Abstract
This paper presents the forms and curve-fitting techniques necessary for the calculation of ray-theory intensities for a curvilinear profile approximation in which continuity of slope as well as velocity is preserved. Using the Epstein profile as a control, this approximation is compared with various approximations that have slope discontinuities. The continuous-slope approximation does not display the artificial effects inherent in approximations with slope discontinuities, such as the introduction of spurious caustics, the omission of real caustics, and the generation of unrealistic regions of low intensity. However, artificial-layering effects in the form of infinite rates of change in intensity appear in the computations for the continuous-slope approximation because of discontinuities in the second derivative. The use of a new profile approximation that can preserve continuity of an arbitrary number of derivatives is suggested.
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