Jongmook Lim and Yudaya Sivathanu

En’Urga, Inc., West Lafayette, Indiana

Douglas Feikema

Glenn Research Center, Cleveland, Ohio

Fan Beam Emission Tomography for Estimating

Scalar Properties in Laminar Flames

NASA/TM—2003-212302

April 2003

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Jongmook Lim and Yudaya Sivathanu

En’Urga, Inc., West Lafayette, Indiana

Douglas Feikema

Glenn Research Center, Cleveland, Ohio

Fan Beam Emission Tomography for Estimating

Scalar Properties in Laminar Flames

NASA/TM—2003-212302

April 2003

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

Third Joint Meeting of the U.S. Sections of the Combustion Institute

sponsored by The Combustion Institute

Chicago, Illinois, March 16–19, 2003
Acknowledgments

This research was sponsored by the NASA contract number NAS3–01085 from NASA’s Microgravity Combustion

Program with Dr. Douglas Feikema as Technical Monitor.

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Available electronically at http://gltrs.grc.nasa.gov
FAN BEAM EMISSION TOMOGRAPHY FOR ESTIMATING SCALAR PROPERTIES IN 

LAMINAR FLAMES 

Jongmook Lim* and Yudaya Sivathanu 

En’Urga, Inc. 

West Lafayette IN 47906 

Douglas Feikema 

NASA Glenn Research Center 

21000 Brook Park Road 

Cleveland, OH 44135 

Abstract 

A new method of estimating temperatures and gas species concentrations (CO2 and H2O) in a laminar flame is 

reported. The path-integrated, spectral radiation intensities emitted from a laminar flame at multiple wavelengths and 

view angles are calculated using a narrow band radiation model. Synthetic data, in the form of radial profiles of 

temperature and gas concentrations, are used in these calculations. The calculations mimic measurements that would 

theoretically be obtained using a mid-infrared spectrometer with a scanner. The path–integrated spectral radiation 

intensities are deconvoluted using a maximum likelihood estimation method in conjunction with an iterative scheme. 

The deconvolution algorithm accounts for the self-absorption of radiation by the intervening gases, and provides the 

local temperature and gas species concentrations. The deconvoluted temperatures and gas concentrations are compared 

with the synthetic data used for calculating the spectral radiation intensities. The deconvoluted temperatures and gas 

species concentrations are within 0.5 % of the synthetic data. The deconvolution algorithm is expected to provide 

combustion researchers with an easy method of obtaining the radial profiles of major gas species concentrations and 

temperatures in laminar flames non-intrusively using a mid-infrared spectrometer with a scanner. 

 

* Corresponding author: jongmook@enurga.com 

Associated Web site: http://www.enurga.com 

Proceedings of the Third Joint Meeting of the U.S. Sections of The Combustion Institute 

Introduction 

 Obtaining information on the instantaneous 

structure of turbulent and transient flames is important in 

a wide variety of applications such as fire safety, pollution 

reduction, flame spread studies, and model validation. 

Durao et al. (1992) has reviewed the different methods of 

obtaining structure information in reacting flows. These 

include Tunable Laser Absorption Spectroscopy (Hanson 

et al., 1980), Laser Induced Fluorescence (Crosley and 

Smith, 1983), Coherent Anti-Raman Spectroscopy 

(Eckbreth et al., 1979), and Fourier Transform Infrared 

Spectroscopy (Best et al., 1991), Laser Induced 

Incandescence (Dasch, 1984), and Emission Spectroscopy 

(Sivathanu and Gore, 1991) to mention a few. 

 LIF and CARS can be used to measure 

temperatures and species concentrations with much higher 

spatial resolution than either absorption or emission 

spectroscopy (Durao et al., 1992). However, the accuracy 

of these two techniques in the presence of interference 

from soot radiation is an unknown factor. These 

techniques in addition require very expensive and bulky 

lasers, detectors and signal processing equipment. 

Therefore, they may not be suitable in drop tower or 

micro-gravity experiments, due to power, volume, and 

mass restrictions. LIF and CARS are ideally suited to 

measure concentrations of minor species and radicals, but 

for temperature and major gas species concentration 

measurements, absorption or emission spectroscopy is the 

more accurate and feasible technique. 

