Laser-absorption tomography beam arrangement optimization using resolution matrices

doi:10.1364/AO.51.007059

Laser-absorption tomography beam arrangement optimization using resolution matrices

Matthew G. Twynstra and Kyle J. Daun »View Author Affiliations

Applied Optics, Vol. 51, Issue 29, pp. 7059-7068 (2012)
http://dx.doi.org/10.1364/AO.51.007059

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Abstract

Laser-absorption tomography experiments infer the concentration distribution of a gas species from the attenuation of lasers transecting the flow field. Although reconstruction accuracy strongly depends on the layout of optical components, to date experimentalists have had no way to predict the performance of a given beam arrangement. This paper shows how the mathematical properties of the coefficient matrix are related to the information content of the attenuation data, which, in turn, forms a basis for a beam-arrangement design algorithm that minimizes the reliance on additional assumed information about the concentration distribution. When applied to a simulated laser-absorption tomography experiment, optimized beam arrangements are shown to produce more accurate reconstructions compared to other beam arrangements presented in the literature.

OCIS Codes
(110.6960) Imaging systems : Tomography
(120.1740) Instrumentation, measurement, and metrology : Combustion diagnostics
(220.4830) Optical design and fabrication : Systems design
(280.2490) Remote sensing and sensors : Flow diagnostics
(300.6360) Spectroscopy : Spectroscopy, laser
(110.6955) Imaging systems : Tomographic imaging

ToC Category:
Spectroscopy

History
Original Manuscript: June 6, 2012
Manuscript Accepted: August 27, 2012
Published: October 9, 2012

Virtual Issues
October 26, 2012 Spotlight on Optics

Citation
Matthew G. Twynstra and Kyle J. Daun, "Laser-absorption tomography beam arrangement optimization using resolution matrices," Appl. Opt. 51, 7059-7068 (2012)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-51-29-7059

