Uncertainties in visibility and phase response functions of optical single-particle counters using the laser Doppler velocimeter optical configuration

Abstract

Particle sizing uncertainties were calculated for the visibility and phase response functions of a dual-beam laser Doppler velocimeter. This uncertainty primarily results from the nonmonotonic behavior of the response functions versus particle size and varies with particle index of refraction and the velocimeter optical configuration, in particular the receiving lens diameter and location. An exact Mie-scattering algorithm predicted the velocimeter response functions for a number of particle indices of refraction and a variety of receiving lens configurations. Uncertainties were determined from the predicted particle size parameter increments corresponding to unit increments in the associated response functions. When examining uncertainties for particles with different refractive indices, the minimum and maximum response function values were used to obtain the associated size parameter increments. Particle sizing uncertainties tend to increase with the particle index of refraction for both visibility and phase. Receiving lens locations for minimal size measurement uncertainties are generally in the backscatter direction for visibility, and in the forward scattering direction near the incident beam plane, with a zenith angle of about 60°, for phase. A large receiving lens (f/♯≊1) minimizes uncertainties for visibility while a moderate lens (f/♯≊2) minimizes uncertainties for phase. Phase generally provides small uncertainties for particles with the same index of refraction but visibility provides smaller uncertainties when the particles have a range of refractive indices.