16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012

Measurements in an IC-engine Flow using Light-field Volumetric Velocimetry

T. Nonn1,*, J. Kitzhofer1, D. Hess2, Ch. Brücker2
1: Dantec Dynamic A/S, Skovlunde, Denmark
2: TU Freiberg, Germany* correspondent author: thomas.nonn@dantecdynamics.com

Abstract The last few years has seen considerable activity regarding light-field cameras and theirapplication to photography. The ability to refocus images over a finite depth range has consequently led tointerest in measuring the distance of objects from the camera. The main limitation of this approach is theinability to determine the distances of occluded objects. In experimental fluid flow measurements thislimitation can be considered negligible for light to moderately seeded flow, and can assist in reconstructing
the measurement volume of interest. This paper will demonstrate the application of a light-field camera on
four-stroke internal combustion engine (ICE) measurements. Measurements were carried out on an indexmatched cylindrical volume as a piston made upward and downward translations. Measurements have shown
the viability of the technique in measuring three velocity components over a finite volume, and to somedegree even in heavily seeded cases. Comparisons were made with scanning light-sheet measurements madeon the same rig.

1. Introduction
Several adaptations of the light-field technique have been described in literature [4-7], having its
origins more than a century ago, but only in the last decade has momentum behind the techniqueincreased, due to advances in optics, sensor resolution and manufacturing techniques. In its originalform the light-field technique sought to capture the 4D light information from a scene. Currently themeasurement of three-dimensional velocity components in experimental flow setups is carried out
using multiple cameras, positioned around a fixed point and carefully aligned and calibrated. A
single light-field camera opens up the possibility of a low-cost, robust and flexible alternative to
multiple camera 3D measurement systems [2]. A single light-field camera significantly reduces thecorrespondence problem associated with stereo matching.
The general principle behind light-field camera can be described as follows: a micro-lens array
placed closely to an image sensor, with the same f-stop as the main objective, reconstructs atselected positions virtual images representing focus planes within the measurement volume, as
shown in figure 1. Particles appear in micro-images within several micro-lenses, at slightly different
perspectives, allowing for depth determination. The downside of light-field cameras, however, isthe loss of spatial resolution. The loss can be mitigated by applying multiple-focus micro-lens
techniques used by a commercially available light-field camera. In such cases 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 monotonically with distance from the main objective, reaching a maximum in the far-1-

16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012

field, as seen in figure 2.

Figure 1

Optical schematic of light-field principle

Figure 2
Resolution(Courtesy Raytrix)

versusdistance

Neighbouring micro-lenses act as local stereo systems, imaging particles at slightly different
perspectives, disclosing not only position in 3D space, but surface features as well. The depth offield of a light-field camera, or measurement depth, is limited by the f-stop of the micro-lens, whichis also the f-stop of the main objective. Otherwise, the micro-images become heavily vignetted or
begin overlapping neighbouring lenses. For the current camera and lens array configuration the fstop was set to f8.
Exploiting a micro-lens array (MLA) with multiple focal lengths, the depth of field can beextended, up to a factor of seven, over the standard camera. Figures 3-4 compares the imaging ofparticles in the micro lenses with those of target dots on a calibration plate. Note that in themicrolens images below the degree of defocusing varies from lens to lens. Organised in a hexagonal
pattern, 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 from the other lens types.

