Stereoscopic PIV Calibration Verification
Daniel C. Bjorkquist
TSI Inc
PO Box 64394
St. Paul MN 55164
USA
dbjorkquist@tsi.com
Abstract
Stereoscopic PIV uses a calibration to combining two 2D vector fields into a 3D vector field. The
calibration is a set of polynomial equations to map locations between a camera pixel (X, Y) location and
world (x, y, z) location. The calibration procedure uses a calibration target with a grid of markers placed
in, or near the lightsheet. A list of image and world point pairs is the input to the calibration. The image
marker locations are found by image processing. The world marker locations are input from the target
geometry and the target location. The target geometry is accurate but the location of the target with respect
to the lightsheet may not be. This paper presents a method for measuring and correcting the target location
error to increase the calibration accuracy and velocity measurement accuracy in stereoscopic PIV.
The flow images have particles illuminated by the lightsheet. These images are in the camera
pixel array coordinate system, that is distorted by the stereoscopic camera configuration. The image
distortion can be corrected, and converted into a world coordinate system by mapping the camera images
into the lightsheet z = 0 plane, a processes known as “warping”. If the calibration is accurate and the
lightsheet has zero thickness, the particle images from the left and right cameras would be at the same
location in the warped images. Crosscorrelation processing, the same processing as is used to measure the
flow velocity is used to measure the displacement in the warped images. The measured X displacements
are assumed to be caused by errors in the z-axis location of the calibration target because of a z-axis
translation or tilt about the x-axis or y-axis are converted into z displacements. The target alignment error
is found by finding the best-fit to the equation: z(x,y) = a + bx + cy. The solution a term is the z translation
error. The solution b term is the tilt about the y-axis. The solution c term is the tilt about the x-axis. The
list of target world marker locations is moved by the best-fit plane solution displacements. This maintains
the geometry of the calibration target, which is accurate, and adjusts the position of the target with respect
to the lightsheet, where alignment errors are likely to occur. The calibration image marker locations are
not changed. The calibration is re-computed using the corrected target location information.
The error caused by calibration target misalignment is investigated using synthetic PIV images.
Six sequences of images, each with flow in one velocity component varied in a sine wave pattern in either
the x or y direction were generated. The 3D vector fields were processed using the same calibration as
used to create the images. A calibration target position error of 2 mm z translation, 2 degrees x tilt and 2
degrees y tilt is then introduced to the calibration, and the images re-processed. With the target misaligned
there are large errors in the w velocity component in the images with du/dx velocity gradients, and large
errors in the residual error in the images with dv/dx velocity gradients. The warped image crosscorrelation,
and target position error analysis are used to correct the target alignment, with 3 optimization iterations,
and the images processed again. The errors are brought back down to near the levels with the correct
calibration location.
The method is demonstrated with experimental data of a downward flowing water jet, with a high
dv/dx velocity gradient. The calibration target was purposefully misaligned by 6 mm. The maximum
residual error was reduced from 3.7 pixel to 0.7 pixel, and the maximum velocity measured increased from
1.6 m/s to 2.8 m/s with the warped crosscorrelation target position correction. In a second test the
calibration target was misaligned by 0.5 mm. The maximum residual error was reduced from 1.1 pixel to
0.6 using the warped image crosscorrelation target position correction. The data for performing this
calibration improvement has always been required for stereoscopic PIV measurements allowing old
experiments to be re-processed to get higher accuracy 3D velocity results.
Introduction
Stereoscopic PIV employs a calibration for mapping locations between the camera and the fluid
(Soloff 1997). The calibration is performed using a target with a grid of markers placed in the laser
lightsheet plane. The target grid parameters and the position of the target in the fluid are entered into the
calibration program and the position of the markers in the images is measured using image processing.
The calibration equations are generated from the calibration marker fluid and image position pairs
(Bjorkquist 1998).
