...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Journal of Modern Optics >Angular distribution of an average solid angle subtended by a circular disc from multiple points uniformly distributed on a planar circular surface coaxial to the disc
【24h】

Angular distribution of an average solid angle subtended by a circular disc from multiple points uniformly distributed on a planar circular surface coaxial to the disc

机译：圆盘从均匀分布在与圆盘同轴的平面圆形表面上的多个点对着的平均立体角的角分布

获取原文
获取原文并翻译 | 示例
   

获取外文期刊封面封底 >>

       
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Average solid angles subtended by an external contour of a given body from several points are required for the calculation of radiation fluxes or particle beams that are incident on the body from multiple-point isotropic emitters of analogous kinds. To consider the refraction effects for fluxes of light propagating through various optical media, knowledge of the angular distributions of such average solid angles is necessary. In this paper the formula describing angular dependence of the average solid angle subtended by a circular disc from uniformly distributed points within the circular surface of a parallel and coaxial disc was derived analytically and used for the calculation of some representative results. The solution has been made in the cylindrical coordinate system. The final and some intermediate formulas were expressed as functions of the polar angle, of the radii of both discs and of the distance between their planes. These formulae were represented by superpositions of simple elementary functions, single integrals of these superpositions and by incomplete and complete Legendre-Jacobi elliptic integrals of all three kinds. Mathematica 2.2.3 software was used to illustrate graphically the relationships between some computed data. These data indicate that the derived formula is directly applicable in any computer programs calculating the Legrendre-Jacobi elliptic integrals to estimate the fluxes of optical radiation and particle beams propagated within a non-absorbing homogeneous medium. The expressions obtained may also be used to calculate the fluxes of optical radiation propagated through various homogeneous media. [References: 20]
机译：给定物体的外部轮廓从几个点对着的平均立体角，对于从类似种类的多点各向同性发射器入射到物体上的辐射通量或粒子束的计算是必需的。为了考虑通过各种光学介质传播的光通量的折射效应，必须知道这种平均立体角的角分布。在本文中，从解析上推导了描述圆盘从平行和同轴圆盘的圆表面内的均匀分布点对着的平均立体角的角度依赖性的公式，并将其用于一些代表性结果的计算。解决方案已在圆柱坐标系中提出。最终和一些中间公式表示为极角，两个圆盘的半径以及它们的平面之间的距离的函数。这些公式由简单基本函数的叠加，这些叠加的单个积分以及所有这三种类型的不完全和完整的Legendre-Jacobi椭圆积分表示。使用Mathematica 2.2.3软件以图形方式说明一些计算数据之间的关系。这些数据表明，导出的公式可直接用于计算Legrendre-Jacobi椭圆形积分的任何计算机程序中，以估计在非吸收性均匀介质中传播的光辐射和粒子束的通量。获得的表达式也可以用于计算通过各种均匀介质传播的光辐射通量。 [参考：20]

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号