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.     

Stereoscopic micro particle image velocimetry

A stereoscopic micro-PIV (stereo-μPIV) system for the simultaneous measurement of all three components of the velocity vector in a measurement plane (2D–3C) in a closed microchannel has been developed and first test measurements were performed on the 3D laminar flow in a T-shaped micromixer. Stereomicroscopy is used to capture PIV images of the flow in a microchannel from two different angles. Stereoscopic viewing is achieved by the use of a large diameter stereo objective lens with two off-axis beam paths. Additional floating lenses in the beam paths in the microscope body allow a magnification up to 23×. The stereo-PIV images are captured simultaneously by two CCD cameras. Due to the very small confinement, a standard calibration procedure for the stereoscopic imaging by means of a calibration target is not feasible, and therefore stereo-μPIV measurements in closed microchannels require a calibration based on the self-calibration of the tracer particle images. In order to include the effects of different refractive indices (of the fluid in the microchannel, the entrance window and the surrounding air) a three-media-model is included in the triangulation procedure of the self-calibration. Test measurement in both an aligned and a tilted channel serve as an accuracy assessment of the proposed method. This shows that the stereo-μPIV results have an RMS error of less than 10% of the expected value of the in-plane velocity component. First measurements in the mixing region of a T-shaped micromixer at Re = 120 show that 3D flow in a microchannel with dimensions of 800 × 200 μm² can be measured with a spatial resolution of 44 × 44 × 15 μm³. The stationary flow in the 200 μm deep channel was scanned in multiple planes at 22 μm separation, providing a full 3D measurement of the averaged velocity distribution in the mixing region of the T-mixer. A limitation is that this approach requires a stereo-objective that typically has a low NA (0.14–0.28) and large depth-of-focus as opposed to high NA lenses (up to 0.95 without immersion) for standard μPIV.     

A method for automatic estimation of instantaneous local uncertainty in particle image velocimetry measurements

The uncertainty of any measurement is the interval in which one believes the actual error lies. Particle image velocimetry (PIV) measurement error depends on the PIV algorithm used, a wide range of user inputs, flow characteristics, and the experimental setup. Since these factors vary in time and space, they lead to nonuniform error throughout the flow field. As such, a universal PIV uncertainty estimate is not adequate and can be misleading. This is of particular interest when PIV data are used for comparison with computational or experimental data. A method to estimate the uncertainty from sources detectable in the raw images and due to the PIV calculation of each individual velocity measurement is presented. The relationship between four error sources and their contribution to PIV error is first determined. The sources, or parameters, considered are particle image diameter, particle density, particle displacement, and velocity gradient, although this choice in parameters is arbitrary and may not be complete. This information provides a four-dimensional “uncertainty surface” specific to the PIV algorithm used. After PIV processing, our code “measures" the value of each of these parameters and estimates the velocity uncertainty due to the PIV algorithm for each vector in the flow field. The reliability of our methodology is validated using known flow fields so the actual error can be determined. Our analysis shows that, for most flows, the uncertainty distribution obtained using this method fits the confidence interval. An experiment is used to show that systematic uncertainties are accurately computed for a jet flow. The method is general and can be adapted to any PIV analysis, provided that the relevant error sources can be identified for a given experiment and the appropriate parameters can be quantified from the images obtained.     

Quantum nanospheres for sub-micron particle image velocimetry

Quantum Nanospheres™ (QNs) have been developed as a new type of flow-tracing particle for micron resolution particle image velocimetry (PIV). The 70 nm diameter QNs were created by conjugating quantum dots to polystyrene beads. The fluorescent QNs have a large Stokes’ shift and are impervious to photobleaching. The use of QNs as flow-tracing particles for micro-PIV was demonstrated by measuring fluid motion in a 30 × 300 μm channel. Using an interrogation region of 1 × 1,024 pixels and ensemble averaging 1,800 image pairs, the physical volume of the interrogation region was 117 μm × 117 μm × 2 μm.     