The accurate positioning of the target in the laser lightsheet is critical for accurate 3D velocity
measurements. Practical considerations can make the accurate positioning of the target difficult. In some
experiments, access to flow area is difficult making target alignment difficult. Wearing laser safety
goggles for alignment makes the laser beam difficult to see. To help align the target with the laser
lightsheet, a mirror placed behind a slit is attached to the side of the target. When the lightsheet is centered
on the slit and light reflects back on the laser the target is aligned. Even with this procedure the target may
not be located accurately enough for a precise calibration. A calibration verification method is desired to
ensure the accuracy of the velocity measurements.
Image Warping
Figure 1 shows a pair of images warped into the lightsheet plane. The pixel values from the two
cameras are interpolated onto a grid of square pixels in the lightsheet plane. The two warped images use
the same number of pixels and pixel spacing so that the images are aligned pixel for pixel. The image area
is the bounding box of the four corners of each camera image mapped into the laser lightsheet plane. The
warped image height in pixels is set equal the camera image height in pixels. The pixel scale factor
(mm/pixel) is set by the warped image height in mm and camera image height in pixels. The image width
is set by this pixel scale factor and the width of the imaged area in mm, so the warped image is the same
height and wider than the camera images keeping the camera images and warped images with
approximately the same pixel scale factor. The warped image pixel values are set by mapping from the
lightsheet to the camera and computing the pixel intensity value using bilinear interpolation at the
floating point mapped pixel location. The rectangular camera images become trapezoidal in the image
warping as shown in figure 1 for a simulation using cameras at +30 degrees and –30 degrees using the
Scheimpflug configuration. The left and right images are now in the same coordinate system. Since the
left and right images are from the same pulse of laser light there is no flow velocity between the images.
Figure 1A Warped Left Image
Figure 1B Warped Right Image
Position of the Target
The accuracy of the image warping can be measured by using crosscorrelation processing (Raffel
1998). This is the same processing as used in PIV to measure particle image displacements due to fluid
motion, except to measure fluid motion the a pair of images come from the same camera imaging the fluid
illuminated by two pulses of laser light. In warped image crosscorrelation the images come from two
cameras imaging the fluid illumined by the same laser pulse. If the calibration is accurate and the laser
lightsheet had zero depth the warped cross correlation vector field would have zero displacement vectors.
If the calibration has errors the warped crosscorrelation vector field will show the error.
One source of calibration error is the calibration target not being accurately placed in the laser
lightsheet plane. Figure 2 shows the warped crosscorrelation vector fields for 4 target position errors. In
figure 2A the target is between the lightsheet and the camera, the X displacement is negative and nearly
constant. In figure 2B the target is tilted about the x-axis with the top closer to the cameras and the bottom
farther away from the cameras, the vector field X displacement shows a negative to positive gradient from
top to bottom. In figure 2C the target is tilted about the y-axis with the left side closer to the camera giving
an X displacement gradient with the minimum on the left and maximum on the right. A combination z
translation, x tilt and y tilt is the sum of the component displacements as shown in figure 2D. The average
X displacement represents the distance from the target to the lightsheet in the z direction. A top to bottom
X displacement gradient represents an x-axis tilt. A left to right X displacement gradient represents a yaxis tilt.
In a typical stereo PIV configuration the cameras are in the x-z plane and the X displacements
dominate the u and w velocity components. Since the Y displacement only has a minor influence on the
measured z displacement analyzing the Y displacements does not provide much information about the
target position error and is not used in this analysis.
