Single-shot , volumetrically illuminated , three-dimensional , tomographic laser-induced-fluorescence imaging in a gaseous free jet

Single-shot, tomographic imaging of the three-dimensional concentration field is demonstrated in a turbulent gaseous free jet in co-flow using volumetrically illuminated laser-induced fluorescence. The fourthharmonic output of an Nd:YAG laser at 266 nm is formed into a collimated 15 × 20 mm beam to excite the ground singlet state of acetone seeded into the central jet. Subsequent fluorescence is collected along eight lines of sight for tomographic reconstruction using a combination of stereoscopes optically coupled to four two-stage intensified CMOS cameras. The performance of the imaging system is evaluated and shown to be sufficient for recording instantaneous three-dimensional features with high signal-tonoise (130:1) and nominal spatial resolution of 0.6–1.5 mm at x/D = 7–15.5. ©2016 Optical Society of America OCIS codes: (110.6880) Three-dimensional image acquisition; (110.6955) Tomographic imaging; (110.6960) Tomography; (280.2490) Flow diagnostics; (300.2530) Fluorescence, laser-induced. References and links 1. M. C. Escoda and M. B. Long, “Rayleigh scattering measurements of the gas concentration field in turbulent jets,” AIAA J. 21(1), 81–84 (1983). 2. I. van Cruyningen, A. Lozano, and R. K. Hanson, “Quantitative imaging of concentration by planar laser-induced fluorescence,” Exp. Fluids 10(1), 41–49 (1990). 3. J. P. Crimaldi, “Planar laser induced fluorescence in aqueous flows,” Exp. Fluids 44(6), 851–863 (2008). 4. W. J. A. Dahm and P. E. Dimotakis, “Mixing at large Schmidt number in the self similar far field of turbulent jets,” J. Fluid Mech. 217(-1), 299–330 (1990). 5. T. R. Meyer, J. C. Dutton, and R. P. Lucht, “Experimental study of the mixing transition in a gaseous axisymmetric jet,” Phys. Fluids 13(11), 3411–3424 (2001). 6. K. M. Tacina and W. J. A. Dahm, “Effects of heat release on turbulent shear flows, Part 1. A general equivalence principle for non-buoyant flows and its application to turbulent jet flames,” J. Fluid Mech. 415, 23–44 (2000). 7. R. L. Gordon, C. Heeger, and A. Dreizler, “High-speed mixture fraction imaging,” Appl. Phys. B 96(4), 745–748 (2009). 8. J. D. Miller, J. B. Michael, M. N. Slipchenko, S. Roy, T. R. Meyer, and J. R. Gord, “Simultaneous high-speed planar imaging of mixture fraction and velocity using a burst-mode laser,” Appl. Phys. B 113(1), 93–97 (2013). 9. T. Ueda, M. Shimura, M. Tanahashi, and T. Miyauchi, “Measurement of three-dimensional flame structure by combined laser diagnostics,” J. Mech. Sci. Technol. 23(7), 1813–1820 (2009). 10. B. Yip, R. L. Schmitt, and M. B. Long, “Instantaneous three-dimensional concentration measurements in turbulent jets and flames,” Opt. Lett. 13(2), 96–98 (1988). 11. L. K. Su and N. T. Clemens, “Planar measurements of the full three-dimensional scalar dissipation rate in gasphase turbulent flows,” Exp. Fluids 27(6), 507–521 (1999). 12. J. Nygren, J. Hult, M. Richter, M. Alden, M. Christensen, A. Hultqvist, and B. Johansson, “Three-dimensional laser induced fluorescence of fuel distributions in an HCCI engine,” Proc. Combust. Inst. 29(1), 679–685 (2002). 13. V. A. Miller, V. A. Troutman, and R. K. Hanson, “Near-kHz 3D tracer-based LIF imaging of a co-flow jet using toluene,” Meas. Sci. Technol. 25(7), 075403 (2014). 14. K. Y. Cho, A. Satija, T. L. Pourpoint, S. F. Son, and R. P. Lucht, “High-repetition-rate three-dimensional OH imaging using scanned planar laser-induced fluorescence system for multiphase combustion,” Appl. Opt. 53(3),


