Particle Image Velocimetry Fundamental Theory and Operation

Outline Definition and Core Concepts of PIV Software Processing- Cross-Correlation Hardware Principles- Basic Operation

Particle Image Velocimetry 4/14/2017 Defn :Experimental means to determine the instantaneous flow field A particle-laden flow is illuminated by a thin sheet of light (2D) Two images are taken with a short time between each capture The two images are compared to determine particle displacement Particle displacement is translated into an instantaneous velocity measurements PIV component technology is continuously evolving and it is a challenge for both the users as well as manufacturers to keep pace with the latest developments. The user is particularly concerned that the PIV system acquired today is not obsolete tomorrow. TSI has factored this need into our PowerView PIV system design and the result is a very versatile and flexible system that can incorporate future developments with minimum cost. TSI’s philosophy has always centered around systems and processing approaches that can extract maximum information from the experiment. In PIV this would require that the raw image information is never lost and is available along with the corresponding vector file. The benefits of such a data management approach are numerous. Having the raw image would mean never having to repeat an experiment. The same image can be processed in several different ways to obtain detailed flow information not extracted during preliminary analysis. Comparing the vector field to the corresponding particle image field offers insight into the nature of the flow, on-line validation and enhances the confidence level in the velocity vector data. Availability of the raw image field offers the ability to get detailed information about the scatterers such as particle image size, concentration etc. It is a misconception that higher speed of processing can be achieved only with dedicated hardware processors and discarding the raw image. Working in the 32-bit NT environment combined with multi-processor support is generating very high processing speeds for on-line data collection, analysis and display without the limitations associated with dedicated hardware of higher cost, loss of raw image and lack of flexibility. The flexible approach offered by the TSI’s PowerView PIV system ensures that the system will grow as camera, interface and processing technologies evolve. 2-velocity component System 3-velocity component System Copyright© 2007 TSI Incorporated

PIV Fundamentals PIV measures are taken very quickly (milliseconds in total) At time t1 Pulsed laser sheet illuminates a planar region of the flow Particles are imaged on the camera (Frame A) At time t1 + Dt A second image (Frame B) is taken of a second light sheet Statistical (Cross-Correlation) methods are used to determine the particle displacement over the time Dt, and thus the local velocity

FRAME A Copyright© 2007 TSI Incorporated

FRAME B Copyright© 2007 TSI Incorporated

Instantaneous Velocity Field Copyright© 2007 TSI Incorporated

Measurement at one point over a period of time PIV LDV Measurement at one point over a period of time Provides time history of the flow and hence time averaged statistics at one point. Flow field mapped by traversing the measuring point Velocity obtained by measuring time to travel a known distance Measurement at many points at one instant of time Provides instantaneous vector fields. Time averaged statistics obtained by averaging several image fields Velocity obtained by measuring image displacement in a known time LDV provides the time history of the flow (velocity components) at the measurement location. The measuring region or the measuring volume is the intersection region of the laser beams. In PIV, measuring the displacement of particle images in the time between two laser flashes (multiple flashes can also be used) that illuminate a plane (in the flow field) provides the velocity information. While the measurement volume size determines the spatial resolution in LDV, the maximum image displacement gives a measure of spatial resolution in PIV. Seeding (adding particles that follow the flow) requirements are comparable for both techniques.

Cross Correlation All particles look alike, so it is hard to find the ‘same’ particle in both Frame A and B (PTV) Instead, PIV uses a statistical approach to find the most likely displacement of a group of particles Frame A is broken up into a grid of ‘interrogation regions’ The group of particles in the interrogation region creates a unique ‘fingerprint’ that we can look for in both frames (PIV)

Cross Correlation Fame B Search Area (“Spot B”) The relative location of the interrogation region in Frame A is known A search area is defined in Frame B. Frame A Interrogation Region (“Spot A”)

Original Particle Positions in Frame A Cross Correlation Original Particle Positions in Frame A

Location of particles in Frame B Cross Correlation Location of particles in Frame B

Cross Correlation A ‘Spot Mask’ (above) created from Frame A, is scanned across the search area of Frame B to form a ‘correlation map’

Cross Correlation The correlation map will have a peak relative to the location where the ‘fingerprint’ of the Spot Mask is identified in Frame B

Cross Correlation The correlation values for different locations of the spot mask can be represented on a “correlation map” In the ideal case, there is a distinct, single, round peak in the correlation map