 Absorption spectroscopy using either tunable laser 

diodes (Hanson et al., 1980) or FTIR (Best et al., 1991) 

can be used with deconvolution to obtain local gas species 

concentrations, soot volume fractions and temperatures in 

laminar flames. However, absorption spectroscopy 

requires a source, with corresponding alignment 

problems. The biggest advantage of absorption 

spectroscopy is that it can be utilized even in low 

temperature flows. In addition, absorption spectroscopy 

is relatively insensitive to temperature variations and is 

ideally suited to measure gas species concentrations 

(Zhang and Cheng, 1986). 

NASA/TM—2003-212302 1
 Most flames emit significant radiation signatures 

that are used in various applications such as fire detection 

(Sivathanu and Tseng, 1996), light-off detection (Vaidya 

et al., 1982), flame diagnostics (Choi et al., 1995), etc. 

Radiation signatures can be utilized to maximum 

advantage for determining structural information in 

turbulent flows (Sivathanu and Faeth, 1990, Sivathanu 

and Gore, 1991, Sivathanu et al., 1991). Emission 

spectroscopy does not require a light source. In addition, 

alignment and data collection are relatively 

straightforward. Emission spectroscopy is most 

advantageous in the infrared regions of the spectra, 

principally because these emission lines arise from 

transitions in the fundamental bands of stable species such 

as CO2 and H2O. Near-Infrared (NIR) and visible 

emission typically arise from transitions in the overtones 

(forbidden transitions) and are from minor species that are 

not in thermodynamic equilibrium with the flow. 

Emission spectroscopy currently offers the most accurate 

method of temperature determination (Zhu et al., 1997). 

 Near-IR emission tomography has been utilized to 

measure the distribution of soot temperature in laminar 

flames (Correia et al., 2001). The deconvolution 

algorithm was based upon the Abel transform, and selfabsorption by soot was incorporated. 

Objective 

 The objective of this work is to develop a 

tomographic algorithm to obtain local scalar properties 

such as gas temperature and mole fractions of major gas 

species from path-integrated multi-wavelength infrared 

radiation measurements. The potential errors in the 

tomographic algorithm are also quantified. 

Tomographic reconstruction algorithm 

 Tomographic reconstruction of local scalar 

properties is based on the deconvolution of a finite 

number of two-dimensional path-integrated multiwavelength radiation measurements that would typically 

be acquired by a mid-infrared spectrometer with a 

scanner. For an axisymmetrical flame, the domain of 

deconvolution is illustrated in Fig. 1. For each ring, 

Figure 1. Schematic of Fan Beam Emission Tomography. 

unique scalars (temperature, mole fraction of CO2 and 

H2O) are defined. In the Fig.1, gas temperature, mole 

fraction of CO2 and H2O are denoted as Ti, Xi1 and Xi2, 

respectively. The spectral radiation intensity emitted 

from a homogeneous path is represented as 

)1(II b λλλ τ−= (1) 

where bλ I is the Planck function (dependent on the gas 

temperature), and λτ is the spectral transmittance of the 

homogeneous path. For a given temperature and mole 

fractions of CO2 and H2O, the spectral transmittance ( λτ ) 

along the optical path can be calculated using a narrow 

band radiation model, RADCAL (Grosshandler, 1993). 

For the two representative homogeneous rings shown in 

Fig. 1, the measured path-integrated intensities are: 

)1(II b,1,1 11 λλ τ−= (2) 

[ ])1()1(II b,1,2 21212223 λλ τ−+τ⋅τ⋅τ−=

b,2 2122 λ )1(I τ⋅τ−+ . (3) 

These two path-integrated intensities are calculated at 

several mid-infrared wavelengths. The iterative 

deconvolution algorithm used to obtain the local scalars 

from the path-integrated intensities involves two steps: 

1. Calculate the local spectral radiation intensities for all 

homogeneous rings, given the value of the 

transmittances for all segments in the optical path. 

Therefore, the two unknown quantities in Eq. (2) and 

Eq. (3) are )1(I b,1 21 λ τ− and )1(I b,2 22 λ τ− , the 

local spectral intensities. The two intensities on the 

left-hand side of Eq. (2) and Eq. (3) are the measured 

or given values. This linear system of equations is 

ill-posed. The solution must be obtained through an 

optimization process. The Maximum Likelihood 

Estimation (MLE) method (Vardi and Lee, 1993) is 

best suited for this problem because of its guaranteed 

convergence and ease of implementation. In Eq. (2) 

and Eq. (3), the transmittances for all segments are 

obtained from the previous iteration. 