Figure 3a-b

Near-field (left) and far-field of a spherical particle (50 micron polyamide)-2-16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012

Figure 4a-b

Near-field (left) and far-field of a 2 mm target dot on a calibration plate

The depth information provided by the light-field camera is not calibrated, and represents a virtual
space specific to the optical construction of the lens array, which changes with focus and objectiveselection. It was found that long focal lengths (i.e. greater than 100 mm) gave reasonably linear
responses and larger working depths when comparing virtual depth response with actual depth.
Shorter focal lengths gave shorter working depths and a more parabolic response. One of thehallmarks of plenoptic imaging is the ability to focus the entire image, an all-in-one focus. Thisfeature greatly simplifies the calibration of the camera. A calibration target with a regular dot
pattern with a known scaling is placed diagonally through the volume so as to cover the working
volume. Unlike multiple camera calibrations where the coordinate system is aligned with the target,
the coordinate system here is rotated to match with the camera. The depth information along thecalibration target is then fitted to the virtual depth response of the camera. The uncertainly in thedepth measurements encountered in many cases was below 0.6 % of the full depth range. A
working depth range of 4 cm would have an uncertainty below 0.2 mm. This is still much larger
than the lateral resolution of the sensor but reasonable for measurements.	   	   	  Figure 6a-b	  Depth determination (left) and resolution from neighbouring micro-lenses with similar focal lengths.

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Lisbon, Portugal, 09-12 July, 2012

A number of tests were conducted to verify the light-field camera's ability to determine depth
positions of particles. Polyamide particles of a uniform size were placed between two laboratory
slides. The slide pair was then mounted onto a micrometer stage and moved from the nearest
measurable position to the farthest. In figure 7a the movement of a single particle from -17 mm to+2 mm can be clearly seen to be linear. In figure 7b the linear calibration fit between the virtual
depth response of the light-field camera and the actual determined depth is seen.
9Virtual depth response

87654

Depth data
Fitted values

3210-16-14-12-10-8-6-4-2024Z pos (mm)Figure 7a-b Depth accuracy of 50 micron polyamide particles translated on a micrometer stage (left) and calibration
fit between virtual depth response of camera and measured depth

As in PIV, the determination of the velocity field of particles in a volume requires the acquisition ofat minimum two light-field images acquired in rapid succession. The depth map determined foreach image is then analysed individually for particle positions and then processed together todetermine the velocity field and particle flow history. Depending on the operating mode of thecamera used the velocity field can be determined either from particle tracking techniques, leastsquare methods (LSM) or three-dimensional cross-correlation techniques. In practice the light-fieldcamera operates best in flows with low to medium seeding densities. In higher densities particles
become difficult to resolve and occlusion makes tracking difficult.

2. Experimental setup
The experiments were carried out on a water analogue 4-stroke CE with 2 fully variable intake
valves. The same setup was used with a single camera scanning lightsheet approach [1] and thus
could give comparisons. Due to the incompressibility of the fluid only the intake stroke can bedetermined. The main test rig was provided by Volkswagen. The design permitted investigation ofthe opening cycle’s equivalent to the different load cases of a real engine in a short period of time.
The cylinder head is a standard head from the 1.6 l TSI engine. It has bore diameter of 76.5 mm anda displacement 87 mm. In order to better fit the region of interest to our field of view thedisplacement is limited to 75.6 mm. The experimental setup is shown in Figure 8a.
A large glass block encloses the piston head and requires that the liquid is index-matched to avoid-4-

16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012

distortion of the optical field due to the cylindrical surface. A 42% water-glycerine mixture
provided the necessary matching, as can be seen (or not seen) in figure 8b. A 100 mm lens applied
to a Raytrix plenoptics camera gave a working volume of 10 cm x 6 cm x 4 cm. A calibration of thevolume was conducted by placing a dot-target with a known dot spacing in the cylinder at an angle
to the camera, covering the depth of interest. A single image taken of the target then gives the fullspatial scaling of the measurement volume as seen if figure 8b. Calibration of the target through theglass yielded a relatively smooth linear fit, giving less than 1% uncertainty on the depthmeasurements.	  

Figure 8a-b. Measurement setup. A modified engine block and Plexiglass casing; Complete engine and running lightfield camera (left); Disassembled engine block during calibration, note index-matched interior (right).	  

