On the effect of particle image intensity and image preprocessing on the depth of correlation in micro-PIV

Abstract

The depth of correlation (DOC) is an experimental parameter, introduced to quantify the thickness of the measurement volume and thus the depth resolution in microscopic particle image velocimetry (lPIV). The theory developed to estimate the value of the DOC relies on some approximations that are not always verified in actual experiments, such as a single thin-lens optical system. In many practical lPIV experiments, a deviation of the actual DOC from its nominal value can be expected, due for instance to additional components present in the optical path of the microscope or to the use of image preprocessing before the PIV evaluation. In the presented paper, the effect of real particle image intensity distribution and image preprocessing on the thickness of the measurement volume is investigated. This is performed studying the defocusing of tracer particles and the DOC-related bias error present in lPIV measurements in a Poiseuille flow. The analysis shows that the DOC predicted using the conventional formulas can be significantly smaller than its actual value. To overcome this problem, the use of an effective NA determined experimentally from the curvature of the image autocorrelations is proposed. The accuracy of this approach to properly predict the actual size of DOC is discussed and validated on the experimental data. The effectiveness of image preprocessing to reduce the DOC-related bias error is tested and discussed as well.

On the resolution limit of digital particle image velocimetry

“…3 correspond to the geometric, diffraction, and defocussing components. The latter shows only significant influence for volume illumination, typically used in micro-PIV (Rossi et al 2011). In macroscopic DPIV, z is usually 1-3 orders of magnitude smaller than s 0 for well-aligned optical systems.…”

“…In a second step, the recorded image pair is subdivided into several thousand interrogation windows, and the average particle image displacement is estimated for each interrogation window by using spatial correlation methods with iterative multi-grid and image deformation techniques. Finally, the local flow velocity for each interrogation window is estimated from the location of the signal peak in the correlation plane by taking into account the optical magnification of the imaging system and the time interval between the two illuminations (Adrian and Westerweel 2010;Raffel et al 2007). Due to the recording principle, each measured velocity vector represents a volume-averaged mean motion of the discretized and quantized tracer particle's diffraction images, rather than the actual velocity of the flow at r. This can be expressed by the following equation:…”

“…However, although it is possible to compute velocity vectors even in smaller scales than a micrometer grid, these vectors are not independent and bias errors can occur in particular situations. Even though many different approaches to increase the accuracy and resolution of DPIV were presented, see Adrian and Westerweel (2010), Keane et al (1995), Raffel et al (2007), Scarano (2001), Stanislas et al (2003Stanislas et al ( , 2005Stanislas et al ( , 2008, Stitou and Riethmuller (2001), Willert (1997), for instance, a detailed analysis of the resolution limit is still lacking and will be the focus of this paper.…”

Particle imaging techniques for volumetric three-component (3D3C) velocity measurements in microfluidics

“…This surely holds for most microscopes where the working distance of the lens is typically at least one order of magnitude larger than the channel width. The diameter is given by the following equation Rossi et al 2011b):…”

“…Applying a proper calibration from image space to the real physical coordinates, the recorded images can be used to estimate the velocity of the fluid by measuring the displacement of the tracer particles, using correlation or particle tracking algorithms. The major difficulty arises from the fact that in contrast to standard PIV, where the measurement plane is defined by a laser light sheet, the measurement plane in lPIV is determined by the depth of focus of the optical system, which can reach several micrometers (Olsen and Adrian 2000;Bourdon et al 2004;Rossi et al 2011b;Kloosterman et al 2010). Out-of-focus particles, as shown on the right side of Fig.…”