2. Estimate the gas temperature and mole fractions of 

CO2 and H2O from the local spectral intensities 

within each homogeneous ring. This process is 

essentially a curve fitting process to find three scalars 

using the multi-spectral radiation intensities using a 

narrow band radiation intensity database. RADCAL 

(Grosshandler, 1993) will be used in these 

calculations as the radiation intensity database. The 

estimated local temperatures and mole fractions are 

used to calculate the transmittances for all segments 

Mid-IR spectrometer

with a scanner

I

1,λ

I

2,λ

τ11

τ21

τ22

τ23

T1, X11, X12

T2, X21, X22

NASA/TM—2003-212302 2
in the domain. These transmittances are then used in 

Step 1. 

 This two-step process is repeated until convergence 

is achieved. At the first iteration, local intensities are 

found only considering emission and neglecting selfabsorption by intervening gaseous components. 

Results and Discussion 

 The performance of the inversion algorithm was 

evaluated using a synthetic dataset. The synthetic dataset 

consists of a 13 point radial profile of gas temperatures 

and mole fractions of CO2 and H2O. The radial profile is 

representative of measurements obtained in a laminar 

ethylene diffusion flame by Santoro et al. (1987). The 

major difference between the measurements (Santoro et 

al., 1987) and the synthetic data set is that soot is absent 

in synthetic data set. The path-integrated radiation 

intensities at 140 wavelengths (2.2-4.8 μm) are computed 

for 25 view angles using the RADCAL database. The 

diameter of the flame is 2 cm. 

 The path-integrated intensities at four 

representative view angles are shown in Fig. 2. These 

2.5 3.0 3.5 4.0 4.5 5.0

0

500

1000

1500

2000

2500

3000

3500

4000

D = 2 cm

Path-integrated intensity (kW/m2/sr/μm)

Wavelength (μm)

 r = -0.92 cm

 r = -0.58 cm

 r = -0.42 cm

 r = 0.0 cm

Figure 2. Path-integrated intensities at four different 

view angles calculated using RADCAL. 

four view angles pass through the radial locations that are 

identified within the figure. The spectral radiation 

intensities were calculated for 140 wavelengths. The 

radiation in the 2.3 to 3.3 μm band has contributions from 

both H2O and CO2. The radiation in the 4.3 to 4.9 μm 

band has contributions only from CO2. Only a portion of 

these two gas bands (that have relatively high radiation 

intensities as shown in Fig. 4) is used by deconvolution 

algorithm. The CO2 band from 4.1 to 4.35 μm is avoided 

because of interference by ambient CO2. 

 The temperatures and gas concentrations obtained 

from the deconvolution algorithm and the synthetic data 

are shown in Fig. 3. The lines represent the synthetic data 

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 600

800

1000

1200

1400

1600

1800

2000 D = 2 cm Line: Synthetic

Symbol: Deconvoluted

Gas temperature (K)

Radial distance (cm)

0.00

0.03

0.06

0.09

0.12

0.15

0.18

0.21

CO2

H2O

 Mole fraction

Figure 3. Synthetic and deconvoluted scalars for D= 2 cm. 

and the symbols represent the deconvoluted results. Since 

radiation intensities at 25 view angles were used in the 

deconvolution algorithm, it is possible to obtain 

temperatures and gas species concentrations for 13 rings. 

For all 13 rings, the deconvoluted scalars are within 0.1% 

of the synthetic data. In general, it is more difficult to 

obtain the scalar property at the center accurately, since 

the volume of gas emitting radiation is the lowest in the 

innermost ring. However, the results obtained are 

accurate to within 0.1%, even for the innermost ring. 

 The synthetic and deconvoluted path-integrated 

intensities, at the point of convergence, for the center of 

the flame are shown in Fig. 4. 

2.5 3.0 3.5 4.0 4.5 5.0

0

500

1000

1500

2000

2500

3000 r = 0.0 D = 2 cm

Path-integrated Intensity (kW/m/sr/μm)

Wavelength (μm)

 Synthetic

 Deconvoluted

Figure 4. Synthetic and deconvoluted path-integrated 

intensities at the center. 

 At the point of convergence, the spectral 

radiation intensities obtained from deconvolution are 

within 0.1% of those obtained from the synthetic data. 