3. Results
A series of double-framed images were taken following the intake of the piston head. Time between
frames was approximately 100 ms. Each pair of frames was separated by nearly 300 msec. The
depth map from each frame would be determined and then converted into a voxel map. The
resulting voxel map had the following dimensions: 1004 x 672 x 256. A pair of voxel maps werethen subjected to least-squares matching procedure to extract the 3D flow gradients. Least-squares
matching is a Gaussian-Markov adjustment procedure [3] that iteratively transforms a volume ofelements in one cuboid (first time-step) until a correspondence is made between cuboids at twotime-steps. The end result is a affine transformation that completely describes the deformation ofthe fluid volume. The voxel volumes were broken up into overlapping cuboids, typically 45-65
voxels in size. With an overlap of 10 voxels, nearly 60000 cuboids would produce an equivalent
number of vectors.
Figures 9-11 highlight the translation of the cylinder head for different crank angles as captured by
the light-field camera and shown as a color-coded depth map and the resulting 3D vector field
determined from least-squares matching.
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Lisbon, Portugal, 09-12 July, 2012

Figure 9a-b. Depth map(left) and vector-field (right). Crank angle = 148º. Depth map coloring scheme: red nearest,
blue farthest. Z-vorticity iso-surfaces .

Figure 10a-b. Depth map(left) and vector-field (right). Crank angle = 156º.

Figure 11a-b. Depth map(left) and vector-field (right). Crank angle = 165º.

As the cylinder becomes fully extended large tumblers are formed, which is expected. The largest
tumbler is sucked toward the cylinder head and then reflected. Measurements carried out using ascanning light sheet approach also exhibited the same structures, as can be seen in figure 12. Alarge, rotating tubular tumbler dominates in the region near the cylinder head. The seeding level inthe scanning light-sheet tests was much higher and offered greater resolution in the end result,though at the cost of system complexity.
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012

Figure 12a-b. Light-field result (left) and scanning light-sheet result (right). Note coordinate system of light-fieldresults is rotated about y-axis.

4. Conclusion
A series of tests were conducted using a commercially available light-field camera and comparedagainst results taken with a scanning light-sheet approach. The light-field technique simplifies thecalibration procedure and data acquisition for 3D velocity measurements, at the cost of someresolution. However, the difficult geometry and limited optical access of these measurements madethe light-field camera a suitable candidate. The 11 MP camera used in the measurements produced
the best results with low to medium particle seeding density. Future tests with a higher resolution
light-field camera are on the roadmap and should improve both the quality and the resolution of themeasured data. Despite the age of the plenoptics theory behind light-field cameras, the technique isstill relatively unknown in the scientific community and much work remains to be done to explore
its range of application.

5. References[1] Hess D, Brücker C, Kitzhofer J, Nonn T: Single-View Volumetric PIV using High-resolution Scanningand Least Squares Matching. In: Proceedings of the 9th International Symposium on Particle Image
Velocimetry (PIV 2011), Kobe, Japan, July 21-23, 2011.
[2] K. Lynch, Development of a 3-D Velocimetry Technique based on Light Field Imaging, Master's thesis,Auburn University, May 9th 2011.

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Lisbon, Portugal, 09-12 July, 2012[3] Westfeld P, Maas HG, Pust O, Kitzhofer J, Brücker C (2010) 3-D Least Squares Matching forVolumetric Velocimetry Data Processing, Proceedings of the 15th International Symposium onApplications of Laser Techniques to Fluid Mechanics, 5-8 July 2010, Lisbon[4] C. Perwass and L. Wietzke, Single Lens 3D-camera with Extended Depth-of-Field, SPIE ElectronicImaging 2012, San Francisco, USA, January 22-26 2012
[5] Adelson & Wang, Single Lens Stereo with a Plenoptic Camera, IEEE Transactions on Pattern Analysis &Machine Intelligence, Volume 14, No. 2, February 1992.

[6] M. Levoy, Light fields and computational imaging," Computer, vol. 39, pp. 46-55,2006.
[7] 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

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