Comparison of volume reconstruction techniques at different particle densitiesltces.dem.ist.utl.pt/lxlaser/lxlaser2010/upload/1708... · 2010. 6. 18. · 15th Int Symp on Applications

15th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 05-08 July, 2010

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Comparison of volume reconstruction techniques at different particle densities

D. Michaelis1, M. Novara2, F. Scarano3, B. Wieneke4

1: LaVision GmbH, Goettingen, Germany, [email protected] 2: Aerospace Engineering Department, Delft University of Technology, Delft, The Netherlands, [email protected] 3: Aerospace Engineering Department, Delft University of Technology, Delft, The Netherlands, [email protected]

4: LaVision GmbH, Goettingen, Germany, [email protected]

Abstract In this study, four different volume reconstruction techniques for tomographic PIV are investigated using synthetic and experimental data at different particle densities. Multiplied line of sight (MLOS) and Minimum line of sight (MinLOS) represent methods that need significant less computation time than the standard MART reconstruction. Motion Tracking Enhancement (MTE) on the other hand needs significant more computational time, but has the potential to achieve more accurate results especially at higher seeding densities. The presented results confirm that the fast MLOS and MinLOS reconstruction are applicable only at low seeding densities, 0.02 particles per pixel (ppp), and achieve a lower accuracy than standard MART. MTE results in most accurate vector fields in a broad density range from 0.01 ppp up to 0.2 ppp. 1. Introduction Since its introduction tomographic particle image velocimetry (tomo PIV) (Elsinga 2006) has widespread as a powerful tool for three-dimensional flow field measurements and has successfully been applied in a wide range of experimental conditions (Elsinga 2008). The main advantage of tomo PIV, when compared to the particle tracking velocimetry approach (PTV) is that it can be used in a wider range of particle tracer concentration. A high seeding density is very desirable in flow field measurements to achieve a high spatial resolution in the measured velocity field. This ability however, comes with a relatively high computational burden of the tomo PIV measurement procedure, mostly the MART tomographic reconstruction as well as the 3D cross correlation (Atkinson 2009). The seeding particle concentration is also known to have a strong impact on the “ghost particles” (Elsinga 2006) being an unavoidable artifact of the reconstruction. Higher seeding densities result in a higher intensity of ghost particles, which will in general degrade the quality of the computed velocity field. The actual amount of ghost particles is affected by the reconstruction algorithm. In fact it can be seen as a quality measure of the reconstruction: the lower the (uncorrelated) ghost particle intensity is, the better is correlation between the reconstructions of two time steps and the higher is the accuracy of the computed velocity field. The quality of a reconstruction algorithm is directly related to its ability to diminish the ghost particle intensity. In this study several algorithms for tomographic reconstruction, requiring rather different computational effort are chosen for comparison. The MART reconstruction algorithm is regarded as the reference method (Elsinga 2006). The assessment of performance focuses on the ability to deal with a chosen level for the seeding density at the source (particles per pixel, ppp). The performance of different reconstruction algorithms is investigated for a wide range of particle densities using synthetic data from numerical simulations and experimental data from a time-resolved free jet in water.


