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18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
Dense Ray Tracing Based Reconstruction Algorithm for Light Field PIV and Comparative Study with Tomo-PIV
Shengxian Shi1*, Junfei Ding1 and T.H. New2 1: Gas Turbine Research Institute, School of Mechanical Engineering, Shanghai Jiao Tong University 200240, Shanghai, China
2: School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798 * Correspondent author: [email protected]
Keywords: 3D-PIV, light field imaging, plenoptic camera, Tomo-PIV, DRT-MART
ABSTRACT
This work presents an in-house developed high resolution light field volumetric PIV system, as well as a new 3D
particle image reconstruction algorithm based on dense ray tracing and multiplicative algebraic reconstruction
technique (DRT-MART). Parametric studies are firstly carried out to access key optical parameters on performance
of the light field volumetric PIV technique, followed by simulation studies that assess the capability of the DRT-
MART algorithm by comparing its reconstruction quality and computational cost with the MART method. In the
last, performance of the new algorithm as well as light field volumetric PIV are further tested with synthetic images
which are generated from a DNS jet flow, and compared with results from Tomo-PIV.
1. Introduction
Many fluid phenomena are inherently complex and three-dimensional, which urges the PIV
technique to progress from planar measurement to fully volumetric velocity measurement. One
of the first efforts was Stereo-PIV, which measures the third velocity component by including
one additional camera to the traditional 2D-PIV system (Prasad et al 1993, Arroyo et al 1996).
Scanning PIV extends such single slice 2D-3C measurement to multiple planes by using a series
of scanning laser sheets and a pair of high speed cameras, however its maximum measurable
velocity is limited by the camera frame rate, laser repetition rate or scanning mirror speed
(Brucker 1996, Hori 2004). Instead of measuring the third velocity component via dual-view
geometry, Defocusing Digital PIV (DDPIV) recovers depth information from defocused particle
images and normally employs a triple-camera arrangement to resolve the flow field with
satisfactory accuracy (Willert et al 1992, Pereira et al 2000). Holographic PIV (HPIV) resolves
volumetric velocity field from particle holograms, which are recorded by in-line or off-axis
holography (Arroyo et al 2008, Katz et al 2010). The application of this technique, however, is
limited by its complex experimental setup. One of widely applied three dimensional velocity
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
measurement techniques is Tomo-graphic PIV (Tomo-PIV), which employs multiple view
geometry (typical 4-8 views) to capture particle images and calculate three dimensional velocity
from multiplicative reconstruction technique (MART) and volumetric cross correlation (Elsinga
et al 2006, Scarano 2013). Tomo-PIV has advantages in high spatial resolution as well as relative
large measurable volume.
Apart from recording tracer particle’s three dimensional position through multiple view
geometry, other techniques record light field of tracer particles. One of such technique is
synthetic aperture PIV (SAPIV), which uses a large camera array (normally 8 to 15 cameras) to
capture the light field image for seeding particles and reconstructs 3D particle image through
synthetic aperture refocusing method. SAPIV can tolerate much higher particle density than
Tomo-PIV and its measurable range along optical axis can be on the same order as lateral
directions (Belden et al 2010). Instead of using camera array system, light field photography
based PIV (shorted as LF-PIV hereafter) records particle light field image through a compact
plenoptic camera, which is the combination of a high resolution micro-lens array (MLA) and a
high resolution CCD sensor. Studies have demonstrated that LF-PIV can resolve 3D velocity
fields through MART based re-construction and 3D cross-correlation (Ding et al 2015, Fahringer
et al 2015, Shi et al 2016).
In the following sections, systematic studies are firstly performed on how key optical parameters
affect resolution of plenoptic camera. In section 3, methodology of dense ray tracing based
MART (DRT-MART) reconstruction method is outlined and its performance is compared with
MART by ray tracing based simulation. In the last, the LF-PIV technique is evaluated by using
synthetic jet flow light field images, the results are compared with Tomo-PIV measurements.
2. Camera prototyping and ray tracing based light field simulation
Fig. 1. In-house developed plenoptic camera
相机机身
CCD平面
镜头安装筒
MLA及调节支架
Lens mount MLA
CCD
Camera body
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
An in-house light field camera shown in Fig. 1 was developed according to plenoptic imaging
(Ng 2006), where a customised micro-lens array (MLA) is precisely positioned one focal length
away from the CCD plane (IMPERX B6640). The MLA consists of 458×301 hexagonal lens unit,
which maximises the pixel usage when compared to a square lens unit. Light field image of
tracer particles can be simulated via linear Gaussian optics according to Eqs.1~5 (Georgiev et al
2003).