Introduction
Laser-based techniques for point-wise, line, or planar measurements have been valuable for studying scalar structure of turbulent flows for quite some time, earlier measurements shown by Escoda and Long [1].Because of relatively strong quantum yields and versatility, planar laser-induced fluorescence (PLIF) has been utilized for measurements of scalar mixing under a wide range of conditions, as summarized early on for gaseous flows by Van Cruyningen and associates [2] and for liquid flows by Crimaldi [3].This has improved the understanding of turbulent flow characteristics, including coherent structures and scaling laws by Dahm and Dimotakis [4], subgrid-scale molecular mixing by Meyer and associates [5], the effects of heat release by Tacina and Dahm [6], and planar time evolution by Gordon and associates [7] and Miller and associates [8], to name only a few.
Because of the inherently three-dimensional structure of turbulent flows, a number of efforts have focused on extending PLIF measurements for use with multiple laser sheets.This has been accomplished by using either multiple fixed sheets or scanning laser sheets with oscillating mirrors to sweep through the region of interest shown by several groups [9][10][11][12][13][14].The former can be accomplished with single-shot time resolution but with limited measurement planes, while the latter can provide many measurement planes but with limited time resolution since the flow can move as the planes are swept through the measurement volume.
In contrast with illumination along multiple planes, stereographic and tomographic measurements utilize a single exposure along multiple lines of sight to provide threedimensional information with single-shot time resolution over a relatively large region of interest.While stereographic imaging provides limited depth information with only two views shown by Ng and Zhang [15] and by Medford and associates [16], the use of three or more views increases the spatial information that can be gained at each time instant.For example, absorption tomography has been applied to combustion and flow environments to track fuel concentration shown by Santoro and associates [17] and water concentration in jet exhaust at high repetition rates shown by Ma and associates [18] and Liu and associates [19].Threedimensional imaging of particle fields has also been acquired via synthetic-aperture imaging with a plenoptic camera shown by Lynch and Thurow [20], which uses a microlens array to capture an image along multiple focal planes onto a single camera.Such information has been acquired from scalar fields using either plenoptic cameras by Greene and Sick [21] as well as using a camera array for tomographic imaging by Elsinga and associates [22], Weinkauff and associates [23], and Klinner and associates [24].While particle fields can be tracked utilizing relatively few (3)(4) camera views or a single plenoptic camera, tomographic reconstruction of gradients within scalar fields requires five or more views with widely varying viewing angles [25][26][27][28][29].A variety of reconstruction algorthims have been applied to chemiluminescence including direct reconstruction by Goyal and associates [25] and iterative multiplicative algebraic reconstruction technique MART by Worth and Dawson [26] to name only a few.The spatial resolution of a reconstructed field using an iterative algorithm has been shown to be approximately the spatial extent of the field divided by the number of views.This estimation was confirmed using synthetic data and previously published results by Floyd and associates [27] and using data collected from a known volume by Cai and associates [28] and Tsekenis and associates [29].
In addition to temporal resolution, depth information, and spatial resolution, another important consideration is the potentially limited signal intensity that may be available for tomographic reconstruction.Volumetric, ultraviolet laser illumination for tracer fluorescence requires substantial laser pulse energies and extremely sensitive detector arrays.Unlike particle scattering, it is more difficult and critical to ensure high signal-to-noise ratio and dynamic range when imaging scalar fields.Hence, potentially weak signals may require single-or dual-stage intensification.Adding intensification is not a limitation for most conventional imaging systems.
In this work, single-shot, volumetrically illuminated tomographic laser-induced fluorescence (LIF) is used to image three-dimensional concentration fields in an acetoneseeded, gaseous free jet.A single excitation pulse illuminates the entire volume within the time span of a nanosecond laser pulse, and up to eight intensified camera views are used to capture the fluorescence signal simultaneously from different horizontal and vertical angles.This provides a pathway to single-shot or high-speed, three-dimensional laser-based imaging with nanosecond time resolution even in flows without high nascent chemiluminescence or incandescence.Laser-induced fluorescence allows excitation of a wide range of potential tracers or chemical species in non-reacting and reacting flows.Illumination with a single excitation beam eliminates the need for multiple sources with varying beam profiles, and avoids nonlinear corrections that must be applied during post-processing.The eight camera views allow widely varying angles for depth information and sufficient spatial resolution to detect coherent structures with varying sizes within the flow.Synthetic data are produced from information known about the flow and investigated to determine the spatial resolution and reconstruction error.The feasibility of tomographic imaging of laser-induced fluorescence, potential limitations, and strategies for improvement are presented and discussed.