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     

Large-scale tomographic particle image velocimetry using helium-filled soap bubbles

To measure large-scale flow structures in air, a tomographic particle image velocimetry (tomographic PIV) system for measurement volumes of the order of one cubic metre is developed, which employs helium-filled soap bubbles (HFSBs) as tracer particles. The technique has several specific characteristics compared to most conventional tomographic PIV systems, which are usually applied to small measurement volumes. One of them is spot lights on the HFSB tracers, which slightly change their position, when the direction of observation is altered. Further issues are the large particle to voxel ratio and the short focal length of the used camera lenses, which result in a noticeable variation of the magnification factor in volume depth direction. Taking the specific characteristics of the HFSBs into account, the feasibility of our large-scale tomographic PIV system is demonstrated by showing that the calibration errors can be reduced down to 0.1 pixels as required. Further, an accurate and fast implementation of the multiplicative algebraic reconstruction technique, which calculates the weighting coefficients when needed instead of storing them, is discussed. The tomographic PIV system is applied to measure forced convection in a convection cell at a Reynolds number of 530 based on the inlet channel height and the mean inlet velocity. The size of the measurement volume and the interrogation volumes amount to 750 mm × 450 mm × 165 mm and 48 mm × 48 mm × 24 mm, respectively. Validation of the tomographic PIV technique employing HFSBs is further provided by comparing profiles of the mean velocity and of the root mean square velocity fluctuations to respective planar PIV data.     

A comparative analysis of the uncertainty of astigmatism-μPTV,stereo-μPIV,and μPIV

Astigmatism or wavefront deformation, microscopic particle tracking velocimetry (A-μPTV) (Chen et al. in Exp Fluids 47:849–863, 2009; Cierpka et al. in Meas Sci Technol 21:045401, 2010b) is a method to determine the complete 3D3C velocity field in micro-fluidic devices with a single camera. By using an intrinsic calibration procedure that enables a robust and precise calibration on the basis of the measured data itself (Cierpka et al. in Meas Sci Technol 22:015401, doi:, 2011), accurate results without errors due to spatial averaging or bias due to the depth of correlation can be obtained. This method takes all image aberrations into account, allows for the use of the whole CCD sensor, and is easy to apply without expert knowledge. In this paper, a comparative study is presented to assess the uncertainties of two state-of-the-art methods for 3C3D velocity field measurements in microscopic flows: stereoscopic micro-particle image velocimetry (S-μPIV) and astigmatism micro-particle tracking velocimetry (A-μPTV). First, the main parameters affecting all methods’ measurement uncertainty are identified, described, and quantified. Second, the test case of the flow over a backward-facing step is analyzed using all methods. For comparison, standard 2D2C μPIV measurements and numerical flow simulations are shown as well. Advantages and disadvantages of both methods are discussed.     

Pseudo turbulence in PIV breaking-wave measurements

 The particle image velocimetry (PIV) technique was employed to measure the instantaneous velocity distribution under nonbreaking and breaking water waves. The corresponding turbulence intensity was calculated by the ensemble average of repeated measurements. The pseudo turbulence found was large enough to affect the accuracy of the turbulence measurements. We follow Prasad et al.'s (1992) approach to demonstrate that the pseudo turbulence is related to the bias error, which is the discrepancy between the true position of the particle image and the position calculated from the pixel array data with inadequate pixel resolution. To reduce the bias error (or the pseudo turbulence), we first calculate it from a turbulence-free flow with the same experimental set-up as that used for the targeted experiments (i.e., we use the same size of field of view, seeding particles, seeding density, lens aperture, and laser wavelength in both experiments). Then we minimize the bias error from the turbulence measurements in the actual experiments. To demonstrate the procedure, the evolution of a breaking wave is investigated. Received: 30 January 1998/Accepted: 28 October 1999     

