Editing Particle image velocimetry (section)

==More complex PIV setups==

===Stereoscopic PIV===
[[Stereoscopic]] PIV utilises two cameras with separate [[angle|viewing angle]]s to extract the z-axis displacement. Both cameras must be focused on the same spot in the flow and must be properly calibrated to have the same point in focus.

In fundamental fluid mechanics, displacement within a unit time in the X, Y and Z directions are commonly defined by the variables U, V and W.  As was previously described, basic PIV extracts the U and V displacements as functions of the in-plane X and Y directions.  This enables calculations of the <math>U_x</math>, <math>V_y</math>, <math>U_y</math> and <math>V_x</math> velocity gradients.  However, the other 5 terms of the velocity gradient tensor are unable to be found from this information.  The stereoscopic PIV analysis also grants the Z-axis displacement component, W, within that plane.  Not only does this grant the Z-axis velocity of the fluid at the plane of interest, but two more velocity gradient terms can be determined:  <math>W_x</math> and <math>W_y</math>.  The velocity gradient components <math>U_z</math>, <math>V_z</math>, and <math>W_z</math> can not be determined.
The velocity gradient components form the tensor:

:<math>
\begin{bmatrix}
 U_x & U_y & U_z \\
 V_x & V_y & V_z \\ 
 W_x & W_y & W_z \\
\end{bmatrix}
</math>

===Dual plane stereoscopic PIV===
This is an expansion of stereoscopic PIV by adding a second plane of investigation directly offset from the first one.  Four cameras are required for this analysis.  The two planes of laser light are created by splitting the laser emission with a beam splitter into two beams.  Each beam is then polarized orthogonally with respect to one another.  Next, they are transmitted through a set of optics and used to illuminate one of the two planes simultaneously.

The four cameras are paired into groups of two.  Each pair focuses on one of the laser sheets in the same manner as single-plane stereoscopic PIV.  Each of the four cameras has a polarizing filter designed to only let pass the polarized scattered light from the respective planes of interest.  This essentially creates a system by which two separate stereoscopic PIV analysis setups are run simultaneously with only a minimal separation distance between the planes of interest.

This technique allows the determination of the three velocity gradient components single-plane stereoscopic PIV could not calculate:  <math>U_z</math>, <math>V_z</math>, and <math>W_z</math>.  With this technique, the entire velocity gradient tensor of the fluid at the 2-dimensional plane of interest can be quantified.  A difficulty arises in that the laser sheets should be maintained close enough together so as to approximate a two-dimensional plane, yet offset enough that meaningful velocity gradients can be found in the z-direction.

===Multi-plane stereoscopic PIV===

There are several extensions of the dual-plane stereoscopic PIV idea available. There is an option to create several parallel laser sheets using a set of beamsplitters and quarter-wave plates, providing three or more planes, using a single laser unit and stereoscopic PIV setup, called XPIV.<ref>{{cite journal | doi=10.1007/s00348-003-0731-9 | volume=36 | issue=2 | title=XPIV?Multi-plane stereoscopic particle image velocimetry | journal=Experiments in Fluids | pages=355–362| bibcode=2004ExFl...36..355L |year = 2004|last1 = Liberzon|first1 = A| last2=Gurka | first2=R | last3=Hetsroni | first3=G | s2cid=122939243 }}</ref>

===Micro PIV===
With the use of an epifluorescent microscope, microscopic flows can be analyzed.  MicroPIV makes use of fluorescing particles that excite at a specific wavelength and emit at another wavelength.  Laser light is reflected through a dichroic mirror, travels through an objective lens that focuses on the point of interest, and illuminates a regional volume.  The emission from the particles, along with reflected laser light, shines back through the objective, the dichroic mirror and through an emission filter that blocks the laser light.  Where PIV draws its 2-dimensional analysis properties from the planar nature of the laser sheet, microPIV utilizes the ability of the objective lens to focus on only one plane at a time, thus creating a 2-dimensional plane of viewable particles.<ref name=Nguyen>{{cite book | author=Nnguyen and Wereley | title=Fundamentals of Microfluidics}}</ref><ref name=Kirby>{{cite book | author=Kirby, B.J. | title=Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices| url=http://www.kirbyresearch.com/textbook| year=2010| publisher=Cambridge University Press| isbn=978-0-521-11903-0}}</ref>

MicroPIV particles are on the order of several hundred nm in diameter, meaning they are extremely susceptible to Brownian motion.  Thus, a special ensemble averaging analysis technique must be utilized for this technique.  The cross-correlation of a series of basic PIV analyses are averaged together to determine the actual velocity field.  Thus, only steady flows can be investigated.  Special preprocessing techniques must also be utilized since the images tend to have a zero-displacement bias from background noise and low signal-noise ratios.  Usually, high numerical aperture objectives are also used to capture the maximum emission light possible.  Optic choice is also critical for the same reasons.

