## Tomographic imaging of temperature and chemical species based on hyperspectral absorption spectroscopy

Optics Express, Vol. 17, Issue 10, pp. 8602-8613 (2009)

http://dx.doi.org/10.1364/OE.17.008602

Acrobat PDF (983 KB)

### Abstract

A novel technique has been developed to obtain simultaneous tomographic images of temperature and species concentration based on hyperspectral absorption spectroscopy. The hyperspectral information enables several key advantages when compared to traditional tomography techniques based on limited spectral information. These advantages include a significant reduction in the number of required projection measurements, and an enhanced insensitivity to measurements/inversion uncertainties. These advantages greatly facilitate the practical implementation and application of the tomography technique. This paper reports the development of the technique, and the experimental demonstration of a prototype sensor in a near-adiabatic, atmospheric-pressure laboratory Hencken burner. The spatial and temporal resolution enabled by this new sensing technique is expected to resolve several key issues in practical combustion devices.

© 2009 Optical Society of America

## 1. Introduction

4. M. Ravichandran and F. C. Gouldin, “Retrieval of asymmetric temperature and concentration profiles from a limited number of absorption-measurements,” Combust. Sci. Technol . **60(1)**, 231–248 (1988). [CrossRef]

5. H. M. Hertz, “Experimental-determination of 2-D flame temperature-fields by interferometric tomography,” Opt. Commun . **54(3)**, 131–136 (1985). [CrossRef]

6. K. B. Chung, F. C. Gouldin, and G. J. Wolga, “Experimental reconstruction of the spatial density distribution of a nonreacting flow with a small number of absorption measurements,” Appl. Opt . **34(24)**, 5492–5500 (1995). [CrossRef]

7. B. Gillet, Y. Hardalupas, C. Kavounides, and A. M. K. P. Taylor, “Infrared absorption for measurement of hydrocarbon concentration in fuel/air mixtures (MAST-B-LIQUID),” Appl. Therm. Eng . **24**(11–12), 1633–1653 (2004). [CrossRef]

8. S. J. Carey, H. McCann, F. P. Hindle, K. B. Ozanyan, D. E. Winterbone, and E. Clough, “Chemical species tomography by near infra-red absorption,” Chem. Eng. J. **77**(1-2), 111–118 (2000). [CrossRef]

11. K. Salem, E. Tsotsas, and D. Mewes, “Tomographic measurement of breakthrough in a packed bed adsorber,” Chem. Eng. Sci . **60**(2), 517–522 (2005). [CrossRef]

12. T. Kraetschmer, D. Dagel, and S. T. Sanders, “Simple multiwavelength time-division multiplexed light source for sensing applications,” Opt. Lett . **33**(7), 738–740 (2008). [CrossRef] [PubMed]

13. W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun . **179**(4), 250–255 (2008). [CrossRef]

15. L. Ma and W. Cai, “Numerical investigation of hyperspectral tomography for simultaneous temperature and concentration imaging,” Appl. Opt . **47**(21), 3751–3759 (2008). [CrossRef] [PubMed]

15. L. Ma and W. Cai, “Numerical investigation of hyperspectral tomography for simultaneous temperature and concentration imaging,” Appl. Opt . **47**(21), 3751–3759 (2008). [CrossRef] [PubMed]

_{2}O) in this spectral region. These measurements were then used as the inputs for a tomographic inversion algorithm to simultaneously reconstruct the distributions of temperature and mole fraction of H

_{2}O. The sensor was demonstrated in a well-controlled near-adiabatic, atmospheric-pressure laboratory flame, and the reconstructed distributions are in good agreement with those obtained via independent methods such as coherent anti-Stoke Raman scattering (CARS) spectroscopy.