Tomographic imaging system
The experimental schematic illustrated in Fig. 1(a) shows the overall optical setup, in which the fourth harmonic, 266-nm output of a Spectra-Physics Pro-350 Series, 10-Hz Nd:YAG laser was used to induce fluorescence of gas-phase acetone seeded in air.The collimated output was shaped into a 15-mm wide by 20-mm tall elliptical beam, which filled the full jet width and a span of 7-15.5 diameters downstream of the nozzle exit.The laser pulse energy at 266 nm was 35 ± 5 mJ, which is readily accessible with conventional 10-30-Hz Nd:YAG lasers or high-power 10-20-kHz burst-mode lasers.Four dual-stage intensified camera systems with stereoscopes were used to acquire eight views simultaneously.Although it is feasible to significantly increase this by coupling as many as four images into a single camera, the number of views in the current proof of concept was limited by the reconstruction software to eight.Figure 1(b) shows an enlarged view of the vertical stereoscope used to couple views from two vertical locations into each of the four cameras.These include a pair of 50-mm mirrors and a pair of 25-mm fused-silica turning prisms.The vertical stereoscopes allowed the number of views to increase two fold while also providing access to unique and readily adjustable viewing angles that lie outside of the horizontal plane.Each detection system comprised a CMOS camera (Photron SA-X, SA-X2, or SA-Z) optically coupled to a high-speed intensifier (LaVision, High-Speed IRO) and an f/5.6, 50-mm Nikon lens with an 8-mm lens extender.The detection systems were placed at varying angles (40°, 75°, 115°, and 140°) within a span of 180° to increase registration accuracy by viewing one side of an alignment test chart.The dot-matrix alignment test chart was imaged by all views resulting in a single coordinate system, increasing the image registration accuracy.The views from the upper and lower 50-mm mirrors in the stereoscope were ± 30° from the horizontal plane.Although images could only be collected at the 10 Hz repetition rate of the Nd:YAG laser, it was of interest to evaluate the use of a detection system capable of high-speed operation.Intensifier gains between 50% and 70% were used to balance the signal levels from the four cameras because of varying detector sensitivities that were tested using a calibration light source.An intensifier gate of 200 ns was used to collect acetone fluorescence, freezing the flow in time, while long-lived acetone phosphorescence was quenched by oxygen in the air jet.Because of the slightly non-linear signal response from the intensified CMOS cameras, it was necessary to correct the signal from each sensor in post-processing.Hence, a relative correction factor, at the condition that signals were recorded, was determined by varying the intensity of a light source with neutral-density filters and relating the relative source intensity to the average pixel intensity.Further improvement of the detector response could be realized by pixel-based characterization, described by Weber and associates [30].The greatest deviation from a linear signal response was a signal intensity deficit of 20% with an intensifier gain of 70%. Figure 2 shows the linear relationship between the acetone vapor concentration and the signal intensity and the consistent acetone concentration used in each measurement.
Air was bubbled through a large volume (8 L) of acetone to a concentration of 0.2 by volume, verified by measuring the absorption through a known path length.The acetone-air mixture was then diluted with air at known varying levels to test the linearity of the signals with concentration.Images were acquired at ratios between zero (background) and 0.2 acetone vapor in air, and the signal increased linearly with concentration.The acetone signal was not found to decrease as the overall flow rate increased, ensuring that a consistent concentration could be maintained at each Reynolds number.The acetone vapor is then fed into the central jet to establish an axisymmetric mixing layer with the unseeded co-flow.The turbulent jet consisted of a D = 2.4-mm-diameter nozzle centered within a 34-mmdiameter co-flow.Fully turbulent flow was achieved by passing the air-acetone mixture through 60 diameters of straight tube upstream of the nozzle exit.Single-shot images were captured for Reynolds numbers Re D = VD/ν of 5,000, 10,000, and 15,000, where V is the jet velocity and ν is the kinematic viscosity.The beam absorption through the potential core was minimal (~3.5%).Figure 3 displays a single-shot image from each of the eight views.These images were processed to ensure a linear relationship with the acetone fluorescence signal.The field of view of a single was 0.13 mm × 0.13 mm.The spatial resolution of each of the eight views prior to reconstruction was determined to be 0.7 mm at the focal plane and 0.85 mm at ± 10 mm from the focal plane using the 50% modulation-transfer function of the images.A USAF 1951 test chart with varying spatial frequencies was imaged without the stereoscope at the focal plane and then translated in 5-mm increments to measure the spatial resolution through the measurement volume.The main loss of spatial resolution was from the use of image intensifiers, which are necessary to ensure sufficient signal levels.
Images from each camera were split into separate viewing frames and corrected for detector nonlinearity, background subtraction, and shot-to-shot laser intensity fluctuations of ~3%.The beam profile was recorded by directly imaging the fluorescence of a diffuser placed in the beam path at the location of the jet by a single, unintensified camera system with no gas flow and no stereoscope.One hundred images were captured at 10 Hz to provide an averaged beam profile.This allowed normalization of the mean spatially fluctuating signal to remove the effect of beam profile non-uniformities.Also it was assumed that the signal from each view should be consistent, so a multiplicative factor was applied to equalize the integrated intensity from each view.This correction is necessary because each camera and intensifier had varying quantum efficiencies and different intensifier gain settings.Due to the difference in magnification from the front of the volume to the back of the volume a small error (less than 2%) was incurred during this process.The final step was to threshold the images to 5% of the maximum value to decrease the computational expense of the reconstruction process.
The signal-to-noise ratio (SNR) in the individual images varied from 6:1 up to 30:1, defined as the ratio of the mean value of 25 pixels around a relatively uniform maximum pixel value in image to the standard deviation over the same pixels.Any variations of the concentration within the 25 pixels would overestimate the apparent noise, meaning that these values represent a conservative estimate of the SNR.Furthermore, the SNR values presented are not the highest in the data set but the average of several realizations.