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2. Reconstruction algorithms In this section the reconstruction algorithms are described that will be compared in this study. 2.1 MART The multiplicative algebraic reconstruction technique MART (Elsinga 2006) is the reconstruction algorithm that has originally been used at the introduction of tomographic PIV. In several studies MART serves as the reference algorithm (Worth 2008, Atkinson 2009, Novara 2009). Worth and Atkinson proposed reconstruction algorithms being faster than the standard MART. However the accuracy of MART is, to the author’s knowledge, still unsurpassed. This is why MART is also regarded as the reference algorithm in this study. Throughout this study five MART iterations have been used for volume reconstruction. 2.2 MLOS Worth (2008) and Atkinson (2009) improved reconstruction speed by applying a procedure to predetermine voxel in the reconstructed volume that are unlikely to get any significant intensity during the reconstruction process (multiplicative first guess MFG-MART and multiplied line of sight MLOS-SMART). Reconstruction is accelerated by excluding these voxel from the further reconstruction. Depending on the seeding density, the amount of the omitted voxel covers about 95% of all voxel, leading to considerable decreased computation times. The resulting accuracy is similar to standard MART and it is expected that the behavior at different seeding densities is similar as well. For this reason and to limit the complexity of this study, these approaches are not applied here, where the focus is on algorithms that may improve or degrade the overall accuracy or that may be more sensitive or more robust at different seeding concentrations compared to MART. However, it should be kept in mind, that the reconstruction speed of standard MART may be improved by these approaches, maintaining the same level of accuracy. Both approaches, MFG-MART and MLOS-MART, use a fast initial reconstruction step to determine the voxel of interest from the initial volume. Atkinson (2009) also uses MLOS reconstruction without further iterations to calculate a velocity field from experimental data, as a reference to MLOS-SMART and MART. Atkinson used MLOS reconstruction to compare computation times and to show the evolution of the reconstructed volume. A larger deviation in the resulting w-component of the velocity field is reported for the MLOS reconstruction. Despite its inferior performance, MLOS reconstruction will be used in this study because the computation is very fast and it is strongly related to the MinLOS reconstruction that is also investigated in this study. MLOS has been used as a reference in a recent study on ghost particle velocity (Elsinga 2009). Elsinga reported that computed velocity fields were more accurate using MART than using MLOS. The dependency on the particle density however has not been examined there. Unlike Atkinson, using nearest neighbor interpolation for MLOS reconstruction, here bilinear interpolation in the particle images is applied to determine the voxel intensities more accurately, accepting a slight increase in computation time. 2.3 MinLOS Maas (2009) proposed a reconstruction method very similar to the initial volume generation with MLOS and MFG. The motivation of using MLOS not as an initial volume generator but as a reconstruction procedure was, to achieve a very fast reconstruction method. Additional to a multiplication of the projected pixel intensity from all cameras (MLOS), the minimum of the


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projected intensities is suggested to determine the voxel intensity in a single step. Maas called this procedure minstore ART or MinART. The procedure is also used in this study. It is labeled MinLOS here to indicate the similarity to MLOS and to avoid confusions with the iterative reconstruction techniques like ART, MART, SMART and MTE-MART. 2.4 MTE While the approaches discussed so far focused on reconstruction-speed improvements, the following method aims at improved reconstruction quality. Motion tracking enhanced MART (MTE, Novara 2009) utilizes the information from multiple time steps to improve the reconstruction at a given time. The method relies on the finding that ghost particles from different time steps tend to be uncorrelated while true particles are strongly correlated by the action of the flow field as long as the shear rate is sufficiently high (Elsinga 2009). The algorithm works as follows: assume a MART reconstruction at two time steps t1 and t2 resulting in 3D objects o1 and o2. The vector field v is calculated by means of 3D cross-correlation between o1 and o2. Now v is used to deform the object o1 (virtually transforming o1 to t2) to get a pseudo simultaneous object (referred to as pso2). Depending on the accuracy of the velocity field v, the actual particles will be found in the same location in the objects o2 and pso2. The same does not happen for the ghost intensities which are not coherent with the flow motion. Now by calculating the average of o2 and pso2 a new initial guess is generated for the next MART iteration. In the same way o2 is deformed by –v to get pso1 and generate an initial guess for object 1. With these initial guesses, another MART-iteration is performed for both objects. The procedure is applied iterative until convergence is achieved, e.g. until the calculated flow field does not change anymore. Calculating the averages of o2 and pso2 as well as o1 and pso1 enhances the true particles and diminishes the ghost particles as long as the ghost particles are uncorrelated under the action of the flow field. Novara (2009) achieved a considerable higher quality factor Q using MTE-MART compared to the simple MART, especially at higher particle densities. Moreover the error of the calculated flow field was significantly reduced. This makes MTE-MART a very interesting candidate for this study on particle densities. Throughout this study 10 MTE steps are used with five MART iterations in each step. These settings are quite conservative to assure convergence of MTE-MART. Optimizing the MTE strategy e.g. using fewer MART iterations or fewer MTE steps may result in much smaller computation times at the same quality level. Such an optimization however, is out of the scope this study. 3. Numerical simulations Synthetic data is generated at 20 different seeding particle concentrations ranging from 0.01 ppp to 0.2 ppp in steps of 0.01 ppp. The synthetic volume has a size of 700 x 700 x 300 voxel. The particle diameter is 1.5 voxel (gaussian shape). The simulated flow field ( u( x, y, z), v( x, y, z), w( x, y, z) )T represents a sinusoidal wave in the v-component with the amplitude changing along the z-direction, u and w are zero (Fig. 1):