## 2. Theoretical background

15. L. Ma and W. Cai, “Numerical investigation of hyperspectral tomography for simultaneous temperature and concentration imaging,” Appl. Opt . **47**(21), 3751–3759 (2008). [CrossRef] [PubMed]

*λ*) generally contains contributions from multiple transitions centered at various wavelengths (including that centered at

_{i}*λ*itself), as schematically shown in the right panel. Here, we use

_{i}*p*(

*L*), termed a projection, to denote the absorbance at a projection location

_{j}, λ_{i}*L*and a wavelength

_{j}*λ*. The projection,

_{i}*p*(

*L*), is expressed by the following integral:

_{j}, λ_{i}*a*and

*b*the integration limits determined by the line of sight and the geometry of the domain of interest,

*S*(

*λ*,

_{k}*T*(1)) is the line strength of the contributing transition centered at a wavelength

*λ*and depends nonlinearly on temperature (

_{k}*T*) [15

**47**(21), 3751–3759 (2008). [CrossRef] [PubMed]

*T*(1) and

*X*(1) the temperature and mole fraction profile of the absorbing species along the line of sight, respectively;

*Φ*the Voigt lineshape function [16

16. M. P. Arroyo and R. K. Hanson, “Absorption-measurements of water-vapor concentration, temperature, and line-shape parameters using a tunable InGaAsP diode-laser,” Appl. Opt . **32**(30), 6104–6116 (1993). [CrossRef] [PubMed]

*P*the pressure, assumed to be uniform. The summation runs over all the transitions with non-negligible contributions. In this work, the domain of interest is discretized by superimposing a square mesh in the Cartesian coordinate, as shown in the left panel of Fig. 1; and the integration in Eq. (1) is also discretized accordingly.

*T*and

*X*over the discretized domain with a finite set of projections as described in Eq. (1). Hence, mathematically, the hyperspectral tomography problem is an inverse problem, which has been studied extensively. However, due to the inclusion of multiple wavelengths and the nonlinear dependence of the line strength on temperature, the hyperspectral tomography problem poses distinct challenges and algorithms designed in the past cannot be readily applied. A new inversion algorithm was therefore developed to address the special challenges of the hyperspectral tomography problem [13

13. W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun . **179**(4), 250–255 (2008). [CrossRef]

**47**(21), 3751–3759 (2008). [CrossRef] [PubMed]

*T*and

*X*distributions are retrieved by minimizing the following function:

*p*(

_{m}*L*) denotes the measured projection at a location

_{j}, λ_{i}*L*and a wavelength

_{j}*λ*;

_{i}*p*(

_{c}*L*) the computed projection based on a reconstructed

_{j}, λ_{i}*T*and

*X*profile (denoted by

*T*and

^{rec}*X*, respectively); and

^{rec}*J*and

*I*the total number of wavelengths and projection locations used in the tomography scheme, respectively. This function,

*D*, provides a quantitative measure of the closeness between the reconstructed and the actual temperature and concentration profiles. The contribution from each wavelength to

*D*is normalized by the projection at this wavelength itself, such that projections measured at all wavelengths are weighted equally in the inversion. When

*T*and

^{rec}*X*match the actual profiles,

^{rec}*D*reaches its global minimum (zero). Note that the formulation in Eq. (2) is designed specifically for the hyperspectral tomography problem. For a general tomography problem, this formulation may encounter singularity issues (i.e.,

*D*(

*T*) → ∞ as

^{rec}, X^{rec}*p*→

_{m}*0*). In the hyperspectral tomography problem (and other sensing techniques based on absorption spectroscopy), the technique is designed such that the minimal absorbance (i.e., the projections,

*p*s) is above a certain level, and consequently, the singularity issue will not occur.

_{m}17. A. Franchois and C. Pichot, “Microwave imaging - complex permittivity reconstruction with a Levenberg-Marquardt method,” IEEE Trans. Antenn. Propag . **45**(2), 203–215 (1997). [CrossRef]

13. W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun . **179**(4), 250–255 (2008). [CrossRef]

**47**(21), 3751–3759 (2008). [CrossRef] [PubMed]

*F*) is minimized instead of

*D*:

*R*and

_{T}*R*are the regularization factors for temperature and concentration, respectively;

_{X}*γ*and

_{T}*γ*are positive constants (regularization parameters) to scale the magnitude of

_{X}*R*and

_{T}*R*properly such that they do not dominate the

_{X}*D*(

*T*) term. In Eq. (3), the regularization factors represent the a priori information (e.g., smoothness of the

^{rec}, X^{rec}*T*and

*X*distributions); and the magnitudes of

*λ*and

_{T}*λ*reflect the relative weights of the

_{X}*a priori*information and the

*a posteriori*knowledge (i.e., measurements). The master function,

*F*, is then minimized using a stochastic algorithm, the simulated annealing algorithm [19

19. A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continuous-variables with the simulated annealing algorithm,” ACM Trans. Math. Softw . **13**(3), 262–280 (1987). [CrossRef]

**179**(4), 250–255 (2008). [CrossRef]

*T*and

*X*distributions.