Cross Correlation DY DX The X and Y displacements of the particles are determined by the offset of the interrogation regions DX

Cross Correlation Since we know the time separation (Dt) between the 2 laser pulses very accurately, we can measure the ‘group’ velocity as the displacement / Dt, and assign a single velocity vector

Cross Correlation A) B) NOTE: Particles and Interrogation region are typically larger than represented here in this simplified example Frame A Spot Mask

Cross Correlation A) B) (1*1) (1*0) + (1*0) 1 Cross Correlation Map Displacement (x,y) = (0,0) 1

Cross Correlation A) B) (1*0) + (1*0) Cross Correlation Map Cross Correlation Map Displacement (x,y) = (0,1) 1

Cross Correlation A) B) (1*1) (1*0) + (1*0) 2 2 Cross Correlation Map Displacement (x,y) = (0,2) 1

Cross Correlation A) B) (1*0) + (1*0) 2 Cross Correlation Map 2 Cross Correlation Map Displacement (x,y) = (1,2) 1

Cross Correlation A) B) (1*1) + (1*1) 5 2 5 Cross Correlation Map Displacement (x,y) = (2,2) 1

Cross Correlation A) B) Cross Correlation Map Displacement (x,y) = (2,2) Peak in the Correlation Map is at (+2,+2), indicating that the particles moved in this direction from Frame A) to Frame B).

Processing Crosscorrelation Spot B Interrogation region Spot A Frame A particle displacement Crosscorrelation Frame B Vector field

Cross Correlation The process is repeated for each interrogation region in Frame A, resulting in a 2-Dimensional velocity field for the imaged region

Hardware Principles 2-component System 3-component System PIV component technology is continuously evolving and it is a challenge for both the users as well as manufacturers to keep pace with the latest developments. The user is particularly concerned that the PIV system acquired today is not obsolete tomorrow. TSI has factored this need into our PowerView PIV system design and the result is a very versatile and flexible system that can incorporate future developments with minimum cost. TSI’s philosophy has always centered around systems and processing approaches that can extract maximum information from the experiment. In PIV this would require that the raw image information is never lost and is available along with the corresponding vector file. The benefits of such a data management approach are numerous. Having the raw image would mean never having to repeat an experiment. The same image can be processed in several different ways to obtain detailed flow information not extracted during preliminary analysis. Comparing the vector field to the corresponding particle image field offers insight into the nature of the flow, on-line validation and enhances the confidence level in the velocity vector data. Availability of the raw image field offers the ability to get detailed information about the scatterers such as particle image size, concentration etc. The flexible approach offered by the TSI’s PowerView PIV system ensures that the system will grow as camera, interface and processing technologies evolve. 2-component System 3-component System

System Components Imaging Subsystem (Laser, Beam delivery system, light optics) Illuminate a plane in the flow (seeded) using a pulsed laser Pulse energy, duration, and repetition rate Typically Nd:YAG laser operating at 532 nm Image Capture Subsystem (CCD Camera, Camera Interface, Synchronizer-Master control unit) Master Timing devise triggers illumination and camera capturing Camera captures particle images and records them Analysis and Display Subsystem Calculates and displays a two dimensional vector field from the particle image fields Capable of processing higher-order statistics of flow field A complete PIV system can be viewed as a combination of three sub-systems. The first and second subsystems (in the list above) are responsible for obtaining good particle image fields, and the third for processing and displaying corresponding velocity fields and their derivatives. While imaging involves on-line set up and optimization, analysis/display can be done on-line or off-line. Laser has become the choice illumination device since it can produce high energy short duration pulses. The laser pulse is delivered to the measurement location using flexible beam guides with mirrors or through optical fibers. Optical elements can convert these pulsed laser beams into pulsing light sheets. CCD cameras are used to record the particle image field. A master control system referred to as a Synchronizer system is used as the timing device to generate the control signals and synchronize the camera with the laser pulses and the camera interface. Camera interface is used to ensure very fast data transfer from the camera to the computer. Image acquisition/analysis/display software is the umbrella program that allows the user to set and optimize the hardware and the experiment, acquire images, process them and display velocity fields.