NASA/TM—2003-212302 3
This indicates that the deconvolution algorithm provides 

scalars that can match the spectral radiation intensities 

provided by the synthetic data set very closely. 

 The diameters of laboratory scales flames are 

relatively small. Therefore, they do not provide a true test 

of the deconvolution algorithm in the presence of strong 

self-absorption. The optical thickness of industrial flames 

is typically an order of magnitude larger than that of 

laboratory flames. An increase in optical thickness 

normally results in slower convergence and decreased 

accuracy for any optical tomographic method. The 

potential degradation in the estimated scalars due to 

increased optical thickness was examined by changing the 

diameter of the flame. The deconvoluted temperature 

profiles for three flames with different diameters are 

shown in Fig. 5. 

-1.0 -0.8 -0.6 -0.4 -0.2 0.0

600

800

1000

1200

1400

1600

1800

2000

Gas temperature (K)

Normalized radial distance (r/R)

 Synthetic

 Deconvoluted, D=2 cm

 Deconvoluted, D=5 cm

 Deconvoluted, D=10 cm

Figure 5. Effects of optical thickness on estimated gas 

temperatures obtained using deconvolution. 

 For flames that are less than 5 cm in diameter, the 

deconvolution algorithm provides excellent results at all 

radial locations. When the diameter of the flame is 10 

cm, there is some error in the deconvoluted temperatures 

near the center of the flame. The primary reason for this 

degradation is that only a small portion of the radiation 

that is emitted from the center of the flame reaches the 

outer surface, resulting in a greater degree of uncertainty 

in estimating the properties at the center of the flame. 

The transmittance at 4.35 μm along the diameter for 10 

cm flame is approximately 0.2. One possible method of 

overcoming this degradation in performance could be to 

use only the portions of the band that are less absorbing. 

However, this was not investigated during this study. 

 All the results discussed so far utilized synthetic 

spectral radiation intensities. However, if these intensities 

were measured using a spectrometer, they are expected to 

have errors, both in the amplitude of the intensities and in 

the wavelengths. In order to better understand the 

sensitivity of the deconvolution algorithm to these 

measurement errors, a random noise was introduced in the 

synthetic path-integrated intensities. 

 A random 1% noise was added to the synthetic 

spectral radiation intensities, and then deconvoluted using 

the algorithm. The synthetic and deconvoluted gas 

temperatures are shown in Fig. 6. At the outer rings, the 

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 600

800

1000

1200

1400

1600

1800

2000 D = 2 cm

Gas temperature (K)

Radial distance (cm)

 Synthetic

 Deconvoluted + 1% noise

Figure 6. Sensitivity of the inversion algorithm to the 

random noise in radiation intensities. 

inversion error for the gas temperatures is less than 1 %. 

However, the inversion error increases toward the center 

of the flame. At the center of the flame, the deviation is 

about 20 %. The higher error at the center could be 

attributed to two reasons. The area of the center ring is 

approximately one tenth of the outermost ring, so the 

contribution of the center ring to the overall pathintegrated intensities is much lower those of outer rings. 

Therefore, any error in the path-integrated spectral 

radiation intensities could lead to high deconvolution 

errors at the center of the flame. The second reason for 

the higher deviation is that the temperature of the center 

ring is lower than the peak temperature. Therefore, noise 

contribution to the local intensity of center ring is higher 

since the random noise 1 % is defined for peak intensities. 

 The measurement of infrared radiation using a 

spectrometer involves errors not only in intensity, but also 

in the wavelengths. The sensitivity of the deconvolution 

algorithm to the uncertainty in the wavelength was also 

evaluated by adding a random noise of 10 nm to each 

wavelength. The synthetic and deconvoluted gas 

temperatures are shown in Fig. 7. The error in the 

deconvoluted gas temperatures is less than 1.7 %. The 

results shown in Fig. 7 indicate that any measurement 

uncertainties in the wavelength of spectral radiation 

intensities do not affect the estimated temperatures 

significantly. 

NASA/TM—2003-212302 4
-1.0 -0.8 -0.6 -0.4 -0.2 0.0

600

800

1000

1200

1400

1600

1800

2000 D = 2 cm

Gas temperature (K)

Radial distance (cm)

 synthetic

 deconvoluted + 10 nm noise

Figure 7. Sensitivity of the inversion algorithm to the 

random noise in the measured wavelengths. 