## 3. Experimental setup

_{2}O concentration over a Hencken flame (top panel of Fig. 2). To facilitate the discussion, we name the laser used here “fiber Fabry-Perot tunable filter laser” (FFP-TFL) (bottom panel of Fig. 2). The fiber-coupled source output was split into 8 similar fiber outputs using a fiber tree coupler. Two of these outputs were used for monitoring: one fed to a Mach-Zehnder interferometer to track the FFP-TFL wavelength and the other fed to a photoreceiver to monitor the FFP-TFL intensity (the so-called reference intensity,

*I*). The six remaining fibers delivered free-space beams (labeled as Beam 1 through 6) to perform projection measurements across the flame region of interest. The flame is produced by a square H

_{O}_{2}/air Hencken burner (2.54 cm × 2.54 cm) and is surrounded by a N

_{2}co-flow. Surrounding the co-flow was a dry N

_{2}purge flow used to eliminate the interference of H

_{2}O in room air. The thickness of the co-flow was 1.27 cm, and that of the purge flow ~2 mm. The transmitted laser beams were registered by six photoreceivers (labeled as Detector 1 through 6), and the signals collected converted into absorption spectra for use in the tomographic reconstruction. Two sets of spectra measured at the 6th beam location are shown in Fig. 3, one measured at an equivalence ratio of 1.0 (

*Φ*= 1.0) and the other at

*Φ*= 0.5, respectively. Note the variations in the relative strengths of the absorption peaks between the spectra at these equivalence ratios. Such variations form the basis of temperature sensing and the tomographic reconstruction.

_{2}O absorption transitions (most belong to the R branch of the

*ν*

_{1}×

*ν*

_{3}band, and some belong to the 2

*ν*

_{1}and 2

*ν*

_{3}bands). The FFP-TFL is similar to a standard external-cavity tunable diode laser (ECDL), with three key differences. First, it is composed entirely of fiber-optic components. Second, the FFP-TF is used to set the instantaneous wavelength rather than a free-space grating. Finally, because standard fiber pigtails were present on all laser components, the laser cavity length is significantly longer than a typical external-cavity laser, ultimately preventing single-mode operation. The cavity length of the laser was ~17 m, which set the cavity mode spacing to ~12 MHz. We operated the FFP-TFL in a multiple-spectral-mode fashion for all the measurements presented here, with the FFP-TF enforcing an instantaneous linewidth of ~5GHz. The multimode operation is not especially desirable, because competition and beating among the multiple (up to ~500 at any instant) modes results in an intensity noise that is higher than in a traditional ECDL;

20. L. A. Kranendonk, X. An, A. W. Caswell, R. E. Herold, S. T. Sanders, R. Huber, J. G. Fujimoto, Y. Okura, and Y. Urata, “High speed engine gas thermometry by Fourier-domain mode-locked laser absorption spectroscopy,” Opt. Express **15**(23), 15115–15128 (2007). [CrossRef] [PubMed]

12. T. Kraetschmer, D. Dagel, and S. T. Sanders, “Simple multiwavelength time-division multiplexed light source for sensing applications,” Opt. Lett . **33**(7), 738–740 (2008). [CrossRef] [PubMed]

_{2}O mole fraction assumed in each zone. The flame was divided into five zones: a 0.85 cm × 0.85 cm square zone at the center, and four symmetric zones around the edges. The N

_{2}co-flow and purge flow were considered as the sixth and seventh zones, respectively. Note that even though the 7-zone scheme shown in Fig. 2 is symmetric, our tomographic technique does not invoke the assumption of symmetry (analogously, setting up a tomographic scheme by imposing a 4-by-4 square mesh does not invoke the symmetry assumption). The assumption of symmetry is only invoked when the tomographic inversion algorithm assumes/forces the values of temperature/concentration of certain zones to be equal; and our technique made no such assumption.

