Particle Displacement and Velocity Measurement Using Holography
Abstract
A method of measuring particle displacements and velocities in the transform plane of a doubleexposure hologram is examined both theoretically and experimentally. The analysis begins with a study of the transform patterns obtained from singleexposure holograms (both inline holograms and offaxis holograms are considered). Although the transform of an inline hologram and an offaxis hologram are similar, the onaxis images of an inline hologram are shown to produce a zone lens which is not observed in the transform plane of an offaxis hologram. The Fourier transform patterns of doubleexposure holograms are then examined, and it is shown that each pair of particle images related by translation contributes a set of cosine fringes to the total diffraction pattern. The frequency and orientation of the fringes are related to the magnitude and direction, respectively, of a given particle's displacement or velocity. The transform patterns corresponding to 1 and 2dimensional distributions of displacement are examined in detail. For the 1dimensional case, a theoretical analysis indicates that the probability density function that characterizes the distribution of displacements may be determined by properly processing intensity data measured in the transform plane of a doubly exposed hologram. For the 2dimensional case it is shown that the marginal density functions may be obtained if the orthogonal components of particle displacement are statistically independent. Experimental results are presented, and good agreement between theory and experiment is observed.
 Publication:

Ph.D. Thesis
 Pub Date:
 December 1985
 Bibcode:
 1985PhDT........39M
 Keywords:

 FARFIELD;
 SPRAY ANALYSIS;
 Physics: Optics;
 Displacement;
 Fourier Transformation;
 Holography;
 Particles;
 Velocity Measurement;
 Diffraction;
 Probability Density Functions;
 Instrumentation and Photography