The target position error can be measured from the warped crosscorrelation vector field if we
assume that all of the X displacement is caused by z positioning errors. Then the measured X displacement
in pixels is converted into dz mm using the calibration equations. The derivatives of the calibration give
the δX/δz gradient for the left and right camera. The sum of the two-δX/δz gradients is the local
calibration factor. The dz value is the X displacement divided by the local δX/δz gradient. The calibration
target position error is defined by the measured z values from the warped crosscorrelation X displacement
field. The target z translation, x-axis tilt and y-axis tilt are found using the a least squares solution to the
equation:
dz = a + bx + cy
Where:
dz = dX / (δX/δz)
dx = measured displacement in pixels
δX/δz = calibration gradient (pixel/mm)
a = z translation error in mm
b = target tilt angle about the y-axis in radians
c = target tilt angle about the x-axis in radians
x = vector x location in world coordinates
y = vector y location in world coordinates
Figure 2 Crosscorrelation Vector Field of Warp Images with Z Translation, X axis Tilt, Y Axis Tilt
Frame 001  28 May 2002  D:ExperimentsTargetSimComponentSineVectorComponentSineAvgZ2target.vec
Frame 001  28 May 2002  D:ExperimentsTargetSimComponentSineVectorComponentSineAvgY2Target.vec
2 mm Z Target Postion
2 degreee Target Y Tilt
20 pixel
7.5 pixel
500
500
450
450
400
400
350
350
Y pixel
Y pixel
300
300
250
250
200
200
150
150
100
100
50
50
0
100
200
300
X pixel
400
0
500
0
100
200
300
X pixel
400
500
Fig 2A Target at Z = 2 mm
dX range –21.87 to –20.44 pixel
dY range –0.18 to 0.15 pixel
Fig 2C Target Y tilt = 2 degrees
dX range –7.62 to 7.56 pixel
dY range –0.11 to 0.12 pixel
Frame 001  28 May 2002  D:ExperimentsTargetSimComponentSineVectorComponentSineAvgX2Target.vec
Frame 001  28 May 2002  D:ExperimentsTargetSimComponentSineVectorComponentSineAvg222Target.vec
2 Degree Target X Tilt
Target Position Z 2mm, X Tilt 2 deg, Y Tilt 2 deg
20 pixel
7.5 pixel
450
450
400
400
350
350
Y pixel
500
Y pixel
500
300
300
250
250
200
200
150
150
100
100
50
0
100
200
300
X pixel
Fig 2B Target X tilt = 2 deg
dX range –7.89 to 7.15 pixel
dY range –0.05 to 0.07 pixel
400
500
50
0
100
200
300
X pixel
400
500
Fig 2D Target Z = 2 mm X tilt = 2 deg, Y tilt = 2
deg
dX range –36.42 to –5.79 pixel
dY range –0.19 to 0.33 pixel
The calibration mapping equations are generated using a list of image and world point pairs. The
target position in the world (x, y, z) is input using the target grid geometry and the target location relative
to the lightsheet. The image target marker locations are found using image processing. The list of point
pairs is used to generate the initial calibration equations. The warped image crosscorrelation results
provide information about the actual position of the target relative to the lightsheet. Translating and
rotating according to the best-fit plane results corrects the target position marker locations. The target
image marker locations are not modified. This preserves the geometry of the calibration target which is
accurate and adjusts its position with respect to the lightsheet, which has some error. After the target world
positions have been modified the calibration is recomputed using the modified target points list. The bestfit plane solution gives a fair estimate of target location error, but it usually takes two to six iterations
before the crosscorrelation of the warped images converges to a solution with a maximum error of less than
1 pixel.
The maximum target location position error that can be corrected is limited by the ability to
crosscorrelate the warped images. When no spot offset is used then the maximum displacement is ½ the
spot size, or 64 pixels for a 128 pixel spot. Offsetting the interrogation spots can increase the maximum
target position error that can be corrected. If good correlation can be found, even if only a portion of the
warped images, then that vector field can be used for the first estimate of the target location error. Usually
if the majority of the error is corrected for the re-warped images will correlate better. And as the
calibration error is reduced the correlations become stronger with each optimization.
Lightsheet Thickness
The lightsheet thickness affects the crosscorrelation peaks of the warped images. The image
warping maps the particles into the lightsheet z = 0 plane. If the particle is not at the center of the
lightsheet then the left and right cameras will map the particle into different warped X image locations.
Because real lightsheets have thickness the there will be some range in peak X location of individual
particles due to particle z position within the lightsheet. With high particle image concentrations there are
many particles contributing to the correlation peak each with an X position determined by the particle z
location elongating the peak in the X direction as show in figure 3. These peaks were created from
simulated PIV images with the cameras at +- 30 degrees in the Scheimpflug configuration. For 100 µm
and 250 µm and 500 µm thick lightsheets the correlation peaks are nearly round. The 1,000 µm and 1,500
µm lightsheets show elongation in the X direction. With low particle image concentrations a splintered
peak will be produced. The measured peak location will be dominated by one or just a few particles and
the location will depend on the particle’s z position.
