Volume self-calibration for 3D particle image velocimetry

Planar self-calibration methods have become standard for stereo PIV to correct misalignments between laser light sheet and calibration plane. Computing cross-correlation between images from camera 1 and 2 taken at the same time, non-zero disparity vectors indicate rotational and translational misalignments relative to the coordinate system defined by a calibration plate. This approach works well for thin light sheets but fails for extended volumes recorded in 3D-PTV or tomographic PIV experiments. Here it is primarily necessary to correct calibration errors leading to triangulation errors in 3D-PTV or in degraded tomographic volume reconstruction. Tomographic PIV requires calibration accuracies of a fraction of a pixel throughout the complete volume, which is difficult to achieve experimentally. A new volumetric self-calibration technique has been developed based on the computation of the 3D position of matching particles by triangulation as in 3D-PTV. The residual triangulation error (‘disparity’) is then used to correct the mapping functions for all cameras. A statistical clustering method suitable for dense particle images has been implemented to find correct disparity map peaks from true particle matches. Disparity maps from multiple recordings are summed for better statistics. This self-calibration scheme has been validated using several tomographic PIV experiments improving the vector quality significantly. The relevance for other 3D velocimetry methods is discussed.     

Deep field noise in holographic particle image velocimetry (HPIV): numerical and experimental particle image field modelling

 Holographic recording overcomes the limits in 2-D particle image velocimetry (PIV) to cover a 3-D flow field volume. Interrogation by focusing on single planes in a reconstructed particle field is disturbed by noise from out-of-focus particles. A numerical simulation models image reconstruction and shows how validation rates depend on aperture and volume depth. An experimental model environment of scattering particles in moveable plastic slices gives support to the numerical results. Simulations and tests are carried out for interrogation by autocorrelation and crosscorrelation techniques and furnish guidelines for system design. Received: 27 December 1996 / Accepted: 14 August 1997     

New tracking algorithm for particle image velocimetry

The cross correlation tracking technique is widely used to analyze image data, in Particle Image Velocimetry (PIV). The technique assumes that the fluid motion, within small regions of the flow field, is parallel over short time intervals. However, actual flow fields may have some distorted motion, such as rotation, shear and expansion. Therefore, if the distortion of the flow field is not negligible, the fluid motion can not be tracked well using the cross correlation technique. In this study, a new algorithm for particle tracking, called the Spring Model technique, has been proposed. The algorithm can be applied to flow fields which exhibit characteristics such as rotation, shear and expansion.The algorithm is based on pattern matching of particle clusters between the first and second image. A particle cluster is composed of particles which are assumed to be connected by invisible elastic springs. Depending on the deformation of the cluster pattern (i.e., the particle positions), the invisible springs have some forces. The smallest force pattern in the second image is the most probable pattern match to the correspondent original pattern in the first image. Therefore, by finding the best matches, particle movements can be tracked between the two images. Three-dimensional flow fields can also be reconstructed with this technique.The effectiveness of the Spring Model technique was verified with synthetic data from both a two-dimensional flow and three-dimensional flow. It showed a high degree of accuracy, even for the three-dimensional calculation. The experimental data from a vortex flow field in a cylinder wake was also measured by the Spring model technique.     

A framework for synthetic validation of 3D echocardiographic particle image velocimetry

Particle image velocimetry (PIV) has been significantly advanced since its conception in early 1990s. With the advancement of imaging modalities, applications of 2D PIV have far expanded into biology and medicine. One example is echocardiographic particle image velocimetry that is used for in vivo mapping of the flow inside the heart chambers with opaque boundaries. Velocimetry methods can help better understanding the biomechanical problems. The current trend is to develop three-dimensional velocimetry techniques that take advantage of modern medical imaging tools. This study provides a novel framework for validation of velocimetry methods that are inherently three dimensional such as but not limited to those acquired by 3D echocardiography machines. This framework creates 3D synthetic fields based on a known 3D velocity field \({\mathbf{V}}\) and a given 3D brightness field \({\mathbf{B}}\). The method begins with computing the inverse flow \({\mathbf{V}}^{\varvec{*}} \) based on the velocity field \({\mathbf{V}}\). Then the transformation of \({\mathbf{B}}\), imposed by \({\mathbf{V}}\), is calculated using the computed inverse flow according to \({\mathbf{B}}^{\varvec{*}} \left( {\mathbf{x}} \right) = {\mathbf{B}}\left( {{\mathbf{x}} + {\mathbf{V}}^{\varvec{*}} \left( {\mathbf{x}} \right)} \right)\), where x is the coordinates of voxels in \({\mathbf{B}}^{\varvec{*}} \), with a 3D weighted average interpolation, which provides high accuracy, low memory requirement, and low computational time. To check the validity of the framework, we generate pairs of 3D brightness fields by employing Hill’s spherical vortex velocity field. \({\mathbf{B}}\) and the generated \({\mathbf{B}}^{\varvec{*}} \) are then processed by our in-house 3D particle image velocimetry software to obtain the interrelated velocity field. The results indicates that the computed and imposed velocity fields are in agreement.     

