Swept-Wavelength Laser Absorption Tomography for
Imaging Rocket Plume Gas Properties
Drew Caswell
Advisor: Scott T. Sanders
Motivation
Experimental Arrangement
To reconstruct the axis-symmetric temperature and water mole fraction radial profiles
in a cross section of a rocket plume
T(r)

Parallel beam and fan beam
geometries provide same information
under axis-symmetric assumption

Data presented below for parallel
beam geometry

Fan beam configuration reduces
optical components and will aid in
reducing unwanted beam steering
effects
XH2O(r)
Parallel Beam
Management of Non-Uniform Flows
Fan Beam
Wavelength [nm]
Wavelength [nm]
Spectral Fitting to HiTRAN Database
1450
0.02
1440
1430
1420
1410
1400
1450
1390
0.02
5

Tomography
Image reconstruction from many line-of-sight
measurements

0.02

0.00
better match to uniformtemperature distribution
(527-1872K)
0.06
0.04
Spectra after Abel inversion are compared to a
database of simulations to find the best fit spectra and
associated gas properties
Higher temperatures near the center of the plume are
visible in the experimental spectra by the increased
absorption at longer wavelengths (nm – top axis) or
lower optical frequencies (cm-1 – bottom axis)
0.02
8
(c)
0.01
0.00
0.03
0.02
11
(b)
0.01
0.00
0.03
Combination
Best of both techniques
1400
1420
1440
(d)
8
(c)
0.02
0.01
0.00
0.03
0.02
11
(b)
0.01
0.00
0.03
0.02
14
(a)
0.01
6900
6950
7000
7050
7100
Wavenumber [cm]
1460
7150
7200
6850 6900 6950 7000 7050 7100 7150 7200 7250
-1
-1
Wavenumber [cm ]
Experimental Spectra
Best Fit Simulated Spectra
100
Experimental Results
0.8

R
3-point Abel inversion
1 N-1
k (ri ; ) 
Dij P ( x j ; )

r j0

D matrix only depends on the number of projections only needs to be computed once
Combining results from all colors produces a complete
spectrum at each radial position


Imaging near the center of the plume is more difficult due to reduced
signal-to-noise ratios caused by shorter optical path lengths and beam
steering from refractive index gradients
Mole Fraction

0.2



20





0
100
3500
3000



80

2500
60

2000
Temperature

1500
40

1000

0
20


MSE
0.0
0.5
1.0
1.5
2.0

2.5
Radial Location [cm]
University of Wisconsin Engine Research Center

MSE
500
0  i, j  N  1
40
9
60
0.4
0.0
Gray area indicates where fit to simulated spectra becomes unreliable and
is indicated by the mean-square-error (MSE) of the fitting routine

MSE*10
Results from outside of plume agree well with ambient conditions
verifying correction scheme for unwanted room water absorption



3.0


3.5
0
4.0
9
 I 
k (r , ) r dr
P( x; )   ln    2 2
2
x r  x 
 I O  , x

Projections need to be uniformly spaced but technique
is not constrained to this

0.6
MSE*10
Variable of interest

Assumed axis-symmetric flow field and infitesimally
narrow laser beam
Temperature [K]
I 


   exp   k ( y, )dy 
 0

 I o 

L
H2O Mole Fraction
80
Beer’s law
1390
0.00
wavelength [nm]
Tomography by means of Abel Inversion
1400
5
0.03
(a)
6850
1380
1410
0.04
0.00
0.00
1420
0.00
0.05
14
0.01
1430
0.01
0.00
0.03
0.02
0.02

(d)
-1
0.04
0.01
Spectral Absorption Coefficient [cm ]
Weighted linear combination of simulated spectra to fit a
single line-of-sight non-uniform measured spectrum.
Temperature distribution is inferred but no spatial
information is gained
poor match to singletemperature simulation
(946 K)
-1
Spectral Absorption Coefficient[cm ]
0.06
Spectral inversion
absorbance

1440