Experimental Study of Effect of Medium Boundary on Light Distribution in Tissue Phantoms

An experimental method for investigating the effect of medium boundary on distributions of light in the biological tissue phantom intralipid is presented. Measurements of distributions of light in intralipid-10% suspensions at 633 nm are described, in which a narrow collimated beam is incident on the surface of the phantoms and into the different depths inside of the phantoms. The experimental results show that the effect of the boundary of the medium on the curves geometry of light distributions is trivial, but the effect on intensity of scattering light is obvious, the maximal relative change of the energy fluence reaches 53.8% and the position of the peak of the energy fluence curve has a shift of 1.1 mm in the reverse direction of incident light for the phantom with albedo a=0.998, and the effect of the boundary is decreased with the increase of the absorption coefficients of tissue phantoms. The experimental results were analysed by the diffusion theory. These studies will be helpful for further understandings of the relation between the boundary of biological tissue and the distribution of light in tissue.     

R~(n+1)中常高阶平均曲率超曲面

本文给出了Rn+1中超曲面的一些积分公式,并利用这些积分公式得到了以球面为边界的常高阶平均曲率超曲面的一些唯一性结果.     

光学非球面二次曲面常数及顶点曲率的研究

受光学非球面制造过程中诸工艺参数的影响,能否保证非球面顶点曲率及二次曲面常数的精度是一个重要问题。基于二次曲面方程,推导出确定光学非球面二次曲面常数k以及顶点曲率半径r的一组算法,并在对一块口径为760mm×200mm标准非球面反射镜的实际测算中进行拟合,经过优化,拟合精度达到Δk=0.015,Δr=0.341mm,从而有效的控制了光学非球面制造过程中的顶点曲率及二次曲面常数的偏差。     

WEIERSTRASS REPRESENTATION FORSURFACES WITH PRESCRIBED NORMALGAUSS MAP AND GAUSS CURVATURE IN H~3

The author obtains a Weierstrass representation for surfaces with prescribed normal Gauss map and Gauss curvature in H3. A differential equation about the hyperbolic Gauss map is also obtained, which characterizes the relation among the hyperbolic Gauss map, the normal Gauss map and Gauss curvature. The author discusses the harmonicity of the normal Gauss map and the hyperbolic Gauss map from surface with constant Gauss curvature in H3 to S2 with certain altered conformal metric. Finally, the author considers the surface whose normal Gauss map is conformal and derives a completely nonlinear differential equation of second order which graph must satisfy.     

非平凡4—调和映照的一个必要条件

本文给出了非平凡４－调和映照的一个必要条件。     

混合曲率曲面变形方程的Tricomi问题——Ⅱ.解的存在性

本文在很弱的条件下,证明对混合曲率曲面无穷小变形方程的Tricomi问题,存在L₂弱解和H₁强解。     

COMPLETE EXTREMAL SURFACES OF MIXED TYPE IN 3-DIMENSIONAL MINKOWSKI SPACE

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双曲空间中的等参子流形

本文相应于文[1]关于 R~(n+p)中等参子流形的分类,讨论了双曲空间 H~(n+p)中等参子流形及其分类问题.