Stable extendibility of vector bundles over lens spaces mod 3 and the stable splitting problem

Let Lⁿ(3) denote the (2n+1)-dimensional standard lens space mod 3. In this paper, we study the conditions for a given real vector bundle over Lⁿ(3) to be stably extendible to L^m(3) for every mn, and establish the formula on the power ζ^k=ζζ (k-fold) of a real vector bundle ζ over Lⁿ(3). Moreover, we answer the stable splitting problem for real vector bundles over Lⁿ(3) by means of arithmetic conditions.     

Line-based camera calibration with lens distortion correction from a single image

Camera calibration is a fundamental and important step in many machine vision applications. For some practical situations, computing camera parameters from merely a single image is becoming increasingly feasible and significant. However, the existing single view based calibration methods have various disadvantages such as ignoring lens distortion, requiring some prior knowledge or special calibration environment, and so on. To address these issues, we propose a line-based camera calibration method with lens distortion correction from a single image using three squares with unknown length. Initially, the radial distortion coefficients are obtained through a non-linear optimization process which is isolated from the pin-hole model calibration, and the detected distorted lines of all the squares are corrected simultaneously. Subsequently, the corresponding lines used for homography estimation are normalized to avoid the specific unstable case, and the intrinsic parameters are calculated from the sufficient restrictions provided by vectors of homography matrix. To evaluate the performance of the proposed method, both simulative and real experiments have been carried out and the results show that the proposed method is robust under general conditions and it achieves comparable measurement accuracy in contrast with the traditional multiple view based calibration method using 2D chessboard target.     

Tight focusing of circularly polarized beam over high NA lens axicon with a diffractive optical element

We propose to use diffractive optical element in combination with high NA lens axicon to achieve a high depth of focus when illuminated by a circularly polarized beam. With this kind of system, the focal depth is increased to 12.816λ and the magnetic spot size is reduced to 0.3764λ. However, in the conventional lens with same NA, the FWHM of the magnetic spot is found to be 0.4308λ and its corresponding magnetization depth is only 0.888λ. The author expects that such a high focal depth strong longitudinal magnetic field with large magnetization depth can be widely used in high density magneto optic recording, laser machining, laser cutting and the scanning near-field magnetic microscope.     

Wave optics analysis by phase-shifting real-time holographic interferometry

The purpose of this work is to study the potentialities in the phase-shifting real-time holographic interferometry using photorefractive crystals as the recording medium for wave-optics analysis in optical elements and non-linear optical materials. This technique was used for obtaining quantitative measurements from the phase distributions of the wave front of lens and lens systems along the propagation direction with in situ visualization, monitoring and analysis in real time.     

Stable extendibility of normal bundles over lens spaces

We study the stable extendibility of R-vector bundles over the (2n+1)-dimensional standard lens space Ln(p) with odd prime p, focusing on the normal bundle to an immersion of Ln(p) in the Euclidean space R2n+1+t. We show several concrete cases in which is stably extendible to Lk(p) for any k with k?n, and in several cases we determine the exact value m for which is stably extendible to Lm(p) but not stably extendible to Lm+1(p).     

应用蛋白质组学方法分析猪晶状体不同区域上皮细胞中蛋白质的表达差异

应用蛋白质组学方法分析比较猪晶状体中央和周边上皮细胞的蛋白质表达差异。将32个正常猪晶状体前囊膜所附着于的上皮细胞分为中央和周边两部分，经二维凝胶电泳分离和凝胶考马斯亮兰染色，质谱（MALDI—TOF—MS）鉴定差异蛋白质斑点，并对鉴定的蛋白质进行分类。结果显示来自中央与周边区域的猪晶体上皮细胞的蛋白在二维凝胶上分别有801和886个蛋白质斑点，鉴定出差异表达蛋白84个：差异表达的蛋白质在功能上有一定趋向性，主要涉及代谢、细胞骨架、信号转导／细胞周期／转录因子等。     

468-W CW operation of a diode-pumped Nd:YAG rod laser with high beam quality and highly efficient concentrator of pump light

A novel design of an efficient, highly reliable, and good beam quality diode-pumped solid-state laser for precise material processing application is presented. Effort has been done to obtain a highly uniform pumping intensity in the active area, which simultaneously reduces the effects of thermal gradient. In this design a novel lens duct configuration which send the light into the center of the rod is used. By this way a uniform power distribution and a maximum absorption of pump power is resulted. Adopting this design, the maximum laser power of 468 W with optical to optical efficiency of 33% in CW mode and M² factor of less than 15 is obtained. Numerical analysis also indicates the superiority of the design to other methods such as direct and diffusive pumping techniques.     

复消色差的短波红外望远物镜设计

分析计算了一些普通光学玻璃及晶体光学材料在0.9~2.5 μm短波红外段的色散特性.在远距型的物镜结构后组中采用的厚弯月镜能产生一定量的反向色差补偿前组中的二级光谱,所设计的物镜在焦距800 mm时的带孔径处最大色差0.13 mm.结果表明,采用氟化物玻璃与重火石玻璃的三片式组合在短波红外段具有较好的消色差能力.     

A Spectrometer Based on Diffractive Lens

A novel spectrometer is designed based on diffractive lens. It is essentially a flat field spectrometer. All the focal points are along the optical axis. Besides, all the asymmetrical aberrations vanish in our mounting. Thus low aberration can be obtained. In this article a diffractive lens is modeled as a special grating and analyzed by using a grating-based method. And a stigmatic point is introduced to reduce the aberrations.     

伴有冰晶生成的第一类冻涨问题解的唯一性

本文研究了伴有冰晶生成的第一类冻涨问题古典解的唯一性问题，当ε＝０临界情况时，作者引入了一种处理问题的新方法即“区域减少法”完成了对该数学模型适定性的论证。