  We show that the shape of P-Cygni line profiles of photospheric phase
supernova can be analytically inverted to extract both the optical depth and
source function of the line -- i.e. all the physical content of the model for
the case when the Sobolev approximation is valid. Under various simplifying
assumptions, we derive formulae that give S(r) and tau(r) in terms of
derivatives of the line flux with respect to wavelength. The transition region
between the minimum and maximum of the line profile turns out to give
especially interesting information on the optical depth near the photosphere.
The formulae give insights into the relationship between line shape and
physical quantities that may be useful in interpreting observed spectra and
detailed numerical calculations.