( u, v, w )T = ( 0, v0 * z/z0 * sin( 2 π x / lx), 0 ) T ( 1 )


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Fig. 1 Synthetic flow field with large flow structures (a) and small flow structures (b): color coded v-component at the front of the volume (z = 150 voxel). The field at the back (z = - 150 voxel) has the opposite direction (not shown here). The scale is set to 1 mm / pixel. with z0 = 150 voxel, v0 = 5 voxel. The amplitude changes linear from +5 voxel at z = +150 voxel to -5 voxel at z = -150 voxel. At z = 0 voxel, the flow is (0, 0, 0) T. The wavelength lx determines the size of the flow structures. In this paper two wavelength are applied simulating large and small structures (lx = 256 voxel and lx = 64 voxel, Fig. 1). The average shift magnitude over the whole volume is

= 1.67 voxel (lx=256) and = 1.61 voxel (lx =64). (2) The virtual cameras have been positioned at the corners of a square: left, right, top bottom, 30° off axis. The camera model used is parallel projection. The volume mapping is modeled by a third order polynomial in x and y at z = -150 voxel and z = +150 voxel, with linear interpolation in between. The camera image size (900 x 900 pixel) is larger than the volume size including a black border (zero counts), minimizing reconstruction border-effects. The particle peak intensity is 4000 counts. According to Elsinga (2009) the present shear rate is high enough to ensure the generation of uncorrelated ghost particles. 4. Experimental setup Experimental data from a time resolved free jet experiment in water is recorded at different seeding densities (Violato 2010). Four LaVision high speed Cameras High Speed Star 6 imaged 56 µm seeding particles at a rate of 1.3kHz, illuminated by a Quantronix Darwin-Duo Nd:YLF laser (2 x 25 mJ/pulse @1kHz) where the beam is expanded to a cylinder of 50 mm diameter using a Linos beam expander (Fig. 2). The seeing density is varied in 15 recordings of 200 images each from 0.005 ppp to 0.17 ppp. The imaged seeding density is computed after detecting the number of particle peaks in the tomographic

a) lx = 256 voxel b) lx = 64 voxel


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images. Since the accuracy of the peak detection operation decreases at high seeding density level, a slit has been used to reduce the illuminated region thickness. The imaged seeding density (ppp*) in this configuration is therefore lower and can be estimated accurately. The actual ppp for the complete volume is then obtained multiplying ppp* by V/V*, ratio between the volume of the cylindrical illuminated region V and the reduced illuminated volume V*. Due to the cylindrical illumination, the seeding density is not constant in the camera images (Fig. 3). The peak ppp is reached on the vertical centerline. A calibration target is recorded at three positions: z = -10 mm, z = 0 mm and z = +10 mm. Volume self calibration (Wieneke 2008) is applied to each recording series achieving a residual calibration error below 0.05 voxel in the complete measurement volume. For simplicity we use the laboratory coordinate system here, so that the y-direction coincides with the flow direction. The size of the reconstructed volumes for the experimental data included slightly more than the illuminated cylinder (diameter 50 mm) and was 60 x 65 x 65 mm³ or 891 x 965 x 966 voxel = 851 Mvoxel. Iso swirl (or λ2) contours in figure 4 (left) illustrate the flow structure: The unstable vortex rings move downstream (upwards in this experiment). At about four diameters distance from the injection point, the vortex rings start to break in smaller vortex structures that travel downstream. Vectors are displayed in the figure only in the central plane for clearness. The highest velocities are observed in the jet core just inside the vortex rings. Small negative v-components are visible at the outer sides of the vortex rings. The seeding density in this case is 0.1 ppp and the displayed results have been obtained from a MART reconstruction.

