Tomographic laser absorption spectroscopy using Tikhonov regularization

The application of tunable diode laser absorption spectroscopy (TDLAS) to flames with non-homogeneous temperature and concentration fields is an area where only few studies exist. Experimental work explores the performance of tomographic reconstructions of concentration and temperature profiles from wavelength-modulated TDLAS measurements within the plume of an axisymmetric McKenna burner. Water vapor transitions at 1391.67 nm and 1442.67 nm are probed using calibration free wavelength modulation spectroscopy with second harmonic detection (WMS-2f). A single collimated laser beam is swept parallel to the burner surface, where scans yield pairs of line-of-sight (LOS) data at multiple radial locations. Radial profiles of absorption data are reconstructed using Tikhonov regularized Abel inversion, which suppresses the amplification of experimental noise that is typically observed for reconstructions with high spatial resolution. Based on spectral data, temperatures and concentrations are calculated point-by-point. Here, a least-squares approach addresses difficulties due to modulation depths that cannot be universally optimized due to a non-uniform domain. Experimental results show successful reconstructions of temperature and concentration profiles based on two-transition, non-optimally modulated WMS-2f and Tikhonov regularized Abel inversion, and thus validate the technique as a viable diagnostic tool for flame measurements.Comment: This paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://dx.doi.org/10.1364/AO.53.008095. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under la

Sequential and Parallel Algorithms for Mixed Packing and Covering

Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set cover, bin-packing, knapsack, scheduling problems, minimum-weight triangulation, etc. This paper gives approximation algorithms for the general class of problems. The sequential algorithm is a simple greedy algorithm that can be implemented to find an epsilon-approximate solution in O(epsilon^-2 log m) linear-time iterations. The parallel algorithm does comparable work but finishes in polylogarithmic time. The results generalize previous work on pure packing and covering (the special case when the constraints are all "less-than" or all "greater-than") by Michael Luby and Noam Nisan (1993) and Naveen Garg and Jochen Konemann (1998)

Efficient and Stable Acoustic Tomography Using Sparse Reconstruction Methods

We study an acoustic tomography problem and propose a new inversion technique based on sparsity. Acoustic tomography observes the parameters of the medium that influence the speed of sound propagation. In the human body, the parameters that mostly influence the sound speed are temperature and density, in the ocean - temperature and current, in the atmosphere - temperature and wind. In this study, we focus on estimating temperature in the atmosphere using the information on the average sound speed along the propagation path. The latter is practically obtained from travel time measurements. We propose a reconstruction algorithm that exploits the concept of sparsity. Namely, the temperature is assumed to be a linear combination of some functions (e.g. bases or set of different bases) where many of the coefficients are known to be zero. The goal is to find the non-zero coefficients. To this end, we apply an algorithm based on linear programming that under some constrains finds the solution with minimum l0 norm. This is actually equivalent to the fact that many of the unknown coefficients are zeros. Finally, we perform numerical simulations to assess the effectiveness of our approach. The simulation results confirm the applicability of the method and demonstrate high reconstruction quality and robustness to noise

Noise Robustness of a Combined Phase Retrieval and Reconstruction Method for Phase-Contrast Tomography

Classical reconstruction methods for phase-contrast tomography consist of two stages: phase retrieval and tomographic reconstruction. A novel algebraic method combining the two was suggested by Kostenko et al. (Opt. Express, 21, 12185, 2013) and preliminary results demonstrating improved reconstruction compared to a two-stage method given. Using simulated free-space propagation experiments with a single sample-detector distance, we thoroughly compare the novel method with the two-stage method to address limitations of the preliminary results. We demonstrate that the novel method is substantially more robust towards noise; our simulations point to a possible reduction in counting times by an order of magnitude