Figure 3 Correlation Peak Elongation with Lightsheet Thickness for High Concentration Spots
100 µm
250 µm
500 µm
1,000 µm
1,500 µm
The measurements in this paper used a 3-point curve fit to the highest intensity correlation map
pixel. The simulated lightsheet and the actual laser lightsheet in the experimental data were about 1 mm
thick. The measured peak location could be anywhere along the elongated peak. Sequences 30 of vector
fields were ensemble averaged to reduce the errors due to lightsheet thickness. Figure 4 shows the range of
vectors in 30 vector fields. The variation is due primarily to the lightsheet thickness.
Frame 001  29 May 2002  01C2ACC8 | 01C2ACC8 | 01C2ACC8 | 01C2ACC8 | 01C2ACC8 | 01C2ACC8 | 01C2ACC8
Aligned Target Vector Range
1 mm thick Lightsheet, 30 Vector Fields
3 pixel
500
450
400
Y pixel
350
300
250
200
150
100
50
0
100
200
300
X pixel
400
500
Fig 4 Target Aligned with Lightsheet 30 Vector Fields dx range –3.55 to 3.64 pixel dy range –0.50 to 0.47
pixel
Residuals Errors
The 3D particle displacement is computed by combining interpolated pixel displacement vectors
from the left and right cameras using the calibration gradients to convert from pixel displacement to world
displacement. The vector grid is defined as a square grid in the fluid coordinates. This world location is
mapped into the left and right cameras using the calibration mapping functions. Bilinear interpolation is
used to estimate the pixel displacement at that location from the four surrounding vectors. Errors in the 3D
velocity vector occur from calibration gradient errors, mapping errors, and pixel displacement
measurement errors in the 2D vector fields.
The 3D particle displacement (dxfluid, dyfluid, dzfluid) is found by solving a set of four equations in
three unknowns:
dXleft =
dYleft =
dXright =
dYright =
Where
dxfluid(δXleft/δxfluid) + dyfluid(δXleft/δyfluid) + dzfluid(δXleft/δzfluid)
dxfluid(δYleft/δxfluid) + dyfluid(δYleft/δyfluid) + dzfluid(δYleft/δzfluid)
dxfluid(δXright/δxfluid) + dyfluid(δXright/δyfluid) + dzfluid(δXright/δzfluid)
dxfluid(δYright/δxfluid) + dyfluid(δYright/δyfluid) + dzfluid(δYright/δzfluid)
dXleft dYleft pixel displacement in left camera
dXright, dYright pixel displacement in right camera
dxfluid, dyfluid, dzfluid particle displacement in the fluid
δXleft/δxfluid, δXleft/δyfluid, δXleft/δzfluid left camera x displacement gradients
δYleft/δxfluid, δYleft/δyfluid, δYleft/δzfluid left camera y displacement gradients
δXright/δxfluid, δXright/δyfluid, δXright/δzfluid right camera x displacement gradients
δYright/δxfluid, δYright/δyfluid ,δYright/δzfluid right camera y displacement gradients
The residual errors are the difference between the measured image displacements and the
displacement computed from the fluid displacement solution and the displacement gradients. The total
residual error is the sum of the absolute values of the four residual errors.
In the typical stereo PIV configuration the cameras are in the x-z plane and the δXimage/δxfluid,
δXimage/δzfluid dominate the dxfluid, dzfluid solutions and the δYimage/δyfluid term dominates the dyfluid solution.
The residual error is a measurement of how well the two Y displacements agree. Errors in the X
displacement appear as errors in the u and w velocity components.
