## Volumetric imaging of turbulent reactive flows at kHz based on computed tomography |

Optics Express, Vol. 22, Issue 4, pp. 4768-4778 (2014)

http://dx.doi.org/10.1364/OE.22.004768

Acrobat PDF (5351 KB)

### Abstract

Diagnostics with three-dimensional (3D) spatial resolution and rapid temporal resolution have been long desired to resolve the complicated turbulence-chemistry interactions. This paper describes a method based on based on tomographic chemiluminescence (TC) to address this diagnostic need. The TC technique used multiple cameras to simultaneously record CH* chemiluminescence emitted by turbulent flames from different view angles. A 3D tomographic algorithm was then applied to reconstruct the instantaneous flame structures volumetrically. Both experimental and computational studies have been conducted to demonstrate and validate the 3D measurements. Experimental results were obtained instantaneously at kHz temporal rate, in a volume of 16 × 16 × 16 cm^{3}, and with a spatial resolution estimated to be 2~3 mm. Computations were conducted to simulate the experimental conditions for comparison and validation.

© 2014 Optical Society of America

## 1. Introduction

1. R. S. Barlow, “Laser diagnostics and their interplay with computations to understand turbulent combustion,” Proc. Combust. Inst. **31**(1), 49–75 (2007). [CrossRef]

3. L. Ma, X. Li, S. Roy, A. Caswell, J. R. Gord, D. Plemmons, X. An, and S. T. Sanders, “Demonstration of High Speed Imaging in Practical Propulsion Systems Using Hyperspectral Tomography,” in *Laser Applications to Chemical, Security and Environmental Analysis*, (Optical Society of America, OSA Technical Digest, paper LM1B.5., 2012)

4. R. Wellander, M. Richter, and M. Aldén, “Time resolved, 3D imaging (4D) of two phase flow at a repetition rate of 1 kHz,” Opt. Express **19**(22), 21508–21514 (2011). [CrossRef] [PubMed]

5. J. Hult, A. Omrane, J. Nygren, C. F. Kaminski, B. Axelsson, R. Collin, P. E. Bengtsson, and M. Alden, “Quantitative three-dimensional imaging of soot volume fraction in turbulent non-premixed flames,” Exp. Fluids **33**(2), 265–269 (2002). [CrossRef]

6. L. Ma, X. Li, S. T. Sanders, A. W. Caswell, S. Roy, D. H. Plemmons, and J. R. Gord, “50-kHz-rate 2D imaging of temperature and H_{2}O concentration at the exhaust plane of a J85 engine using hyperspectral tomography,” Opt. Express **21**(1), 1152–1162 (2013). [CrossRef] [PubMed]

7. F. Li, X. Yu, H. Gu, Z. Li, Y. Zhao, L. Ma, L. Chen, and X. Chang, “Simultaneous Measurements of Multiple Flow Parameters for Scramjet Characterization Using Tunable Diode-laser Sensors,” Appl. Opt. **50**(36), 6697–6707 (2011). [CrossRef] [PubMed]

8. D. P. Correia, P. Ferrao, and A. Caldeira-Pires, “Advanced 3D emission tomography flame temperature sensor,” Combust. Sci. Technol. **163**(1), 1–24 (2001). [CrossRef]

11. W. Cai, X. Li, F. Li, and L. Ma, “Numerical and experimental validation of a three-dimensional combustion diagnostic based on tomographic chemiluminescence,” Opt. Express **21**(6), 7050–7064 (2013). [CrossRef] [PubMed]

12. Y. Hardalupas and M. Orain, “Local measurements of the time-dependent heat release rate and equivalence ratio using chemiluminescent emission from a flame,” Combust. Flame **139**(3), 188–207 (2004). [CrossRef]

13. Y. Hardalupas, M. Orain, C. S. Panoutsos, A. Taylor, J. Olofsson, H. Seyfried, M. Richter, J. Hult, M. Alden, F. Hermann, and J. Klingmann, “Chemiluminescence sensor for local equivalence ratio of reacting mixtures of fuel and air (FLAMESEEK),” Appl. Therm. Eng. **24**, 1619–1632 (2004). [CrossRef]