The fully digital evaluation of photographic PIV recordings

The performance of a purely digital evaluation system for photographic PIV recordings is described. High resolution digital images are obtained from the 35 mm negatives using a commonly available slide scanner. Together with the continually improving capabilities of standard computers, this evaluation system is a cost effective alternative to the traditional analog optical/digital (Young's fringe method) and purely optical PIV interrogation systems. Compared to the optical systems the fully digital evaluation can provide a higher spatial resolution while maintaining a similar measurement uncertainty. Using actual PIV recordings absolute measurement uncertainties are obtained and further predictions toward optimal displacement data recovery are made with the aid of Monte-Carlo simulations. Measurement uncertainties are minimized for particle image diameters on the order of 2 pixels while the reduction of the image depth (i.e. bits/pixel) has little effect. The overall performance of the described digital evaluation is compared to two types of optical evaluation systems.Affiliated with DNW-NWB, DLR-Braunschweig.     

Acceleration of Tomo-PIV by estimating the initial volume intensity distribution

Tomographic particle image velocimetry (Tomo-PIV) is a promising new PIV technique. However, its high computational costs often make time-resolved measurements impractical. In this paper, a new preprocessing method is proposed to estimate the initial volume intensity distribution. This relatively inexpensive “first guess” procedure significantly reduces the computational costs, accelerates solution convergence, and can be used directly to obtain results up to 35 times faster than an iterative reconstruction algorithm (with only a slight accuracy penalty). Reconstruction accuracy is also assessed by examining the errors in recovering velocity fields from artificial data (rather than errors in the particle reconstructions themselves).     

Quantification of dispersed phase concentration using light sheet imaging methods

With the prevalence of particle image velocimetry (PIV) as a quantitative tool for fluid mechanics diagnostics, its application for analyzing complicated multiphase flows has been steadily increasing over the last several decades. While the primary issue in using PIV for multiphase flows is in separating the information of the phases for independent analysis with a minimum of spurious “cross-talk,” an equally crucial but often overlooked point is in the accurate quantitative measurement of the dispersed phase concentration. Accurate concentration measurement is important due to the fact that the dispersed phase is often heterogeneously distributed in both space and time, either due to a non-uniformity of the source of particulates (such as a spray nozzle or sediment boundary) or due to inertial migration of the particles even from originally homogeneous spatial distributions. In the current work, we examine the effects of light sheet profile distortion and attenuation by tracer seeding particles, as well as reflected light from local wall boundaries on the effective light sheet thickness. The effective thickness is critical for concentration measurements, as it dictates the dispersed phase detection volume. A direct calibration method is demonstrated to measure the effective light sheet thickness in a water/glass bead system, which shows that systematic bias errors on the order of 30% can result if the reflective bed condition is not accounted for, and the errors can be as high as 50% or more if a single-point measure of the sheet width is used.     

The accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer

To investigate the accuracy of tomographic particle image velocimetry (Tomo-PIV) for turbulent boundary layer measurements, a series of synthetic image-based simulations and practical experiments are performed on a high Reynolds number turbulent boundary layer at Re_θ = 7,800. Two different approaches to Tomo-PIV are examined using a full-volume slab measurement and a thin-volume “fat” light sheet approach. Tomographic reconstruction is performed using both the standard MART technique and the more efficient MLOS-SMART approach, showing a 10-time increase in processing speed. Random and bias errors are quantified under the influence of the near-wall velocity gradient, reconstruction method, ghost particles, seeding density and volume thickness, using synthetic images. Experimental Tomo-PIV results are compared with hot-wire measurements and errors are examined in terms of the measured mean and fluctuating profiles, probability density functions of the fluctuations, distributions of fluctuating divergence through the volume and velocity power spectra. Velocity gradients have a large effect on errors near the wall and also increase the errors associated with ghost particles, which convect at mean velocities through the volume thickness. Tomo-PIV provides accurate experimental measurements at low wave numbers; however, reconstruction introduces high noise levels that reduces the effective spatial resolution. A thinner volume is shown to provide a higher measurement accuracy at the expense of the measurement domain, albeit still at a lower effective spatial resolution than planar and Stereo-PIV.     