## 4. Results and discussions

### 4.1 Tomographic imaging of temperature and chemical species

22. L. A. Kranendonk, A. W. Caswell, and S. T. Sanders, “Robust method for calculating temperature, pressure, and absorber mole fraction from broadband spectra,” Appl. Opt . **46**(19), 4117–4124 (2007). [CrossRef] [PubMed]

23. R. J. Barber, J. Tennyson, G. J. Harris, and R. N. Tolchenov, “A high-accuracy computed water line list,” Mon. Not. R. Astron. Soc . **368**(3), 1087–1094 (2006). [CrossRef]

*F*to obtain

*T*and

*X*requires calculating the spectra at all six beam locations for a large number of times. Such a computational cost is beyond our existing capability. With both reasons considered, here the strongest 100 absorption peaks in the measured spectra were selected and used in the analysis. This selection reduced the computational cost by a factor of ~3000, and the peaks selected can still provide a reasonable overall representation of the spectra. Though this current method is simple and practical, research is underway to refine the selection of transitions for use in the hyperspectral tomography technique. Besides the measurement uncertainty and computational cost, the selection method should also consider the response of the line strength of the selected transitions with respect to temperature (which is mainly controlled by a parameter named the lower state energy). Intuitively, transitions with line strength varying more sensitively to temperature change should provide more accurate temperature measurements.

*Φ*= 1.0) and the other at

*Φ*= 0.5. As can be seen, the line-of-sight-averaged analysis yields a different temperature and concentration when the measured spectra at different beam locations are used. Such variation is partly due to measurement uncertainties, but primarily due to the nonuniformity over the measurement region (including the purge flow and co-flow zones).

*T*and

*X*distributions over the measurement region, using measured spectra at all six beam locations as inputs. Two sets of results are shown in Fig. 5, again at

*Φ*= 1.0 and

*Φ*= 0.5, respectively. In this figure,

*T*and

_{i}*X*represent the temperature and H

_{i}_{2}O concentration in the

*i*th zone, respectively. The results confirm that a certain degree of nonuniformity exists in the test region, and also the insulating effects of the purge flow and co-flow. The results shown are in reasonable agreement with the adiabatic flame calculations and past measurements using CARS [24

24. S. Roy, P. J. Kinnius, R. P. Lucht, and J. R. Gord, “Temperature measurements in reacting flows by time-resolved femtosecond coherent anti-Stokes Raman scattering (fs-CARS) spectroscopy,” Opt. Commun . **281**(2), 319–325 (2008). [CrossRef]

24. S. Roy, P. J. Kinnius, R. P. Lucht, and J. R. Gord, “Temperature measurements in reacting flows by time-resolved femtosecond coherent anti-Stokes Raman scattering (fs-CARS) spectroscopy,” Opt. Commun . **281**(2), 319–325 (2008). [CrossRef]

*T*and

*X*distributions reconstructed are in good agreement (within ~7%) with those reconstructed using all six projection measurements. The reduction in the number of projections becomes more dramatic when the scale of the problem increases [15

**47**(21), 3751–3759 (2008). [CrossRef] [PubMed]

### 4.2 Insensitivity of the tomography algorithm to initial guesses

**47**(21), 3751–3759 (2008). [CrossRef] [PubMed]

*F*in Eq. (3) using the simulated annealing technique, an initial guess of the

*T*and

*X*distributions must first be made to start the algorithm. Therefore, a practical concern is whether the tomographic reconstruction is sensitive to the initial guesses. This section uses both numerical simulation and the experimental results obtained above to address this concern.