Tomographic reconstruction
To accurately reconstruct the images into a single volume, the view angles and distances need to be known to within ~1 pixel.A dot-matrix test chart was placed directly over the center of the jet and imaged at each viewing angle.The plane of the test chart was set parallel to the direction of laser propagation and then translated in 5-mm increments through a range of ± 25 mm from the central axis of the jet normal to the plane of the test chart.Images collected at each 5-mm increment were used to correlate all detection systems relative to each other for the entire imaging volume.
Tomographic reconstruction was accomplished using the DaVis 8 software (LaVision) employing a Simultaneous Multiplicative Algebraic Reconstruction Technique (SMART) [31] and image registration.An iterative algorithm with optional volume spatial smoothing, SMART is a relatively fast algorithm commonly used for tomographic particle-image velocimetry (PIV).The software currently limits the number of views to eight; the smoothing is limited to a 3x3x3 filter of variable shape.The reconstruction process assumes an initial field that is constant over the entire volume.Projections of that volume are compared with the images from each view.The voxels that are spatially correlated to the pixels are adjusted based on how the projections compare with the images.For example, the intensities of the pixels, in the images and projections for each view, are compared at locations associated with a given voxel.If on average the pixel intensity is greater in the image than in the projection, the voxel value is increased by a multiplicative factor related to that difference.After 5-10 iterations, the pixel values from the projection equal the pixel values from the image on average over all views.After this point the voxel values remain unchanged and the process is complete.
The volume can be spatially smoothed between iterations by the Davis 8 software to reduce the effects of image noise and imperfect calibration.The smoothing is an averaging filter, three pixels wide, applied individually to each of the three spatial coordinates, resulting in 3 × 3 × 3 smoothing.The shape of the smoothing function is (S,1.0,S),where S is the smoothing strength, determined by the experimenter.For example, when S is zero, there is no smoothing; when S is one, there is boxcar spatial averaging with a window of 3 pixels.The SNR and contrast resolution of the volume are functions of the individual images, the number of views, and the amount of smoothing performed between iterations during the reconstruction process.Figure 4 shows the effects of smoothing between iterations on the SNR and contrast.The signal noise was calculated as the standard deviation of the signal in an area where the signal was nearly constant.The peak signal was the average of the peak signals from 100 unique reconstructions.A smoothing strength of 0.5 was selected to reduce artifacts in the reconstruction due to image noise while maintaining sufficient spatial resolution.The resulting SNR of the reconstructed volumes was determined to be 130:1.The contrast shown in Fig. 4 was determined by examining a oscillation in the voxel intensity, representing a variation in the acetone concentration along the centerline of the jet.The relative contrast was calculated by comparing the same peak and valley in a single volume.