Holographic particle image velocimetry system for measurements of hairpin vortices in air channel flow

A holographic particle image velocimetry system for investigating hairpin vortices, artificially generated in a subcritical plane Poiseuille air flow, is presented. The optical setup is a modified version of the hybrid scheme, previously employed in turbulent water flows. Accordingly, separate reconstruction of holograms, successively recorded on the same photoplate, is provided by using two reference beams. The positioning of the photoplate within the image of the sample volume accompanied by special alignment procedures, minimizes the apparent displacement caused by the misalignment of the reconstruction waves. A novel method is employed for detecting in-focus particles. Testing the system with a fixed 5 μm diameter wire, results in a corresponding 3D wire image having a diameter of ≈25 μm. Finally, the instantaneous topology and 3D distribution of the two velocity components associated with the hairpin vortex are presented.     

Quantitative evaluation of PIV peak locking through a multiple Δ<Emphasis Type="Italic">t</Emphasis> strategy: relevance of the rms component

The possibility of using different times between laser pulses (Δt) in a PIV (Particle Image Velocimetry) measurement of the same real flow field for error assessment has already been proposed by the authors in a recent paper Nogueira et al. (Meas Sci Technol 20, 2009). It is a simple procedure that is available with the usual PIV setup. In that work, peak locking was considered basically as a bias error. Later measurements indicated that, using appropriate processing algorithms, this error is not the main peak-locking effect. Scenarios with the rms (root mean square) error due to peak locking as the most relevant contribution are more common than initially expected and require a differentiated approach. This issue is relevant due to the impact of the rms error in the evaluation of flow quantities like turbulent kinetic energy. The first part of this work is centred on showing that peak-locking error in PIV is not always a measurement bias towards the closest pixel integer displacement. Insight in the subject indicates that this is the case only for algorithm-induced peak locking. The peak locking coming out of image acquisition limitations (i.e. resolution) is not ‘a priory’ biased. It is a random error with a peculiar probability density function. Discussion on the subject is offered, and a particular approach to use a simple multiple Δt strategy to asses this error is proposed. The results reveal that in real images where amplitude of the peak-locking bias error is assessed to be as small as 0.02 pixels, rms errors can be in the order of 0.1 pixels. As PIV approaches maturity, providing a quantitative confidence interval by estimating measurement error seems essential. The method developed is robust enough to quantify these values in the presence of turbulence with rms up to ~0.6 pixels. This proposal constitutes a relevant step forward from the traditional histogram-based considerations that only reveal whether strong peak-locking error is present or not, without any information on its magnitude or whether its origin is bias or rms.     

PIV图像粒子像斑定位偏差综合评估试验及其测速误差评估

本文针对ＰＩＶ技术的直接测量法中图像的可读性和可测性，讨论了从模拟图像到数字图像，最后到粒子像斑中心位置的确定过程中的误差规律；并提出了一种称之为粒子像斑定位偏差综合评估的试验方法。     

Improvement of measurement accuracy in micro PIV by image overlapping

Micro PIV uses volume illumination; therefore, the velocity measured at the focal plane is a weighted average of the velocities within the measurement volume. The contribution of out-of-focus particles to the PIV correlation can generate significant measurement errors particularly in near wall regions. We present a new application of image overlapping, which is shown to be very effective in improving the accuracy of time-averaged velocity measurements by effectively reducing the measurement depth. The performance of image overlapping and correlation averaging were studied using synthetic and experimental images of micro channel flow, both with and without image pre-processing. The results show that for flows without particle clumping, image overlapping provides the best measurement accuracy without any need for image pre-processing. For flows with particle clumping, image overlapping combined with band-pass filtering provides the best measurement accuracy. When overlapped images are saturated with particles due to a large number of image pairs, image overlapping measurement still does not show any visible pixel-locking effect. Image overlapping was found to have comparable or slightly reduced pixel-locking effects compared to correlation averaging. In addition, image overlapping utilizes significantly fewer computational resources than the other techniques.     

