A simple way of quantification is to carry out Mott-Schottky analysis using electrochemical impedance spectroscopy and determine charge carrier density. However, here the assumption is that oxygen vacancies are the charge carriers. The assumption can be supported by XPS, Raman, or EPR (paramagnetic resonance) results.
Raman and XPS can be very helpful in calculation of oxygen vacancy. Also, the concentrations of different oxidation state of metal ions can also be calculated via XPS. Here I am sharing some articles that might help you
Article Electronic Structure and Photocatalytic Activity of Samarium...