Spline function methods are presented for the analysis of optical spectra of solids. Algorithms for differential energy spectra

Kramers-Kronig transform and sum ruls are developed on the basis of the third spline interpolation. We demonstrated the first and the third differential spectra

Kramers-Kronig transformation and other integral relations of Si dielectric function measured by ellipsometric spectroscopy and compared them with those by other numerical methods. Spline function methods have the merits of flexibility

high speed and high accuracy. By means of optimization

the electronic critical point parameters can be determined from the differential spectra obtained using spline function.