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Newrad 2011, Maui, Hawaii
Heather J. Patrick, Leonard Hanssen, Jinan Zeng and Thomas A. Germer
National Institute of Standards and Technology, Gaithersburg, MD 20899 USA
email: [email protected]
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Motivation and Overview
In this work:
In-plane and hemispherically-scanned BRDF (full hemisphere of polar, azimuthal scattering angles)
Ambient temperature, 405 nm and 658 nm wavelengths
4 samples, of two graphite types: 7ST-1, 7ST-2, SGL-1, SGL-2
Seven values of qi (0°, 8°, 15°, 30°, 45°, 60°, 70°)
Two incident polarizations: s-polarized, p-polarized
Integrate BRDF to DHR (r)
Graphite samples measured
High-Temperature Fixed Point (HTFP) cavities
Courtesy Y. Yamada
Potential eutectic reference points: Co-C 1597 K Pt-C 2011 K Re-C 2747 K
A critical issue is the knowledge of the emissivity of the graphite blackbody radiator cavities. Modeling of the emissivity requires characterization of the reflectance of the graphite walls of the cavity, ideally as a function of incident angle, scattering angle, polarization, wavelength and temperature.
Example HTFP, Batuello et al., Metrologia 2011
Heather J. Patrick, NIST, Newrad 2011 2
Only a subset of the data will be shown!
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Previous BRDF Models for Monte Carlo Studies
Heather J. Patrick, NIST, Newrad 2011 3
(Lambertian diffuse+ non-varying
specular)
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Goniometric Optical Scatter Instrument (GOSI)
Used 405 nm, 658 nm lasers Few millimeter illuminated spot on sample Linearly polarized incident light Power monitor to normalize for source
fluctuations 5-dof sample positioning for in-plane and
out-of-plane BRDF
Heather J. Patrick, NIST, Newrad 2011 4
Receiver (Ps position)
Ps
(Pi position)
Goniometer with sample
polarizer
monitor beamsplitter
From laser
Monitor Detector
Spatial filter/focus
l/2 waveplate
Pi
BRDF D = aperture to receiver A = aperture area qr = scattering polar angle
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BRDF coordinates
z is sample normal
x-z plane is plane of incidence
Incident polar angle (qi) and polar scattering angle (qr) measured from z
Azimuthal scattering angle (fi) measured from x
For in-plane measurements, take negative qr to be scattering with fr = 180°
Heather J. Patrick, NIST, Newrad 2011 5
q iq r
f r x
y
zd
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In-plane BRDF
405 nm data shown, unpolarized incident light (average of s-pol and p-pol incident results) Graphite BRDF is highly non-Lambertian at high qi, qs
Not a good fit to uniform specular diffuse models! May be able to adapt GSD model to approximate this behavior
SGL samples a little less forward scatter enhancement 405 nm and 658 nm show similar trends Grey sample; BRDF values around 10% of pressed PTFE
Heather J. Patrick, NIST, Newrad 2011 6
405 nm, graphite
0.01
0.1
1
-80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80
BR
DF,
sr-
1
qr, degrees
7ST-1 incident 0 degrees
7ST-1 incident 45 degrees
7ST-1 incident 70 degrees
0.01
0.1
1
-80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80
BR
DF,
sr-
1
qr, degrees
7ST-1 incident 0 degrees
7ST-1 incident 45 degrees
7ST-1 incident 70 degrees
SGL-1 incident 0 degrees
SGL-1 incident 45 degrees
SGL-1 incident 70 degrees
658 nm, graphite
0.01
0.1
1
-80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80
BR
DF,
sr-
1
qr, degrees
7ST-1 incident 0 degrees
7ST-1 incident 45 degrees
7ST-1 incident 70 degrees
SGL-1 incident 0 degrees
SGL-1 incident 45 degrees
SGL-1 incident 70 degrees
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-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0q
