Nils Damaschke Æ Holger Nobach Æ Thomas I. Nonn Nikolay Semidetnov Æ Cameron Tropea Multi-dimensional particle sizing techniques Published online: 17 June 2005 Ó Springer-Verlag 2005 Abstract Two techniques for multi-dimensional sizing of spherical particles are discussed and compared with one another: interferometric particle imaging (IPI) and a novel technique known as global phase Doppler (GPD). Whereas the IPI technique is known from various previous studies and uses a laser light sheet illumination of the particle field, the GPD technique is a new method and employs two intersecting laser light sheets. The resulting far-field interference pattern arises from the interference of like scattering orders from the particle, similar to the phase Doppler technique. A description of this far-field interference is given for both techniques. Both multi-dimensional particle sizing techniques sample the scattered light in the far-field by means of a defocused imaging system. The diameter of each droplet illuminated by the laser light sheet(s) is determined by measuring the angular frequency of the interference fringes in the defocused images. Combined with a pulsed laser, the technique also allows the velocity of the particle to be determined, similar to particle tracking velocimetry (PTV). However, the size of the defocused image of each particle also depends on the position of the particle perpendicular to the laser sheet, hence, with appropriate calibration, the third component of velocity is also accessible. The two techniques, IPI and GPD, are compared to one another in terms of implementation and expected accuracy. Possibilities of combining the two techniques are also discussed. Some novel approaches for the signal processing have been introduced and demonstrated with simulated and real signals. 1 Introduction Multi-dimensional particle sizing refers to the possibility of sizing a number of particles simultaneously within a defined observation volume, while still retaining information about each individual particle size. This is in contrast to single-point counting techniques, such as the phase Doppler technique or photon correlation spectroscopy, which sample only those particles passing through a very small volume, one at a time, and to ensemble techniques, such as diffraction spectroscopy, which yield only overall size distributions, but with no direct counting of the number of particles sampled. There are several techniques which can be classed as multi-dimensional particle sizing; perhaps the most intuitive being direct imaging, e.g., Nishino et al. (2000) and Pan et al. (2002). This technique is not yet wide- spread for particle sizing; it has only become feasible with high-resolution CCD cameras and fast image pro- cessing possibilities. However, direct imaging potentially offers size estimates of irregularly shaped particles. Difficulties arise with the definition of the size of the observation volume and with optical access, and a compromise is made between observation area and size resolution. Therefore, this technique is more applicable for sizing larger particles and only for dilute systems. In the present study, two interferometric techniques will be examined, which observe the scattered light from homogeneous spherical particles in the far field. The first of these techniques has been previously described under various names: planar Mie scattering interferometry (PMSI), planar interferometric imaging (PII), Mie scat- tering imaging, planar particle image analysis (PPIA), interferometric light imaging for droplet sizing (ILIDS), This manuscript was submitted following the 11th International Symposium on Applications of Laser Techniques to Fluid Me- chanics-July 2002, Lisbon, Portugal. N. Damaschke (&) Æ H. Nobach Æ N. Semidetnov Æ C. Tropea Chair of Fluid Mechanics and Aerodynamics, Darmstadt University of Technology, Petersenstr. 30, 64287 Darmstadt, Germany E-mail: damaschke@sla.tu-darmstadt.de Tel.: +49-6151-166558 Fax: +49-6151-164754 T. I. Nonn Dantec Dynamics A/S, Tonsbakken 16-18, P.O. Box 121, 2740 Skovlunde, Denmark Experiments in Fluids (2005) 39: 336–350 DOI 10.1007/s00348-005-1009-1