Determination of the Size of Irregular Particles Using Interferometric Out-of-Focus Imaging

We present a mathematical formalism to predict speckle-like interferometric out-of-focus patterns created by irregular scattering objects. We describe the objects by an ensemble of Dirac emitters. We show that it is not necessary to describe rigorously the scattering properties of an elliptical irregular object to predict some physical properties of the interferometric out-of-focus pattern. The fit of the central peak of the 2D autocorrelation of the pattern allows the prediction of the size of the scattering element. The method can be applied to particles in a size range from a tenth of micrometers to the millimeter. 1. Introduction Interferometric laser imaging for droplet or bubble sizing is a very convenient technique. It is relatively simple to develop and gives accurate evaluations of the size of these scattering particles in a wide range of configurations [1–7]. In addition, real-time algorithms can be developed to investigate a whole image directly using Fourier transforms instead of investigating the interferogram droplet per droplet or bubble per bubble [8]. Unfortunately, this technique is limited to the analysis of simple scattering objects as spherical droplets or bubbles. The deformation of these objects can affect significantly the interferometric patterns (orientation and frequency of the fringes) and the analysis of complex irregular objects does not seem to be possible. In this paper, we show however that interferometric out-of-focus imaging can allow the determination of some simple morphological information of irregular particles (size and global form of the envelope). It is well established that interferometric out-of-focus imaging of droplets is based on the observation of interferences produced by the two “glare points” produced by the illumination beam on the droplet [9, 10]. Under a geometrical optics approximation, these emitters correspond to the ray reflected on the particle and the ray refracted within the droplet [11]. These emitters can be further defined using Lorenz-Mie theory expressed in terms of Debye series [10]. In the case of droplets in air, the scattering angle of 66° is currently chosen. It is indeed the angle leading to the amplitudes of the reflected beam and the refracted beam having the same magnitude. The interferences that are recorded present then a contrast reaching unity. For irregular particles, there is unfortunately no general solution to the field scattered by the particles when they are illuminated by a coherent plane wave, Gaussian beam, or laser sheet. The interferometric out-of-focus images are