i = 45
0, s-pol
y =
sin
qr*
sin
fr
x = sinqr*cosf
r
0.01800
0.02084
0.02413
0.02795
0.03236
0.03747
0.04339
0.05024
0.05817
0.06736
0.07800
BRDF, sr-1
Hemispherically-scanned BRDF - overview
Hemispherically scanned qr and fr for fixed qi Measured at points evenly spaced in x,y space where
x = sinqr cosfr y = sinqr sinfr Spacing of x,y eases integration to total directional-hemispherical
reflectance (DHR)
Heather J. Patrick, NIST, Newrad 2011 7
In-plane
Example: SGL-1 405 nm qi = 45° s-pol incident
fr = 0° fr = 180°
r = sinqs
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Hemispherically-scanned BRDF: example qi = 0°
Sample 7ST-1, 405 nm “s-pol” electric field along y, “p-pol” electric field along x See preference to scatter perpendicular to electric field (higher BRDF values) Slight asymmetry about x,y may indicate “lay” to surface finish at measured
point, or surface nonuniformity
Heather J. Patrick, NIST, Newrad 2011 8
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
y =
sin
qr*
sin
fr
x = sinqr*cosf
r
0.01800
0.01912
0.02032
0.02159
0.02294
0.02437
0.02590
0.02751
0.02923
0.03106
0.03300
BRDF, sr-1
qi = 0
0, s-pol
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0q
i = 0
0, p-pol
y =
sin
qr*
sin
fr
x = sinqr*cosf
r
0.01800
0.01912
0.02032
0.02159
0.02294
0.02437
0.02590
0.02751
0.02923
0.03106
0.03300
BRDF, sr-1
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Hemispherically-scanned BRDF: example qi = 45°
Sample 7ST-1, 405 nm Much higher BRDF values for s-polarized incident light (note scales are
not same) Observed asymmetries, more pronounced when looking at p-
polarization
Heather J. Patrick, NIST, Newrad 2011 9
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0q
i = 45
0, s-pol
y =
sin
qr*
sin
fr
x = sinqr*cosf
r
0.01500
0.01822
0.02214
0.02689
0.03267
0.03969
0.04821
0.05857
0.07115
0.08643
0.1050
BRDF, sr-1
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0q
i = 45
0, p-pol
y =
sin
qr*
sin
fr
x = sinqr*cosf
r
0.018000.019360.020810.022380.024060.025880.027820.029920.032170.034590.037200.04000
BRDF, sr-1
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Hemispherically-scanned BRDF: example qi = 70°
Sample 7ST-1, 405 nm Greatly enhanced BRDF values for s-polarized incident light vs. p-polarized (note scales
are not same) Unpolarized (averaged) result will be dominated by s-polarization; strong dependence of
observed BRDF on fr at given qr Observed asymmetries, more pronounced when looking at p-polarization
Heather J. Patrick, NIST, Newrad 2011 10
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0q
i = 70
0, s-pol
y =
sin
qr*
sin
fr
x = sinqr*cosf
r
0.01400
0.01913
0.02614
0.03573
0.04883
0.06672
0.09118
0.1246
0.1703
0.2327
0.3180
BRDF, sr-1
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0q
i = 70
0, p-pol
y =
sin
qr*
sin
fr
x = sinqr*cosf
r
0.01560
0.01857
0.02210
0.02630
0.03131
0.03726
0.04435
0.05278
0.06283
0.07478
0.08900
BRDF, sr-1
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Integrating BRDF to obtain DHR
For white Lambertian reflector, DHR r = 1
rrrrrrr ddf fqfqfqr sincos),(DHR from BRDF*
Variable substitution rrx fq cossin rry fq sinsin
dxdyyy
xx
yxfr fq
fq
fqr cossin),(
1
since BRDF measured at evenly spaced pts in x,y
Heather J. Patrick, NIST, Newrad 2011 11
*ASTM E2387-05, “Standard practice for goniometric optical scatter measurements,” ASTM International, West Conshoken, PA, 2005.
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DHR, polarization-resolved
Results for all samples, wavelengths investigated
Two samples within type (7ST or SGL) show similar trends
7ST polarization dependence more pronounced (different surface finish?)
