Hyperspectral tomography based on proper orthogonal decomposition as motivated by imaging diagnostics of unsteady reactive flows.

A series of previous studies, both numerical and experimental, have demonstrated the advantages of hyperspectral tomography (HT) as a promising technique to measure the two-dimensional distributions of temperature and species concentration in reacting flows. This paper intends to prepare the mathematical groundwork for extended use of the HT technique for three-dimensional and/or time-correlated measurements. Direct application of the methods developed previously encounters both experimental and computational difficulties. Numerical studies reported in this paper suggest that the use of proper orthogonal decomposition (POD) is effective to overcome these difficulties. The use of POD in HT significantly reduces the computational cost, enhances the fidelity of the tomographic reconstructions, and improves the stability of the reconstruction in the presence of measurement noise. Implications of these results for practical applications are also discussed.

[1]  Michael Lindenbaum,et al.  Sequential Karhunen-Loeve basis extraction and its application to images , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[2]  C. Kaminski,et al.  Characterisation of a spark ignition system by planar laser-induced fluorescence of OH at high repetition rates and comparison with chemical kinetic calculations , 2000 .

[3]  Stephen J Carey,et al.  Toward in-cylinder absorption tomography in a production engine. , 2005, Applied optics.

[4]  J. Fujimoto,et al.  High speed engine gas thermometry by Fourier-domain mode-locked laser absorption spectroscopy. , 2007, Optics express.

[5]  Lin Ma,et al.  Determination of the optimal regularization parameters in hyperspectral tomography. , 2008, Applied optics.

[6]  Sandro Ridella,et al.  Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithmCorrigenda for this article is available here , 1987, TOMS.

[7]  D. Dagel,et al.  Simple multiwavelength time-division multiplexed light source for sensing applications. , 2008, Optics letters.

[8]  Lin Ma,et al.  Application of simulated annealing for multispectral tomography , 2008, Comput. Phys. Commun..

[9]  Lin Ma,et al.  Tomographic imaging of temperature and chemical species based on hyperspectral absorption spectroscopy. , 2009, Optics express.

[10]  Weiwei Cai,et al.  Numerical investigation of hyperspectral tomography for simultaneous temperature and concentration imaging. , 2008, Applied optics.

[11]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[12]  A. Chatterjee.  An introduction to the proper orthogonal decomposition , 2000 .

[13]  M. Ravichandran,et al.  Retrieval of asymmetric temperature and concentration profiles from a limited number of absorption measurements , 1988 .