14. O. Stein, A. M. Kempf, and J. Janicka, “LES of the sydney swirl flame series: An initial investigation of the fluid dynamics,” Combust. Sci. Technol. **179**, 173–189 (2007). [CrossRef]

9. J. Floyd, P. Geipel, and A. M. Kempf, “Computed Tomography of Chemiluminescence (CTC): Instantaneous 3D measurements and Phantom studies of a turbulent opposed jet flame,” Combust. Flame **158**(2), 376–391 (2011). [CrossRef]

15. J. Floyd and A. M. Kempf, “Computed Tomography of Chemiluminescence (CTC): High resolution and instantaneous 3-D measurements of a Matrix burner,” Proc. Combust. Inst. **33**(1), 751–758 (2011). [CrossRef]

16. N. Denisova, P. Tretyakov, and A. Tupikin, “Emission tomography in flame diagnostics,” Combust. Flame **160**(3), 577–588 (2013). [CrossRef]

17. N. A. Worth and J. R. Dawson, “Tomographic reconstruction of OH* chemiluminescence in two interacting turbulent flames,” Meas. Sci. Technol. **24**(2), 024013 (2013). [CrossRef]

11. W. Cai, X. Li, F. Li, and L. Ma, “Numerical and experimental validation of a three-dimensional combustion diagnostic based on tomographic chemiluminescence,” Opt. Express **21**(6), 7050–7064 (2013). [CrossRef] [PubMed]

18. W. Cai, A. J. Wickersham, and L. Ma, “Three-Dimensional Combustion Diagnostics Based on Computed Tomography of Chemiluminescence,” in *51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition**,* (Dallas Region, TX, 2013). [CrossRef]

9. J. Floyd, P. Geipel, and A. M. Kempf, “Computed Tomography of Chemiluminescence (CTC): Instantaneous 3D measurements and Phantom studies of a turbulent opposed jet flame,” Combust. Flame **158**(2), 376–391 (2011). [CrossRef]

15. J. Floyd and A. M. Kempf, “Computed Tomography of Chemiluminescence (CTC): High resolution and instantaneous 3-D measurements of a Matrix burner,” Proc. Combust. Inst. **33**(1), 751–758 (2011). [CrossRef]

## 2. TC technique fundamentals

*F(x,y,z)*, which is discretized into voxels in the measurement volume. Line-of-sight images of

*F*are measured as 2D

*projections*on cameras, and the projections formed depend on the location and orientation of the cameras, specified by

*r*(distance),

*θ*(azimuth angle), and

*ϕ*(inclination angle). The relationship between a projection (

*P*) and

*F*is:where

*x*,

_{i}*y*,

_{i}*z*represent the voxel centered at (

_{i}*x*,

_{i}*y*,

_{i}*z*); and

_{i}*PSF*is the

*point spread function*defined as the projection formed by a point-source located at (

*x*,

_{i}*y*,

_{i}*z*) with unity intensity.

_{i}*PSF*across all voxels, and the weights are the value of the sought distribution. In this work the PSF was obtained using a Monte Carlo method. Calculating the

*PSF*is computationally intensive for the scale of problem under consideration in this work, and a Monte Carlo method was adopted to calculate the

*PSFs*due to its flexibility and relative ease of programming. Photons were generated at each voxel in random directions one by one. The program then tracked the propagation of each photon through all the optical elements in the imaging system until it landed on a pixel on the camera chip. The location of the pixel was then recorded. By generating a large number of photons, a distribution of their landing pixels was obtained and was used as the

*PSF*for the given pixel after normalization by the number of photons generated on this given pixel. After obtaining the

*PSF*, the 3D TC problem is then formulated as: given a set of projections (

*P*s) measured at various distances and orientations, find

*F(x,y,z)*.

