Measurement and prediction of the gaussian beam effect in the phase Doppler technique
Under certain circumstances, particle size measurements using a phase Doppler instrument can be erroneous due to the Gaussian beam effect, sometimes referred to as the trajectory effect. This is especially true under extenuating circumstances such as when
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Abstract. Under certain circumstances, particle size measurements using a phase Doppler instrument can be erroneous due to the Gaussian beam effect, sometimes referred to as the trajectory effect. This is especially true under extenuating circumstances such as when, for cost reasons, only two detectors are being used, when the choice of detector off-axis and/or elevation angle is limited through the application, when the signal processing has only limited validation possibilities or if a particularly small measurement volume must be employed. All of these factors may be disadvantageous for measuring larger particles. In this study the physical origins of the Gaussian beam effect are examined anew. The interpretation is based on determining for each light scattering order the position of the detection volume and their separation distances from each other. Using this information and the analysis of so-called dual-burst signals, a method of estimating the maximum allowable particle size to avoid such effects is proposed. This estimation should aid users in evaluating or configuring their system for a particular application. In this method a tolerance limit is prescribed, under which the measured phase difference can vary due to unwanted scattering orders. For variations exceeding this limit, the respective particle size is considered to be too large to be reliably measured using the specified detection positions (symmetric detectors in elevation angle). These results, and also the shift of the detection volume position based on a geometrical optics analysis, have been experimentally verified. The Gaussian beam effect has been systematically demonstrated in the experiment using a stream of monodispersed droplets traversed through the measurement volume.
Introduction The phase Doppler technique is now well established as a non-intrusive method for sizing spherical, homogeneous particles and deriving corresponding volume and mass fluxes. The principle of the phase Doppler technique is based on light scattering from two plane light beams incident on the particle. The simplest phase Doppler configuration involves two detectors, placed such that a single scattering order dominates on both. Under these conditions, a linear relation between the phase difference of the detector signals and the particle diameter exists. The layout of phase Doppler systems is aided by computer programs, which compute the light scattered from spherical particles. One of the main design targets is to insure that only one scattering order dominates the light collected at the detector. For this purpose either computations according to geometrical optics (van de R. J. Adrian et al., Laser Techniques for Fluid Mechanics © Springer-Verlag Berlin Heidelberg 2002
190 Hulst 1981) for particles significantly larger than the wavelength of light, or the Lorenz-Mie theory with a Debye series expansion (Lock 1988; Hovenac and Lock 1992) can be used. In reality however, the incident beams in a phase Doppler system cannot always be approximated by a homogeneo
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