Lab Methods Day
June 25, 2014
Optical Thermometry
Haiqing Guo
Dept. of Fire Protection Engineering
hguo@umd.edu
1/24
Introduction
• Optical thermometry, i.e. soot pyrometry, provides soot
temperature and soot concentration information in flames.
• Soot radiance in flames was detected and converted to
soot temperature (K) and soot volume fraction (ppm).
• This technique is nonintrusive.
2/24
Soot Radiance
The spectral radiance of hot soot
is:
W   B 
2hc 2
5 exp(hc / kT )  1
For hot regions in the visible or
near-IR:
wikipedia.org
exp(hc / kT )  1
• Choose wavelength
• Determine emissivity
• Measure radiance (e.g., with
filtered digital camera)
Bλ
c
h
k
T
ε
λ
Blackbody spectral radiance
Speed of light
Planck’s constant
Boltzmann’s constant
Temperature
Emissivity
Wavelength
3/24
Bandpass Filters
newport.com
wikipedia.org
• Choose two or more bandpass filters, e.g., at 450, 650, and 900 nm.
• Bandwidth choice involves a tradeoff between error and signal
strength. A FWHM of 10 nm is most common.
• Avoid chemiluminescence spectra (e.g., Swan Bands) and should be
far separated.
4/24
Soot Emissivity
• Determine emissivity
Rayleigh scattering can be assumed because soot primary particles
(dp  30 nm) are smaller than the Rayleigh limit.
 ( x, y )  1  exp( K abs ( x, y )dy )  K abs ( x, y )dy
Assume: K abs  K ext  6E (m) f s / 
 ( x, y)  6E(m) f s ( x, y)dy / 
E(m)
fs
Kabs
Kext
Refractive index absorption function
Soot volume fraction
Absorption coefficient
Extinction coefficient
Notes:
• The variation of E(m) with soot morphology, soot age, and other
conditions is not fully understood.
• Soot volume fraction fs is unknown.
5/24
Camera Signal
• Measure soot radiance
CCD/CMOS cameras are attractive owing to high bit depth (e.g,
14), higher pixel counts (12M), larger sensor arrays (36 x 24 mm),
and decreased noise.
Irradiance incident on the CMOS sensor I:


I    W d
0
GS  aI 
a
GS


Constant that accounts for pixel size, fill factor, and sensitivity
Grayscale divided by shutter time
Constant that accounts for magnification and lens light losses
Bandpass filter transmissivity
6/24
Camera Calibration
• Constant a obtained from blackbody furnace
calibration.
– Emissivity of ε = 0.99 ± 0.01
– Uniform and stable temperature
T range: 900 − 1200 ºC
T increment: 25 ºC
T accuracy: ± 0.1 ºC
7/24
Line-of-Sight Radiance
Bandpass Filter
Flame cross section
x
x
(x,y)dy
y
I ( x)

 

 
K abs ( x, y ) B ( x, y ) exp  K ext ( x, y ' ) dy ' dy

 y

 12 2 E ( m) hc 2 f ( x, y )
  6E (m) f s ( x, y ' )

s
 
exp 
dy ' dy
  6 exp[hc / kT ( x, y )]
 y







The exponent term describes the extinction effect from
soot. For optically thin cases, it is negligible.
8/24
GS to T Conversion
For optically thin conditions:
I ( x)

 

12 2 E (m)hc 2 f s ( x, y )

 exp[hc / kT ( x, y )]

6
dy
Tomography can convert the line-of-sight integrated irradiance I(x)
into the local irradiance I(x,y).
Required
High uncertainty
GS( x, y )
a

I ( x, y )


12 2 E (m)hc 2 f s ( x, y )
From filter
manufacturer
6 exp[hc / kT ( x, y )]
Objective
From measured grayscale, blackbody
calibration, and tomography
9/24
Ratio Pyrometry
• With multiple bandpass filters, ratio pyrometry allows fs
and E(m) to be cancelled:
GS 1 ( x, y ) a2
GS 2 ( x, y ) a1

 112 6 exp( hc / k2T )
 2 216 exp( hc / k1T )
and
T ( x, y ) 
hc1 / 1  1 / 2 
k lnC1GS2 ( x, y ) C 2 GS1 ( x, y )
where C = a τ Δλ / λ6 is a constant for each filter and
camera that does not vary with T or E(m).
10/24
fs from Emissions
• The pyrometry determined temperature can be used to
obtain the soot volume fraction for each filter.
f s ( x, y ) 
GS( x, y ) exphc / kT ( x, y ) 
12 2 hc 2 E (m)C
• A soot refractive index of m = 1.57 – 0.56 i is commonly
assumed, which yields E(m) = 0.26.
• Any uncertainty in T is amplified in determining fs.
11/24
Camera Tradeoffs
• Digital cameras require considering:
– Response linearity (gamma correction must be avoided)
– Parallel light collection (small aperture)
– Sufficient depth-of-field (small aperture)
– High spatial resolution (big sensor, small object distance)
– High temporal resolution (fast shutter)
– High signal resolution (high color bit-depth)
– Ideal exposures should have high GS but not be
saturated in any color plane. This presents tradeoffs with
aperture, shutter, and ISO.
12/24
Deconvolution
• 3D tomographic reconstruction requires multiple imaging
at different locations.
• For axisymmetric flames, tomography from I(x) to I(r) can
be simplified and requires only one image.
• Commonly used deconvolution algorithms:
– Abel transform
– Onion peeling
– Filtered back projection
13/24
Abel Transform
• Based on an exact solution
• Requires discretization
Line-of-sight integration of the flame property f(r) is:
p ( x) 