11. W. Cai, X. Li, F. Li, and L. Ma, “Numerical and experimental validation of a three-dimensional combustion diagnostic based on tomographic chemiluminescence,” Opt. Express **21**(6), 7050–7064 (2013). [CrossRef] [PubMed]

16. N. Denisova, P. Tretyakov, and A. Tupikin, “Emission tomography in flame diagnostics,” Combust. Flame **160**(3), 577–588 (2013). [CrossRef]

20. W. Cai and L. Ma, “Comparison of approaches based on optimization and algebraic iteration for binary tomography,” Comput. Phys. Commun. **181**(12), 1974–1981 (2010). [CrossRef]

21. W. Cai, D. J. Ewing, and L. Ma, “Investigation of temperature parallel simulated annealing for optimizing continuous functions with application to hyperspectral tomography,” Appl. Math. Comput. **217**(12), 5754–5767 (2011). [CrossRef]

**21**(6), 7050–7064 (2013). [CrossRef] [PubMed]

24. L. Ma, X. Li, S. T. Sanders, A. W. Caswell, S. Roy, D. H. Plemmons, and J. R. Gord, “50-kHz-rate 2D imaging of temperature and H_{2}O concentration at the exhaust plane of a J85 engine using hyperspectral tomography,” Opt. Express **21**(1), 1152–1162 (2013). [CrossRef] [PubMed]

24. L. Ma, X. Li, S. T. Sanders, A. W. Caswell, S. Roy, D. H. Plemmons, and J. R. Gord, “50-kHz-rate 2D imaging of temperature and H_{2}O concentration at the exhaust plane of a J85 engine using hyperspectral tomography,” Opt. Express **21**(1), 1152–1162 (2013). [CrossRef] [PubMed]

*P*represents the measured projections at (

_{m}*r*,

*θ*,

*ϕ*),

*P*the projection calculated at (

_{c}*r*,

*θ*,

*ϕ*) with a given distribution according to Eq. (1), and the summation runs over all locations and orientations of measurements. Equation (2) essentially seeks the

*F*that best (in the least squares sense) reproduces the projection measurements. Solving Eq. (2) is nontrivial due to the scale of the problem, and the Simulated Annealing [11

**21**(6), 7050–7064 (2013). [CrossRef] [PubMed]

*x*direction) × 54 (

*y*direction) × 4 (

*z*direction) voxels, resulting in a total of 11,664 voxels. Each voxel has a dimension of 1.25 mm in both the

*x*and

*y*directions and 0.25 mm in the

*z*direction. The size of the voxels is limited by both practical and fundamental factors. Practically, the computational cost and memory requirement scales to the third power of voxel size (or more precisely, the inversion of voxel size). Fundamentally, the number of unknowns in the tomography problem also scales to the third power of the inverse of the voxel size. So if the voxel size becomes too small, it leads to more unknowns than the available equations (i.e., number of pixels in the projections), the tomography problem becomes under-determined.

*N*) are used in the reconstruction. For this particular flame as shown in Fig. 2(a), the TC technique can resolve its finest 1.25 mm feature with 8 views. The same trend as shown in Fig. 3 has been observed by numerical simulations. Besides experimental and numerical results, theoretical results are also available to predict the spatial resolution of tomographic reconstructions. For example, the Fourier Slice Theorem [25

25. G. Frieder and G. T. Herman, “Resolution in reconstructing objects from electron micrographs,” J. Theor. Biol. **33**(1), 189–211 (1971). [CrossRef] [PubMed]

26. G. T. Herman and S. Rowland, “Resolution in algebraic reconstruction techchqique an experimental investigation of the resolving power of an algebraic picture reconstruction techniuqe,” J. Theor. Biol. **33**, 213–223 (1971). [CrossRef] [PubMed]

*πλ/N*, where

*λ*is a characteristic spatial scale. A fit of the experimental data in Fig. 3 according to this theorem indicates that the data were reasonably captured. Note that the spatial resolution usually is defined by the minimum distance between line pairs. Here the thickness of a feature was used instead due to the experimental difficulty of creating controlled line pairs in gaseous and/or combustion flows. A method to overcome such difficulty will definitely benefit not only this work, but also a wide range of other flow/flame diagnostics.