Fig. 2 Four high speed cameras imaging a free jet (10 mm diameter) inside the illuminated cylinder (50 mm diameter) at 1.3 kHz recording rate.


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Fig. 3 Raw particle images. Top: complete image from camera 1 (1 K x 1 K) at ppp = 0.17. Bottom: small stripes from camera 1 at different seeding particle densities: ppp = [0.005, 0.17].

0.17 ppp


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Fig. 4 Free Jet. Left: Iso λ2 surface (yellow), v-component coded in the color of the vector arrows. Right: Planar cut of the jet axial velocity component. Particle density 0.1 ppp, MART reconstruction, interrogation volume size = 48³ voxel. About four diameters downstream (~ y = 20 mm), the unstable vortex rings break down and split in smaller vortex structures. 5. Velocity field calculation Three dimensional velocity fields are calculated from the reconstructed objects by a multi pass correlation scheme using deformed interrogation volumes with decreasing window size. The interrogation volume overlap factor is set to 75 % to minimize truncation errors when evaluating the velocity gradient by finite differences. Moreover, spatial correlation between neighboring vectors enables a more efficient outlier detection and removal. The interrogation at the final grid is repeated twice. 6. Results from numerical simulations The computation time for the different reconstruction methods using synthetic data is summarized in table 1. MLOS and MinLOS only need 9 sec for the reconstruction of two exposures. This is about 25 times faster than the MART reconstruction. The considerable higher speed qualifies these techniques for a closer investigation. MTE-MART on the other hand is 15 times slower than MART or 375 times slower than MLOS and MinLOS. The computing time of 60 min results from ten times five MART iterations plus the time needed for nine vector field calculations. MTE-MART has the potential for considerable computing time reduction (e.g. Worth 2008, Atkinson 2009) which will be studied in the future.


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Table 1: Reconstruction time. Volume size: 700 x 700 x 300 voxel = 147 Mvoxel. MLOS MinLOS MART MTE MART

Reconst. time 9 sec 9 sec 4 min 60 min The effect of the reconstruction algorithm on the resulting velocity field is quantified by calculating the difference vector field from the original velocity field and the velocity field calculated from the reconstructed volumes. To reduce the influence of spurious vectors, the difference fields have been calculated after outlier removal. The average magnitude of the difference fields (Error) is plotted versus the particle density in figure 5. For the case with large flow structures (lx=256 voxel), velocity fields at three different interrogation volumes sizes (IV) have been calculated: 64³, 32³ and 24³ voxel (Fig. 5a, b and c). For the case with small flow structures (lx=64 voxel) velocity fields have been calculated only for an interrogation volumes size of 24³ voxel (Fig. 5d). Larger interrogation volumes were not suitable to resolve the small flow structures. In each plot a baseline is included, that results from a vector calculation using the original synthetic volume. No reconstruction algorithm can be expected to perform better than the baseline. However the closer an algorithm can get to the baseline, the better is the reconstruction quality. The baseline error always shows a maximum at low densities and a minimum at high ppp. The reason for the higher deviation at low particle density is the small number of particles contributing to an interrogation volume at low densities. As in planar PIV the accuracy increases with an increasing number of particles per interrogation window. The reference algorithm MART shows small deviations from the true velocity field of about 0.1 voxel at moderate seeding densities in the range from 0.02 ppp up to 0.09 ppp (interrogation volume size 64³ voxel, Fig. 5a). Up to ppp = 0.07 the MART error is close to the baseline error. At 0.01 ppp MART deviates about 0.14 voxel from the true velocity field. The error increases gradually for ppp values greater 0.09, reaching 0.2 voxel at ppp = 0.13. From there the error increases approximately linear to nearly 0.4 voxel at ppp = 0.2. The error for the MinLOS reconstruction is close to the baseline only at low densities of ppp = 0.01 to 0.02 (Fig. 5a). For higher densities (ppp > 0.02) the error increases rapidly, saturating at an error of about 0.8 voxel at ppp = 0.2. The error resulting from MLOS reconstruction is minimal (about 0.2 voxel) at the lowest density of ppp = 0.01 (Fig. 5a). Then the error increases even faster than for MinLOS reaching the maximum of about 0.8 voxel already at ppp = 0.14. The error curve from the MTE reconstruction is below the minimum of 0.13 voxel from MinLOS in nearly the complete particle density range from 0.02 ppp to 0.19 ppp (Fig. 5a). An error of about 0.1 voxel is achieved in a relatively wide range of particle densities from 0.02 ppp to 0.16 ppp. As expected, the MTE error is always equal or smaller than the error from pure MART. While the errors from MART and MTE are similar at low particle densities (up to 0.06 ppp), the differences becomes larger for higher densities reaching a maximum of about 0.2 voxel at ppp = 0.2. Overall MTE shows the smallest errors of all reconstruction techniques in the complete particle density range from 0.01 ppp to 0.2 ppp.