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References

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P. Wright, N. Terzija, J. L. Davidson, S. Garcia-Castillo, C. A. Garcia-Stewart, S. H. Pegrum, S. M. Colbourne, P. J. Turner, S. D. Crossley, T. J. Litt, S. C. Muray, K. B. Ozanya, and H. McCann, “High-speed chemical species tomography in a multi-cylinder automotive engine,” Chemical Engineering J. 158, 2–10 (2010). [CrossRef]
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S. Pal, K. B. Ozanyan, and H. McCann, “A computational study of tomographic measurement of carbon monoxide at minor concentrations,” Meas. Sci. Technol. 19, 094018 (2008). [CrossRef]
D. Verhoeven, “Limited-data computed tomography algorithms for the physical sciences,” Appl. Opt. 32, 3736–3754 (1993). [CrossRef]
S. Ibrahim, R. G. Green, K. Dutton, K. Evans, R. Abdul Rahim, and A. Goude, “Optical sensor configurations for process tomography,” Meas. Sci. Technol. 10, 1079–1086 (1999). [CrossRef]
W. Menke, Geophysical Data Analysis: Discrete Inverse Theory (Academic, 1989), pp. 51–65.
M. F. Modest, Radiative Heat Transfer (Academic, 2003), pp. 289–291.
L. S. Rothman, I. E. Gordon, A. Barbe, D. C. Benner, P. F. Bernath, M. Birk, V. Boudon, L. R. Brown, A. Campargue, J.-P. Champion, K. Chance, L. H. Coudert, V. Dana, V. M. Devi, S. Fally, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner, N. Lacome, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, S. N. Mikhailenko, C. E. Miller, N. Moazzen-Ahmadi, O. V. Naumenko, A. V. Nitikin, J. Orphal, V. I. Perevalov, A. Perrin, A. Predoi-Cross, C. P. Rinsland, M. Rotger, M. Šimečková, M. A. H. Smith, K. Sung, S. A. Tashkun, J. Tennyson, R. A. Toth, A. C. Vandaele, and J. Vander Auwera, “The HITRAN 2008 Molecular Spectroscopic Database,” J. Quant. Spectrosc. Radiat. Transfer 110, 533–572 (2009). [CrossRef]
A. E. Klingbeil, J. B. Jeffries, and R. K. Hanson, “Temperature- and pressure-dependent absorption cross sections of gaseous hydrocarbons at 3.39 μm,” Meas. Sci. Technol. 17, 1950–1957 (2006). [CrossRef]
L. Ma, W. Cai, A. W. Caswell, T. Kraetschmer, S. T. Sanders, S. Roy, and J. R. Gord, “Tomographic imaging of temperature and chemical species based on hyperspectral absorption spectroscopy,” Opt. Express 17, 8602–8613 (2009). [CrossRef]
P. C. Hansen, Rank-Deficient and Discrete Ill-posed Problems (Siam, 1998), pp. 99–105.
C. A. Garcia-Stewart, N. Polydorides, K. B. Ozanyan, and H. McCann, “Image reconstruction algorithms for high-speed chemical species tomography,” in Proceedings of 3rd World Conference on Industrial Process Tomography (Virtual Centre for Industrial and Process Tomography, 2003), pp. 80–85.
N. Terzija and H. McCann, “Wavelet-based image reconstruction for hard-field tomography with severely limited data,” IEEE Sens. 11, 1885–1893 (2011). [CrossRef]
K. Salem, E. Tsotsas, and D. Mewes, “Tomographic measurement of breakthrough in a packed bed absorber,” Chem. Eng. Sci. 60, 517–522 (2005). [CrossRef]
R. Zdunek, “Multigrid regularized image reconstruction for limited-data tomography,” Comp. Meth. Sci. Tech. 13, 67–77 (2007).
K. J. Daun, S. L. Waslander, and B. B. Tulloch, “Infrared species tomography of a transient flow field using Kalman filtering,” Appl. Opt. 50, 891–900 (2011). [CrossRef]
M. Bertero and P. Boccacci, Inverse Problems in Imaging(Institute of Physics Publishing, 1998), pp. 200.
J. M. Lees and R. S. Crosson, “Bayesian ART versus conjugate gradient methods in tomographic seismic imaging: an application at Mount St. Helens, Washington,” in Spatial Statistics and Imaging, A. Possolo, ed. (Institute of Mathematical Statistics, 1991), pp. 186–208.
R. S. Crosson, “Crustal structure modeling of earthquake data 1. Simultaneous least squares estimation of hypocenter and velocity measurements,” J. Geophys. Res. 81, 3036–3046 (1976). [CrossRef]
R. A. Wiggins, “The general linear inverse problem: implication of surface waves and free oscillations for earth structure,” Rev. Geophys. Space Phys. 10, 251–285 (1972). [CrossRef]
J. K. MacCarthy, B. Borchers, and R. C. Aster, “Efficient stochastic estimation of the model resolution matrix diagonal and generalized cross-validation for large geophysical inverse problems,” J. Geophys. Res. 116, B10304 (2011). [CrossRef]
J. G. Berryman, “Tomographic resolution without singular value decomposition,” Proc. SPIE 2301, 1–13 (1994). [CrossRef]
W. Annicchiarico, J. Périaux, M. Cerrolaza, and G. Winter, Evolutionary Algorithms and Intelligent Tools for Engineering Optimization (WIT, 2005).