*T*and

*X*phantoms were generated over a 10-by-10 square grid, with a set of samples shown in Fig. 7. These distribution phantoms were created by superimposing two Gaussian peaks on a paraboloid to simulate a representative multi-modal and asymmetric temperature distribution of H

_{2}O that could be encountered in practical combustion devices. Other distribution phantoms have been tested and the results obtained are similar to those obtained with the phantoms shown here. A hypothetical tomography sensor with 20 beams is applied to probe the phantom

*T*and

*X*distributions. Each beam contains 10 wavelengths, probing 10 different transitions of H

_{2}O. More details of the setup of the simulation can be found in [15

**47**(21), 3751–3759 (2008). [CrossRef] [PubMed]

*T*and

*X*distributions with different initial guesses. The evolutions of the value of

*F*at three different initial guesses (a Gaussian, a uniform, and a parabolic distribution) were recorded and plotted in Fig. 8. As can be seen from Fig. 7, the values of

*F*were considerably different at the beginning of the minimization (at the first iteration), because of the different initial guesses used. As the tomographic algorithm proceeded, the values of

*F*converged; and at the end of the algorithm, the values of

*F*became within 2% across all three initial guesses.

*T*distributions, corresponding to that obtained with a uniform initial guess and that with a parabolic initial guess, respectively, are shown in Fig. 9, together with their differences. Figure 9 indicates that the retrieved

*T*distributions agree well with each other, and the maximum difference between these two distributions is within ± 60 K. The same observations were made with the

*X*distributions. Also note that according to Fig. 8, the uniform and parabolic initial guesses resulted in the largest

*F*discrepancy, and consequently the largest discrepancy in

*T*and

*X*distributions. Therefore, the level of difference shown in Fig. 9 represents the worst scenario for the cases simulated here.

*T*and

*X*distributions compared. Due to the relative simplicity of the problem compared with the 10-by-10 problem simulated above, the retrieved

*T*and

*X*distributions are essentially the same across all the different initial guesses. For example, when a uniform, a Gaussian, and a random initial guess were used to process the experimental data at

*Φ*= 1.0 and

*Φ*= 0.5, the retrieved

*T*and

*X*distributions agree with those shown in Fig. 5 to within 0.1%.

## 5. Summary

## Acknowledgements

## References and links

1. | F. Mayinger and O. Feldmann, eds., |

2. | A. C. Eckbreth, |

3. | M. G. Allen, E. R. Furlong, and R. K. Hanson, “Tunable diode laser sensing and combustion control,” in |

4. | M. Ravichandran and F. C. Gouldin, “Retrieval of asymmetric temperature and concentration profiles from a limited number of absorption-measurements,” Combust. Sci. Technol . |

5. | H. M. Hertz, “Experimental-determination of 2-D flame temperature-fields by interferometric tomography,” Opt. Commun . |

6. | K. B. Chung, F. C. Gouldin, and G. J. Wolga, “Experimental reconstruction of the spatial density distribution of a nonreacting flow with a small number of absorption measurements,” Appl. Opt . |

7. | B. Gillet, Y. Hardalupas, C. Kavounides, and A. M. K. P. Taylor, “Infrared absorption for measurement of hydrocarbon concentration in fuel/air mixtures (MAST-B-LIQUID),” Appl. Therm. Eng . |

8. | S. J. Carey, H. McCann, F. P. Hindle, K. B. Ozanyan, D. E. Winterbone, and E. Clough, “Chemical species tomography by near infra-red absorption,” Chem. Eng. J. |

9. | P. Wright, C. A. Garcia-Stewart, S. J. Carey, F. P. Hindle, S. H. Pegrum, S. M. Colbourne, P. J. Turner, W. J. Hurr, T. J. Litt, S. C. Murray, S. D. Crossley, K. B. Ozanyan, and H. McCann, “Toward in-cylinder absorption tomography in a production engine,” Appl. Opt . |

10. | P. Wright, N. Terzija, J. L. Davidson, S. Garcia-Castillo, C. Garcia-Stewart, S. Pegrum, S. Colbourne, P. Turner, S. D. Crossley, T. Litt, S. Murray, K. B. Ozanyan, and H. McCann, “High-speed chemical species tomography in a multi-cylinder automotive engine,” Chem. Eng. J. in press . |

11. | K. Salem, E. Tsotsas, and D. Mewes, “Tomographic measurement of breakthrough in a packed bed adsorber,” Chem. Eng. Sci . |

12. | T. Kraetschmer, D. Dagel, and S. T. Sanders, “Simple multiwavelength time-division multiplexed light source for sensing applications,” Opt. Lett . |

13. | W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun . |

14. | L. Ma and W. Cai, “Determination of the optimal regularization parameters in hyperspectral tomography,” Appl. Opt . |

