Uncertainty analysis of microsphere circumference diameter measurement based on Whispering-Gallery-Mode resonance

Microspheres are widely used as reference artefacts in microscale three-dimensional metrology, yet accurate diameter measurement remains challenging. This study presents a method for evaluating the circumferential diameter of microspheres based on whispering-gallery-mode (WGM) resonance, in which the sphere itself functions as an optical resonator and its effective resonator length is derived from measured resonance wavelengths. Resonant wavelengths are measured with sub-picometer resolution using evanescent coupling via a micro-optical fiber, and the associated angular, azimuthal, and radial mode numbers are uniquely identified through near-field observation of the surface electric field intensity distribution. A Monte Carlo–based uncertainty analysis is performed to quantify the contributions of resonance wavelength measurement, refractive index variation, and mode identification. Experimental results demonstrate nanometer-scale consistency among independently evaluated modes, and the expanded uncertainty of the circumferential diameter measurement is on the order of several 10 nm. The proposed method provides a reliable and high-precision approach for microsphere diameter evaluation, suitable for dimensional metrology and calibration applications. • A circumferential diameter measurement method for microspheres based on whispering-gallery-mode resonance is proposed. • Angular, azimuthal, and radial mode numbers are uniquely identified via near-field electric field observation. • Monte Carlo–based uncertainty analysis quantitatively evaluates wavelength, refractive index, and mode identification effects. • Nanometer-scale consistency and expanded uncertainty of several tens of nanometers are demonstrated.