Conclusions 

 

A tomographic algorithm was developed to estimate 

local scalars from the multi-wavelength path-integrated 

spectral radiation intensities. The algorithm was 

evaluated using calculated spectral radiation intensities 

from a synthetic data set. The spectral radiation 

intensities were deconvoluted using the maximum 

likelihood estimation method in conjunction with an 

iterative scheme. The deconvolution accounts for the 

self-absorption of radiation by the intervening gases. The 

deconvolution algorithm successfully recovers the 

temperature and gas concentrations within 0.1 % for a 

laboratory flame. The algorithm achieves reasonable 

results for flames up to 10 cm in diameter. The sensitivity 

of the algorithm to random errors in the amplitude and 

spectral location of the radiation intensities was also 

tested. The deconvolution error in gas temperatures, with 

the addition of 1% random error in the spectral radiation 

intensities, was less than 1%, except at the center of the 

flame. The error in the deconvoluted gas temperatures 

with the addition of a 10 nm random noise in the 

wavelength was found to be less than two percent (2 %) at 

all locations within the flame. 

References 

Best, P. E., Chien, P. L., Carangelo, R. M., Solomon, P. 

R., Danchak, M. and Ilovici, I 1991, Combust. 

Flame, vol. 85, pp. 309-318. 

Bishop, Y. M. M., Fienber, S. E., and Holland, P. W., 

1975, Discrete Multivariate Analysis: Theory 

and Practice, MIT Press, Cambridge. 

Chen, F. P., and Goulard, R., 1976, JQSRT, vol. 16, pp. 

819-827. 

Choi, M. Y., Hamins, A., Mullholland, G. W., and 

Kashiwagi, T., 1995, Combust. Flame, vol. 99, 

pp. 174-186 

Cover, T. M.,1984, IEEE Trans. Inform. Theory, vol. 30, 

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Crosley, D. R., and Smith, G. P., 1983, Opt. Eng., vol. 22, 

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Deans, S. R., 1983, The Radon Transform and Some of its 

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Witze, P. O., 1992, Combustion Flow 

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fire93/ art096.html. 

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Falcone, F. K., 1980, Laser Probes for 

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OH, pp. 333-336. 

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JQSRT, vol. 55, pp. 345-356. 

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89. 

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Journal, vol. 29, pp. 301-315. 

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pp. 483-492. 

NASA/TM—2003-212302 5
Sivathanu, Y. R., and Gore, J. P., 1991, Combust. Sci. & 

Tech., vol. 80, pp. 1-21 

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310, pp. 120-127, ASME, New York, NY. 

NASA/TM—2003-212302 6
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E–13873

WBS–22–101–12–17

12

Fan Beam Emission Tomography for Estimating Scalar Properties in

Laminar Flames

Jongmook Lim, Yudaya Sivathanu, and Douglas Feikema

Combustion; Spectroscopic analysis; Flame spectroscopy; Emission spectra

Unclassified -Unlimited

Subject Categories: 31 and 34 Distribution: Nonstandard

Prepared for the Third Joint Meeting of the U.S. Sections of the Combustion Institute sponsored by The Combustion

Institute, Chicago, Illinois, March 16–19, 2003. Jongmook Lim and Yudaya Sivathanu, En’Urga, Inc., West Lafayette,

Indiana 47906; Douglas Feikema, NASA Glenn Research Center. Responsible person, Douglas Feikema, organization

code 6711, 216–433–5707.

A new method of estimating temperatures and gas species concentrations in a laminar flame is reported. The spectral

radiation intensities emitted from a laminar flame is measured at multiple wavelengths using a mid infrared spectrometer. The spectrometer obtains the spectral radiation intensities from 1.3 to 4.8 microns with a scanner attached

to the front of the spectrometer. The measurements are deconvoluted using a maximum likelihood estimation method

in conjunction with an iterative scheme. The deconvolution accounts for the self-absorption of radiation by the

intervening gases. The fan beam emission tomography (FBET) is validated using synthetic data created using a

narrow band radiation model (RADCAL). The results obtained from the deconvolution successfully recovered the

original synthetic data within 0.5 percent for the temperature and the concentrations of CO2 and H2O. The method is

expected to provide combustion researchers an easy method of obtaining the major gas species concentrations,

temperatures, and soot volume fractions in laminar flames non-intrusively with one instrument.