Nd:YAG Laser 15 mJ - 400 mJ per pulse 4 ns - 20 ns pulse duration Acts like strobe light freezes the particle images Wide range of T to measure flow velocities from mm/s to supersonic speeds 10 - 30 Hz Pulse Repetition Rate 532 nm Wavelength (Frequency Doubled) Most visible wavelength The dual Nd:YAG laser is the preferred light source for most PIV experiments. This integrated laser houses two separate laser heads whose pulses are combined with built-in beam combination optics to produce a coaxial pulse train. The very short pulse duration is fast enough to “freeze” even particle images in supersonic flow without image streaking. The high pulse energy is able to illuminate small particles for either air or water flows. Because two lasers are used any time between pulses is possible, with the full energy in each pulse. Lower power (10 to 100 mJ ) Nd:YAG lasers are now available for water flow experiments or small air flow experiments. These small Nd:YAG lasers are able to deliver much higher pulse energy than even a 10 Watt argon laser. Dual Nd:YAG s can come with variable repetition rate from 10-30 Hz. A dual YAG laser with 15 Hz rep rate per laser works well with the special 30 Hz cross correlation camera, when two images are captured on separate frames. This would give 15 velocity fields per second.

Energy vs. Q-switch delay Hi Med Low 100% 80% 60% Pulse energy - % of maximum 40% 20% Nd:YAG lasers use two trigger signals in generating a pulse of light. The first trigger fires a flash lamp. Photons from the flash lamp are absorbed by the Nd:YAG rod where this energy is stored. The second trigger opens the Q-Switch releasing the stored energy as a laser pulse. The light discharge from the flash lamp takes some time to reach maximum brightness and then decreases. The pulse energy depends on flash lamp brightness when the Q-Switch is opened. The figure above shows the relationship between pulse energy and Q-Switch delay. By setting the Q-Switch delay time the pulse energy is selected. This allows a minimum energy pulse to be used for alignment and setup, and a high energy pulse to be used for the experiment. The Synchronizer and LaserPulse software set the laser pulse energy by setting the Q-Switch delay time. The pulse energy can also be set (on some laser models) by setting the flash lamp voltage. Adjusting the pulse energy with Q-Switch delay is recommended because it keeps the laser at the operating temperature it was tuned for. This maintains the best beam quality. 0% 50 100 150 200 250 300 Q-Switch delay (microsec)

Light sheet Optics “Fan” laser light to create 2D measurement plane Combination of cylindrical and spherical lenses Cylindrical lens diverges (fans) light in one direction Dictates measurement area Spherical lens waists (thins) light sheet Achieves “2D” sheet (very thin) Cylindrical lens Spherical lens waist Laser light sheet optics are used to control the dimensions of the illuminated area. A cylindrical lens controls the light sheet height. A spherical lens is used to control the light sheet thickness. The top view shows the thickness of the light sheet. The cylindrical lens has no effect on the light sheet thickness. The spherical lens forms a waist in the light sheet at its focal point. The bottom view shows the light sheet height. The beam diverges in the vertical direction after passing through the negative focal length cylindrical lens. The positive focal length spherical lens reduces this height divergence only a little. Typically the cylindrical lens has a much shorter focal length than the spherical lens. Typically the camera views the light sheet near the thickness waist, where the intensity is highest, but any place along the light sheet can be used. When selecting the light sheet optics and camera viewing position the light sheet intensity should not be allowed to vary too much over the field of view. Fan

PIV Image Capture Synchronizer controls timing with high precision Controls laser power and “que” timing Initiates camera capture Camera captures 2 images “back to back” upon trigger Frame A exposure Independent (user defined) Frame B exposure Dependent (fixed) Laser light intensity determines particle image brightness NOT exposure time Timing parameters chosen so that one laser pulse appears in frame A and another in frame B

Synchronization Camera Exposures Camera Image Readout Pulse separation 4/14/2017 Image 1 Exposure Image 2 Exposure Camera Exposures Camera Image Readout Image 1 Readout Image 2 Readout Pulse separation LaserPulses Frame straddling technique allows very short time between laser pulses and thus provides the capability to measure higher and higher speed flows. Frame Straddling requires a close synchronization between the camera exposure and the pulsing of the laser. Key camera specification is the time from the end of one exposure to the start of the next exposure, the minimum frame straddle time. When trying to make the highest flow velocity measurement the first pulse is delayed until the last moment of exposure 1, and the second pulse happens at the first moment of exposure 2. Actual frame straddle time requires that Image1 be removed from the pixels before the second exposure starts. The time to move the image from the pixels depends on the image brightness. Actual frame straddle times can vary with experimental setup. Camera Trigger: The Synchronizer Triggers the camera to start a double exposure sequence. The Frame Grabber is also triggered at this time to capture the next two images. An external trigger can initiate the camera trigger. Camera Shutter Feedback: After a short time the Shutter Feedback signals the start of the first frame exposure. Camera Exposure: The two frame exposure includes a short frame 1 exposure and a longer frame 2 exposure. The first exposure is just long enough to Q-Switch a Nd:YAG laser. During the second exposure image in frame 1 is readout. Camera Digital Video Image output: The first image(frame 1) moves quickly from the light sensitive pixels to the readout registers. It then takes one frame time to transfer the image out of the camera and to the frame grabber. The second image cannot end until all of the first image has been read out of the camera. Laser Pulses: The first laser pulse must end before the end of exposure 1. The second pulse must start after the beginning of exposure 2

