  Identifying the mode numbers in whispering-gallery mode resonators (WGMRs) is
important for tailoring them to experimental needs. Here we report on a novel
experimental mode analysis technique based on the combination of frequency
analysis and far-field imaging for high mode numbers of large WGMRs. The radial
mode numbers q and the angular mode numbers p=$\ell$-m are identified and
labeled via far-field imaging. The polar mode numbers $\ell$ are determined
unambiguously by fitting the frequency differences between individual
whispering gallery modes (WGMs). This allows for the accurate determination of
the geometry and the refractive index at different temperatures of the WGMR.
For future applications in classical and quantum optics, this mode analysis
enables one to control the narrow-band phase-matching conditions in nonlinear
processes such as second-harmonic generation or parametric down-conversion.
