The complex optical conductivity may be obtained via a Kramers–Kronig transformation –– see, for example, F. Wooten, Optical Properties of Solids (Academic Press, New York, 1972).
You will need to fit the optical data with a Lorentz-Drude model in order to get the optical conductivity.
There is a straight forward software available for free called REFFIT
Tha manual is easy to understand and contains some examples. You can also refer to the following paper which is published by the programmer of the software himself.
The optical response of a material is mainly studied in terms of the optical conductivity (σ)which is given by the relation
σ=αnc/ 4π
where c is the velocity of light,α is the absorption coefficient and n is the refractive index. It can be seen clearly that the optical conductivity directly depends on the absorption coefficient and the refractive index of the material.
P.Sharma and S.C.Katyal,J.Phys.D:Appl.Phys.40,2115(2007)