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Development of a fan-beam TDLAS-based tomographic sensor for rapid imaging of temperature and gas concentration

Chang Liu, Lijun Xu, Jianliang Chen, Zhang Cao, Yuzhen Lin, and Weiwei Cai

Open Access Open Access

Abstract

This work aims to develop a fan-beam tomographic sensor using tunable diode lasers that can simultaneously image temperature and gas concentration with both high spatial and temporal resolutions. The sensor features three key advantages. First, the sensor bases on a stationary fan-beam arrangement, by which a high spatial resolution is guaranteed because the distance between two neighboring detectors in a view is approximately reduced to the size of a photodiode. Second, fan-beam illumination from five views is simultaneously generated instead of rotating either the fanned beams or the target, which significantly enhances the temporal resolution. Third, a novel set of optics with the combination of anamorphic prism pair and cylindrical lens is designed, which greatly improves the uniformity of the planar beams, and hence improves the reconstruction fidelity. This paper reports the tomographic model, optics design, numerical simulation and experimental validation of the sensor. The sensor exhibits good applicability for flame monitoring and combustion diagnosis.

© 2015 Optical Society of America

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Figures (16)
Fig. 1
Fig. 1 Definitions of the coordinate system and the discretization configuration.

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Fig. 2
Fig. 2 Schematic of the fan-beam generator. Panel (a): the optics design. Panel (b): the circular and elliptical beam at location 1 and 2 in Panel (a). Panel (c): uniformity of the fan-shaped planar illumination obtained with and without the use of the anamorphic prism pair (APP).

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Fig. 3
Fig. 3 (a) Schematic and (b) layout of the five-view stationary fan-beam TDLAS-based tomographic sensor.

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Fig. 4
Fig. 4 Qualification of the spatial resolution of the tomographic image. Panel (a): expected distribution of H2O concentration with a rectangular sharp-edged feature. Panel (b): the reconstructed distribution of H2O concentration and two sampled tracks to calculate the spatial resolution. Panel (c): edge spread functions and corresponding spatial resolution in the two sampled tracks.

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Fig. 5
Fig. 5 Phantoms of asymmetric distributions of (a) temperature and (b) H2O concentration in the simulation.

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Fig. 6
Fig. 6 Reconstructed distributions of (a) temperature and (b) H2O concentration with noise-free projections in the simulation.

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Fig. 7
Fig. 7 Dependence of cT and cX on the number of grids with the designed tomographic sensor.

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Fig. 8
Fig. 8 Reconstructed temperature distributions with noise-free projections when the number of grids equals (a) 124, (b) 332 and (c) 560, respectively.

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Fig. 9
Fig. 9 Evaluation of the accuracy and robustness of the fan-beam TDLAS-based tomography sensor at different noise levels.

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Fig. 10
Fig. 10 Reconstructed distributions of (a) temperature and (b) H2O concentration with 5% random noise adding on the noise-free projections in the simulation.

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Fig. 11
Fig. 11 Flame generated by using a McKenna flat flame burner. In the experiment, the flow rates of methane, air and shrouding nitrogen were set to 1.2, 15.25 and 22.5 L/min, respectively.

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Fig. 12
Fig. 12 Reconstructed distributions of (a) temperature and (b) H2O concentration at the height of 3 cm above the burner plug when the equivalence was set to 0.749.

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Fig. 13
Fig. 13 Sampled TDLAS data obtained by a photodiode in room air and in the premixed flame for transitions at (a) v 1 = 7444.36 cm−1 and (b) v 2 = 7185.6 cm−1, respectively.

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Fig. 14
Fig. 14 Experimental setup and tomographic results by putting a cube on the center of the burner plug. Panel (a) and Panel (b) show the schematic diagram and photo of the experimental setup, respectively. Panel (c) and Panel (d) show the reconstructed distributions of temperature and H2O concentrations, respectively.

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Fig. 15
Fig. 15 Experimental setup and tomographic results by putting a cube on one side of the burner plug. Panel (a) and Panel (b) show the schematic diagram and photo of the experimental setup, respectively. Panel (c) and Panel (d) show the reconstructed distributions of temperature and H2O concentrations, respectively.

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Fig. 16
Fig. 16 Experimental setup and tomographic results by putting two cubes on the burner plug. Panel (a) and Panel (b) show the schematic diagram and photo of the experimental setup, respectively. Panel (c) and Panel (d) show the reconstructed distributions of temperature and H2O concentrations, respectively.

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Tables (3)

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Table 1 Dependence of cT on the number of views, noted as N v, and the number of laser beams in each view, noted as N l.

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Table 2 Dependence of cX on the number of views, noted as N v, and the number of laser beams in each view, noted as N l.

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Table 3 List of values of cT and convergence time of the modified Landweber algorithm, ART and SMART, respectively.

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Equations (15)

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α v = ∫ 0 L P ( x ) X ( x ) S [ T ( x ) ] ϕ d l ,
S ( T ) = S ( T 0 ) Q ( T 0 ) Q ( T ) ( T 0 T ) exp [ − h c E ' ' k ( 1 T − 1 T 0 ) ] × 1 − exp ( − h c v 0 / k T ) 1 − exp ( − h c v 0 / k T 0 ) ,
A v = ∫ − ∞ ∞ α v d v = ∫ 0 L P ( x ) X a b s ( x ) S [ T ( x ) ] d l .
A v , i = ∑ j = 1 N a v , j L i j = ∑ j = 1 N [ P S ( T ) X ] v , j L i j ,
L a v = A v ,
L = [ L 11 L 12 ⋯ L 1 N L 21 L 22 ⋯ L 2 N ⋮ ⋮ ⋱ ⋮ L M 1 L M 2 ⋯ L M N ] ,
a v k + 1 = a v k + λ k L T ( A v − L a v k ) ,
Δ = ∑ j = 1 N | a v , j k + 1 − a v , j k | / ∑ j = 1 N ( a v , j k ) .
R j = a v 1 , j a v 2 , j = S 1 ( T j ) S 2 ( T j ) = S 1 ( T 0 ) S 2 ( T 0 ) exp [ − h c ( E 1 '' − E 2 ' ' ) k ( 1 T j − 1 T 0 ) ] .
T j = h c k ( E 2 ' ' − E 1 ' ' ) / [ ln a v 1 , j a v 2 , j + ln S 2 ( T 0 ) S 1 ( T 0 ) + h c k ( E 2 ' ' − E 1 ' ' ) T 0 ] .
X j = a v 1 , j / S 1 ( T j ) .
c T = ∑ j = 1 N p ( | T j r e c − T j e x p | / T j e x p ) / N p ,
c X = ∑ j = 1 N p ( | X j r e c − X j e x p | / X j e x p ) / N p ,
e T = ∑ j = 1 N ( | T j r e c − T j M _ r e c | / T j M _ r e c ) / N ,
e X = ∑ j = 1 N ( | X j r e c − X j M _ r e c | / X j M _ r e c ) / N ,
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