Influence of the Measurement Volume on the Phase Error in Phase Doppler Anemometry. Part 1: Reflective mode operation

Abstract

In phase Doppler anemometry (PDA), phase difference errors are caused by the Gaussian intensity distribution of the laser beam and the curvature of the phase fronts outside of the beam waist. This results in erroneous particle sizes. Based on a physical analysis by geometrical optics [1], this phase difference error is evaluated for reflected mode operation (Part I) and for refracted mode operation (Part II). By varying the particle trajectories statistically, the error in determining the particle size and the mass flow can be simulated. By the method described the error in the measured phase difference can easily be estimated.

The imaging properties of scattering particles in laser beams

“…The computation of the interaction points on the surface of a spherical particle for given detector and particle positions is therefore an iterative process, since the incident wavevector is not known until the incident interaction point is known. The rules of geometrical optics for plane waves have to be applied for each calculated incident interaction point separately [15,25,26]. In the case of plane-wave illumination, the determination of the interaction points and the light path through the particle is not necessary; for the EGO it is the basis of the calculation.…”

“…For a particle at position 1 in figure 10, the incident interaction point for the dominant scattering order lies outside a region of significant incident amplitude, whereas for position 2 the incident interaction point is well within the bounds of the beam. The exact position of the incident interaction point depends on the scattering order considered, the particle diameter, the relative refractive index and the point-detector position [25,26]. The positions of the interaction points can be determined using methods of geometrical optics (ray tracing) [15].…”

“…For reflection the location of the incident interaction and glare point with respect to the centre of the particle is given by [25] r (1) br = r p e (1) br = r p e (1) sr − e (1) W |e (1) Sr − e (1) W |…”