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At the smaller interrogation volume sizes (32³ and 24³ voxel, Fig.5b and c) the error curves are very similar to the curves discussed above. An obvious difference is that the error curves show higher error values at the lowest particle densities of 0.01 and 0.02 ppp. This is a clear indication that the number of particle per interrogation volume is too small at these densities. Also the minimal error from MinLOS increases to 0.2 voxel and nearly 0.3 voxel, for MLOS to 0.4 voxel and 0.5 voxel, while the minimal errors for MART and MTE stay close to 0.1 voxel. For the smaller flow structure size (Fig. 5d) the errors increase by more than a factor of two (relative to Fig. 5c). The minima are shifted to higher seeding densities, e.g. from 0.04 ppp to 0.07 ppp for the MART reference reconstruction. The minimum for MTE with about 0.2 voxel is clearly lower than the minimum for MART with about 0.3 voxel.

Fig. 5 Synthetic data: The displayed error is the average difference of calculated vector fields from known field. Baseline: cross correlation vector calculation from known original volume. IV = Interrogation volume, lx = wavelength (see equation 1), 75 % overlap, three passes. Post processing: outlier removal.

a) IV = 64³ voxel, lx = 256 voxel b) IV = 32³ voxel, lx = 256 voxel

c) IV = 24³ voxel, lx = 256 voxel d) IV = 24³ voxel, lx = 64 voxel


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Fig. 6 Front z-plane of the calculated vector fields for large flow structures (a) and small structures (b). The optimal particle density pppopt is the density at the error minimum for the different reconstruction techniques (Fig. 5 b and d).