Synchronization-Example Timing 4/14/2017 400 ns 2 ms Camera Exposures 400 us Camera Image Readout 2 ms 500 us LaserPulses Frame straddling technique allows very short time between laser pulses and thus provides the capability to measure higher and higher speed flows. Frame Straddling requires a close synchronization between the camera exposure and the pulsing of the laser. Key camera specification is the time from the end of one exposure to the start of the next exposure, the minimum frame straddle time. When trying to make the highest flow velocity measurement the first pulse is delayed until the last moment of exposure 1, and the second pulse happens at the first moment of exposure 2. Actual frame straddle time requires that Image1 be removed from the pixels before the second exposure starts. The time to move the image from the pixels depends on the image brightness. Actual frame straddle times can vary with experimental setup. Camera Trigger: The Synchronizer Triggers the camera to start a double exposure sequence. The Frame Grabber is also triggered at this time to capture the next two images. An external trigger can initiate the camera trigger. Camera Shutter Feedback: After a short time the Shutter Feedback signals the start of the first frame exposure. Camera Exposure: The two frame exposure includes a short frame 1 exposure and a longer frame 2 exposure. The first exposure is just long enough to Q-Switch a Nd:YAG laser. During the second exposure image in frame 1 is readout. Camera Digital Video Image output: The first image(frame 1) moves quickly from the light sensitive pixels to the readout registers. It then takes one frame time to transfer the image out of the camera and to the frame grabber. The second image cannot end until all of the first image has been read out of the camera. Laser Pulses: The first laser pulse must end before the end of exposure 1. The second pulse must start after the beginning of exposure 2

Synchronizer System External trigger -or- Insight3G Software Capture interface Computer The computer controlled Synchronizer is at the heart of all PIV systems. The primary function of a Synchronizer system is that of a precise timer and a master system controller. It synchronizes the timing of image capture with the pulsing of the laser. Acting as the master controller for system components, it automates control of the timing between laser pulses, camera, camera interfaces and any external device during system set-up and image acquisition. The Synchronizer enables the system to be completely computer controlled via a serial interface. Special crosscorrelation cameras are employed in PIV which enable pairs of images be taken with short time between pulses. Control of such cameras is built into the synchronizer. Signals for the laser flash lamps and Q-switches, the camera and the frame grabber are generated and automatically synchronized for effortless image acquisition. For PIV applications, pulse delay time and the time between pulses necessary to collect frame-straddling images, are controlled visa TSI’s INSIGHT software. The synchronizer has an auxiliary output for controlling various devices in an experimental rig. For periodic flows, where phase locked velocity measurements are desirable, the Laserpulse synchronizer can be externally triggered using a TTL signal from the experimental apparatus. For example, in an IC engine experiment, images are captured at a certain crank angle position to be ensemble averaged. In bio-fluid mechanics relating to heart valve flows, images are captured at certain events in the systolic/diastolic cycle. The synchronizer system provides all the needed control signals – and does not need adjustments – for the cameras, lasers and other devices supplied as part of the TSI PIV system. Laser control

PIV Rules of Thumb for great results The key to good measurements is good raw data The raw data of PIV measurements are particle images In the Ideal Case Seed particle images are 3 – 5 pixels in diameter 5 – 15 particles per interrogation region Maximum particle displacement approximately 25% of size of interrogation region It is not always possible to satisfy these in all measurements, but they are good experimental goals

Experiment Considerations Important considerations: What size field of view? What desired spatial resolution? Are the above 2 realistic together? Appropriate seeding Optical access Camera 90 degrees with respect to laser sheet View is not distorted What does it look like when you view the measurement region from the perspective of the camera? 0.2 m 0.2 m Field of View Using 4MP (2k x 2k) Camera… …apply 32pxl x 32pxl interrogation region …apply 64pxl x 64pxl interrogation region

