I think it is the Raman shift that can be used to detect diamond and non-diamond phases.

I would suggest infrared spectroscopic ellipsometry for that type of characterization; it is non-destructive and the substrate/interlayer materials might not "interfere" with what you want to measure.  You should be able to quantify the diamond/non-diamond ratio with the ratio of well-identified IR peaks.

XRD might be useful as well.

Knight, D. S. and W. B. White. 1989. Characterization of diamond films by Raman spectroscopy. Journal of Materials Research, Volume 4, begins on page 385.

This was the first and is still likely the best reference for your question.

For general references on the subject you can look up:

Phelps, A. W., Diamond Films, in Handbook of Materials Selection, edited by Myer Kutz, John Wiley, NY, Chapter 42, pp. 1287-1301 (2002)

https://www.academia.edu/1403125/Diamond_Films

Thank you, dear colleagues, for your valuable answers