a) IV = 32³ vox, lx = 256 vox b) IV = 24³ vox, lx = 64

MLOS

MinLOS

MART

MTE

pppopt = 0.01, err = 0.42 vox pppopt = 0.03, err = 0.96 vox





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The v-component of the calculated flow at the frontal z-plane is displayed in Fig. 6. Results at optimal ppp values (minimal error) are selected for the different reconstruction techniques. Outliers have not been removed for this illustration. The MTE results (Fig. 6, bottom) show no or very few distortions. The MART results include a few more distortions but still look acceptable. MinLOS and MLOS results show very strong distortions especially for the small flow structures (Fig. 6b). 7. Results from turbulent jet Figure 7 displays the color coded jet axial velocity component in the central vector plane from recordings at seeding densities of 0.02 ppp (top) to 0.17 ppp (bottom). The interrogation volume size is always 48³ voxel. The resulting vector spacing is 0.8 mm. In the ppp = 0.02 case (Fig. 7, top), all algorithms result in very similar velocity fields. In the lower jet core (marked with the red rectangle in figure 7, top-right) the difference between MTE and the other reconstruction techniques is about 0.3 voxel, for MART even below 0.04 voxel. The obvious difference between MLOS and MinLOS found for the synthetic data is not confirmed by the results from the experimental data at a density of 0.02 ppp which are quite similar for both techniques. The overall picture is already very different at moderate seeding density of 0.055 ppp (Fig. 7 second from top): While the velocity field from MTE is still reasonable for the jet flow, the velocity fields resulting from MLOS and MinLOS reconstruction are very different from the expected flow field. The average difference to the MTE result is 1.2 voxel for MLOS and 1.6 voxel for MinLOS in the jet core. The MART reconstruction still results at approximately the same vector field as MTE-MART (avg. difference of 0.03 voxel in the jet core). At seeding densities of 0.1 and 0.17 ppp MLOS and MinLOS fail to give reasonable results. The avg. difference of the MART results from MTE is still very small at ppp = 0.1 (0.1 voxel) and hardly visible. Finally at ppp = 0.17 the difference increases to 0.7 voxel and becomes visible (Fig. 7, bottom), where the MTE result looks more reasonable. Given, that the true velocity field is unknown in the experiments, MTE is chosen as a reference in the quantitative interpretation of the results (Fig. 8). This is justified by the findings from synthetic experiments, where MTE proofed its ability to produce results closest to the true velocity field at particle densities used in this experiment and by the visual inspection of the MTE results (Fig. 7, right). The average voxel shift in the jet core region is about 2.8 voxel. The measured shift is nearly constant for MTE (Fig. 8, left). The other reconstruction techniques show smaller measured core velocities for increasing densities. This tendency is relatively small for MART (below 1.5% until 0.1 ppp, about 20% at ppp = 0.17), but quite substantial for MLOS and MinLOS with more than 40% reduction already at 0.055 ppp.


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MLOS MinLOS MART MTE-MART

Fig. 7 Planar cut of the jet axial velocity component. The jet core region (red rectangle at the top, right) is used for further analysis (Fig. 8)). Size and color map as in Fig. 4, right.

0.022 ppp

0.055 ppp

0.10 ppp

0.17 ppp


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Fig. 8 Average measured voxel shift (left) and deviation from MTE results (right) in the jet core region (Fig. 7, red rectangle, top-right) 8. Discussion The numerical simulations reveal that at low seeding density the MinLOS method offers an acceptable accuracy, which is interesting, when considering the lower computational cost of such approach. Instead the MLOS technique fails to produce acceptable results for the synthetic data even at such low seeding density and the minimum precision error observed is just below half a voxel (IV = 32³). Results with accuracy comparable to that of planar PIV (RMS error in the order of 0.1 voxel) are only achieved using the MART algorithm. The increase of the error at very low seeding density (ppp < 0.02) is ascribed to the lack of particle tracers in the interrogation volumes, whereby the particle tracer concentration is not sufficient to spatially sample the chosen velocity field. At a seeding density of ppp = 0.05 (corresponding to the criterion suggested by Elsinga et al., 2006) no appreciable difference can be observed between the MART method and MTE-MART. This is probably due to the combined choice of four cameras and relatively low density of particle images. At a seeding density exceeding 0.05 the MinLOS approach becomes not viable (errors beyond half a voxel) and also the MART technique becomes increasingly inaccurate with the error increasing about linearly at a rate of 2 voxel/ppp (0.2 voxel increase within an increase of ppp of 0.1) The MTE-MART technique on the other hand can be applied at high particle densities resulting in an even higher accuracy than MART. Moreover, a high accuracy can be achieved in a wide range of particle densities. The price is here the higher computation time. For experimental data at low seeding density (0.02 ppp), MinLOS and MLOS reconstruction results in vector fields consistent with the expected flow and with results from MART and MTE. At higher seeding density (> 0.055 ppp) only MART and MTE reconstructions still allow the calculation of a reasonable vector field, whereas no meaningful field can be calculated from the MinLOS or MLOS reconstruction above densities of 0.37 ppp. At the highest measured seeding density (0.17 ppp) only MTE reconstruction results in a reasonable and undisturbed velocity field (Fig. 7, bottom-right). 9. Conclusion In this study, different reconstruction techniques were investigated using synthetic and experimental data at different particle densities. From the presented results, the following conclusions are drawn for flow field measurements using tomographic PIV:


