  We performed a reverse process of a usual optical data analysis of
boson-exchange superconductors. We calculated the optical self-energy from two
(MMP and MMP+peak) input model electron-boson spectral density functions using
Allen's formula for one normal and two ($s$- and $d$-wave) superconducting
cases. We obtained the optical constants including the optical conductivity and
the dynamic dielectric function from the optical self-energy using an extended
Drude model, and finally calculated reflectance spectrum. Furthermore to
investigate impurity effects on optical quantities we added various levels of
impurities (from the clean to the dirty limit) in the optical self-energy and
performed the same reverse process to obtain the optical conductivity, the
dielectric function, and reflectance. We observed that impurities give similar
effects on various optical constants of $s$- and $d$-wave superconductors; the
more impurities give the more distinct gap feature and the less superfluid
density. However, the $s$-wave superconductor gives the superconducting gap
feature more clearly than the $d$-wave superconductor because in the $d$-wave
superconductors the optical quantities are averaged over the anisotropic Fermi
surface. Our results also supply helpful information to see how characteristic
features of the electron-boson spectral function and the $s$- and $d$-wave
superconducting gaps appear in various optical constants including raw
reflectance spectrum. Our study also may help to understand the usual optical
analysis process thoroughly. Further systematic study of experimental data
collected at various conditions using the optical analysis process will help to
reveal the origin of the mediated boson in the boson-exchange superconductors.
