Is this primarily done analyzing the Voigt profiles absorption bands on background of stellar spectra or on re-emission bands of atmospheric compounds? Assuming Pluto's atmosphere behaves like an ideal gas, one is dealing with three unknowns - pressure, particle density, and temperature. Looking at the Lorentzian portion of curve, one can get the product of particle density and relative velocity. While looking at the Gaussian portion of the curve, one can get the temperature. Just curious how this is actually done.
Stellar occultations of distant atmospheres produce light curves that are almost entirely due to refraction, not opacity (absorption), in those atmospheres. Ray paths of light rays encountering the atmosphere bend slightly toward the planet (or moon, in cases like Triton) due to refraction. During immersion (movement of the ray path deeper into the atmosphere), the deeper that ray path goes, the larger the bend angle. Also, the larger the derivative of the refractive index with respect to radius from the planet's center, the greater the bend angle.
If you assume that the receiving aperture is circular, such as a telescope mirror, or an antenna aperture for a radio telescope or DSN station, then before the occultation starts, the rays of light arriving at the receiving aperture are confined essentially to a cylinder of the same radius as the aperture. At the distance of the occulting planet they are also confined to a cylinder, so all the energy arriving at the aperture passes through that cylinder near the planet. The intensity of that signal yields a total signal power arriving at the aperture, pre-occultation.
When the near-planet cylinder encounters the planet's atmosphere, the rays in the part of the cylinder nearest the planet are bent more than those at the other side of the cylinder, so they begin to diverge. The angles involved are extremely small, but over the distance to Earth the divergence can become large. What was formerly a circular cylinder of ray paths between the planet and Earth becomes elliptical in cross-section, with its short dimension the same as the cylinder's diameter, and the long dimension greater than the cylinder's diameter. Thus the signal's energy flux (intensity) that was once spread over the circular cross-section of the cylinder is now spread over an elliptical cross-section of larger area, so the signal power per unit area decreases: the signal intensity decreases. Signal intensity is the quantity measured by the instrument (a photometer) at the telescope. In the radio occultation community, this elongation of the signal envelope, and the subsequent decrease in signal intensity, is called "beam spreading".
The mathematics involved was first presented by W.A. Baum and A.D. Code in 1953, soon after equipment became available to record time series of signal intensity ("occultation profiles"). It is covered in exquisite detail in abundant papers from the 1950's and 1960's by researchers such as Von. R. Eshleman, H. Taylor Howard, G. Leonard Tyler, and G. Fjeldbo, notably a 1982 review paper by Tyler. Since their primary interest was for spacecraft-based radio occultation, their solutions are for a general case where the "star" (the signal source) is at a finite distance behind the planet. For stellar occultations the stars are so distant that they can be considered at infinite distance. A 1979 review paper by James L. Elliot, and a subsequent one by Elliot and C.B. Olkin, do a good job of summarizing the stellar occultation technique. Data reduction algorithms for converting occultation profiles to vertical profiles of refractive index at the planet are not simple for non-infinite sources, usually involving numerical solutions to integral equations. The radio occultation data reduction equations are still valid for stellar occultation, and in fact are somewhat simpler for a fixed, infinite-distance source, but usually the Baum-Code solutions are sufficient.
Most stellar occultations occur with fairly faint stars, so there isn't sufficient signal intensity to do high-resolution (in wavelength) spectroscopy with the occultation data. Without high-resolution data you just can't analyze narrow line shapes to infer atmospheric characteristics from them.
For infinite-distance sources the depth of penetration, i.e. the minimum planet-centered radius the ray path achieves before the signal intensitiy is lost in noise, is typically quite high in the atmosphere, where pressures are measured in microbars. Usually there is little signal exinction there from mechanisms such as continuum signal absorption or scattering from particulates, though it is possible that stellar occultations of Pluto and Triton have seen extinction due to atmospheric hazes.