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: heather.patrick@nist.gov

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!

Previous BRDF Models for Monte Carlo Studies

Heather J. Patrick, NIST, Newrad 2011 3

(Lambertian diffuse+ non-varying

specular)

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

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

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

-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

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

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

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

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.

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

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

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

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

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

Thank you!

Heather J. Patrick, NIST, Newrad 2011 17