Abdul Rahim, R.
Annicchiarico, W.
Aster, R. C.
Barbe, A.
Benner, D. C.
Bernath, P. F.
Berryman, J. G.
Bertero, M.
Birk, M.
Boccacci, P.
Borchers, B.
Boudon, V.
Brown, L. R.
Cai, W.
Campargue, A.
Carey, J. S.
Caswell, A. W.
Cerrolaza, M.
Champion, J.-P.
Chance, K.
Colbourne, S. M.
Coudert, L. H.
Crossley, S. D.
Crosson, R. S.
Dana, V.
Daun, K. J.
Davidson, J. L.
Devi, V. M.
Dutton, K.
Evans, K.
Fally, S.
Flaud, J.-M.
Gamache, R. R.
Garcia-Castillo, S.
Garcia-Stewart, C. A.
Garcia-Stuart, C. A.
Gibbs, B. M.
Goldman, A.
Gord, J. R.
Gordon, I. E.
Goude, A.
Green, R. G.
Hansen, P. C.
Hanson, R. K.
Hindle, F. P.
Hurr, W. J.
Ibrahim, S.
Irfan, N.
Jacquemart, D.
Javed, M. T.
Jeffries, J. B.
Kirby, B. J.
Kleiner, I.
Klingbeil, A. E.
Kraetschmer, T.
Lacome, N.
Lafferty, W. J.
Lees, J. M.
Litt, T. J.
Ma, L.
MacCarthy, J. K.
Mandin, J.-Y.
Massie, S. T.
McCann, H.
Menke, W.
Mewes, D.
Mikhailenko, S. N.
Miller, C. E.
Moazzen-Ahmadi, N.
Modest, M. F.
Muray, S. C.
Naumenko, O. V.
Nitikin, A. V.
Orphal, J.
Ozanya, K. B.
Ozanyan, K. B.
Pal, S.
Pegrum, S. H.
Perevalov, V. I.
Pergrum, S.
Périaux, J.
Perrin, A.
Polydorides, N.
Predoi-Cross, A.
Rinsland, C. P.
Rotger, M.
Rothman, L. S.
Roy, S.
Salem, K.
Sanders, S. T.
Šimecková, M.
Smith, M. A. H.
Sung, K.
Tashkun, S. A.
Tennyson, J.
Terzija, N.
Toth, R. A.
Tsotsas, E.
Tulloch, B. B.
Turner, P. J.
Vandaele, A. C.
Vander Auwera, J.
Verhoeven, D.
Waslander, S. L.
Wiggins, R. A.
Winter, G.
Wright, P.
Zdunek, R.

Appl. Opt.

Appl. Phys. B

B. J. Kirby and R. K. Hanson, “Planar laser-induced fluorescence imaging of carbon monoxide using vibrational (infrared) transitions,” Appl. Phys. B 69, 505–507 (1999). [CrossRef]

Chem. Eng. Sci.

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

Chemical Engineering J.

P. Wright, N. Terzija, J. L. Davidson, S. Garcia-Castillo, C. A. Garcia-Stewart, S. H. Pegrum, S. M. Colbourne, P. J. Turner, S. D. Crossley, T. J. Litt, S. C. Muray, K. B. Ozanya, and H. McCann, “High-speed chemical species tomography in a multi-cylinder automotive engine,” Chemical Engineering J. 158, 2–10 (2010). [CrossRef]

Comp. Meth. Sci. Tech.

R. Zdunek, “Multigrid regularized image reconstruction for limited-data tomography,” Comp. Meth. Sci. Tech. 13, 67–77 (2007).

IEEE Sens.

N. Terzija and H. McCann, “Wavelet-based image reconstruction for hard-field tomography with severely limited data,” IEEE Sens. 11, 1885–1893 (2011). [CrossRef]

J. Environ. Manag.

M. T. Javed, N. Irfan, and B. M. Gibbs, “Control of combustion-generated nitrogen oxides by selective non-catalytic reduction,” J. Environ. Manag. 83, 251–289 (2007). [CrossRef]

J. Geophys. Res.

J. K. MacCarthy, B. Borchers, and R. C. Aster, “Efficient stochastic estimation of the model resolution matrix diagonal and generalized cross-validation for large geophysical inverse problems,” J. Geophys. Res. 116, B10304 (2011). [CrossRef]
R. S. Crosson, “Crustal structure modeling of earthquake data 1. Simultaneous least squares estimation of hypocenter and velocity measurements,” J. Geophys. Res. 81, 3036–3046 (1976). [CrossRef]

J. Quant. Spectrosc. Radiat. Tranfer

K. J. Daun, “Infrared species limited data tomography through Tikhonov regularization,” J. Quant. Spectrosc. Radiat. Tranfer 111, 105–115 (2010). [CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