Experimental Setup General Setup Setup Tips Laser illuminates plane of interest Camera 90 degrees to light sheet Good optical access (no distortions) Camera is focused on ‘waist’ of the light sheet Setup Tips Initial setup: steps should be performed in ‘free; continuous’ mode of the Insight 3G software Use room light, no laser Final setup: the best practice is to focus camera on seed particles in the flow This assures that the focus is optimized to the laser sheet

Experimental Setup When setting up the cameras to view laser light scattered from particles: Start on a large f-number (small aperture) and low laser energy Increase alternately until seed particles are well-illuminated with minimal pixel saturation WARNING: IF LARGE REGIONS OF SATURATED (PINK) PIXELS APPEAR, STOP CAPTURE IMMEDIATELY Laser light can damage camera pixels Reduce laser energy and/or increase f-number

Calibration What are we ‘calibrating’? We need to show the software how to convert from pixel units to the physical units relevant to our flow space We are considering the simplest case in 2D PIV, where we view the light sheet at 90 degrees with good optical access Off-axis viewing and optical distortions are sometimes unavoidable, and appropriate corrections can be made In these cases, we need to give the software more information to be able to convert pixels to mm over the entire image region Addressed in future webinars

Calibration Procedure Assumption: Cameras focused on laser light sheet Calibration Steps Capture and save image of “Ruler” in plane of laser light sheet Create a calibration file with the saved image Use the 2D-Calibration software tool to measure across a known distance in the calibration image

Seed Density Considerations for Seeding Density: The true test of appropriate seed particle density is examining the Particle Images Considerations for Seeding Density: Field of View is known Desired Spatial Resolution known Interrogation Region Size Do I have enough particles in each interrogation region? 5-15 particles per region

Optimizing Dt In addition to imaging the flow field, we must also determine the timing between Frame A and Frame B. This parameter is called Δt We must select a Δt so that the displacement follows our “rule of thumb” of 25% of our intended interrogation region Ensure consistency with experimental objectives Field of view Spatial resolution Appropriate limits on particle displacement Maximum particle displacement should be approximately 25% of the interrogation region

Optimizing Dt The first step in optimizing Dt is developing “an eye for it” Can you see the displacement? Although qualitative, this is a critical step in optimizing a PIV measurement If displacements appears random, reduce Dt If there is little / no displacement, increase Dt

Optimizing Dt There are several ways to ‘measure’ the displacement for a more quantitative assessment Zoom into individual particles Perform ‘Point Processing’ and assess displacement of individual spots Remember, this process is iterative. Expect to alternate between experimental optimization and processing adjustments

Optimizing Dt Timing Setup The Timing Setup Window in Insight 3G Dt

Basic PIV Processing Start with “general purpose” settings Basic processing lets you know what the flow is doing and how well your images process A good foundation for further optimization Iteratively optimize This may include making experimental changes and acquiring new images

PIV Rules of Thumb Review Seed particle images are 3 – 5 pixels in diameter 5 – 15 particles per interrogation region Maximum particle displacement approximately 25% of size of interrogation region 3-5 pixel particles allows for a Gaussian ‘fit’ to determine location to subpixel accuracy, but still allows for a high seeding density Multiple particles per interrogation region strengthen the correlation 25% displacements keep most particles within the interrogation region, allowing the search to match with most of the spots

Basic PIV Processing Insight3G’s default settings are a good starting point Classic PIV produces 1 vector field from 1 image 64x64 pixel size for both spot A and spot B works well for moderately-seeded flows with similar x and y velocity ranges The Nyquist grid setting gives us 50% overlap between neighboring spots Since we are using NyquistGrid, the starting spots are the final spots The FFT correlator is a good general-purpose choice. This enforces our 25% rule of thumb The Gaussian peak engine is normally the best choice for obtaining accurate velocities.

Evaluating Processing The easiest way to evaluate your processing settings is to process a vector field. Adjust the scale of the vectors for a clear view Do the generated vectors appear physically reasonable? Are there many “red” vectors that failed validation?

Evaluating Processing Vector Statistics provide more useful information Maximum U and V pixel displacements Number and percentage good vectors

Evaluating Processing This image is a good candidate for increasing the spatial resolution by decreasing interrogation region size 99.6% valid vectors maximum particle displacements of >5 pixels High seeding density suggests 5-15 particle rule of thumb possible for smaller interrogation region What to consider: How much smaller? Spot A? Spot B?