Reconstructed volumes
Three representative volumetric images displaying isocontours of acetone tomographic-LIF delineating variation of LIF signals from high to low from the central core to the outer region are shown in Fig. 5.The volume represents an underdetermined matrix of intensity values; the reconstructed volume is spatially blurred because of the limited number of views and from any interiteration smoothing.As shown in [27][28][29], the spatial resolution of the volume will be approximately the diameter of the reconstructed volume divided by the number of views in a single plane when the image spatial resolution is not the limiting factor.The voxel size correlated to a volume of 0.2 × 0.2 × 0.2 mm 3 and, therefore, was not the primary factor restricting the spatial resolution.Hence, the spatial resolution in each direction is expected to be of the order 1-1.5 mm in the reconstructed volume based on the number of views and the approximate size of the jet at x/D = 7-15.5,where x is the axial distance from the jet exit.The spatial resolution was also shown to depend on the local field geometry; for example, simple or symmetric shapes can be reconstructed with greater accuracy and spatial resolution [27].The estimated spatial resolution is verified by predicting regions of steep gradient shown in   5 in the lower right edge of the Re D = 5,000 jet.The concentration rises by 50% over a distance of 0.3 mm, implying a spatial resolution of ~0.6 mm from the full width at half maximum rise and fall of an isolated feature.This approach of testing the spatial resolution has been utilized in prior work using chemiluminescence tomography [Cai et al., 2013].For more complex flow structures, however, it may be difficult for the imaging system to capture spatial features with sizes less than 1-1.5 mm due to the limited number of views (Floyd et al., 2011).
To further evaluate the spatial resolution, synthetic data were developed to have similar spatial characteristics of the volumes of interest.The volumes, having been smoothed through the reconstruction process, were not suitable candidates for synthetic data; however, they did have the correct overall concentration profile.A typical reconstructed volume was modified, therefore, to create synthetic data with enhanced spatial variations using a Lucy-Richardson deconvolution algorithm in Matlab.This resulted in high intensity peaks near the edge of the jet that were reduced by a multiplicative factor related to the original volume.Finally the volume was reconstructed from the same viewing angles except they were shifted by 18 degrees so any artifacts in the original volume that were created along the lines of sight would not match the new lines of sight.Representative images of the central plane from an original reconstructed volume, the synthetic volume, and the reconstructed synthetic volume are shown in Fig. 6.To evaluate the smoothing induced by the reconstruction process, Fig. 7 shows horizontal line plots taken from the volume slice at the location highlighted in Fig. 6 by the red dashed line.The synthetic reconstruction shows how the spatial resolution and accuracy vary within the probe volume.The leftmost feature at radial location −3.5 mm is characterized by a full width at half maximum (FWHM) of 0.6 mm and is almost completely resolved.This is consistent with the resolution measured form a region of steep concentration gradient, which showed a resolution of ~0.6 mm at the edge of the original jet.However, other features near the centerline are not completely resolved and lead to errors of ~25% near the peak of the signal.This error is not unexpected because of the limited number of views, which limits the ability of the reconstruction to capture the precise concentrations, feature locations, and gradients within the flow.For example, the dual peak in the synthetic data at radial locations of ~1 mm and ~2.2 mm, shown in Fig. 7, are reconstructed with a single, shifted peak that spatially averages the two features.This is consistent with a spatial resolution of 1-1.5 mm estimated from the number of views and illustrates how the spatial resolution of the reconstruction can vary throughout the flowfield.As such, the reconstructed concentrations should not be used to infer local gradients and peak concentrations but rather large-scale features of the flow.In addition to showing the turbulent jet structure from the isocontours of acetone concentration, it is possible to highlight coherent structures in the flow as represented by deviations in signal from the mean.An example of the normalized deviation from the mean LIF signal is presented in Fig. 8 for Re D = 10,000 at different viewing angles to show the internal structure of the flow.A thick slice of the volume or slab has been shown to reveal central contours; note that some contours are not fully enclosed and white space is seen in the background.The blue and red colors represent signals above and below the mean, respectively.The slab is rotated 45 and 90 degrees for perspective.The same volume at Re D = 10,000 in Fig. 8 is presented in Fig. 9 as planar slices at various parallel planes from the centerline to highlight the benefits of three-dimensional imaging.What appear to be elongated features in two dimensions in Fig. 9 are seen as highly irregular three-dimensional shapes in Fig. 8. Hence, a distinct advantage of three-dimensional measurements is the preservation of out-of-plane information.The three planes separated by 0.6 mm in Fig. 9 reveal correlated features for a particular structure highlighted with a black box on the right edge of the jet.This highlighted feature appears to be composed of two separate islands at 0 mm and 0.6 mm but is part of a larger structure, as shown in the planar slice at −0.6 mm.
The measurement uncertainty in the tomographic reconstruction includes: 1) temporal resolution, 2) spatial resolution, 3) random noise, and 4) bias errors.The temporal resolution in the single-shot images is determined by the intensifier gate width of 200 ns, which is sufficient to freeze the flow in time.The spatial resolution of the volume was estimated to be ~0.6 mm based on the ability to capture steep gradients near the edge of the jet, with a resolution of 1-1.5 mm for more complex features based on the number of views and evaluation of synthetic data.The SNR of the reconstructed three-dimensional images was 130:1 due to signal averaging across the eight views, although smoothing of flow features led to errors of ~25% in peak concentration.A potential source of bias error was from beam absorption through the non-uniform acetone concentration field, which was not accounted for in experiment and could lead to a total variation of ~3.5% in the concentration measurement across the turbulent jet.Shot-to-shot beam profile variations resulted in an additional potential error of ~1%.Finally, the view-to-view correction did not account for non-uniformities along the depth of field of each image.Because objects further from the camera would be less intense than objects near the camera, the signal intensity could vary by ~2% within the depth of field.As such, the uncertainty in concentration measurements is dominated by errors associated with spatial smoothing occurring during the reconstruction process, and interpretation of the flow structure should be limited to analysis of millimeter-scale features.