Particle O Main lens
(
x′y′
θ′φ′
) = (
10
01
So
0
0So
00
00
10
01
) (
xyθφ
) (1)
Through Main lens
(
x′y′
θ′φ′
) = (
10
01
00
00
−1/fm
0
0−1/fm
10
01
) (
xyθφ
) (2)
Main lens MLA
(
x′y′
θ′φ′
) = (
10
01
Si
0
0Si
00
00
10
01
) (
xyθφ
) (3)
Through MLA
(
x′y′
θ′φ′
) = (
10
01
00
00
−1/fl
0
0−1/fl
10
01
) (
xyθφ
) + (
00
Sx/fl
Sy/fl
) (4)
MLA CCD
(
x′y′
θ′φ′
) = (
10
01
fl
0
0fl
00
00
10
01
) (
xyθφ
) (5)
where x,y is the spatial location of particle O. θ, φ is the orientation angle of light ray emitted
from the particle. Geometry of a representative light ray is plotted in Fig. 2. For simulation
studies in the paper, a series of synthetic light field images are generated using ray tracing
method with key parameters listed in Table 1.
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
Fig. 2. Schematic of ray tracing for plenoptic camera
Table 1 Optical parameters for ray tracing simulation
Symbol Parameter Pixel Microlens Ratio
PMR8 PMR14 PMR28
nlx MLA resolution: X 63 31 15
nly MLA resolution: Y 63 31 15
pl Microlens pitch 44μm 77μm 154μm
fl Microlens focal length 308μm
npx Camera resolution: X 448
npy Camera resolution: Y 448
pp Pixel pitch 5.5μm
fm Main lens focal length 50mm
Pm Main lens aperture 25mm
So Object distance 100mm
Sl Image distance 100mm
M Magnification factor -1
(f/#)m Main lens f number 3.5 2 1
(f/#)l Microlens f number 7 4 2
Ray
pl
pp
Si So
Z
fm
Pm
Focal Plane
dy
dz
Sy
MLA CCD
VB
YCCD
Yl O
Main Lens
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
According to the studies made by Georgeiv et al (2006), spatial and angular resolution of a
plenoptic camera is determined by the resolution of MLA and number of pixels beneath each
microlens (pixel microlens ration, PMR) respectively. As these spatial and angular resolution
will greatly affect the reconstruction performance of plenoptic camera, detailed ray tracing
analysis is made in this section to study the effect of PMR on y-z and x-y plane resolution. For
illustration purpose, analysis is only made for square microlens, but conclusions can be generally
extent to hexagonal microlens as well.
Fig. 3. Formation of an unresolvable block by back ray tracing
Two spatially separated point light sources are said to be resolved if the location variation results
in any light columns be captured by different microlens. To illustrate the resolution limit, the
outermost light rays (or boundary) of the discretized light columns are plotted in Fig. 3. Take the
top green line as an example, which is plotted by tracing a light ray from the lower edge of the
center microlens through the top portion of the discretized main lens, and back to the object side.
It is clear that any point light source moving across such line will result in the top light column
moving across the center microlens, and hence leads to pixel intensity variations. Based on such
analysis, performing back ray tracing for outermost light rays of the discretized light columns at
the upper edge of the center microlens would form a series of closed blocks. Any point light
sources inside these blocks cannot be distinguished. Extend such analysis to a small region (-
1mm<z<1mm and -0.3mm<y<0.3mm), discretized light columns for PMR=8, 14 and 28 can be
plotted in Figs. 4, 5 and 6, where blank blocks represent unresolvable areas, and separation
between two red lines represents one micro-lens size. An instant observation from Figs. 4, 5 and
6 is that resolution in x-y plane decreases with the increase of PMR. The reason is very
straightforward, for a fixed image sensor size and fixed pixel pitch, increase of PMR will reduce
lenslet number of the correspondent MLA, and hence will reduce planar resolution of plenoptic
camera. On the other hand, higher PMR will generally leads to higher resolution along optical
Focal Plane Main lens MLA CCD
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
axis, except on the focal plane. As such a very small pixel size as well as densely packed MLA is
preferred. However, too small pixel size will greatly reduce the camera sensitivity and densely
packed microlens array will significantly increase the manufacturing cost or even impossible to
fabricate.
