ILASS Americas, 24th Annual Conference on Liquid Atomization and Spray Systems, San Antonio, TX, May 2012

Particle Size and Velocity Measurements using Light-Field Velocimetry
T. Nonn*, V. Jaunet, C. Weissman
Dantec Dynamics A/S
2740 Skovlunde, Denmark

Abstract
The last few years have seen considerable activity regarding light-field cameras and their application to photography. The ability to refocus images over a finite depth range has consequently led to interest in measuring the distance of objects from the camera. While originally developed for imaging textured opaque surfaces, interest has led
to successful application in volumetric flow-fields using a commercially developed plenoptics camera. It is then
expected that once particles are successfully imaged in 3D PIV flows, 2-phase and spray flows naturally follow.
This paper focuses on measurement of spray particle flow velocity and size using a single light-field camera. Whileprevious techniques utilised a limiting 2D shadowing technique, measuring the size and velocity of particles silhouetted from behind with uniform illumination, light-field measurements open the possibility of accessing the depth
position, and thus the 3D position and velocity of individual bubbles and droplets.

*Corresponding author: thomas.nonn@dantecdynamics.com

Introduction
The light-field (LF) technique has been describedwidely in literature [1,2,3], having its origins more thana century ago, but only in the last decade has momentum behind the technique increased, due to advances in
optics, sensor resolution and manufacturing techniques.
Currently the measurement of three-dimensional velocity components in experimental flow setups is carriedout using multiple cameras, positioned around a fixed
point and carefully aligned and calibrated. A single
light-field camera opens up the possibility of a lowcost, robust and flexible alternative to multiple camera
3D measurement systems. A single camera capturing
3D events simplifies both physical access and calibration.
The general principle behind light-field camera canbe described as follows: a micro-lens array placed
closely to an image sensor, with the same f-stop as themain objective, reconstructs at selected positions virtualimages representing focus planes within the measurement volume, as shown in figure 1.

camera. In the worst case (near-field) roughly 25 percent of the spatial resolution is retained, thus the 11 MP
camera used in this study had an effective resolution of
2.6 MP. The depth resolution through the measurement
volume is not constant, but increases monotonicallywith distance from the main objective, reaching amaximum in the far-field, as seen in figure 2.
Neighbouring micro-lenses act as local stereo systems, imaging large particles such as bubbles or droplets at slightly different perspectives, disclosing not
only position in 3D space, but surface features as well.
The depth of field of a light-field camera, or measurement depth, is limited by the f-stop of the microlens,
which is also the f-stop of the main objective. Exploiting a micro-lens array (MLA) with multiple focal
lengths, the depth of field can be extended, up to afactor of seven with three focal lengths. Figures 3 and 4compare the imaging of seeding particles and dropletson the micro-lenses. Note that in the micro-lens images
below the degree of defocusing varies from lens to lens.
Due to the hexagonal arrangement of the micro-lenses,
no two lens of the same focal length are ever in contact.
Images from lenses with the same focal lengths are
examined together and compared against results fromthe other lens types.

Figure 1. Optical schematic of light-field principle.
Particles appear in micro-images within several microlenses, at slightly different perspectives, allowing for
depth determination. The downside of light-field cameras, however, is the loss of spatial resolution. The loss
can be mitigated by applying multiple-focus micro-lenstechniques used by a commercially available plenoptics

Figure 3. Near-field and far-field images of a 30 micron spherical particle.

Figure 4. Micro-lens image of a droplet in a spray..

Figure 2. Resolution versus depth (courtesy Raytrix)

As in PIV, the determination of the velocity fieldof particles in a volume requires the acquisition of at
minimum two light-field images acquired in rapid succession. The depth map determined for each image isthen analysed individually for particle positions andthen processed together to determine the velocity fieldand particle flow history. Depending on the operating
mode of the camera used the velocity field can the beExperimental setup
The investigation consisted of measuring dropletsfrom a aerated spray nozzle typically found in agriculture. A Raytrix light-field camera used in combination
with a Dantec imaging system was used for acquisitionof data. Illumination was provided by a pulsed shadow
strobe combined with a diffuser. For comparison purposes, 2D measurements on the nozzle were also carried with a phase-Doppler (PDA) system.
The imaging system was calibrated with a textured
dot target commonly used in stereo PIV. The calibration process consists of three independent processes: (1)software alignment of the micro-lens array (MLA); (2)calibration of the depth space based on the pinholemodel; (3) Matching of the depth response of the lightfield camera with the depth determined from the target
calibration. The entire calibration process consists ofacquiring two images: a target image and a white image. The calibration target is placed diagonally acrossthe measurement volume. The focus is adjusted so that
dots farthest from the camera are nearly in focus. As
one moves to the near-field dots begin to occupy everlarger rings of lenses. The depth volume depends on thefocal length of the objective selected and the working
distance