===Holographic PIV===
Holographic PIV (HPIV) encompasses a variety of experimental techniques which use the interference of coherent light scattered by a particle and a reference beam to encode information of the amplitude and phase of the scattered light incident on a sensor plane. This encoded information, known as a [[hologram]], can then be used to reconstruct the original intensity field by illuminating the hologram with the original reference beam via optical methods or digital approximations. The intensity field is interrogated using 3-D cross-correlation techniques to yield a velocity field.

Off-axis HPIV uses separate beams to provide the object and reference waves. This setup is used to avoid [[speckle noise]] form being generated from interference of the two waves within the scattering medium, which would occur if they were both propagated through the medium. An off-axis experiment is a highly complex optical system comprising numerous optical elements, and the reader is referred to an example schematic in Sheng et al.<ref name=sheng_2008>{{cite journal | last1 = Sheng | first1 = J. | last2 = Malkiel | first2 = E. | last3 = Katz | first3 = J. | year = 2008 | title = Using digital holographic microscopy for simultaneous measurements of 3D near wall velocity and wall shear stress in a turbulent boundary layer | journal = Experiments in Fluids | volume = 45 | issue = 6| pages = 1023–1035 | doi=10.1007/s00348-008-0524-2| bibcode = 2008ExFl...45.1023S | s2cid = 123170183 }}</ref> for a more complete presentation.

In-line holography is another approach that provides some unique advantages for particle imaging. Perhaps the largest of these is the use of forward scattered light, which is orders of magnitude brighter than scattering oriented normal to the beam direction. Additionally, the optical setup of such systems is much simpler because the residual light does not need to be separated and recombined at a different location. The in-line configuration also provides a relatively easy extension to apply CCD sensors, creating a separate class of experiments known as digital in-line holography. The complexity of such setups shifts from the optical setup to image post-processing, which involves the use of simulated reference beams. Further discussion of these topics is beyond the scope of this article and is treated in Arroyo and Hinsch<ref>M. P. Arroyo and K. D. Hinsch, "Recent Developments of PIV towards 3D Measurements, pp. 127-154, Springer, 2008.</ref>

A variety of issues degrade the quality of HPIV results. The first class of issues involves the reconstruction itself. In holography, the object wave of a particle is typically assumed to be spherical; however, due to Mie scattering theory, this wave is a complex shape which can distort the reconstructed particle. Another issue is the presence of substantial speckle noise which lowers the overall signal-to-noise ratio of particle images. This effect is of greater concern for in-line holographic systems because the reference beam is propagated through the volume along with the scattered object beam. Noise can also be introduced through impurities in the scattering medium, such as temperature variations and window blemishes. Because holography requires coherent imaging, these effects are much more severe than traditional imaging conditions. The combination of these factors increases the complexity of the correlation process. In particular, the speckle noise in an HPIV recording often prevents traditional image-based correlation methods from being used. Instead, single particle identification and correlation are implemented, which set limits on particle number density. A more comprehensive outline of these error sources is given in Meng et al.<ref>{{cite journal | last1 = Meng | first1 = H. | last2 = Pan | first2 = G. | last3 = Pu | first3 = Y. | last4 = Woodward | first4 = S. H. | year = 2004 | title = Holographic particle image velocimetry: from film to digital recording | journal = Measurement Science and Technology | volume = 15 | issue = 4| pages = 673–685 | doi=10.1088/0957-0233/15/4/009| bibcode = 2004MeScT..15..673M | s2cid = 250922660 }}</ref>

In light of these issues, it may seem that HPIV is too complicated and error-prone to be used for flow measurements. However, many impressive results have been obtained with all holographic approaches. Svizher and Cohen<ref>{{cite journal | last1 = Svizher | first1 = A. | last2 = Cohen | first2 = J. | year = 2006 | title = Holographic particle image velocimetry system for measurement of hairpin vortices in air channel flow | journal = Experiments in Fluids | volume = 40 | issue = 5| pages = 708–722 | doi=10.1007/s00348-006-0108-y| bibcode = 2006ExFl...40..708S | s2cid = 125034239 }}</ref> used a hybrid HPIV system to study the physics of hairpin vortices. Tao et al.<ref>{{cite journal | last1 = Tao | first1 = B. | last2 = Katz | first2 = J. | last3 = Meneveau | first3 = C. | year = 2000 | title = Geometry and scale relationships in high reynolds number turbulence determined from three-dimensional holographic velocimetry | journal = Physics of Fluids | volume = 12 | issue = 5| pages = 941–944 | doi=10.1063/1.870348| bibcode = 2000PhFl...12..941T }}</ref> investigated the alignment of vorticity and strain rate tensors in high Reynolds number turbulence. As a final example, Sheng et al.<ref name=sheng_2008 /> used holographic microscopy to perform near-wall measurements of turbulent shear stress and velocity in turbulent boundary layers.

