Sara Profile Analytic (or semi-analytic) version

[jdtsmith]

@sarduval:

The "Sara Profile" is what we call a Drude * Gaussian convolution, and is what instruments really deliver. To ensure the science pack is a physical description of the Universe, and all instrument-specific information is kept in the instrument pack(s), we need an analytic Sara profile, S. S takes wavelength, instrumental FWHM (probably just a single value at feature center), power, and feature intrinsic FWHM*, and produces a functional form that approximates a Drude * Gaussian (or is a real analytic function if such can be found). Key features of S:

• Must be possible to compute its integral power (semi-)analytically.
• Must be able to handle the "transition" wing vs. core power fraction between Gaussian and Drude's. Voigt profiles have this "flavor" (but not the asymmetry of a Drude).
• Be reasonably fast to compute, ideally just a "kind of Drude with extra terms".