本文中應用雷建德多項式展開可變折射率平板的輻射熱傳遞方程式中的角度再分配項，藉由此種展開方式，本文得到一種新的解折射平板中之輻射熱傳遞的離散方向法。產生的差分方程式則以有限差分方法求解。而有限雷建德轉換的離散方向法也可以結合Chandrasekhar的方法成為修正的有限雷建德轉換的離散方向法。文中以上述方法應用於各種非等向散射相函數的折射介質。首先，本文的結果顯示上述方法可以產生精確的結果，而修正的離散方向法之結果較未修正的離散方向法之結果更加準確。然後本文檢驗光學厚度與散射比對折射平板之反射率與穿透率的影響。

In this work, an expression of the angular redistribution term appearing in the radiative transfer equation for radiation transfer in a refractive planar medium is derived from the expansion of the radiative intensity on the basic of Legendre polynomials. Using the expression, we obtain a new discrete ordinates representation of the radiative transfer equation for radiation transfer in a refractive planar medium. The set of the resulting differential equation are solved by finite difference method. The present discrete ordinates method (DOM) associated with the finite Legendre transform can also be applied to the Chandrasekhar’s modified discrete ordinates method. We apply the above methods to radiative transfer in refractive media with various scattering phase functions and distributions of refractive index. First, we show that the above method can generate accurate results and the results of modified DOM are usually more accurate than those obtained by the original DOM. The effects of the optical thickness and the scattering albedo on the reflectance and the transmittance of a refractive slab are then examined.

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