f (r )dy
Substituting y with x and r following r2 = x2 + y2 yields:
p( x)  2


rf (r )
r 2  x2
x
dr
Analytical inverse of the above equation yields:
f (r )  
1


r
p ' ( x)
x2  r 2
dx
Sensitive to noise
Singularity at x = r
14/24
Abel Transform
f (r )  
r h
p( x)  p(r )
  x
1
r
2
r

2 3/ 2
xdx 
L
  x
1
r h
p( x)
2
r

2 3/ 2
xdx 
p(r )
 h( 2r  h)
Lower integration limit region,
solved with a open type numeric
integration (e.g. Steffensen’s
formula).
Solved with a regular closed type integration scheme (e.g. Simpson’s rule).
• Alternatively, a discretized form is simpler and more commonly
used.
f (ri ) 
2

L 1

j i




p( j  1)  p( j ) 
2
2 1/ 2
2
2 1/ 2 
r j 1  ri
 r j  ri
2
2



r j 1  r j
15/24
Onion Peeling
• Based on numerical approximation.
• The domain is divided into a series of
concentric rings.
• Within each ring, the value of the
spatial function f(r) is assumed to be
constant.
• For the i-th cord and the j-th ring:

p( xi ) 
s
ij
f ( j )
r j   j  r j 1
j i
sij is a geometric matrix
Deconvolve Form:
f ( j ) 

1


s
 ji p( xi )
r j   j  r j 1
i j
16/24
Deconvolution
• Sufficient spatial resolution is required for enough accuracy.
• Due to the differentiation, deconvolution is very sensitive to noise. Data
smoothing can help:
 Low-pass filter
5.E+18
2.0E+19
 Gaussian filter
 Savitzky-Golay filter
TRUE
4.E+18
Deconvolution
Abel transform
3.E+18
1.0E+19
Projection
2.E+18
Projection
1.5E+19
Onion peeling
5.0E+18
1.E+18
0.E+00
0.0E+00
0
0.5
1
1.5
2
2.5
3
3.5
4
r (mm)
Deconvolution results from prescribed projection
data. Spatial resolution is 0.05 mm/pixel.
17/24
Laminar Jet Diffusion Flame
• A Santoro coflow burner
was used.
• The flame was steady
and axisymmetric.
Glass
beads
• Fuel tube: 11.1 mm ID
Air
• Air tube: 101 mm ID
Fuel
18/24
C2H4 Flame
• Fuel: ethylene
• Oxidizer: coflowing air.
• Flame height: 88 mm
Steady
Optically thin
Axisymmetric
Visible
(a)
650 nm
(b)
632.8 nm
(c)
19/24
Soot Temperatures
2500
z = 50 mm
T (K)
2000
1500
1000
500
450/650
450/900
650/900
0
0
0.5
1
1.5
2
2.5
3
r (mm)
2500
z = 15 mm
T (K)
2000
1500
1000
Low soot concentration
500
450/650
450/900
650/900
0
Visible
(a)
0
650 nm
(b)
0.5 nm1
632.8
(c)
1.5
2
2.5
r (mm)
3
3.5
4
4.5
5
20/24
T Contours
• T range: 1600-1850 K.
• Spatial resolution: 23 µm
• Longest shutter time:
125 ms
• Precision: ± 0.1 K
• Uncertainty: ± 50 K (95%
confidence)
21/24
Soot Emission Concentrations
12
fs (ppm)
10
fs450
8
fs650
6
fs900
4
2
0
0
0.5
1
1.5
2
2.5
3
2
2.5
3
r (mm)
3.0
fs (ppm)
2.5
2.0
fs450
1.5
fs650
1.0
fs900
0.5
0.0
Visible
(a)
0
650 nm
(b)
0.5 nm
632.8
(c)
1
1.5
r (mm)
3.5
4
4.5
5
22/24
fs results Results
Emission
Extinction
fs (ppm)
0.1-10
0.2-10
Res. (µm)
23
34
t (ms)
125
167
Precision
(ppm)
± 4×10-4
± 6×10-4
Uncertainty
± 30%
± 10%
23/24
Limitations
• Only applicable for sooting flame.
• Needs to be optically thin (otherwise
complicated corrections are required).
• Needs to be steady.
• Needs to be axisymmetric.
For detailed information, please refer to “H. Guo, J.A. Castillo, P.B. Sunderland, Digital
Camera Measurements of Soot Temperature and Soot Volume Fraction in
Axisymmetric Flames, Applied Optics 52 (2013) 8040-8047.”
24/24