Fig. 4. Resolution variation for PMR=8
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
pl / p
p = 8
Z (mm)
Y (
mm
)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
pl / p
p = 8
Z (mm)
Y (
mm
) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
pl / p
p = 8
Z (mm)
Y (
mm
)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
Z (mm)
Y (
mm
)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
Z (mm)
Y (
mm
)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
Z (mm)
Y (
mm
)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
Z (mm)
Y (
mm
)
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
Fig. 5. Resolution variation for PMR=14
Fig. 6. Resolution variation for PMR=28
3. Dense ray tracing based MART reconstruction method (DRT-MART)
Similar to particle reconstruction in Tomo-PIV, the MART reconstruction for light field PIV is
very time consuming, if not worse. As reported by Fahringer et al (2015), weighting matrix of a
300 × 200 × 200 voxels volume takes 350 GB, for only storing non-zero voxel values. The MART
reconstruction took 1.5hrs on a 12 cores work stations. As a matter of fact, tracer particles are
sparsely distributed in the measurement volume, and only a small portion of voxels have non-
zero values. Hence the computational load and storage request can be greatly reduced if only
non-zero voxels are reconstructed. This has been proved to be an efficient reconstruction
method by Atkinson et al (2009), who proposed an MLOS approach to pre-determine the non-
zero voxels.
The proposed dense ray tracing based reconstruction method employs similar idea, but it is
fundamentally different from MLOS on how is implemented. For Tomo-PIV, pixel line of sight
can be easily determined by camera calibration, the line of sight of each pixel is fixed for a
specific experimental set-up. However, this is not the case for light field PIV. As demonstrated in
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
pl / p
p = 28
Z (mm)
Y (
mm
)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
pl / p
p = 28
Z (mm)
Y (
mm
)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
pl / p
p = 28
Z (mm)
Y (
mm
)
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
Fig. 7, pixel line of sight varies with the spatial location of tracer particles. Hence, all affected
pixels must be taken into account for reconstructing a specific voxel.
Fig. 7. Light field images generated by ray tracing simulation
Figure 8 illustrates the principle of the DRT method. To determine the pixel line of sight for the
red voxel, three representative light rays (nine light rays for 3D case) were drawn for each
discretised main lens portion so as to find the affected micro-lens units. Once this is
accomplished, the affected pixels can be easily located according to the analysis made in the
previous section. With the affected pixels available, a simple multiplication of their values would
help picking out the non-zero voxels.
(a) Light source on the focal plane
(b) Light source offset to the focal plane, dz=0.385mm
Focal Plane Main lens MLA CCD
dz
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
Fig. 8. Principle of the DRT method
To evaluate the performance for DRT-MART reconstruction algorithm, a small plenoptic camera
(31×31 micro-lens units, 448×448 pixels) was simulated by ray tracing. A small volume measured
2mm×2mm×4mm was discretized into 385×385×57voxels. Note that the voxel size in z direction
is the same as micro-lens pith, whereas the voxel size x and y direction is the same as pixel pitch.
For brevity, weighting coefficients were calculated by the new weighting algorithm for both
DRT-MART and MART reconstruction results. To explore the effect of resolution variation along
optical axis on the proposed new reconstruction algorithm, A series of light field images were
generated by ray tracing simulation for particle location varies from z=-2 ~ 2mm along the
optical axis with a step of 0.077mm. Note that the focal plane locates at z=0. Fig. 9a plots the
accuracy of the reconstructed particle image center for DRT-MART and MART algorithms, and
Fig. 9b shows the reconstruction quality for the two methods.
An instant observation from Fig. 9 is that the accuracy of reconstructed particle image center as
well as reconstruction quality reach to the lowest level near the focal plane (z =-0.308~
0.308mm). This is because that all light rays from particles in this range were all focused onto a
single micro-lens, and subsequently being captured by the same group of pixels, as illustrated in
Fig. 7a. As such, the reconstructed voxel intensity distribution is nearly the same for particles
located in this range.
For particles outside the focal plane region (z <-0.308, z >0.308mm), the reconstructed particle
image centre of the two algorithms matches well with real values. But the DRT-MART algorithm
shows considerably higher reconstruction quality than MART in these regions. The reason is that
DRT-MART could successfully filter out the zero voxels which surround around the affected
voxels. On the other hand, however, these neighboring voxels are also included by MART
Focal Plane Main lens MLA CCD
Reconstruction area
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
during its reconstruction iterations. With particle moves away from the focal plane, the voxel
intensity reconstructed by the DRT-MART algorithm starts to expand due to the decrease of
resolution in x and y direction and results in slight decrease in Q value.