## 3. Turbulent flame measurement

*r*for each camera is shown in units of mm). Measurements were made with various flames and view arrangements up to 5 kHz (5 kHz frame rate and 0.2 ms exposure time). The temporal rate was largely determined by the intensity of the flame and

*r*, so projections can be measured with sufficient SNR). Use of intensifiers and a different set of lenses can further enhance the temporal rate. Before each measurement, the cameras were calibrated using a uniform illuminator on a pixel-by-pixel basis as described in [27

27. V. Weber, J. Bruebach, R. L. Gordon, and A. Dreizler, “Pixel-based characterisation of CMOS high-speed camera systems,” Appl. Phys. B **103**(2), 421–433 (2011). [CrossRef]

^{3}as shown. However, the dark regions where no flame was present were clipped before tomographic inversion to save computational cost, resulting in an actual measurement volume of 16 × 16 × 16 cm

^{3}for the data shown here. The azimuth angles were

*θ*= 0°, 21.66°, 90°, 119.25°, and 161.37

^{0,}respectively for camera 1 through 5. Finally note that the results shown here were taken with

*Φ*= 90° for all five cameras (i.e., in a coplanar fashion), with the intent of facilitating the intuitive interpretation of the results. Though as discussed in [11

**21**(6), 7050–7064 (2013). [CrossRef] [PubMed]

^{5}equations in the form of Eq. (1). Thus, the projections from all five cameras provide a total of ~1 million equations to solve for the 262,144 unknowns, and the TISA algorithm [11

**21**(6), 7050–7064 (2013). [CrossRef] [PubMed]

*Φ*= 90° based on the 3D data used in Fig. 6. The results (the rendering and media) shown here illustrate TC’s ability to obtain 4D flame measurements, also the challenge of visualizing high dimensional large data sets encountered in flow and flame measurements, a discussion beyond the scope of this current paper [28, 30

30. J. Kitzhofer, T. Nonn, and C. Bruecker, “Generation and visualization of volumetric PIV data fields,” Exp. Fluids **51**(6), 1471–1492 (2011). [CrossRef]

*x-z*plane taken from 10 consecutive frames of the 3D reconstructions, each again obtained at 1 kHz frame rate and 1 ms exposure. The pixel resolution here was 64×64. The

*y*position of these cross-sectional views was

*y*= 0, i.e., along the center of the jet exit. The orientation of these cross-sectional views was therefore along the axis of the V-gutter, just as that of camera 3. These cross-sectional views again show the frame to frame temporal correlation, and comparing them with the projection data shown in Fig. 5 reveals features at this particular location that camera 3 was unable to resolved via line-of-sight measurements.

## 4. Validation of 3D measurements

*Φ*= 90° to facilitate such comparison. The most intuitive comparison can be made between the projections on cameras 1 and 3 (Fig. 4) versus the side and axial view of the 3D reconstructions (Fig. 6(a) and 6(c), respectively). The projection from camera 1 suggests the flame is slightly tilted towards the left (at that moment), and that from camera 3 suggests the left branch of the flame is taller and larger than the right branch. These features are observed in the 3D reconstruction shown in Fig. 6(c) and 6(d). The top view (Fig. 6(d)) further confirms the left branch is larger than the right. Closer examination provides verification at a more detailed level. For instance, the projection measured by camera 2 shows some cavities in the flame when viewed from

*θ*= 21.66°, and these cavities were correctly captured by the reconstruction as highlighted by the circled regions in Fig. 6(b). As another example, the projection measured by camera 3 shows the right branch of the flame, when viewed axially, had two disjointed regions of intense combustion. The circled region in Fig. 6(c) correctly captured this feature.

*F*. The calculated projections were then used as inputs in the tomographic algorithm to obtain 3D reconstructions. The uncertainties in the experimental measurements were estimated to be less than 5%. Therefore, these simulations were performed both with noiseless projections and also with 5% random Gaussian noise artificially added to the projections.

*e*) and correlation coefficients (

*r*) as defined below:where

*F*represents the known phantom,

*F*the reconstruction, and

^{rec}*σ*and

_{F}*F*and

*F*, respectively. Additionally, these phantoms can also be generated to simulate small scale turbulent fluctuations (e.g., by using results from DNS, direct numerical simulations, as phantom) that are difficulty to generated in a controlled fashion experimentally. However, these phantom studies encounter the same computation and memory challenges as the analysis of the experimental data, really a generic challenge to all multi-scale and multi-dimensional problems in general. With the computational resources we have, these phantom studies were conducted under similar configurations as the analysis of the experimental data. The sought

^{rec}*F*was discretized into 64 × 64 × 64 ( = 262,144) voxels, and projections were calculated with 500 × 500 ( = 250,000) pixels. With 10 projections, the PSF has ~6 × 10

^{11}(262,144 × 250,000 × 10) elements, a significant requirement on computational and memory resources.

