The determination for the presence of FeO can be realized by two approaches. One is in the presence of a real experiment in which we have a reaction with Fe and O. The reading of this phase can be realized by X-ray structural analysis (X-RAY). Another approach is by simulating the process, using research data or literature for input data in the software. In this variant, a mathematical model can be created for the optimized variant, which can be verified experimentally. When differences arise, new adjustments are made to the mathematical model. This is repeated until a similarity is found between the experiment and the mathematical model.
Olivine structure contains only 2-valent iron and can be written in sub-lattice form of (Fe,Mg)2(Si)(O)4. Thus, the molar fraction of (Fe+Mg) to Si is always constant and the fact can be used for estimating the total concentration of olivine in a system.
Pekka's suggestion would work well if you need a rough estimate of FeO concentration. Natural olivines would also have small amount of NiO, MnO, CaO, TiO2, Al2O3, you'll get more accurate result if these minor elements concentrations are known.