One Component Gradient Simulation
To see the affect of calibration accuracy a set of synthetic six image sequences were generated and
processed. Each sequence had one component of velocity that was varied in a sinusoidal pattern from –1
m/s to +1 m/s over 2 cycles. Velocity gradients in the x and y directions were generated for each velocity
component; the results are summarized in table 2. The aligned values are from 3D vector fields processed
using the same calibration used to generate the synthetic images. The 222 values are from 3D vector fields
processed with a target location error of 2 mm z translation, 2 degrees x tilt and 2 degrees y tilt as in figure
2D. The 3 iterations of optimization used are shown in table 1. The warped crosscorrelation target
position correction procedure was then used to correct the target location and the 3D vector fields are
shown as the corrected values. The table shows the rms error for the zero velocity components and the
residual rms error. The errors are also shown as a percentage of the aligned vector field to show the
change due to the calibration error.
Table 1 One Componet Sine Target Optimization Target at 2 mm z, 2 deg x tilt, 2 deg y tilt
dX Mean
dY Mean
Z translation
X tilt degree
pixel
pixel
mm
Pass1
-22.7853
0.0373
-2.2923
-2.2784
Pass2
-1.5855
0.0030
0.1690
0.2647
Pass3
0.1985
0.0013
0.0202
0.0047
Y tilt degree
-2.3247
0.2658
0.0229
Error
0.0787
-0.0090
-0.0360
Velocity gradient flow field simulations were tested to see the full affect of mapping errors.
When uniform translation is tested the mapping error only creates a relatively small error because the
velocity at a point and all of the surrounding area is nearly the same. This error can be seen in figures 5B
and 6B as an increase in the errors from the lower right to upper left corners, following the pattern seen in
the warped crosscorrelation vector field in figure 2D. When the flow has a strong gradient then the
velocity may be very different between the correct location and the mapped location. The du/dx gradient
flow shown in figure 5 and the dv/dx gradient flow shown in figure 6, show that the errors can be much
higher where there are velocity gradients. In the du/dx gradient flow the mapping error causes errors in the
u velocity component, which becomes a w velocity error. In the dv/dx gradient flow the mapping error
causes the v vectors to come from areas with different velocities and a large residual error results.
Table 2 of One Component Sine Velocity Gradient Flow Vector Field Errors
flow/calibration
u rms v rms w rms residual u %
v%
w%
residual %
m/s
m/s
m/s
aligned
rms pixel aligned aligned aligned
du/dx aligned
0.0061 0.0158
0.0403
du/dx 222
0.0200 0.2697
0.0407
228.7% 1603.2%
0.9%
du/dx corrected
0.0061 0.0158
0.0394
0.7%
-0.5%
-2.3%
du/dy aligned
0.0061 0.0159
0.0393
du/dy 222
0.0061 0.0289
0.0397
0.2%
81.6%
1.0%
du/dy corrected
0.0061 0.0158
0.0394
0.7%
-1.0%
0.2%
dv/dx aligned
0.0062
0.0104
0.0446
dv/dx 222
0.0073
0.0252
143.3%
0.3640 19.0%
715.3%
dv/dx corrected
0.0062
0.0104
0.0448
1.1%
0.0%
0.3%
dv/dy aligned
0.0060
0.0102
0.0420
dv/dy 222
0.0060
0.0262
0.0481
0.2%
157.7%
14.3%
dv/dy corrected
0.0061
0.0101
0.0419
1.3%
-0.2%
-0.2%
dw/dx aligned
0.0171 0.0145
0.0848
dw/dx 222
0.0827 0.0253
0.0926 384.1% 74.1%
9.3%
dw/dx corrected
0.0170 0.0146
0.0848 -0.4%
0.4%
0.1%
dw/dy aligned
0.0184 0.0144
0.0845
dw/dy 222
0.0291 0.0259
0.0890 58.0% 79.9%
5.2%
dw/dy corrected
0.0185 0.0143
0.0844
0.5% -0.4%
-0.2%
The errors are highest with horizontal gradients because target-positioning errors show up as Z
location errors. The target grid defines the X-axis and Y-axis so positioning errors are calibrated out.
Another way of thinking about is the target defines the X-axis and Y-axes but the lightsheet defines the Z =
0 plane. Z position, tilt and tilt about the X-axis and Y-axis are all recognizable by their dx displacement
pattern. When the calibration is off it is the X displacement in the warped crosscorrelation images that
shows the error. It is therefore horizontal velocity gradients that show the largest 3D errors.