*e*= 0%, and a perfect reconstruction that is different from the phantom by a shift results in

*r*= 100%. Figure 9(a) and 9(b) show the

*e*and

*r*obtained in these simulations, respectively. These results shows that reconstruction performance increases (both reflected in decreasing

*e*and increasing

*r*) as more projections are available, corrugating the results shown in Fig. 3. Figure 9 also shows that with noiseless projections at 5 views, reconstruction with

*e*= 2.5 and 5.8% can be obtained with noiseless projections and projections with 5% noise, respectively. Since the uncertainties in the measurements were estimated to be within 5%, the overall

*e*for the experimental results shown in Fig. 6 was estimated to be between 2.5 and 5.8%. The overall error can be reduced either by reducing the measurement uncertainty or more cameras to obtain more projections. These results also provide insights into the effects of temporal resolution of the technique, as the measurement uncertainty improves with longer integration time (thusly slower temporal response). Furthermore, it becomes easier to gather more projections at more views at slower temporal resolution. Also note that Fig. 9(a) shows

*r*is above 99% when five or more projections are used, indicating that a substantial portion of

*e*may be due to a shift between the reconstruction and phantom, and a detailed analysis into the interpretation of these criteria are undergoing.

## 5. Summary

^{3}using five high speed cameras. Computations have been conducted using phantoms simulating the experimental flames for comparison and validation purposes. The simulation results suggest an overall reconstruction error within 5.8%, and a high degree of correlation. These simulation results, besides providing validation and uncertainty analysis to the experimental data, also provide insights into the effects of temporal resolution of the technique. Ongoing research efforts are investigating the relationship of the reconstruction error and the correlation, and designing new experiments and simulations that can be directly compared against the volumetric measurement. A possible strategy is to compare a cross-section of the 3D measurements against a 2D planar technique (such as PLIF, planar laser induced fluorescence).

## Acknowledgement

## References and links

1. | R. S. Barlow, “Laser diagnostics and their interplay with computations to understand turbulent combustion,” Proc. Combust. Inst. |

2. | L. Ma, “High Speed Imaging in Reactive Flows Using Hyperspectral Tomography and Photodissociation Spectroscopy,” in |

3. | L. Ma, X. Li, S. Roy, A. Caswell, J. R. Gord, D. Plemmons, X. An, and S. T. Sanders, “Demonstration of High Speed Imaging in Practical Propulsion Systems Using Hyperspectral Tomography,” in |

4. | R. Wellander, M. Richter, and M. Aldén, “Time resolved, 3D imaging (4D) of two phase flow at a repetition rate of 1 kHz,” Opt. Express |

5. | J. Hult, A. Omrane, J. Nygren, C. F. Kaminski, B. Axelsson, R. Collin, P. E. Bengtsson, and M. Alden, “Quantitative three-dimensional imaging of soot volume fraction in turbulent non-premixed flames,” Exp. Fluids |

6. | L. Ma, X. Li, S. T. Sanders, A. W. Caswell, S. Roy, D. H. Plemmons, and J. R. Gord, “50-kHz-rate 2D imaging of temperature and H |

7. | F. Li, X. Yu, H. Gu, Z. Li, Y. Zhao, L. Ma, L. Chen, and X. Chang, “Simultaneous Measurements of Multiple Flow Parameters for Scramjet Characterization Using Tunable Diode-laser Sensors,” Appl. Opt. |

8. | D. P. Correia, P. Ferrao, and A. Caldeira-Pires, “Advanced 3D emission tomography flame temperature sensor,” Combust. Sci. Technol. |

9. | J. Floyd, P. Geipel, and A. M. Kempf, “Computed Tomography of Chemiluminescence (CTC): Instantaneous 3D measurements and Phantom studies of a turbulent opposed jet flame,” Combust. Flame |

