氏条纹。该杨氏条纹能够用数字傅里叶变换结合条纹重构进行自动分析。此外，给出一种条纹质量增强的方法。     

光谱辐射照度标准灯的数据插值与曲线拟合方法研究

介绍了多种插值方法与曲线拟合方法,对光谱辐射照度标准灯在所需波长间隔上的照度值进行内插运算,包括这些方法的模型建立、参数计算及误差分析过程。得到了效果较好的插值方法及分段普朗克曲线拟合模型,其中拟合模型较好地体现了光谱辐射照度标准灯的灯丝发射率及灯壳的光谱透射比。最终结果的相对偏差接近国家级计量院提供标准灯的最佳不确定度0.2%。     

He-NO体系一种拟合的各向异性相互作用势

根据MS(Maitland Smith)势模型拟合出了He -NO系统一种形式简单的各向异性相互作用势 ,利用拟合的势能计算了基态氦原子和NO分子碰撞的散射截面 ,计算结果表明拟合势能较好的描写了He -NO系统相互作用的特征。