椭圆积分表示的点源处圆柱形探测器对向立体角
Solid angle subtended by a cylindrical detector at a point source in terms of elliptic integrals
摘要：
位于任意位置的点源处的直圆柱所对的立体角通常由两项之和组成：由圆柱表面（$Ω_{cyl}$）定义的立体角和由任一端圆（$Ω_{circ}$）定义的立体角。我们推导出一个表达式$Ω_{cyl}$的第一和第三类椭圆积分，并给出类似的表达式$Ω_{circ}$使用的第一和第二类积分。这些后者可以用来替代表达式也在椭圆积分方面，由于菲利普A。麦克林和包括作为一个脚注在面具（修订版科学。仪器，28（3），191-197，1957）。当源位于任意位置时，整个圆柱体所对的立体角可以使用椭圆积分来计算。
英文摘要：
The solid angle subtended by a right circular cylinder at a point source located at an arbitrary position generally consists of a sum of two terms: that defined by the cylindrical surface ($Ω_{cyl}$) and the other by either of the end circles ($Ω_{circ}$). We derive an expression for $Ω_{cyl}$ in terms of elliptic integrals of the first and third kinds and give similar expressions for $Ω_{circ}$ using integrals of the first and second kinds. These latter can be used alternatively to an expression also in terms of elliptic integrals, due to Philip A. Macklin and included as a footnote in Masket (Rev. Sci. Instr., 28 (3), 191-197, 1957). The solid angle subtended by the whole cylinder when the source is located at an arbitrary location can then be calculated using elliptic integrals.
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