Self-calibrated microscopic dual-view tomographic holography for 3D flow measurements

Abstract

This paper introduces the application of microscopic dual-view tomographic holography (M-DTH) to measure the 3D position and motion of micro-particles located in dense suspensions. Pairing of elongated traces of the same particle in the two inclined reconstructed fields requires precise matching of the entire sample volume that accounts for the inherent distortions in each view. It is achieved by an iterative volumetric self-calibration method, consisting of mapping one view onto the next, dividing the sample volume into slabs, and cross-correlating the two views. Testing of the procedures using synthetic particle fields with imposed distortion and realistic errors in particle locations shows that the self-calibration method achieves a 3D uncertainty of about 1µm, a third of the particle diameter. Multiplying the corrected intensity fields is used for truncating the elongated traces, whose centers are located within 1µm of the exact value. Without correction, only a small fraction of the traces even overlap. The distortion correction also increases the number of intersecting traces in experimental data along with their intensity. Application of this method for 3D velocity measurements is based on the centroids of the truncated/shortened particle traces. Matching of these traces in successive fields is guided by several criteria, including results of volumetric cross-correlation of the multiplied intensity fields. The resulting 3D velocity distribution is substantially more divergence-free, i.e., satisfies conservation of mass, compared to analysis performed using single-view data. Sample application of the new method shows the 3D flow structure around a pair of cubic roughness elements embedded in the inner part of a high Reynolds number turbulent boundary layer.