10. | R. Snyder and L. Hesselink, “Measurement of mixing fluid flows with optical tomography,” Opt. Lett. |

11. | W. Cai, X. Li, F. Li, and L. Ma, “Numerical and experimental validation of a three-dimensional combustion diagnostic based on tomographic chemiluminescence,” Opt. Express |

12. | Y. Hardalupas and M. Orain, “Local measurements of the time-dependent heat release rate and equivalence ratio using chemiluminescent emission from a flame,” Combust. Flame |

13. | Y. Hardalupas, M. Orain, C. S. Panoutsos, A. Taylor, J. Olofsson, H. Seyfried, M. Richter, J. Hult, M. Alden, F. Hermann, and J. Klingmann, “Chemiluminescence sensor for local equivalence ratio of reacting mixtures of fuel and air (FLAMESEEK),” Appl. Therm. Eng. |

14. | O. Stein, A. M. Kempf, and J. Janicka, “LES of the sydney swirl flame series: An initial investigation of the fluid dynamics,” Combust. Sci. Technol. |

15. | J. Floyd and A. M. Kempf, “Computed Tomography of Chemiluminescence (CTC): High resolution and instantaneous 3-D measurements of a Matrix burner,” Proc. Combust. Inst. |

16. | N. Denisova, P. Tretyakov, and A. Tupikin, “Emission tomography in flame diagnostics,” Combust. Flame |

17. | N. A. Worth and J. R. Dawson, “Tomographic reconstruction of OH* chemiluminescence in two interacting turbulent flames,” Meas. Sci. Technol. |

18. | W. Cai, A. J. Wickersham, and L. Ma, “Three-Dimensional Combustion Diagnostics Based on Computed Tomography of Chemiluminescence,” in |

19. | X. Li and L. Ma, Three-Dimensional Measurements of Turbulent Jet Flames at kHz Rate Based on Tomographic Chemiluminescence ” in |

20. | W. Cai and L. Ma, “Comparison of approaches based on optimization and algebraic iteration for binary tomography,” Comput. Phys. Commun. |

21. | W. Cai, D. J. Ewing, and L. Ma, “Investigation of temperature parallel simulated annealing for optimizing continuous functions with application to hyperspectral tomography,” Appl. Math. Comput. |

22. | L. Ma, L. Kranendonk, W. Cai, Y. Zhao, and J. Baba, “Application of simulated annealing for simultaneous retrieval of particle size distribution and refractive index,” J. Aerosol Sci. |

23. | X. An, T. Kraetschmer, K. Takami, S. T. Sanders, L. Ma, W. Cai, X. Li, S. Roy, and J. R. Gord, “Validation of temperature imaging by H |

24. | L. Ma, X. Li, S. T. Sanders, A. W. Caswell, S. Roy, D. H. Plemmons, and J. R. Gord, “50-kHz-rate 2D imaging of temperature and H |

25. | G. Frieder and G. T. Herman, “Resolution in reconstructing objects from electron micrographs,” J. Theor. Biol. |

26. | G. T. Herman and S. Rowland, “Resolution in algebraic reconstruction techchqique an experimental investigation of the resolving power of an algebraic picture reconstruction techniuqe,” J. Theor. Biol. |

27. | V. Weber, J. Bruebach, R. L. Gordon, and A. Dreizler, “Pixel-based characterisation of CMOS high-speed camera systems,” Appl. Phys. B |

28. | W. Cai, X. Li, Y. Cao, J. Wang, and L. Ma, “Practical aspects of three-dimensional flame imaging using tomographic chemiluminescence ” in |

29. | M. Kang, X. Li, and L. Ma, “Calibration of Fiber Bundles for Flow and Combustion Measurements,” in |

30. | J. Kitzhofer, T. Nonn, and C. Bruecker, “Generation and visualization of volumetric PIV data fields,” Exp. Fluids |