Summary
Single-shot, volumetrically-illuminated tomographic laser-induced fluorescence (LIF) measurements were presented in a free jet in co-flow.Eight views of the fluorescence signal were collected through stereoscopes mounted in front of four high-speed CMOS cameras coupled to high-speed dual-stage intensifiers to allow for temporally resolved volumetric reconstructions of the flow field.Further improvements include increasing the number of views as well as shot-to-shot beam profile corrections to allow quantitative measurement of mixture fraction.The number of views and corresponding spatial resolution can be increased by the use of more cameras or dual stereoscopes to couple four images (instead of two) into a single camera.The use of dual stereoscopes may also be used to reduce the number of cameras and optical access requirements.Increasing the number of views increases the optical complexity but reduces the reconstruction error and improves the spatial resolution.Ongoing work includes coupling the tomographic imaging system to a burst-mode laser for high-speed three-dimensional tomographic-LIF measurements, as well as development of a more accurate ART algorithm for optimizing the reconstruction of scalar field data.

Fig. 1 .
Fig. 1.(a) Schematic of laser and multiple-intensified-camera detection system and (b) close up of stereoscope used to couple two views into a single lens objective.

Fig. 2 .
Fig. 2. Line plots showing (a) the linear relationship between the acetone concentration and signal intensity and (b) the consistency of the concentration of acetone in the measurements.

Fig. 3 .
Fig. 3. Single-shot processed images from each detector and viewing angle at Re D = 10,000.

Fig. 4 .
Fig. 4. Line plots displaying the effects of smoothing strength on the (a) SNR and (b) relative contrast.

Fig.
Fig.5in the lower right edge of the Re D = 5,000 jet.The concentration rises by 50% over a distance of 0.3 mm, implying a spatial resolution of ~0.6 mm from the full width at half maximum rise and fall of an isolated feature.This approach of testing the spatial resolution has been utilized in prior work using chemiluminescence tomography[Cai et al., 2013].For more complex flow structures, however, it may be difficult for the imaging system to capture spatial features with sizes less than 1-1.5 mm due to the limited number of views(Floyd et al., 2011).To further evaluate the spatial resolution, synthetic data were developed to have similar spatial characteristics of the volumes of interest.The volumes, having been smoothed through the reconstruction process, were not suitable candidates for synthetic data; however, they did have the correct overall concentration profile.A typical reconstructed volume was modified, therefore, to create synthetic data with enhanced spatial variations using a Lucy-Richardson deconvolution algorithm in Matlab.This resulted in high intensity peaks near the edge of the jet that were reduced by a multiplicative factor related to the original volume.Finally the volume was reconstructed from the same viewing angles except they were shifted by 18 degrees so any artifacts in the original volume that were created along the lines of sight would not match the new lines of sight.Representative images of the central plane from an original reconstructed volume, the synthetic volume, and the reconstructed synthetic volume are shown in Fig.6.

Fig. 6 .
Fig. 6.Planar slices through the central plane of (a) the original reconstructed volume, (b) the synthetic volume, and (c) the reconstruction of the synthetic volume.

Fig. 7 .
Fig. 7. Line plots of central slice from volumes shown in Fig. 6 at the location of the red dashed line.

Fig. 8 .
Fig. 8. Volume slab rendering of isocontours of deviations from the mean signal at Re D = 10,000 for various rotated views.Blue represents positive deviations from the mean and red represents negative deviations.

Fig. 9 .
Fig. 9. Planar slices separated by 0.6 mm, with blue representing positive deviations from the mean and red representing negative deviations.The scale of the black box is 4.5 mm × 8 mm.