L. S. Rothman, I. E. Gordon, A. Barbe, D. C. Benner, P. F. Bernath, M. Birk, V. Boudon, L. R. Brown, A. Campargue, J.-P. Champion, K. Chance, L. H. Coudert, V. Dana, V. M. Devi, S. Fally, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner, N. Lacome, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, S. N. Mikhailenko, C. E. Miller, N. Moazzen-Ahmadi, O. V. Naumenko, A. V. Nitikin, J. Orphal, V. I. Perevalov, A. Perrin, A. Predoi-Cross, C. P. Rinsland, M. Rotger, M. Šimečková, M. A. H. Smith, K. Sung, S. A. Tashkun, J. Tennyson, R. A. Toth, A. C. Vandaele, and J. Vander Auwera, “The HITRAN 2008 Molecular Spectroscopic Database,” J. Quant. Spectrosc. Radiat. Transfer 110, 533–572 (2009). [CrossRef]

Meas. Sci. Technol.

A. E. Klingbeil, J. B. Jeffries, and R. K. Hanson, “Temperature- and pressure-dependent absorption cross sections of gaseous hydrocarbons at 3.39 μm,” Meas. Sci. Technol. 17, 1950–1957 (2006). [CrossRef]
N. Terzija, J. L. Davidson, C. A. Garcia-Stuart, P. Wright, K. B. Ozanyan, S. Pergrum, T. J. Litt, and H. McCann, “Image optimization for chemical species tomography with an irregular and sparse beam array,” Meas. Sci. Technol. 19, 094007 (2008). [CrossRef]
S. Pal, K. B. Ozanyan, and H. McCann, “A computational study of tomographic measurement of carbon monoxide at minor concentrations,” Meas. Sci. Technol. 19, 094018 (2008). [CrossRef]
S. Ibrahim, R. G. Green, K. Dutton, K. Evans, R. Abdul Rahim, and A. Goude, “Optical sensor configurations for process tomography,” Meas. Sci. Technol. 10, 1079–1086 (1999). [CrossRef]

Opt. Express

L. Ma, W. Cai, A. W. Caswell, T. Kraetschmer, S. T. Sanders, S. Roy, and J. R. Gord, “Tomographic imaging of temperature and chemical species based on hyperspectral absorption spectroscopy,” Opt. Express 17, 8602–8613 (2009). [CrossRef]

Proc. SPIE

J. G. Berryman, “Tomographic resolution without singular value decomposition,” Proc. SPIE 2301, 1–13 (1994). [CrossRef]

Rev. Geophys. Space Phys.

R. A. Wiggins, “The general linear inverse problem: implication of surface waves and free oscillations for earth structure,” Rev. Geophys. Space Phys. 10, 251–285 (1972). [CrossRef]

Other

M. Bertero and P. Boccacci, Inverse Problems in Imaging(Institute of Physics Publishing, 1998), pp. 200.
J. M. Lees and R. S. Crosson, “Bayesian ART versus conjugate gradient methods in tomographic seismic imaging: an application at Mount St. Helens, Washington,” in Spatial Statistics and Imaging, A. Possolo, ed. (Institute of Mathematical Statistics, 1991), pp. 186–208.
W. Annicchiarico, J. Périaux, M. Cerrolaza, and G. Winter, Evolutionary Algorithms and Intelligent Tools for Engineering Optimization (WIT, 2005).
P. C. Hansen, Rank-Deficient and Discrete Ill-posed Problems (Siam, 1998), pp. 99–105.
C. A. Garcia-Stewart, N. Polydorides, K. B. Ozanyan, and H. McCann, “Image reconstruction algorithms for high-speed chemical species tomography,” in Proceedings of 3rd World Conference on Industrial Process Tomography (Virtual Centre for Industrial and Process Tomography, 2003), pp. 80–85.
W. Menke, Geophysical Data Analysis: Discrete Inverse Theory (Academic, 1989), pp. 51–65.
M. F. Modest, Radiative Heat Transfer (Academic, 2003), pp. 289–291.

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