**OCIS Codes**

(100.6890) Image processing : Three-dimensional image processing

(100.6950) Image processing : Tomographic image processing

(120.1740) Instrumentation, measurement, and metrology : Combustion diagnostics

(300.2140) Spectroscopy : Emission

**ToC Category:**

Image Processing

**History**

Original Manuscript: December 5, 2013

Revised Manuscript: January 27, 2014

Manuscript Accepted: January 27, 2014

Published: February 21, 2014

**Citation**

Xuesong Li and Lin Ma, "Volumetric imaging of turbulent reactive flows at kHz based on computed tomography," Opt. Express **22**, 4768-4778 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-4-4768

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### References

- R. S. Barlow, “Laser diagnostics and their interplay with computations to understand turbulent combustion,” Proc. Combust. Inst. 31(1), 49–75 (2007). [CrossRef]
- L. Ma, “High Speed Imaging in Reactive Flows Using Hyperspectral Tomography and Photodissociation Spectroscopy,” in Laser Applications to Chemical, Security and Environmental Analysis, (Optical Society of America, OSA Technical Digest Series, Paper LWA3, 2010)
- L. Ma, X. Li, S. Roy, A. Caswell, J. R. Gord, D. Plemmons, X. An, and S. T. Sanders, “Demonstration of High Speed Imaging in Practical Propulsion Systems Using Hyperspectral Tomography,” in Laser Applications to Chemical, Security and Environmental Analysis, (Optical Society of America, OSA Technical Digest, paper LM1B.5., 2012)
- R. Wellander, M. Richter, M. Aldén, “Time resolved, 3D imaging (4D) of two phase flow at a repetition rate of 1 kHz,” Opt. Express 19(22), 21508–21514 (2011). [CrossRef] [PubMed]
- J. Hult, A. Omrane, J. Nygren, C. F. Kaminski, B. Axelsson, R. Collin, P. E. Bengtsson, M. Alden, “Quantitative three-dimensional imaging of soot volume fraction in turbulent non-premixed flames,” Exp. Fluids 33(2), 265–269 (2002). [CrossRef]
- L. Ma, X. Li, S. T. Sanders, A. W. Caswell, S. Roy, D. H. Plemmons, J. R. Gord, “50-kHz-rate 2D imaging of temperature and H2O concentration at the exhaust plane of a J85 engine using hyperspectral tomography,” Opt. Express 21(1), 1152–1162 (2013). [CrossRef] [PubMed]
- F. Li, X. Yu, H. Gu, Z. Li, Y. Zhao, L. Ma, L. Chen, X. Chang, “Simultaneous Measurements of Multiple Flow Parameters for Scramjet Characterization Using Tunable Diode-laser Sensors,” Appl. Opt. 50(36), 6697–6707 (2011). [CrossRef] [PubMed]
- D. P. Correia, P. Ferrao, A. Caldeira-Pires, “Advanced 3D emission tomography flame temperature sensor,” Combust. Sci. Technol. 163(1), 1–24 (2001). [CrossRef]
- J. Floyd, P. Geipel, A. M. Kempf, “Computed Tomography of Chemiluminescence (CTC): Instantaneous 3D measurements and Phantom studies of a turbulent opposed jet flame,” Combust. Flame 158(2), 376–391 (2011). [CrossRef]
- R. Snyder, L. Hesselink, “Measurement of mixing fluid flows with optical tomography,” Opt. Lett. 13(2), 87–89 (1988). [CrossRef] [PubMed]
- W. Cai, X. Li, F. Li, L. Ma, “Numerical and experimental validation of a three-dimensional combustion diagnostic based on tomographic chemiluminescence,” Opt. Express 21(6), 7050–7064 (2013). [CrossRef] [PubMed]
- Y. Hardalupas, M. Orain, “Local measurements of the time-dependent heat release rate and equivalence ratio using chemiluminescent emission from a flame,” Combust. Flame 139(3), 188–207 (2004). [CrossRef]
- Y. Hardalupas, M. Orain, C. S. Panoutsos, A. Taylor, J. Olofsson, H. Seyfried, M. Richter, J. Hult, M. Alden, F. Hermann, J. Klingmann, “Chemiluminescence sensor for local equivalence ratio of reacting mixtures of fuel and air (FLAMESEEK),” Appl. Therm. Eng. 24, 1619–1632 (2004). [CrossRef]