Fig. 9. (a) Accuracy of reconstructed particle image centre coordinate; (b) Reconstruction quality;
(c) computational efficiency of the DRT-MART method for various particle density cases
(a)
Real center (Z, mm)
Re
co
ns
tru
cti
on
ce
nte
r(Z
,m
m)
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2
-1.5
-1
-0.5
0
0.5
1
1.5
2Real
DRT-MART
MART
Z (mm)
Q
-2 -1.5 -1 -0.5 0 0.5 1 1.5 20
0.2
0.4
0.6
0.8
1 DRT-MART
MART
(b)
Particles per microlens (ppm)
Co
mp
uta
tio
na
lti
me
rati
o(T
MA
RT/T
DR
T-M
AR
T)
1 2 3 4123456789
101112131415
(c)
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
Further away from the focal plane, either in the far field or near field, the reconstruction quality
decreases for both algorithms. However, there are discernible local minimums for the DRT-
MART algorithm. For instance, at z =-1.078mm the reconstructed intensity expands to even
larger amount of voxels. This is due to the fact that, further away from the focal plane, when
there is a small change in particle’s z location, the affected micro-lens units remain the same with
only a slight change in the distribution of surrounding pixels’ intensity. This fractional pixel
intensity variation is normally difficult to be resolved by reconstruction methods. The
improvement in computation efficiency is very promising, for example, when the particle
density is 1ppm which is the density used for the following simulation studies, DRT-MART is 10
times faster than the MART method as shown in Fig. 9c.
4. Comparison between LF-PIV and Tomo-PIV
In this section, a pair of synthetic light field images is generated by ray tracing simulation. The
simulated plenoptic camera has the same resolution as our in-house developed camera (Shi et al
2016). The first synthetic light field image is generated by randomly scatter tracer particles in a
volume of 36×24×20mm with a particle density of 1 particle per microlens (1ppm). A known
velocity field is imposed on the particles, and new locations of the particles is determined by
giving a short time interval of ∆t=0.5ms. Flow field of a jet issued from a D=6mm circular nozzle
at Re=2500 is simulated by DNS and serves as the exact velocity field. Three dimensional particle
images are reconstructed from these two synthetic light field images by the DRT-MART
algorithm with a reconstruction resolution of 2100×1400×260 voxel. A three dimensional version
of multi-grid cross correlation is then used to calculated the raw instantaneous velocity volume
with 50% overlap and an initial and final interrogation window size of 128×128×32 and
64×64×16, respectively. The raw velocity volume is then further processed by median filter and
linear interpolation to identify and replace any incorrect velocity vectors. Consider very
intensive calculations involved in the reconstruction and cross correlation steps, GPU parallel
processing (Geforce980) is applied to the to improve the computational efficiency.
On the other hand, two sets of synthetic Tomo-PIV particle images are generated for comparison.
To do that, camera calibration matrix is calculated for four Imperx B2041 cameras by using a 110
× 110 mm calibration board and pinhole camera model. A magnification factor of 0.074
mm/pixel is used for capturing the calibration board images to ensure a similar measurement
resolution as LF-PIV. The first four Tomo-PIV images are generated by projecting a group of
randomly scattered particles to four cameras by using the camera calibration matrix with a
particle image density of 0.05ppp. The DNS jet flow is then imposed on the particles in a similar
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
fashion as LF-PIV to generate the second four Tomo-PIV images. Three dimensional particle
images are reconstructed by the MLOS-MART method and then process by multi-grid cross
correlation with 75% overlap and an initial and final interrogation window size of 64×64×64 and
32×32×32, respectively. Median filter and linear interpolation are also applied to smooth the raw
velocity volume. GPU parallel computation is also applied to Tomo-PIV process to increase the
efficiency. The DNS velocity field and calculation results from LF-PIV and Tomo-PIV is
presented in Fig. 9. The overall flow structure measured by LF-PIV matches generally well with
the DNS data and Tomo-PIV result, which proves the validity of the proposed DRT-MART
method. However, there are discernable differences in velocity contour between the LF-PIV and
Tomo-PIV results, which is due to the inhomogeneous voxel intensity distribution along the z-
axis. Further analysis is underway to normalize the voxel intensity after it is reconstructed by the
DRT-MART method.
5. Conclusion
This paper conducted a detailed simulation of the effect of pixel-microlens-ratio on plenoptic
camera resolution, showing this factor greatly affect the planar and spatial resolution. Based on
such ray tracing analysis method, a dense ray tracing based reconstruction algorithm namely
DRT-MART is proposed to improve the computational efficiency. The performance of DRT-
MART is firstly studied by using a series of synthetic light field particle images, showing that it
is capable of reconstructing particle image at a higher accuracy than MART but with lower
computational cost. Finally, a set of synthetic jet flow light field images is used to evaluate the
overall performance of LF-PIV. Preliminary studies show that the DRT-MART based LF-PIV
technique can provide satisfactory results when compared with the traditional Tomo-PIV
method.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No.
11472175) and the Shanghai Raising Star Program (Grant No. 15QA1402400).
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
Fig. 10. Instantaneous velocity volume for (a) DNS results, (b) LF-PIV measurment and (c)
Tomo-PIV measurement
(a)
(c) (b)
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
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