Digital holographic particle image velocimetry: eliminating a sign-ambiguity error and a bias error from the measured particle field displacement

Abstract

In a typical digital holographic PIV recording set-up, the reference beam and the object beam propagate towards the recording device along parallel axes. Consequently, in a reconstructed volume, the real image of the recorded particle field and the speckle pattern that originates from the virtual image of the recorded particle field overlap. If the recorded particle field experiences a longitudinal displacement between two recordings and if the two reconstructed complex-amplitude fields are analysed with a 3D correlation analysis, two separate peaks appear in the resulting correlation-coefficient volume. The two peaks are located at opposite longitudinal positions. One peak is related to the displacement of the real image and the other peak is related to the displacement of the speckle pattern that originates from the virtual image. Because both peaks have a comparable height, a sign ambiguity appears in the longitudinal component of the measured particle field displacement. Additionally, the measured longitudinal particle field displacement suffers from a bias error. The sign ambiguity and the bias error can be suppressed by applying a threshold operation to the reconstructed amplitude. The sign ambiguity, characterized by , is suppressed by more than a factor of 60. The dimensionless bias error is reduced by a factor of 5.

Applications of Holography in Fluid Mechanics and Particle Dynamics

“…Because the real and virtual images are located symmetrically on both sides of the hologram, the virtual image generates a series of faint interference fringes in the real image plane and vice versa. These fringes have an adverse effect on the quality of images and may introduce a bias in some applications of holography to 3D velocity measurements (Ooms et al 2008). Figure 3d is an axial cut through the center of the reconstructed image, showing the ∼1-mm long, elongated peak causing the DOF problem.…”

“…Finally, we note that research to improve the accuracy of data-analysis procedures is still ongoing, including the development of procedures that follow substantially different paths. Ooms et al (2008) attempted to deal with challenges involved with 3D correlation-based analysis in in-line digital holograms analyzed using the complex amplitude field (as opposed to intensity distributions). Included were potential problems of directional ambiguity and bias error introduced by the presence of a virtual image.…”

Structurally controlled synthesis of synthetic gypsum derived from industrial wastes: sustainable approach

“…The decrease in size of crystals with an increase in supersaturation in the system during the deposition of poorly soluble salts has been reported in the literature. [33][34][35][36] The oversaturation of the solution with Ca 2+ and SO 4 2− ions also affects the shape of the crystals. Based on the statistical calculation of deposited gypsum crystals, it was found 22 that with a decrease in the concentrations of the initial components, the ratio of the length of the crystals to their diameter decreases by 25% from 2.00 to 1.55.…”

Direct particle depth displacement measurement in DHPTV using spatial correlation of focus metric curves

“…The depth position of a particle is enclosed in the chirp frequency of the hologram fringes, and it is difficult to obtain its exact value due to various noises, such as twin image noises, finite hologram aperture and sampling rate of CCD. Thus, various focus detection methods have been proposed to improve the accuracy of depth position [13,[24][25][26][27], and each claimed it can accurately locate the particles with a small error of z err , especially referring to the relative depth error z z / err . In the Gabor inline holography configuration, the depth position uncertainty z err usually equals to several times of the particle diameter and increases with the particle size, ranging from dozens of up to thousands of micrometers [12,20,21].…”