were heavily vignetted (i.e. defocused). The next step inthe calibration requires that the object to image coordinate relationship be determined. An interesting propertyof light-field technology is the so-called "all-in-one"
focus. Instead of focusing on a particular plane thedepth map determined from the light-field data is usedto put all objects in an image in focus. In this case all of
the dots on the target are focused. This image is thenprocessed using a pinhole camera model to extract atransformation between image and object space. Thisessentially contains all our scaling information for 3D
measurements. Typical reprojection errors were on theorder of 0.5 - 0.8 pixels. It is expected that this uncertainty can be improved using a specially designed target
with a finer dot distribution.
The last step of the calibration involves matching
the virtual depth values returned by the camera with theactual depth values determined by the camera model. It
was found for longer focal length objectives (> 100mm) the relationship between virtual depth and actual
depth was approximately linear, as is evident in figure
6. For shorter focal length lenses the relationship wasparabolic. Once the calibration procedure is complete
the target used can be reconstructed in 3D as verification (figure 7). Typical residuals for the fit were between 0.5 - 1.0 %.
98

Virtual depth response

determined from particle tracking techniques, leastsquare methods (LSM) or three-dimensional crosscorrelation techniques. In practice the light-field camera
operates best in flows with low to medium seedingdensities. In higher densities particles become difficult
to resolve and occlusion makes tracking difficult.
For particle size measurements the particles need
to be sufficiently large so that the reconstructed focus
images produce particle images that can be analyzed byconventional edge detection techniques.

7654
Depth data
Fitted values

32
10-16-14-12-10-8-6-4-2

0

24Z pos (mm)Backlight
sourceFigure 6. Calibration fit between virtual depth andmeasured depth.
PDA
ReceiverTransmitter

NozzleLight-field camera

Figure 5. Layout of spray experiment.
The alignment process ensures that the lenses areproperly specified in the software during the reconstruction of the focus images. The near-field lenses

Figure 7. 3D Reconstruction of calibration target.

Results
For the current investigation a series of images wastaken of the entire spray. Thereafter, several runs of 200
images were acquired from a subset of the whole fieldusing the light-field camera, as shown in figures 8 and
9. In the subset ROI roughly 10-15 droplets were captured in each image. The working volume of the ROIsubset was 3.8 cm x 2.5 cm x 1.4 cm. The minimum
diameter that could be effectively evaluated with thecurrent optical setup was 10 microns. A higher resolution camera would have assisted in recovering more ofthe smaller droplets. A series of measurements with aPDA (phase-Doppler) system were carried out over theentire spray. Two vertical slices of the volume giving
32 positions in total were used for comparisons. An
example is given in Figure 10 comparing diameter
distributions between the PDA and LF system.
A time-averaged result of the ROI data sequence,
figure 11,shows the characteristic distribution of larger
droplets in the outer region of the spray cone and thegradual falling off toward the center of the spray.
Conclusion
This investigation introduces the light-field camera to
3D spray measurement. It could be seen that not only
droplets are useful subjects of this technology, but thatthe depth measurement could also determine positionsof structures such as ligaments and the sheath of thespray.
In general, the light-field camera simplifies the measurement and calibration process for 3D analysis. Another added value of LF over the shadow measurement
technique is in resolving out-of-focus particles, a persistent problem for conventional imaging. The investigation also focused on the uncertainties involved with LF
measurement. This work is still preliminary and reconstruction of the results in a 3D format remains to bedone. However, these early results show promise andpoint to the practical usefulness of light-field technology in 3D measurement.
References1. T. Nonn, J. Kitzhofer and D. Hess, "Measurements
in an IC-engine Flow using Light Field Volumetric
Velocimetry", Laser Appl. Fluid Flows, Lisbon
2012.
2. M. Levoy, "Light fields and computational imaging," Computer, vol. 39, pp. 46-55, 2006.
3. R. Ng, M. Levoy, M. Bredif, G. Duval, M.
Horowitz, and P. Hanrahan, "Light field photography with a hand-held plenoptic camera," tech. rep.,
Stanford University, 2005
4. Haeyoung Jeong, Kihyung Lee and Yuji Ikeda,"Investigation of the spray characteristics for a sec-ondary fuel injector using a digital image processingmethod", Measurement Science and Tech.", vol. 18,pp.1591-1602, 2007.

Figure 8. Focus and color-mapped depth map of spray from light-field results.

Figure 9. Subset ROI of spray with color mapped depth and 2D vectors.

Figure 10. Comparison of spray particle diameter distributions between data acquired from PDA and Light-fieldcamera.

14D [um]

123230282624222018161412108642Y [mm]1086420051015X [mm]Figure 11. Time-averaged velocity and diameter data (200 images).