===Scanning PIV===
By using a rotating mirror, a high-speed camera and correcting for geometric changes, PIV can be performed nearly instantly on a set of planes throughout the flow field.  Fluid properties between the planes can then be interpolated.  Thus, a quasi-volumetric analysis can be performed on a target volume.  Scanning PIV can be performed in conjunction with the other 2-dimensional PIV methods described to approximate a 3-dimensional volumetric analysis.

===Tomographic PIV===
Tomographic PIV is based on the illumination, recording, and reconstruction of tracer particles within a 3-D measurement volume. The technique uses several cameras to record simultaneous views of the illuminated volume, which is then reconstructed to yield a discretized 3-D intensity field. A pair of intensity fields are analyzed using 3-D cross-correlation algorithms to calculate the 3-D, 3-C velocity field within the volume. The technique was originally developed<ref name=scarano_2013>
{{cite journal
 |last=Scarano |first=F.
 |year=2013
 |title=Tomographic PIV: principles and practice
 |journal=[[Measurement Science and Technology]]
 |volume=24 |issue=1 |pages=012001 |doi=10.1088/0957-0233/24/1/012001
 |bibcode = 2013MeScT..24a2001S |s2cid=119509301
 }}</ref>
by Elsinga et al.<ref name=elsinga_2006>{{cite journal | last1 = Elsinga | first1 = G. E. | last2 = Scarano | first2 = F. | last3 = Wieneke | first3 = B. | last4 = van Oudheusden | first4 = B. W. | year = 2006 | title = Tomographic particle image velocimetry | journal = Experiments in Fluids | volume = 41 | issue = 6| pages = 933–947 | doi=10.1007/s00348-006-0212-z| bibcode = 2006ExFl...41..933E | s2cid = 53701882 }}</ref> in 2006.

The reconstruction procedure is a complex under-determined inverse problem.{{citation needed|date=September 2014}} The primary complication is that a single set of views can result from a large number of 3-D volumes. Procedures to properly determine the unique volume from a set of views are the foundation for the field of tomography. In most Tomo-PIV experiments, the multiplicative algebraic reconstruction technique (MART) is used. The advantage of this pixel-by-pixel reconstruction technique is that it avoids the need to identify individual particles.{{citation needed|date=September 2014}} Reconstructing the discretized 3-D intensity field is computationally intensive and, beyond MART, several developments have sought to significantly reduce this computational expense, for example the multiple line-of-sight simultaneous multiplicative algebraic reconstruction technique (MLOS-SMART)<ref name=atkinson_2009>
{{cite journal
 |last1=Atkinson |first1=C. |last2=Soria |first2=J. 
 |year=2009
 |title=An efficient simultaneous reconstruction technique for tomographic particle image velocimetry
 |journal=[[Experiments in Fluids]]
 |volume=47 |issue=4–5 |pages=553–568 |doi=10.1007/s00348-009-0728-0
 |bibcode = 2009ExFl...47..553A |s2cid=120737581 }}</ref>
which takes advantage of the sparsity of the 3-D intensity field to reduce memory storage and calculation requirements.

As a rule of thumb, at least four cameras are needed for acceptable reconstruction accuracy, and best results are obtained when the cameras are placed at approximately 30 degrees normal to the measurement volume.<ref name=elsinga_2006/> Many additional factors are necessary to consider for a successful experiment.{{citation needed|date=September 2014}}

