Optical studies of a liquid crystalline compound 6O.6

A detailed optical study for a Schiff's base liquid crystalline nO.m compound (6O.6) is reported in this article. The phase transition temperatures for the compound were investigated using a polarising microscopy and differential scanning calorimetry (DSC). Refractive index studies were conducted using the thin prism method with the 633 nm line from a He–Ne laser. The order parameters of the compound were calculated from the refractive index data. Order parameters calculated by two methods, namely, direct extrapolation method and modified Vuks’ method were found to be in close agreement. The normalised polarisabilities for extraordinary and ordinary rays and their ratio for the sample were also calculated. The order parameters are found to be reasonably high and the trend shown by normalised polarisabilities substantiates the correctness of our results. From the methods we adopted, the order parameters and the normalised polarisabilities could be determined directly from the refractive index measurements without doing the density studies. Both these methods are found to be highly suitable for the calculation of order parameters of liquid crystalline compounds having high clearing temperature where density studies are difficult and hazardous.     

若干倍图的均匀染色

用归纳法完全解决了星、扇、轮和棱柱这4类图的倍图的均匀染色问题，对这些图给出了均匀色数，并对相应的图给出了具体的染色方法，这些结果部分支持了均匀染色猜想．     

Comparison of Si_n~+ and Ge_n~+(n=2―15) Cationic Structures

We designed and optimized a large number of the isomers of Si12+ at the level of density functional theory (DFT)-B3LYP/6-311++G(d) using the Gaussian 03 software package. An unambiguous structure of the Si12+ cluster is presented, whose IR spectrum agrees well with the experiment result. The most stable geometric structures of Gen+(n=2―15) clusters were determined by the all-electron PBE/DND method in DMol3 of the Material Studio Package, and compared with those of the corresponding Sin+ geometries. Most st...     

残棱柱体模和数的上界

各种和图标号都可用作图的压缩表示.一个图G称为和图,若它同构于某个SN的和图.一个图G称为模和图,若它同构于某个S{1,2,……,m-1}且所有算术运算均取模m(≥S 1)的和图.图G的模和数ρ(G)是使得G∪ρK1是模和图的非负整数ρ的最小值.Cn×K2称为棱柱体,将棱柱体上下底面的棱Cn进行一次剖分所形成的图形称为残棱柱体.给出了残棱柱体的模和标号,从而证明了残棱柱体的模和数的上界为4.     

前视悬挂棱镜测距法在矿山井下测量中的应用

以马兰矿井下30s导线距离测量前视悬挂棱镜测距的应用为例,重点介绍了前视悬挂棱镜测量距离的操作方法和数据处理,指出该操作方法有效地提高了矿山井下测量作业效率和测量成果质量,并在此基础上分析了前视悬挂棱镜测距法作业的优点,探讨了在作业过程中存在的一些问题及在测量方面的局限性,展望了今后的发展方向。     

光波导技术同步测量棱镜及波导薄膜参数

依据全反射理论和棱镜耦合原理,实现了对棱镜折射率及波导薄膜材料折射率和厚度的同步测量。使用高准直半导体激光器激光入射到棱镜内部与波导膜的分界面上,逐步旋转棱镜或改变棱镜的入射角,得到棱镜耦合M线,曲线前面几组的波谷为波导模激发,在M线左侧收尾处有一个不完整波峰,其反射光强随入射角迅速衰减,为全反射时的临界点,由此可实现棱镜及波导薄膜参数的同步测量;用此法测量了棱镜耦合一体化平面波导棱镜的折射率和聚甲基丙烯酸甲酯(PMMA)聚合物波导薄膜的折射率和厚度。测量棱镜折射率精度为±1.9×10-4,波导薄膜折射率和厚度的精度分别为±6.2×10-4 μm和±1.6×10-2 μm。     

空间外差光谱仪视场展宽棱镜设计理论与方法

空间外差光谱仪采用特定楔角的棱镜实现视场拓展是提高仪器通量和辐射灵敏度的重要手段之一。借鉴传统傅里叶变换光谱仪视场展宽基础理论,结合空间外差光谱仪的技术特点,研究了基于数值归纳方法进行视场展宽棱镜设计的理论依据和实现途径。分析了不同Littrow角和目标波数下视场展宽棱镜顶角的最优取值及最大视场展宽容限。结果表明数值归纳方法全面衡量各级次视场对相位差的影响给出视场展宽棱镜顶角的最优取值,与传统理论推导方法相比,沿色散主截面方向视场容限提高了10%～30%,且数值归纳方法设计空间外差视场展宽棱镜简单、直观,在设计过程中可同时分析仪器参数对视场展宽容限的影响。     

A displacement measurement system, utilizing a Wollaston interferometer

A dual interferometric displacement measurement system is presented where a Wollaston prism interferometer is employed in conjunction with a normal Michelson interferometer. The system operates without the use of external polarizers, apart from those associated with the Wollaston prism interferometer itself. It is shown that an optical path difference induced in the Michelson interferometer can be detected using the Wollaston prism in a normal interferometer arrangement. Further, the interference pattern produced by the Wollaston prism interferometer changes in a measurable, linear fashion as the optical path difference from the Michelson interferometer alters. A simple theoretical analysis of the system is presented and used to derive a computer model of the optical arrangement. Results from an experimental implementation of the system, using a Wollaston prism with a beam separation of 0.5 degrees and a superluminescent diode, of wavelength 825 nm, as a light source, are included and compared to the results from the computer model.     

Quantitative characterization of optical anisotropy in high refractive index films

Waveguide coupling measurements of polymers have largely concentrated on the application of mode analysis to the study of thin supported films (such as spin coatings). The use of prism coupling to study thick, freestanding polymer films, however, has not been reported. In this paper, the ability of prism coupling to characterize the three-dimensional optical properties of thick, freestanding polymer films and sheets is demonstrated. A modified prism coupling procedure is described that allows the determination of all three principal refractive indices in thick, three-dimensionally anisotropic freestanding films. A Metricon prism coupler is used in a manner similar to an Abbé refractometer for the measurement of isotactic polypropylene, poly(ethylene terephthalate), PMDA-ODA polyimide, and poly(phenylene sulfide). Three series of PMDA-ODA films are also investigated in this study. The first series has been drawn to different extensions from three-dimensionally random films. The second series has random orientation in the plane of the film but different degrees of planarity with respect to the through direction. The third series are commercial films of varying thickness. These three series of films are compared as to the optical an-isotropy that is developed from the three different fabrication processes. © 1993 John Wiley & Sons, Inc.     

棱镜型光热偏振光谱法

提出了一种高灵敏度的棱镜型光热偏转光谱法,给出了系统的理论分析,导出了由泵浦光引起的探测光的偏向角表达式.并与普通型光热偏转技术作了比较,理论分析结果表明,棱镜型光热偏转检测方法比普通型光热偏转技术具有更高的灵敏度.