Choice of the reduction and of the representation in centrifugal distortion analysis: A case study of dimethylsulfoxide

The millimeter-wave and submillimeter-wave spectra of dimethylsulfoxide have been measured up to 660 GHz, corresponding to maximum values of J = 70 and K_c = 68. A total of 3331 transitions (corresponding to 2133 distinct frequencies) were fit to a standard Watson Hamiltonian using the S- and A-reductions and the representations I^r and III^r. Although dimethylsulfoxide is an asymmetric oblate top, the combination (A, III^r) gives the worst results. From the point of view of the convergence of the Hamiltonian, the best results are obtained with the combination (S, III^r) but the least-squares system of normal equations is better conditioned with representation I^r. These results are compared to those obtained for a few typical molecules.     

Correcting non-linear lens distortion in cameras without using a model

Camera lens distortion calibration is the first step in resolving any metric application with a camera. To date, lens distortion was corrected using some existing lens distortion non-metric or self-calibration methods. Using a lens distortion model means defining a global rule to correct the entire image. This global rule does not take into account particular lens distortion effects not represented by the model. Moreover, to calibrate the model, only some features of the scene such as straight lines, circles or vanishing points are used. Since only the feature of the scene used to calibrate the model is guaranteed by the distortion rectification, it is certain that the model will not be precise. The result is an approximation of the real image distortion.To improve the lens distortion rectification, a method without using a model is proposed. Using a set of control points distributed across the entire image, they are corrected to assure all the restrictions of the scene. With both sets of points, the points detected in the image and the undistorted ones, image local transformations are defined considering only nearby control points. Rather than calibrating a global model, local functions are characterized. The distortion correction is defined by a rectification surface composed of local surface patches each influenced by nearby control points. This method is more sensitive to local deformations and allows the image to be corrected in accordance with its distortion.     

Polarization phase-shifting Jamin shearing interferometer

The Jamin shearing interferometer is very useful in wavefront testing, especially for the low coherent light. Based on this interferometer, a polarization phase-shifting Jamin shearing interferometer is proposed to improve the performance. In the interferometer, two interference beams are linearly polarized and a polarization phase shifter is applied to realize the phase shifting. Different types of configurations of the interferometer are given. With phase-shifting interferograms, the precision of the interferometer can be improved. The interferometer is kept as an equal optical path system and its shearing amount remains changeable with simple structure and easy operation. In experiments, phase-shifting interferograms are obtained by rotating the analyzer. The usefulness of the interferometer is verified.     

两矩形上的全偏差

考虑如下极值问题的存在性和唯一性:■,其中h代表从矩形Q_1到矩形Q_2并保持端点且具有有限偏差的所有同胚映射的集合.     

Bi-Sobolev mappings with differential matrices in Orlicz Zygmund classes

Bi-Sobolev mappings have been defined as those homeomorphisms such that f and f−1 belong to . We deduce regularity properties of the distortion of f from the regularity of the differential matrix Df−1 and conversely.     

一种寻找星图光斑质心的高精度算法及在成像畸变矫正中的应用

首先讨论星图识别中的质心寻找问题,提出了一种改进的匹配算法.使用高斯分布对光斑内像素点的强度分布进行近似模拟, 并采用最小二乘法中的法方程法对光斑图像质心坐标进行优化计算.算例表明该算法可以得到更为精确的结果, 在噪声小于最大像素值的$5\%$时,质心坐标计算精度高于0.04个像素, 优于以往的匹配算法的结果.最后讨论了算法在望远镜光学成像畸变矫正中的应用, 设计了矫正算法, 并通过算例验证了算法的合理性.     

Distortion control of conjugacies between quadratic polynomials

We use a new type of distortion control of univalent functions to give an alternative proof of Douady-Hubbard’s ray-landing theorem for quadratic Misiurewicz polynomials. The univalent maps arise from Thurston’s iterated algorithm on perturbation of such polynomials.     

Analysis of ray tube area in geometrical shock dynamics

We provide a rigorous analysis of structure of a ray tube in geometrical shock dynamics. Our aim is to shed more lights on the cross-sectional area function of a ray tube. We have shown that for a given ray tube and a given initial value of cross-sectional area, then its cross-sectional area can be determined uniquely everywhere. We give a definition of cross-sectional area of a ray tube in precise mathematical terms and from that we derive a set of relations, each describing the cross-sectional area for an arbitrary ray tube in geometrical shock dynamics. We have shown that from our results one can deduce Whitham’s area function relation as a partial differential equation from our general formulations. Some applications are discussed.     

利用分形法表征光学元件中高频相位畸变

针对神光Ⅲ主机装置使用的光学元件,基于分形理论,分析中高频相位畸变的统计分布特征,指出其满足分数布朗随机场,并利用结构函数法对分形维数进行计算,统计结果显示,大口径钕玻璃片的分形维数在2.34~2.43之间。利用局部稳态的随机中点位移法,提出一种新的表征光学元件相位的方法,将分形维数作为参数,可衡量中高频相位畸变,对高功率激光光学元件的评价有参考意义。     

Determination of the Molecular Arrangement in Liquid Crystals by Polarization of Fluorescence

Polarized luminescence intensity reading and the polarized absorbance spectra of 4-diethyl-amino-4′-nitrostilbene “impurity” in the n-butyl-p/p-hexyloxyphenyloxycarbonyl/-phenyl-carbonate liquid crystal were measured. Degrees of orientational order, S₁ and S₂, of the nematic liquid were calculated from relative values of the absorbance and luminescence intensity components. A function, which describes the angular molecular distribution with respect to a preferred direction in the liquid crystal, is plotted.