Bartell F O, Wolfe W L
Appl Opt. 1976 Jan 1;15(1):84-8. doi: 10.1364/AO.15.000084.
Multiple reflection considerations give cavity emissivity as an infinite series of nested integrals. The Liou-ville-Neumann series solution to the Fredholm integral equation of the second kind gives the same series for integral equation formulation of the cavity problem when the walls are gray, Lambertian, and isothermal. A compact solution, derived from the series, stimulates interesting comparisons among the multiple reflection analyses of Gouffé, De Vos, Treuenfels, Kelly, and Bartell and Wolfe and the integral equation theories of Sparrow, Albers, and Eckert; Sparrow and Jonsson; Syndor; Bedford and Ma; and Chandos and Chandos.
多次反射因素将腔体发射率表示为一系列无穷嵌套积分。当壁面为灰色、朗伯型且等温时，第二类弗雷德霍姆积分方程的刘维尔 - 诺伊曼级数解为腔体问题的积分方程形式给出了相同的级数。从该级数推导得出的一个简洁解激发了古费、德沃斯、特罗伊恩费尔斯、凯利、巴特尔和沃尔夫的多次反射分析与斯帕罗、阿尔伯斯和埃克特；斯帕罗和琼森；辛多尔；贝德福德和马；以及钱多斯和钱多斯的积分方程理论之间有趣的比较。