- O. Stein, A. M. Kempf, J. Janicka, “LES of the sydney swirl flame series: An initial investigation of the fluid dynamics,” Combust. Sci. Technol. 179, 173–189 (2007). [CrossRef]
- J. Floyd, A. M. Kempf, “Computed Tomography of Chemiluminescence (CTC): High resolution and instantaneous 3-D measurements of a Matrix burner,” Proc. Combust. Inst. 33(1), 751–758 (2011). [CrossRef]
- N. Denisova, P. Tretyakov, A. Tupikin, “Emission tomography in flame diagnostics,” Combust. Flame 160(3), 577–588 (2013). [CrossRef]
- N. A. Worth, J. R. Dawson, “Tomographic reconstruction of OH* chemiluminescence in two interacting turbulent flames,” Meas. Sci. Technol. 24(2), 024013 (2013). [CrossRef]
- W. Cai, A. J. Wickersham, and L. Ma, “Three-Dimensional Combustion Diagnostics Based on Computed Tomography of Chemiluminescence,” in 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, (Dallas Region, TX, 2013). [CrossRef]
- X. Li and L. Ma, Three-Dimensional Measurements of Turbulent Jet Flames at kHz Rate Based on Tomographic Chemiluminescence ” in AIAA SciTech 2014, Paper AIAA-2014–0735, (National Harbor, MD, 2014).
- W. Cai, L. Ma, “Comparison of approaches based on optimization and algebraic iteration for binary tomography,” Comput. Phys. Commun. 181(12), 1974–1981 (2010). [CrossRef]
- W. Cai, D. J. Ewing, L. Ma, “Investigation of temperature parallel simulated annealing for optimizing continuous functions with application to hyperspectral tomography,” Appl. Math. Comput. 217(12), 5754–5767 (2011). [CrossRef]
- L. Ma, L. Kranendonk, W. Cai, Y. Zhao, J. Baba, “Application of simulated annealing for simultaneous retrieval of particle size distribution and refractive index,” J. Aerosol Sci. 2009, 588–596 (2009).
- X. An, T. Kraetschmer, K. Takami, S. T. Sanders, L. Ma, W. Cai, X. Li, S. Roy, J. R. Gord, “Validation of temperature imaging by H2O absorption spectroscopy using hyperspectral tomography in controlled experiments,” Appl. Opt. 50(4), A29–A37 (2011). [CrossRef] [PubMed]
- L. Ma, X. Li, S. T. Sanders, A. W. Caswell, S. Roy, D. H. Plemmons, J. R. Gord, “50-kHz-rate 2D imaging of temperature and H2O concentration at the exhaust plane of a J85 engine using hyperspectral tomography,” Opt. Express 21(1), 1152–1162 (2013). [CrossRef] [PubMed]
- G. Frieder, G. T. Herman, “Resolution in reconstructing objects from electron micrographs,” J. Theor. Biol. 33(1), 189–211 (1971). [CrossRef] [PubMed]
- G. T. Herman, S. Rowland, “Resolution in algebraic reconstruction techchqique an experimental investigation of the resolving power of an algebraic picture reconstruction techniuqe,” J. Theor. Biol. 33, 213–223 (1971). [CrossRef] [PubMed]
- V. Weber, J. Bruebach, R. L. Gordon, A. Dreizler, “Pixel-based characterisation of CMOS high-speed camera systems,” Appl. Phys. B 103(2), 421–433 (2011). [CrossRef]
- W. Cai, X. Li, Y. Cao, J. Wang, and L. Ma, “Practical aspects of three-dimensional flame imaging using tomographic chemiluminescence ” in AIAA SciTech 2014, Paper AIAA-2014–0394, (National Harbor, MD, USA, 2014).
- M. Kang, X. Li, and L. Ma, “Calibration of Fiber Bundles for Flow and Combustion Measurements,” in AIAA SciTech 2014, Paper AIAA-2014–0397, (National Harbor, MD, 2014).
- J. Kitzhofer, T. Nonn, C. Bruecker, “Generation and visualization of volumetric PIV data fields,” Exp. Fluids 51(6), 1471–1492 (2011). [CrossRef]

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