Nichelatti E, Pozzi G
Ente per le Nuove Tecnologie, l'Energia e l'Ambiente, Centro Ricerche Energia Casaccia, Via Anguillarese, 301, 00060 Roma, Italy.
Appl Opt. 1998 Jan 1;37(1):9-21. doi: 10.1364/ao.37.000009.
Improved beam propagation method (BPM) equations are derived for the general case of arbitrary refractive-index spatial distributions. It is shown that in the paraxial approximation the discrete equations admit an analytical solution for the propagation of a paraxial spherical wave, which converges to the analytical solution of the paraxial Helmholtz equation. The generalized Kirchhoff-Fresnel diffraction integral between the object and the image planes can be derived, with its coefficients expressed in terms of the standard ABCD matrix. This result allows the substitution, in the case of an unaberrated system, of the many numerical steps with a single analytical step. We compared the predictions of the standard and improved BPM equations by considering the cases of a Maxwell fish-eye and of a Luneburg lens.
针对任意折射率空间分布的一般情况，推导了改进的光束传播法（BPM）方程。结果表明，在傍轴近似下，离散方程对于傍轴球面波的传播有解析解，该解收敛于傍轴亥姆霍兹方程的解析解。可以推导出物平面和像平面之间的广义基尔霍夫 - 菲涅耳衍射积分，其系数用标准ABCD矩阵表示。这一结果使得在无像差系统的情况下，能用单个解析步骤替代许多数值步骤。我们通过考虑麦克斯韦鱼眼透镜和伦伯格透镜的情况，比较了标准BPM方程和改进BPM方程的预测结果。
