Efficient automated algorithm for the sizing of dielectric microspheres using the resonance spectrum

Abstract

We describe an efficient algorithm for the sizing of single microspheres having a known index of refraction as a function of wavelength. The algorithm employs a peak-detection routine that determines several resonant frequencies in the radiation scattered from the particle. These measured resonances are then compared with entries from a library of stored resonance locations in order to determine a few neighborhoods within which the size of the particle is likely to lie. A final step finds a local minimum of the cost function within each neighborhood, and the size estimate is determined by selecting the smallest of these local minima. The algorithm has modest computational and memory requirements, and it requires no analysis of complicated features of the resonance spectrum that would call for human intervention. Hence it could be automated for nearly real-time operation using a microprocessor. When applied to the measured resonance spectrum of a fluorescent polystyrene sphere, the algorithm finds the radius with an accuracy limited only by such factors as surface roughness, asphericity, and imperfect knowledge of the refractive index. The algorithm is currently limited to use with first-order resonances.