Tomo-PIV has been applied to a broad range of flows. Examples include the structure of a turbulent boundary layer/shock wave interaction,<ref>{{cite journal | last1 = Humble | first1 = R. A. | last2 = Elsinga | first2 = G. E. | last3 = Scarano | first3 = F. | last4 = van Oudheusden | first4 = B. W. | year = 2009 | title = Three-dimensional instantaneous structure of a shock wave/turbulent boundary layer interaction | url = http://resolver.tudelft.nl/uuid:1ea2ab47-a595-46f9-a162-039c860512c9| journal = Journal of Fluid Mechanics | volume = 622 | pages = 33–62 | doi=10.1017/s0022112008005090| bibcode = 2009JFM...622...33H | s2cid = 52556611 }}</ref> the vorticity of a cylinder wake<ref>{{cite journal | last1 = Scarano | first1 = F. | last2 = Poelma | first2 = C. | year = 2009 | title = Three-dimensional vorticity patterns of cylinder wakes | journal = Experiments in Fluids | volume = 47 | issue = 1| pages = 69–83 | doi=10.1007/s00348-009-0629-2| bibcode = 2009ExFl...47...69S | doi-access = free }}</ref> or pitching airfoil,<ref>
{{cite journal
 |last1=Buchner |first1=A-J. |last2=Buchmann |first2=N. A. |last3=Kilany |first3=K. |last4=Atkinson |first4=C. |last5=Soria |first5=J.
 |year=2012
 |title=Stereoscopic and tomographic PIV of a pitching plate
 |journal=[[Experiments in Fluids]]
 |volume=52 |issue=2 |pages=299–314 |doi=10.1007/s00348-011-1218-8
 |bibcode = 2012ExFl...52..299B |s2cid=121719586 }}</ref>
rod-airfoil aeroacoustic experiments,<ref>D. Violato, P. Moore, and F. Scarano, "Lagrangian and Eulerian pressure field evaluation of rod-airfoil flow from time-resolved tomographic PIV," Experiments in Fluids, 2010</ref> and to measure small-scale, micro flows.<ref>{{cite journal | last1 = Kim | first1 = S. Große S | last2 = Elsinga | first2 = G.E. | last3 = Westerweel | first3 = J. | year = 2011 | title = Full 3D-3C velocity measurement inside a liquid immersion droplet | journal = Experiments in Fluids | volume = 51 | issue = 2| pages = 395–405 | doi=10.1007/s00348-011-1053-y| bibcode = 2011ExFl...51..395K | doi-access = free }}</ref>  More recently, Tomo-PIV has been used together with 3-D particle tracking velocimetry to understand predator-prey interactions,<ref>{{cite journal | last1 = Adhikari | first1 = D. | last2 = Longmire | first2 = E. | year = 2013| title = Infrared tomographic PIV and 3D motion tracking system applied to aquatic predator–prey interaction | journal = Measurement Science and Technology | volume = 24 | issue = 2| page = 024011 | doi = 10.1088/0957-0233/24/2/024011 | bibcode = 2013MeScT..24b4011A | s2cid = 122840639 }}</ref><ref>{{cite journal | last1 = Adhikari | first1 = D. | last2 = Gemmell | first2 = B. | last3 = Hallberg | first3 = M. | last4 = Longmire | first4 = E. |last5 = Buskey | first5 = E. | year = 2015 | title = Simultaneous measurement of 3D zooplankton trajectories and surrounding fluid velocity field in complex flows | journal = Journal of Experimental Biology | volume = 218 | issue = 22| pages = 3534–3540| doi = 10.1242/jeb.121707 | pmid = 26486364 | doi-access = free }}</ref> and portable version of Tomo-PIV has been used to study unique swimming organisms in Antarctica.<ref>{{cite journal | last1 = Adhikari | first1 = D. | last2 = Webster | first2 = D. | last3 = Yen | first3 = J. |year =2016 | title = Portable tomographic PIV measurements of swimming shelled Antarctic pteropods | journal = Experiments in Fluids | volume = 57 | issue = 12| page = 180| bibcode = 2016ExFl...57..180A | doi = 10.1007/s00348-016-2269-7 | s2cid = 125624301 }}</ref>

===Thermographic PIV===
Thermographic PIV is based on the use of thermographic phosphors as seeding particles. The use of these thermographic phosphors permits simultaneous measurement of velocity and temperature in a flow.

Thermographic phosphors consist of ceramic host materials doped with rare-earth or transition metal ions, which exhibit phosphorescence when they are illuminated with UV-light. The decay time and the spectra of this phosphorescence are temperature sensitive and offer two different methods to measure temperature. The decay time method consists on the fitting of the phosphorescence decay to an exponential function and is normally used in point measurements, although it has been demonstrated in surface measurements. The intensity ratio between two different spectral lines of the phosphorescence emission, tracked using spectral filters, is also temperature-dependent and can be employed for surface measurements.

The micrometre-sized phosphor particles used in thermographic PIV are seeded into the flow as a tracer and, after illumination with a thin laser light sheet, the temperature of the particles can be measured from the phosphorescence, normally using an intensity ratio technique. It is important that the particles are of small size so that not only they follow the flow satisfactorily but also they rapidly assume its temperature. For a diameter of 2&nbsp;μm, the thermal slip between particle and gas is as small as the velocity slip.