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• MinLOS may be used when a relative low spatial resolution and a lower accuracy is acceptable in favor of high computation speed. The acceptable accuracy is achieved in a small range of seeding density, so that the seeding concentration needs to be controlled carefully. Small deviations from the optimal seeding density will result in considerable lower accuracy. • MLOS is outperformed by MinLOS in the synthetic data experiments. The difference is however not visible or even reversed using experimental data at low seeding concentration, so that we cannot draw a final conclusion here in favor for MLOS or MinLOS. • MART achieves a good compromise between computational effort, spatial resolution and accuracy. The accuracy is comparable to planar PIV at moderate seeding concentrations up to 0.05 ppp. MART will be more robust than MinLOS under conditions where the seeding density cannot be controlled very precisely and more accurate at higher seeding densities. • The highest spatial resolution and the highest accuracy are achieved using MTE reconstruction. Since MTE is also very accurate at low seeding densities, it is the most flexible technique. Flexibility concerning seeding density is of practical importance, especially for experiments in air: While it is possible to control the seeding density in water applications quite well, this is not the case in air applications where it is much harder to achieve constant seeding conditions. Often the seeding concentration varies during a single recording series or even inside a single image. In such situations MTE is recommended as the most reliable method. Computation time is high for MTE in the configuration used in this study. However, the authors see a high potential of speed optimization for this method using faster reconstruction techniques (Worth 2008, Atkinson 2009) and by optimizing the MTE-MART strategy. Results from this study may illuminate the flexibility of tomographic PIV: Depending on the reconstruction algorithm, it can be quite fast on one hand or it can achieve very accurate results at high spatial resolution on the other hand. References Atkinson C., Soria J., (2009) An efficient simultaneous reconstruction technique for tomographic particle image velocimetry. Exp in Fluids 47: 553-568 Elsinga G. E., Scarano F., Wieneke B., van Oudheusden B.W., (2006) Tomographic particle image Velocimetry. Exp in Fluids 41: 933-947 Elsinga G.E., Wieneke B., Scarano F., Schröder A., (2008) Tomographic 3D-PIV and Applications. In Particle Image Velocimetry - New Developments and Recent Applications, Schröder, Andreas; Willert, Christian E. (Eds.), Topics in Applied Physics, Vol. 112, Springer Elsinga G.E., Westerweel1 J., Scarano F., Novara M. (2009) On the velocity of ghost particles. In proceedings of PIV09, Melbourne, Australia Maas H.G., Westfeld P., Putze T., Boetkjaer N., Kitzhofer J., Brücker C., (2009) Photogrammetric techniques in multi-camera tomographic PIV. In proceedings of PIV09, Melbourne, Australia Novara M., Scarano F., (2009) Ghost intensity reduction by means of motion tracking enhanced MART tomography. In proceedings of PIV09, Melbourne, Australia Violato D., Moore P. and Bryon K. and Scarano F. (2010) Application of Powell's analogy for the prediction of vortex-pairing sound in a low-Mach number jet based on time-resolved planar and tomographic PIV, 16th AIAA/CEAS Aeroacoustics Conference. Wieneke B., (2008) Volume Self-Calibration for 3D Particle Image Velocimetry. Exp in Fluids 45: 549-556 Worth N. A., Nickels T.B., (2008) Accelaration of tomo-PIV by estimating the initial volume intensity distribution. Exp in Fluids 45: 847-856

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Comparison of volume reconstruction techniques at different particle densitiesltces.dem.ist.utl.pt/lxlaser/lxlaser2010/upload/1708... · 2010. 6. 18. · 15th Int Symp on Applications