Improved numerical techniques for the calculation of the reflection of electromagnetic waves by an arbitrary stratified inhomogeneity are derived and assessed. The inhomogeneity is sectioned into thin layers, in each of which the dielectric function is taken to vary linearly, or cubically, with depth. The matrices representing each layer are calculated to third order in layer thickness. Some general properties of the matrices used in these calculations are also presented.
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Lekner et al. (1987) studied this question.