The calibration equations are used to map points between the lightsheet and the cameras, and the
derivatives of the calibration equation are used as the pixel displacement to world displacement conversion
factors. For a uniform translation flow the mapping errors will make little difference, as velocity does not
change much from vector to vector. As the velocity gradients increase the mapping errors have a greater
affect.
Frame 001  30 May 2002  D:ExperimentsTargetSimComponentSineVectorComponentSineAvgA222.v3s
Frame 001  30 May 2002  D:ExperimentsTargetSimComponentSineVectorComponentSineAvgA222.v3s
du/dx Gradient Flow W Velocity Errors
Target Aligment Error 2 mm z, 2 deg x tilt, 2 deg y tilt
du/dx Gradient Flow
1 m/s
1 m/s
W
0.619101
20
20
0.371461
0.12382
10
10
-0.12382
0
10
20
30
-10
-10
-20
-20
0
-20
-10
0
10
20
30
0
Y mm
-0.619101
Z mm
-10
0
Z mm
-20
Y mm
-0.371461
0
X mm
X mm
figure 5A du/dx Vector Field
Figure 5B du/dx Vector Field w Velocity Errors
Frame 001  30 May 2002  D:ExperimentsTargetSimComponentSineVectorComponentSineAvgC222.v3d
dv/dx Flow
1 m/s
Frame 001  30 May 2002  D:ExperimentsTargetSimComponentSineVectorComponentSineAvgC222.v3d
dv/dx Gradient Flow, Residual Error Contour
Target Position Error Z 2 mm, X Tilt 2 deg, Y Tilt 2 deg
30
Residual Error Pixe
0.966837
20
20
0.77347
0.580102
10
10
0
-10
10
20
30
0
-20
X mm
-20
-10
0
10
20
30
0
Z mm
0
0
Z mm
-10
0.193367
-10
-20
-20
Y mm
Y mm
0
0.386735
X mm
Figure 6A dv/dx Vector Field
Figure 6B dv/dx Vector Field Residual Errors
Experimental Results
To test this calibration verification and correction method an experiment was performed. A water
jet shooting down was measured with a stereo PIV system. The TSI PIVCAM 1030 cameras were at +-30
degrees in the Scheimpflug configuration. The water jet has a high du/dx gradient and should produce
relatively large residual errors if the calibration is off. The calibration target was purposefully misaligned
to produce the calibration errors and allow them to be corrected. Table 3 shows the measured target
location errors in 3 optimization iterations.
Table 3 Optimization of Target Position
dX Mean
dY Mean
pixel
pixel
Pass1
48.5
-0.241
Pass2
0.3749
-0.8934
Pass3
0.008
-0.7449
Z translation
mm
6.270
0.0319
-0.0108
X tilt degree
Y tilt degree
-0.0028
-0.457
0.0084
-1.498
-0.1096
0.0186
The velocity magnitude for the flow as calibrated and after the warped crosscorrelation target optimization
is shown in figure 7A and 7B. Optimizing the calibration increased the maximum 3D velocity from 1.63
m/s to 2.86 m/s. The 3D residual errors were greatly reduced from a maximum of 3.71 pixels with
standard deviation of 0.611 pixels to a maximum of 0.681 pixels with a standard deviation of 0.060 pixel.
Frame 001  30 May 2002  C:Experimentswjv100wjAvgECal.v3d
Frame 001  30 May 2002  C:Experimentswjv100wjAvgEOptimized.v3d
Velocity Magnitude, Target Position Optimized
Vel Mag
3
60
0.6
2.4
0.6
Vel Mag
3
60
2.4
Velocity Magnitude, Original Target Position
2.4
2.4
1.2
0.6
50
1.8
0.6
1.2
1.8
40
40
1.2
1.2
0
20
Y mm
0.6
0.6
Y mm
0.6
0.6
0
0.6
0.6
20
0.6
30
10
0
-10
0
10
20
30
40
50
-20
20
0
-20
Z mm
-20
-20
0
Figure 7A Velocity Magnitude As Calibrated
Frame 001  30 May 2002  C:Experimentswjv100wjAvgEOptimized.v3d
3D Residual Error, Original Target Position
Residual Error, Target Position Optimized
3.5
2.8
Residual Error Pixel
2.1
60
Residual Error Pixel
60
2.8
1.4 2.8
3.5
50
3.5
2.8
2.8
2.1
40
2.1
0.7
-20
20
0
-20
Figure 7B Velocity Magnitude Optimized Target
Position.
