Particle sizing by interference fringes and signal coherence in Doppler velocimetry

Abstract

To supplement another paper presented at this Symposium (which deals with sizing suspended particles by light scattering), a new optical method is proposed for sizes larger than a few wavelengths. To this end, conditions under which the alternating light signal generated by a particle traversing a fringe pattern falls to zero are examined with a view to measuring such particle sizes by varying fringe spacing. The a.c. frequency is a measure of the particle velocity and can be expressed, with identical results, either as a beat note caused by Doppler shift or in terms of the varying illumination of the particle due to its movement across the light grid. The theory, giving the a.c. amplitude for two infinitesimal particles moving with a common velocity as a function of their separation, is extended to a variable number of particles moving together. This provides the basis not only for an assessment of how the signal legibility in Doppler velocimetry falls off as the number of scatterers increases but also for the integration which treats particles of finite size as the sum of their infinitesimal elements.A variety of optical systems are proposed for measuring the size of particles, droplets, fibres, etc. under different conditions. For some purposes, fringe systems of non-uniform spacing may be advantageous and the use of a dark field schlieren image which shows the particle as a thin circumferential line—in place of the illuminated area produced by normal imaging—is often valuable. Such a schlieren system is used in a simple experimental test of the method; the results accurately conform to the theoretical predictions.