Particle positioning from charge-coupled device images by the generalized Lorenz–Mie theory and comparison with experiment

Abstract

Three-dimensional position and velocity information can be extracted by direct analysis of the diffraction patterns of seeding particles in imaging velocimetry with real-time CCD cameras. The generalized Lorenz-Mie theory is shown to yield quantitatively accurate models of particle position, such that it can be deduced from typical experimental particle images with an accuracy of the order of 20 microm and an error of 11 gray levels rms, data obtained by comparison of theoretical and experimental images. Both the theory and an experimental verification of the problem presented here are discussed.

Characterizing and tracking single colloidal particles with video holographic microscopy

“…Others require better ways to measure particles' sizes and to characterize their optical properties, particularly if these measurements can be performed on individual particles in situ. This Article demonstrates that images obtained with in-line holographic microscopy 1,2 can be interpreted with Lorenz-Mie theory 3,4 to obtain exceptionally precise measurements of individual colloidal spheres' dimensions and optical properties 5,6 while simultaneously tracking their three dimensional motions with nanometer-scale spatial resolution at video rates 7 . This method works over the entire range of particle sizes and compositions for which Mie scattering theory applies, and requires only a single calibration of the optical train's magnification.…”

“…is dominated by long-wavelength variations in |u 0 (ρ)| 2 . The resulting distortions have been characterized 12 , but were not corrected in previous analyses of I(ρ) 5, 6,7,12,13 . Fortunately, |u 0 (ρ)| 2 can be measured in an empty field of view, and the in-line hologram can be normalized to obtain the undistorted image…”

Robust genetic algorithm for high-accuracy particle position estimation in three-dimensional particle image velocimetry applications

“…Previous works employing a more detailed treatment 4,7 have shown that the scattered intensity field produced by micronsized particles is not symmetric about the focus plane. Therefore, there can be no ambiguity of particle position for particles on either side of the focus plane.…”

“…A program for calculating the GLMT scattering field of particles at any given position when illuminated by plane, Guassian, spherical, or elliptically shaped incident beams has been previously reported by our group for particle image velocimetry applications. 4 However, a detailed model of the behavior of illuminated particles is insufficient to produce a practical positioning algorithm, unless means are found to make it applicable for low-magnification conditions, so that correspondingly large investigation volumes can be achieved.…”

Particle positioning from CCD images: experiments and comparison with the generalized Lorenz-Mie theory

“…The GLMT deals with arbitrarily shaped incident beams [25,26]. It is thoroughly covered in a complementary paper applied to velocimetry [27], in which the full mathematical approach is described. Simplifications in formulating the physical problem to be solved were considered, e.g.…”