A generalized processing technique in digital particle image velocimetry with direct estimation of velocity gradients

A technique is proposed for the processing of digital particle image velocimetry (PIV) images, in one single step providing direct estimates of fluid velocity, out-of-plane vorticity and in-plane shear rate tensor. The method is based on a generalization of the standard PIV cross-correlation technique and substitutes the usual discrete cross-correlation of image pairs with a correlation of interpolated two-dimensional image intensity functions, being subject to affine transformations. The correlation is implemented by using collocation points, on which image intensity values are interpolated. The resulting six-dimensional correlation function is maximized using a general purpose optimization algorithm. The use of the method is demonstrated by application to different types of synthetically generated image pairs constructed with known particle displacement functions. The resulting errors are assessed and compared with those of a representative standard PIV method as well as with those of the present technique using no differential quantities in the search of the peak location. The examples demonstrate that significant improvements in accuracy can be obtained for flow fields with regions containing strong velocity gradients.     

A new artificial neural network tracking technique for particle image velocimetry

 The analysis of Particle Image Velocimetry (PIV) data requires effective algorithms to track efficiently the particles suspended in the fluid flow. The artificial neural network algorithm method described here presents a new approach to solve this problem. Contrary to the classic cross correlation method, this new method does not require a large number of particles per frame, it can handle flows with large velocity gradients, and is suited for tracking images with multiple exposures as well as tracking through consecutive images. The algorithm was tested on synthetic and available experimental data to provide a thorough performance analysis. Received: 28 May 1996/Accepted: 25 December 1996     

3-Component acceleration field measurement by dual-time stereoscopic particle image velocimetry

In this article, a multiplane stereo-particle image velocimetry (PIV) system was implemented and validated to measure the three-component acceleration field in a plane of turbulent flows. The employed technique relies on the use of two stereoscopic particle image velocimetry (SPIV) systems to measure pairs of velocity fields superimposed in space but shifted in time. The time delay between the two velocity fields enables the implementation of a finite difference scheme to compute temporal derivatives. The use of two synchronized SPIV systems allows us to overcome the limited acquisition rate of PIV systems when dealing with highly turbulent flows. Moreover, a methodology based on the analysis of the spectral error distribution is described here to determine the optimal time delay to compute time derivatives. The present dual-time SPIV arrangement and the proposed analysis method are applied to measure three-component acceleration fields in a cross section of a subsonic plane turbulent mixing layer.     

An advanced off-axis holographic particle image velocimetry (HPIV) system

Holographic PIV (HPIV) is the most promising candidate for the next generation full-field velocimetry that can measure high spatial resolution instantaneous three-dimensional (3D) velocity fields. To explore the maximum performance capabilities of HPIV including spatial resolution, off-axis holography based HPIV has become a major direction of development. A fully automated off-axis HPIV system based on an injection-seeded dual-pulsed YAG laser and 3D data processing software has been implemented in the laser flow diagnostics lab (LFD). In our system, 90-degree particle scattering, dual reference beams, in situ reconstruction/data processing, and 3D velocity extraction based on a fast “concise cross correlation” (CCC) algorithm are utilized. The off-axis HPIV system is tested for an acoustically excited air jet and the wake of a surface-mounted tab in a water channel flow, giving instantaneous 3D velocity fields for both flows. Experimental data of instantaneously measured 3D flow structures using this technique show great promise. Received: 12 August 1998/Accepted: 20 October 1999     

A particle image velocimetry system for microfluidics

 A micron-resolution particle image velocimetry (micro-PIV) system has been developed to measure instantaneous and ensemble-averaged flow fields in micron-scale fluidic devices. The system utilizes an epifluorescent microscope, 100–300 nm diameter seed particles, and an intensified CCD camera to record high-resolution particle-image fields. Velocity vector fields can be measured with spatial resolutions down to 6.9×6.9×1.5 μm. The vector fields are analyzed using a double-frame cross-correlation algorithm. In this technique, the spatial resolution and the accuracy of the velocity measurements is limited by the diffraction limit of the recording optics, noise in the particle image field, and the interaction of the fluid with the finite-sized seed particles. The stochastic influence of Brownian motion plays a significant role in the accuracy of instantaneous velocity measurements. The micro-PIV technique is applied to measure velocities in a Hele–Shaw flow around a 30 μm (major diameter) elliptical cylinder, with a bulk velocity of approximately 50 μm s^-1. Received: 26 November 1997/Accepted: 26 February 1998     

An efficient simultaneous reconstruction technique for tomographic particle image velocimetry