Frame 001  30 May 2002  C:Experimentswjv100wjAvgECal.v3d
2.1
2.1
1.4
40
X mm
X mm
0.7
20
Z mm
0.6 0.6
0.6
1.2
-10
-30
0
2
1.
2.1
40
1.4
1.4
0.7
20
0
Y mm
Y mm
20
0.7
0.7 0.7
1.4
30
0.7
0
0.7
10
0.7
-10
0
10
20
30
40
50
-20
20
0
-20
-20
20
40
-20
20
0
-20
X mm
X mm
Figure 8A Residual Error as Calibrated
0
Z mm
-20
Z mm
-10
0. 0.7
7
-30
0
0
Figure 8B Residual Error Optimized Target Position
The calibration was performed a second time, with a much smaller, .5 mm, positioning error. The
two target position optimization iterations are shown in table 4. In this case the maximum residual error
was reduced from 1.14 pixel to 0.64 pixel, the residual error standard deviation was reduced from 0.10
pixel to to 0.06 pixel as shown in figure 9A and 9B.
Table 4 Optimization of Target Position
dX Mean
dY Mean
pixel
pixel
Pass1
-3.638
-0.1633
Pass2
-0.1751
-0.1595
Z translation
mm
-0.5497
-0.0183
X tilt degree
Y tilt degree
-0.1167
-0.0198
-0.1735
-0.0039
Frame 001  30 May 2002  C:Experimentswjv100wjAvgBCal.v3d
Frame 001  30 May 2002  D:ExperimentswjVectorwjAvgBOpt.v3d
Residual Error Pixel
1.2
60
0.24
0.48
0.96
0.96
0.2
0.20.24
4
0.24
0.24
0.48
Residual Error Pixel
1.2
60
0.4
8
0.24
Cal B Optimized Calibration Residual Error
0.48
0.2
4
0.72
Cal B Residual Calibration, Residual Error
4
0.72
0.2
4
0.72
40
0.48
0.24
0.48
40
20
40
-20
20
0
-20
Z mm
0
0.24
0
0
0
-20
Y mm
20
0
X mm
Figure 9A Residual Error Original Figure
Calibration B
-20
0
20
40
-20
20
0
-20
Z mm
0.24
20
Y mm
0.24
0.24
0.2
4
0.24
X mm
9B Residual Error Optimized Calibration B
Conclusion
A method of verifying the stereoscopic PIV camera calibration is presented. The verification
using the crosscorrelation of images warped from the left and right cameras into the laser lightsheet plane.
The warped crosscorrelation vector field can be analyzed to find the calibration target position error, with
respect to the laser lightsheet plane. The analysis gives the target z-axis translation, x-axis tilt angle and yaxis tilt angle. The position of the target is then adjusted to reflect its true location and the calibration
equations re-computed using the corrected target location. Correcting the target location was shown to
improve the 3D velocity measurements and decrease the 3D residual errors.
This calibration improvement process uses the flow images that are also required to measure the
flow velocity. If the images were archived, it is possible to go back to old experiments and verify and
correct the calibration target location errors to increase the accuracy of past experiments.
References:
Soloff S. M, Adrian, R. J., Liu, Z-C, 1997 Distortion compensation for generalized stereoscopic particle
image velocimetry, Measurement Science and Technology December 1997 Vol. 8 Number 12 pages 14411454
Bjorkquist D. C. 1998 Design and Calibration Of A Stereoscopic PIV System, Ninth In International
Symposium on Applications of Laser Techniques to Fluid Mechanics July 13-16 1998 Lisbon, Portugal
Raffel M, Willert C, Kompenhans J, 1998 Particle Image Velocimetry A Practical Guide, Springer ISBN
3-540-63683-8