15. | L. Ma and W. Cai, “Numerical investigation of hyperspectral tomography for simultaneous temperature and concentration imaging,” Appl. Opt . |

16. | M. P. Arroyo and R. K. Hanson, “Absorption-measurements of water-vapor concentration, temperature, and line-shape parameters using a tunable InGaAsP diode-laser,” Appl. Opt . |

17. | A. Franchois and C. Pichot, “Microwave imaging - complex permittivity reconstruction with a Levenberg-Marquardt method,” IEEE Trans. Antenn. Propag . |

18. | W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, |

19. | A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continuous-variables with the simulated annealing algorithm,” ACM Trans. Math. Softw . |

20. | L. A. Kranendonk, X. An, A. W. Caswell, R. E. Herold, S. T. Sanders, R. Huber, J. G. Fujimoto, Y. Okura, and Y. Urata, “High speed engine gas thermometry by Fourier-domain mode-locked laser absorption spectroscopy,” Opt. Express |

21. | T. Kraetschmer and S. T. Sanders, “Ultrastable Fourier domain mode locking observed in a laser sweeping 1363.8 - 1367.3 nm,” in |

22. | L. A. Kranendonk, A. W. Caswell, and S. T. Sanders, “Robust method for calculating temperature, pressure, and absorber mole fraction from broadband spectra,” Appl. Opt . |

23. | R. J. Barber, J. Tennyson, G. J. Harris, and R. N. Tolchenov, “A high-accuracy computed water line list,” Mon. Not. R. Astron. Soc . |

24. | S. Roy, P. J. Kinnius, R. P. Lucht, and J. R. Gord, “Temperature measurements in reacting flows by time-resolved femtosecond coherent anti-Stokes Raman scattering (fs-CARS) spectroscopy,” Opt. Commun . |

**OCIS Codes**

(100.6950) Image processing : Tomographic image processing

(280.1740) Remote sensing and sensors : Combustion diagnostics

**ToC Category:**

Image Processing

**History**

Original Manuscript: March 12, 2009

Revised Manuscript: April 29, 2009

Manuscript Accepted: May 3, 2009

Published: May 6, 2009

**Citation**

Lin Ma, Weiwei Cai, Andrew W. Caswell, Thilo Kraetschmer, Scott T. Sanders, Sukesh Roy, and James R. Gord, "Tomographic imaging of temperature and chemical species based on hyperspectral absorption spectroscopy," Opt. Express **17**, 8602-8613 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-10-8602

