Generally no, since the thin film made will be mostly without inherent color, any color you see is most likely due to optical interference due to the thin layer.
As such, there is no specific formulae. However, if you apply Raman Specroscopy, I think you will attain some result. By comparing two Gaussians around G-peak and D-peak, you can have ratio of areas (intensity) giving information of sp3 and sp2 bonds content in DLC films. However, it is going to be more qualitative than quantitative.
UV excitation gives rise to an extra Raman peak (the so called T-peak) that is indicative of sp3 bonding, and along with the C-Hx stretching mode at 2920 cm-1, it can be used to study relative changes in sp2/sp3 ratios. The following references provide further detail.
Ferrari, A.C. and J. Robertson, Interpretation of Raman spectra of disordered and amorphous carbon. Phys. Rev. B, 61(20): 14095-14107. (2000).
Ferrari, A.C. and J. Robertson, Resonant Raman spectroscopy of disordered, amorphous, and diamondlike carbon. Phys. Rev. B, 64(7). (2001).