Illumination of the phosphor is achieved using UV light. Most thermographic phosphors absorb light in a broad band in the UV and therefore can be excited using a YAG:Nd laser. Theoretically, the same light can be used both for PIV and temperature measurements, but this would mean that UV-sensitive cameras are needed. In practice, two different beams originated in separate lasers are overlapped. While one of the beams is used for velocity measurements, the other is used to measure the temperature.

The use of thermographic phosphors offers some advantageous features including ability to survive in reactive and high temperature environments, chemical stability and insensitivity of their phosphorescence emission to pressure and gas composition. In addition, thermographic phosphors emit light at different wavelengths, allowing spectral discrimination against excitation light and background.

Thermographic PIV has been demonstrated for time averaged
<ref>
{{cite journal
 |last1=Omrane |first1=A. |last2=Petersson |first2=P. |last3=Aldén |first3=M. |last4=Linne |first4=M.A.
 |year=2008
 |title=Simultaneous 2D flow velocity and gas temperature measurements using thermographic phosphors
 |journal=[[Applied Physics B: Lasers and Optics]]
 |volume=92 |issue=1 |pages=99–102 |doi=10.1007/s00340-008-3051-1
|bibcode = 2008ApPhB..92...99O |s2cid=121374427 }}</ref>
and single shot
<ref>
{{cite journal
 |last1=Fond |first1=B. |last2=Abram |first2=C. |last3=Heyes |first3=A.L. |last4=Kempf |first4=A.M. |last5=Beyrau |first5=F.
 |year=2012
 |title=Simultaneous temperature, mixture fraction and velocity imaging in turbulent flows using thermographic phosphor tracer particles
 |journal=[[Optics Express]]
 |volume=20 |issue=20 |pages=22118–22133 |doi=10.1364/oe.20.022118
|pmid=23037361 |bibcode = 2012OExpr..2022118F |doi-access=free }}</ref>
measurements. Recently, also time-resolved high speed (3&nbsp;kHz) measurements
<ref>
{{cite journal
 |last1=Abram |first1=C. |last2=Fond |first2=B. |last3=Heyes |first3=A.L. |last4=Beyrau |first4=F.
 |year=2013
 |title=High-speed planar thermometry and velocimetry using thermographic phosphor particles
 |journal=[[Applied Physics B: Lasers and Optics]]
 |volume=111 |issue=2 |pages=155–160 |doi=10.1007/s00340-013-5411-8
|bibcode = 2013ApPhB.111..155A |doi-access=free }}</ref>
have been successfully performed.

=== Artificial Intelligence PIV ===
With the development of artificial intelligence, there have been scientific publications and commercial software proposing PIV calculations based on deep learning and convolutional neural networks. The methodology used stems mainly from optical flow neural networks popular in machine vision. A data set that includes particle images is generated to train the parameters of the networks. The result is a deep neural network for PIV which can provide estimation of dense motion, down to a maximum of one vector for one pixel if the recorded images allow. AI PIV promises a dense velocity field, not limited by the size of the interrogation window, which limits traditional PIV to one vector per 16 x 16 pixels.<ref>{{Cite web|last=LTD|first=WOJCIECH MAJEWSKI, MICROVEC PTE|title=Artificial Intelligence in Particle Image Velocimetry|url=https://www.photonics.com/Articles/Artificial_Intelligence_in_Particle_Image/a65407|access-date=2021-03-17|website=www.photonics.com}}</ref>

===Real time processing and applications of PIV===
With the advance of digital technologies, real time processing and applications of PIV became possible. For instance, GPUs can be used to speed up substantially the direct of Fourier transform based correlations of single interrogation windows. Similarly multi-processing, parallel or multi-threading processes on several CPUs or multi-core CPUs are beneficial for the distributed processing of multiple interrogation windows or multiple images. Some of the applications use real time image processing methods, such as FPGA based on-the-fly image compression or image processing. More recently, the PIV real time measurement and processing capabilities are implemented for the future use in active flow control with the flow based feedback.<ref>{{cite journal | title=Real-time processing methods to characterize streamwise vortices | journal=Journal of Wind Engineering and Industrial Aerodynamics | pages=14–25| year = 2018|volume= 179|last1 = Braud|first1 = C |last2 = Liberzon|first2 = A| doi=10.1016/j.jweia.2018.05.006 | arxiv=1612.05826 | bibcode=2018JWEIA.179...14B | s2cid=116053665 }}</ref>