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### References

- F. Mayinger and O. Feldmann, eds., Optical Measurements: Techniques and Applications (Springer, Berlin, 2001).
- A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Gordon and Breach Publishers, The Netherlands, 1996).
- M. G. Allen, E. R. Furlong, and R. K. Hanson, "Tunable diode laser sensing and combustion control," in Applied Combustion Diagnostics, K. Kohse-Hoinghaus, and J. B. Jeffries, eds., (Taylor & Francis, New York, 2002), Chap. 18.
- M. Ravichandran and F. C. Gouldin, "Retrieval of asymmetric temperature and concentration profiles from a limited number of absorption-measurements," Combust. Sci. Technol. 60(1), 231-248 (1988). [CrossRef]
- H. M. Hertz, "Experimental-determination of 2-D flame temperature-fields by interferometric tomography," Opt. Commun. 54(3), 131-136 (1985). [CrossRef]
- K. B. Chung, F. C. Gouldin, and G. J. Wolga, "Experimental reconstruction of the spatial density distribution of a nonreacting flow with a small number of absorption measurements," Appl. Opt. 34(24), 5492-5500 (1995). [CrossRef]
- B. Gillet, Y. Hardalupas, C. Kavounides, and A. M. K. P. Taylor, "Infrared absorption for measurement of hydrocarbon concentration in fuel/air mixtures (MAST-B-LIQUID)," Appl. Therm. Eng. 24(11-12), 1633-1653 (2004). [CrossRef]
- S. J. Carey, H. McCann, F. P. Hindle, K. B. Ozanyan, D. E. Winterbone, and E. Clough, "Chemical species tomography by near infra-red absorption," Chem. Eng. J. 77(1-2), 111-118 (2000). [CrossRef]
- P. Wright, C. A. Garcia-Stewart, S. J. Carey, F. P. Hindle, S. H. Pegrum, S. M. Colbourne, P. J. Turner, W. J. Hurr, T. J. Litt, S. C. Murray, S. D. Crossley, K. B. Ozanyan, and H. McCann, "Toward in-cylinder absorption tomography in a production engine," Appl. Opt. 44(31), 6578-6592 (2005). [CrossRef] [PubMed]
- P. Wright, N. Terzija, J. L. Davidson, S. Garcia-Castillo, C. Garcia-Stewart, S. Pegrum, S. Colbourne, P. Turner, S. D. Crossley, T. Litt, S. Murray, K. B. Ozanyan, and H. McCann, "High-speed chemical species tomography in a multi-cylinder automotive engine," Chem. Eng. J.in press.
- K. Salem, E. Tsotsas, and D. Mewes, "Tomographic measurement of breakthrough in a packed bed adsorber," Chem. Eng. Sci. 60(2), 517-522 (2005). [CrossRef]
- T. Kraetschmer, D. Dagel, and S. T. Sanders, "Simple multiwavelength time-division multiplexed light source for sensing applications," Opt. Lett. 33(7), 738-740 (2008). [CrossRef] [PubMed]
- W. Cai, D. J. Ewing, and L. Ma, "Application of simulated annealing for multispectral tomography," Comput. Phys. Commun. 179(4), 250-255 (2008). [CrossRef]
- L. Ma, and W. Cai, "Determination of the optimal regularization parameters in hyperspectral tomography," Appl. Opt. 47(23), 4186-4192 (2008). [CrossRef] [PubMed]
- L. Ma, and W. Cai, "Numerical investigation of hyperspectral tomography for simultaneous temperature and concentration imaging," Appl. Opt. 47(21), 3751-3759 (2008). [CrossRef] [PubMed]
- M. P. Arroyo, and R. K. Hanson, "Absorption-measurements of water-vapor concentration, temperature, and line-shape parameters using a tunable InGaAsP diode-laser," Appl. Opt. 32(30), 6104-6116 (1993). [CrossRef] [PubMed]
- A. Franchois, and C. Pichot, "Microwave imaging - complex permittivity reconstruction with a Levenberg-Marquardt method," IEEE Trans. Antenn. Propag. 45(2), 203-215 (1997). [CrossRef]
- W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in FORTRAN: The Art of Scientific Computing (Cambridge University Press, New York, USA, 1992).
- A. Corana, M. Marchesi, C. Martini, and S. Ridella, "Minimizing multimodal functions of continuous-variables with the simulated annealing algorithm," ACM Trans. Math. Softw. 13(3), 262-280 (1987). [CrossRef]
- L. A. Kranendonk, X. An, A. W. Caswell, R. E. Herold, S. T. Sanders, R. Huber, J. G. Fujimoto, Y. Okura, and Y. Urata, "High speed engine gas thermometry by Fourier-domain mode-locked laser absorption spectroscopy," Opt. Express 15(23), 15115-15128 (2007). [CrossRef] [PubMed]
- T. Kraetschmer, and S. T. Sanders, "Ultrastable Fourier domain mode locking observed in a laser sweeping 1363.8 - 1367.3 nm," in Conference on Lasers and Electro-Optics (CLEO), submitted (Baltimore, 2009).
- L. A. Kranendonk, A. W. Caswell, and S. T. Sanders, "Robust method for calculating temperature, pressure, and absorber mole fraction from broadband spectra," Appl. Opt. 46(19), 4117-4124 (2007). [CrossRef] [PubMed]
- R. J. Barber, J. Tennyson, G. J. Harris, and R. N. Tolchenov, "A high-accuracy computed water line list," Mon. Not. R. Astron. Soc. 368(3), 1087-1094 (2006). [CrossRef]
- S. Roy, P. J. Kinnius, R. P. Lucht, and J. R. Gord, "Temperature measurements in reacting flows by time-resolved femtosecond coherent anti-Stokes Raman scattering (fs-CARS) spectroscopy," Opt. Commun. 281(2), 319-325 (2008). [CrossRef]

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