Heather J. Patrick, NIST, Newrad 2011 12
0.065
0.075
0.085
0.095
0.105
0.115
0.125
0.135
0 8 15 30 45 60 70
r
qi, degrees
405 nm, p-polarization incident
7ST-1
7ST-2
SGL-1
SGL-2
0.065
0.075
0.085
0.095
0.105
0.115
0.125
0.135
0 8 15 30 45 60 70
r
qi, degrees
405 nm, s-polarization incident
7ST-1
7ST-2
SGL-1
SGL-2
0.065
0.075
0.085
0.095
0.105
0.115
0.125
0.135
0 8 15 30 45 60 70
r
qi, degrees
658 nm, p-polarization incident
7ST-1
7ST-2
SGL-1
SGL-2
0.065
0.075
0.085
0.095
0.105
0.115
0.125
0.135
0 8 15 30 45 60 70
r
qi, degrees
658 nm, s-polarization incident
7ST-1
7ST-2
SGL-1
SGL-2
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DHR, unpolarized incident light
Results for all samples, wavelengths investigated
Two samples within type (7ST or SGL) show similar trends
DHR 0.083 to 0.101 for all samples/wavelengths/incident angles
Heather J. Patrick, NIST, Newrad 2011 13
0.08
0.085
0.09
0.095
0.1
0.105
0 8 15 30 45 60 70
r
qi, degrees
405 nm, polarization averaged
7ST-1
7ST-2
SGL-1
SGL-2
0.08
0.085
0.09
0.095
0.1
0.105
0 8 15 30 45 60 70
r
qi, degrees
405 nm, polarization averaged
7ST-1
7ST-2
SGL-1
SGL-2
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Variation of DHR over surface?
405 nm DHR for unpolarized incident light, qi = 0° Graphite SGL-2 sample showed ≈ 5% Dr vs. position In contrast, a Spectralon sample showed ≈ 0.3% Dr vs. position Surface non-uniformity of graphite samples plays a role! Surface non-uniformity may also contribute to apparent asymmetries
in hemispherically –scanned BRDF, as illuminated area expands with qi
Heather J. Patrick, NIST, Newrad 2011 14
405 nm, graphite 405 nm, spectralon
0.09
0.091
0.092
0.093
0.094
0.095
0.096
0.097
0.098
0.099
0.1
position 1 position 2 position 3
DHR, 405 nm, qi = 0°, SGL-2
0.9
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
position 1 position 2 position 3
Spectralon, 405 nm, qi = 0°, SGL-2
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Dependence of DHR on scanning range?
658 nm DHR for unpolarized incident light, qi = 70°, sample 7ST-2 On left, 0.1 spacing x,y grid (typical). On right, 0.05 spacing (accesses
higher qs) Dr ≈ +6% when spacing decreased (for sample with largest effect) Only affects qi = 70° May need to consider for very non-Lambertian BRDF, highest
Heather J. Patrick, NIST, Newrad 2011 15
Typical, 305 pts
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
y =
sin
qr*
sin
fr
x = sinqr*cosf
r
0.01500
0.02169
0.03137
0.04536
0.06560
0.09487
0.1372
0.1984
0.2869
0.4149
0.6000
BRDF, sr-1
r = 0.01
Fine spacing, 1245 pts
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
y =
sin
qr*
sin
fr
x = sinqr*cosf
r
0.01500
0.02169
0.03137
0.04536
0.06560
0.09487
0.1372
0.1984
0.2869
0.4149
0.6000
BRDF, sr-1
r = 0.0106
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Discussion Graphite samples show strongly non-Lambertian BRDF
Strong enhancement of forward-scattering, dominated by BRDF from s-pol component of incident light
DHR from 0.083 to 0.101 calculated from BRDF measurements
Dependent on qi, polarization, sample type, position on sample Likely also very dependent on exact surface finish
Hanssen et al. report 0.1 to 0.3 rough-polished at 2 mm wavelength
Effect on models of emissivity/blackbody temperature? TBD! Plan to adjust models to more appropriately account for BRDF
measurements – may be able to adapt GSD model to approximate our results Also compare elevated T measurements with these room T results One study showed changing DHR from 0.2 to 0.3 gave ≈ 20 mK change in T –
but assumed a Uniform Specular Diffuse model. Goals for all source-based components of uncertainty budget 30 mK – 110 mK
Ability to hemispherically scan BRDF gives more detailed BRDF picture compared to sphere-based and in-plane measurements
Heather J. Patrick, NIST, Newrad 2011 16
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Thank you!
Heather J. Patrick, NIST, Newrad 2011 17