Bias and precision errors of digital particle image velocimetry

The bias and precision errors of digital particle image velocimetry are quantified. Uniform displacement images are used to evaluate the uncertainty attributed to various sub-pixel peak finding algorithms. Bias errors are found to exist for all algorithms, and the presence of bias error tends to affect the precision error. The ability to “calibrate” out the bias error is explored using a rectangular free jet experiment. The calibration was effective in removing the bias error in the potential core and less effective in the shear layer. The bias error is found to functionally depend on the displacement gradients present in the interrogation region. The study stresses the need for in situ quantification of DPIV uncertainty. Received: 3 November 1998 / Accepted: 26 June 1999     

Application of numerical and optical evaluation schemes for particle image velocimetry

Application of particle image velocimetry (PIV) techniques for measurement of fluid velocities typically requires two steps. The first of these is the photography step in which one or more exposures of a particle field are taken. The second step is the evaluation of the particle pattern and production of appropriate velocities. Each of these steps involves optimization which is usually specific to the experiment being conducted and there is significant interaction between photographic parameters and evaluation characteristics.Among the various evaluation techniques suggested for analysis of PIV images is the evaluation of the scattered interference pattern (Young's fringes) by numerical Fourier transform. An alternative to the numerical calculation of the Fourier transform of the Young's fringes has been suggested, using a modified liquid crystal television as an optical correlator to allow the transform to be performed optically. Both transform techniques are affected by the quality of the input function, specifically the Young's fringes.This paper will compare the performance of optical and numerical Fourier transform analysis of Young's fringes using speckle images. The repeatability and an estimate of the accuracy of the particle displacement will be shown for each method. A brief examination of the effects of small particle number density of PIV evaluation will also be presented. Finally, for a small part of an actual unsteady flow, the optical and numerical Fourier transform analysis methods will be compared.     

A correlation-based central difference image correction (CDIC) method and application in a four-roll mill flow PIV measurement

An experiment is conducted in a four-roll mill to verify a novel particle image velocimetry (PIV) recording evaluation method that combines the advantages of central difference interrogation and an image correction technique. Simulations and experiments in the four-roll mill geometry demonstrate that the central difference image correction method described in this paper can not only avoid the bias error resulting from the curvature and high-velocity-gradient flow but also effectively reduce the random error resulting from particle image distortion. Two image correction schemes and two base algorithms are discussed. A four-point image correction scheme is suggested on the basis of the traditional correlation-based interrogation algorithm to enable a fast, high-accuracy evaluation of PIV recordings in complex flows. In addition, the PIV experiment accurately determines the velocity field in the four-roll mill and confirms the linear distributions of the velocity components and the roller speed.     

Particle tracer response across shocks measured by PIV

The experimental approach used for the evaluation of the particle response time across a stationary shock wave is assessed by means of PIV measurements. The study focuses on the experimental requirements for a reliable and unbiased measurement of the particle response time τ _p and length ξ _p based on a single-exponent decaying law. A numerical simulation of the particle response experiment returns the parameters governing the measurement: namely the normalized spatial and temporal resolution, shock strength, and digital resolution. Representing the velocity decay in logarithmic coordinates it is shown that measurements performed with laser pulse separation time up to τ _p and interrogation window up to ξ _p still yield unbiased results for the particle response. A set of experiments on the particle response across a planar oblique shock wave was conducted to verify the results from the numerical assessment. Liquid droplets of DEHS and solid tracer particles of silicon and titanium dioxide with different primary crystal size are compared. The resulting temporal response ranges from 2 to 3 μs, corresponding to values commonly reported in literature, to almost 0.3 μs when particles are properly dehydrated and a filter is applied before injection into the wind tunnel. It is the first experimental evidence of particle tracers with a measured response time lower than 0.4 μs. The same procedure is applied to attempt the measurement of individual particle tracers by particle tracking velocimetry to estimate the spread in the distribution of tracer time response. The latter analysis is limited by the particle image tracking precision error, which biases the results introducing a wider broadening of the particle velocity distribution.