To date, Tomo-PIV has involved the use of the multiplicative algebraic reconstruction technique (MART), where the intensity of each 3D voxel is iteratively corrected to satisfy one recorded projection, or pixel intensity, at a time. This results in reconstruction times of multiple hours for each velocity field and requires considerable computer memory in order to store the associated weighting coefficients and intensity values for each point in the volume. In this paper, a rapid and less memory intensive reconstruction algorithm is presented based on a multiplicative line-of-sight (MLOS) estimation that determines possible particle locations in the volume, followed by simultaneous iterative correction. Reconstructions of simulated images are presented for two simultaneous algorithms (SART and SMART) as well as the now standard MART algorithm, which indicate that the same accuracy as MART can be achieved 5.5 times faster or 77 times faster with 15 times less memory if the processing and storage of the weighting matrix is considered. Application of MLOS-SMART and MART to a turbulent boundary layer at Re _θ = 2200 using a 4 camera Tomo-PIV system with a volume of 1,000 × 1,000 × 160 voxels is discussed. Results indicate improvements in reconstruction speed of 15 times that of MART with precalculated weighting matrix, or 65 times if calculation of the weighting matrix is considered. Furthermore the memory needed to store a large weighting matrix and volume intensity is reduced by almost 40 times in this case.     

Two-color particle image velocimetry technique for an internal combustion engine

A two-color particle image velocimetry (PIV) technique has been applied to a single-cylinder motored research engine. Two-color PIV is a quantitative planar velocity measurement technique that can unambiguously determine the velocity magnitude and direction.

The work includes the development of an interrogation system, a series of computer simulations to determine the performance of the technique under various conditions, the comparison of these results to similar ones obtained for an autocorrelation PIV system, and a test of the technique by reconstructing the velocity field of a uniform jet flow.

The technique was then applied to the in-cylinder flow field of a motored single-cylinder, cup-in-head, research engine. A total of 27 instantaneous velocity fields were obtained at a single measurement plane for a single operating condition of the engine. The data were analyzed to yield ensemble-averaged velocity and velocity fluctuation.     

3D scanning particle tracking velocimetry

In this article, we present an experimental setup and data processing schemes for 3D scanning particle tracking velocimetry (SPTV), which expands on the classical 3D particle tracking velocimetry (PTV) through changes in the illumination, image acquisition and analysis. 3D PTV is a flexible flow measurement technique based on the processing of stereoscopic images of flow tracer particles. The technique allows obtaining Lagrangian flow information directly from measured 3D trajectories of individual particles. While for a classical PTV the entire region of interest is simultaneously illuminated and recorded, in SPTV the flow field is recorded by sequential tomographic high-speed imaging of the region of interest. The advantage of the presented method is a considerable increase in maximum feasible seeding density. Results are shown for an experiment in homogenous turbulence and compared with PTV. SPTV yielded an average 3,500 tracked particles per time step, which implies a significant enhancement of the spatial resolution for Lagrangian flow measurements.     

Endoscopic 2D particle image velocimetry (PIV) flow field measurements in IC engines

The paper describes camera and laser endoscopes designed for particle image velocimetry (PIV) applications like measurements in IC engines or turbomachinery. Endoscopic PIV measurements through 8-mm optical access on an IC engine are presented and compared with the measurements using standard optical access through a window.     

A cross-correlation technique for velocity field extraction from particulate visualization

A rapid time series of photographs of the horizontal cross-sections of several y ⁺ locations were taken of a turbulent open-channel water flow with Re _d = 3,900. A pair of photographic images were obtained with a time difference of 1.3 v/u ² at each y ⁺ locations. The pictures were digitized into 8 bit data with a spatial resolution of 2.5 viscous scales. Instead of identifying discrete particles, a variable interval spatial correlation technique was used to extract the velocity components. With this technique, two-dimensional spatial cross-correlations of the illumination intensities were taken between a pair of picture images. The correlations were taken over small areas and the peak of the correlation coefficients were used to obtain the convection velocity yielding the u and w components of velocity. Some statistical properties were calculated and are shown to be comparable with previous data. Spatial correlations of the velocity components revealed some unique characteristics related to the structure of turbulence.     

A calibration procedure for millimeter-scale stereomicroscopic particle image velocimetry

A stereomicroscopic particle image velocimetry (SμPIV) system has been developed for millimeter scale flows. The SμPIV system is based on an off-the-shelf stereomicroscope, with magnification between 0.69× and 30×, and a field of view between 7.5 × 6 mm and 250 × 200 μm. Custom calibration targets were devised using printed circuit board technology, and applied at a magnification factor of 1.74, with a field of view of 4.75 × 3.8 mm. Measurement errors were assessed by moving a test block with fixed particles. Total system uncertainty in test block displacement transverse to the optical axis was 0.5% of the field of view, and 3% of the depth of field for motion along the optical axis. Approximately 20% of this uncertainty was due to the calibration target quality and test block procedures.     

A simple particle image velocimetry instrument for low-velocity flows

 A P.I.V. instrument using two synchronized CCD video cameras is described. The same field of view is imaged onto each CCD array with an image splitter and one imaging lens. The delay between two exposures can be adjusted from 0.5 to 20 ms depending on the flow velocity to be measured. Received: 12 February 1999/Accepted: 20 March 1999