Spot Dimensions The Spot A size is used to determine spatial resolution Velocity of all particles in Spot A is averaged into a single vector The Spot B size and maximum dx, dy determine search area size Larger sizes slow down processing, only help with large displacements Spot A Spot B

Adjusting spot dimensions Dimensions of Spot A determines: How many particles in the interrogation region (5-15) Smallest resolvable flow features (spatial resolution) Maximum allowed displacement (dx, dy): Maximum measurable particle displacements (dynamic range) in X and Y 25% spot width, height Adjusting these features can accommodate processing smaller interrogation regions.

Adjusting Spot Dimensions Reprocessed with 32x32 Now we are starting to get more invalid vectors. Why? Let’s look closer: Uneven seeding leaves some spots empty

Adjusting Spot Dimensions Point Processing lets us evaluate the outcome of processing at a given spot. Here we see how low seeding density affects the correlation map Multiple peaks Lumpy Background

Point Processing Point Processing shows us other information as well Peak Ratio Processing Algorithms Input and as-processed spots Location of the correlation peak within the map Near the center is best Dx, Dy

Adjusting Spot Dimensions For some flows, square spots may not be optimal For example, a boundary layer Large displacements, low gradients in X (need large spot size) Small displacements, sharp gradients in Y (need small spot size) Can use rectangular spots to optimize both dimensions Rectangular spot A averages velocities over a rectangular region Rectangular spot B combined with larger allowed displacements looks for a correlation over a larger area

Adjusting spot dimensions This flow is sufficiently seeded for 32x32 (or even 24x24) interrogation, but we still get many invalid vectors. Dx is too large for 32x32 spot A and spot B size Try different spotA and spotB sizes Here we could also offset the search region in spot B Requires knowledge of the flow field Only works in flows with a dominant flow direction

Adjusting spot dimensions 64x24 Spot A 64x24 Spot B 0.25 Maximum dx 32x32 Spot A 64x32 Spot B 0.49 Maximum dx

Single-Pass drawbacks With a fixed spot size and single pass, smaller interrogation regions give higher spatial resolution but reduced dynamic range There are workarounds We can relax the 25% rule of thumb and use a larger spot B if the image quality is high We can use rectangular interrogation regions if the flow geometry permits We can offset spot B There is a better option – Multi-pass processing Can optimize for both spatial resolution and dynamic range Improves SNR for better quality vector fields Operates like a dynamic spot offset

Multi-Pass PIV Processing Using the RecursiveNyquist-Grid Multi-pass PIV processing lets us increase our spatial resolution

Multi-pass PIV Processing Process PIV image multiple times in sequence Successive passes use the initial results as a starting guess The search area in Spot B is “offset” relative to Spot A – centered on the displacement “guess” Spot A and Spot B will contain only the “fingerprint” Higher SNR, more and better vectors 25% rule of thumb only applies to first pass Spot B Spot A

Vector Post Processing Vector Validation Basic PIV processing checks only SNR to validate vectors Need a way to “weed out” invalid vectors In final data In between passes Vector Conditioning Interpolation to replace discarded vectors Smoothing Especially important for intermediate passes in multi-pass techniques Avoids using a bad vector as a guess for additional processing

Vector Validation Global Validation Check velocity against specified range or number of standard deviations from the mean Good when you know what range of velocities to expect

Vector Validation Local Validation More flexible, compares a vector with its neighbors Discriminates based on difference between the vector and the median or mean displacement (in pixels), or dimensionless “Universal” median Decrease neighborhood size for flows with high gradients Option to replace discarded vectors with local median or secondary correlation peak

Vector Conditioning Apply After discarding invalid vectors Replace discarded vectors with the local median or mean velocity Optionally apply a low-pass filter to the vector field for smoothing Keep in mind that smoothing changes all vectors – modifying your data

Deformation Grid Processing Means to sharpen peak of correlation map Accounts for high rotation or velocity gradients within interrogation regions Anticipates displacement of particles, and deforms Spot B to account for such gradients Surrounding velocities used to determine deformation Spot A Sharpen peak of correlation function Deformed Spot B “Traditional” Spot B (Overlaid Spot Masks)

Deformation Grid Processing Stronger correlation peak and better accuracy with high gradients Higher computational cost

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