The generalized Darwin-Hamilton equations [Wuttke (2014). Acta Cryst. A70, 429-440] describe multiple Bragg reflection from a thick, ideally imperfect crystal. These equations are simplified by making full use of energy conservation, and it is demonstrated that the conventional two-ray Darwin-Hamilton equations are obtained as a first-order approximation. Then an efficient numeric solution method is presented, based on a transfer matrix for discretized directional distribution functions and on spectral collocation in the depth coordinate. Example solutions illustrate the orientational spread of multiply reflected rays and the distortion of rocking curves, especially if the detector only covers a finite solid angle.

中文翻译：

---

厚厚的镶嵌水晶多次布拉格反射。二。在网格上求解的简化输运方程。

广义达尔文-汉密尔顿方程[Wuttke（2014）。Acta Cryst。[A70，429-440]描述了从厚的，理想的不完美晶体产生的多次布拉格反射。通过充分利用能量守恒简化了这些方程，并且证明了常规的两射线达尔文-汉密尔顿方程是作为一阶近似获得的。然后，基于离散方向分布函数的传递矩阵和深度坐标中的光谱配置，提出了一种有效的数值求解方法。示例解决方案说明了多重反射射线的定向散布和摇摆曲线的畸变，尤其是在检测器仅覆盖有限立体角的情况下。