Methods for quantitative infrared directional-hemispherical
and diffuse reflectance measurements using an FTIR and a commercial
integrating sphere

Thomas A. Blake, Timothy J. Johnson, Russell G. Tonkyn, Brenda M. Forland, Tanya L. Myers, Carolyn S. Brauer, Yin-Fong Su, Bruce E. Bernacki, Leonard Hanssen, and Gerardo Gonzalez

Author Affiliations

Thomas A. Blake,^{1,}^{*} Timothy J. Johnson,^{1} Russell G. Tonkyn,^{1} Brenda M. Forland,^{1,}^{2} Tanya L. Myers,^{1} Carolyn S. Brauer,^{1} Yin-Fong Su,^{1} Bruce E. Bernacki,^{1} Leonard Hanssen,^{3} and Gerardo Gonzalez^{4}

^{1}Pacific Northwest National Laboratory, 902
Battelle Blvd., Richland, Washington 99354, USA

^{2}Current address: Red Rocks Community
College, 13300 West 6th Avenue, Lakewood, Colorado 80228, USA

^{3}Optical Technology Division, National
Institute of Standards and Technology, Gaithersburg, Maryland 20899,
USA

^{4}Alecam FTIR Services and Consulting, The
Woodlands, Texas 77381, USA

Thomas A. Blake, Timothy J. Johnson, Russell G. Tonkyn, Brenda M. Forland, Tanya L. Myers, Carolyn S. Brauer, Yin-Fong Su, Bruce E. Bernacki, Leonard Hanssen, and Gerardo Gonzalez, "Methods for quantitative infrared directional-hemispherical and diffuse reflectance measurements using an FTIR and a commercial integrating sphere," Appl. Opt. 57, 432-446 (2018)

We have developed methods to measure the directional-hemispherical
($\rho $) and diffuse
(${\rho}_{d}$) reflectances of powders, liquids,
and disks of powders and solid materials using a commercially
available, matte gold-coated integrating sphere and Fourier transform
infrared spectrometer. To determine how well the sphere and protocols
produce quantitative reflectance data, measurements were made of three
diffuse and two specular standards prepared by the National Institute
of Standards and Technology (NIST), LabSphere Infragold and Spectralon
standards, hand-loaded sulfur and talc powder samples, and water.
Relative to the NIST measurements of the NIST standards, our
directional hemispherical reflectance values are within
$\pm 4\%$ for four of the standards and within
$\pm 7\%$ for a low reflectance diffuse
standard. For the three diffuse reflectance NIST standards, our
diffuse reflectance values are within $\pm 5\%$ of the NIST values. For the two
specular NIST standards, our diffuse reflectance values are an order
of magnitude larger than those of NIST, pointing to a systematic error
in the manner in which diffuse reflectance measurements are made for
specular samples using our methods and sphere. Sources of uncertainty
are discussed in the paper.

John A. Jacquez, Wayne McKeehan, John Huss, James M. Dimitroff, and Hans F. Kuppenheim J. Opt. Soc. Am. 45(10) 781-785 (1955)

References

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Fractional Uncertainties Used for Calculating Systematic
Uncertainties When Using the Bruker Sphere for DHR and Diffuse
Reflectance Measurements^{a}

Source of Systematic Uncertainty

DHR Configuration

Diffuse Configuration

Knife edges/flat specular port edges

0.0294

0.0135

Curved sample/flat sample

0.0020

0.00106

Detector FOV and baffle position

0.0078

0.0155

FTIR baseline drift

0.0020

0.0020

Fractional uncertainties for the sphere are calculated from
ray trace simulations of the Bruker integrating sphere
assuming a Lambertian wall interior and Lambertian sample
surface both with $R=0.97$. For specular samples,
the fractional uncertainty associated with knife edges and
port edges is assumed to be zero.

Table 2.

Average DHR and Diffuse Reflectance and Percent Change Between
PNNL and NIST Measurement of the Five NIST Standards^{a}

Averages calculated between $1000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$7000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$. The values in
parenthesis after the reflectances are the two standard
deviation ($k=2$ coverage factor) expanded
uncertainties.
Percent change, $\%\mathrm{\Delta}\rho =\{({\rho}_{\mathrm{PNNL}}-{\rho}_{\mathrm{NIST}})/{\rho}_{\mathrm{NIST}}\}\times 100\%$.
The diffuseness spectrum is defined as
$D={\rho}_{d}/\rho $ and measured by the
Bruker sphere. $D$ is averaged between
$1000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$7000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ to give the values
shown.

Table 3.

Average Scaled DHR and Diffuse Reflectance Values for
Infragold, Bruker Diffuse Gold, Spectralon 99% Reflectance
Standard, Hand-Loaded Sulfur, Hand-Loaded Talc, and Water^{a}

Average DHR values for calibration spectra, where
available, and percent change with the PNNL results are
given. Calculated diffuseness values are also given. The
values in parenthesis after the reflectances are the two
standard deviation ($k=2$ coverage factor) expanded
uncertainties.
Percent change, $\%\mathrm{\Delta}\rho =\{({\rho}_{\mathrm{PNNL}}-{\rho}_{\text{calib}})/{\rho}_{\text{calib}}\}\times 100\%$.
The diffuseness spectrum is defined as
$D={\rho}_{d}/\rho $ and measured by the
Bruker sphere. $D$ is averaged over the
wavenumber ranges noted to give the values shown.
Averaged between $1000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$7000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$.
Averaged between $5000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$9000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$.
Averaged between $4000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$7000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$.
Averaged between $1500\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$7000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$.
Averaged between $5000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$7500\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$.
Averaged between $5000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$7000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$.
Averaged between $1000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$5000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$.

Tables (3)

Table 1.

Fractional Uncertainties Used for Calculating Systematic
Uncertainties When Using the Bruker Sphere for DHR and Diffuse
Reflectance Measurements^{a}

Source of Systematic Uncertainty

DHR Configuration

Diffuse Configuration

Knife edges/flat specular port edges

0.0294

0.0135

Curved sample/flat sample

0.0020

0.00106

Detector FOV and baffle position

0.0078

0.0155

FTIR baseline drift

0.0020

0.0020

Fractional uncertainties for the sphere are calculated from
ray trace simulations of the Bruker integrating sphere
assuming a Lambertian wall interior and Lambertian sample
surface both with $R=0.97$. For specular samples,
the fractional uncertainty associated with knife edges and
port edges is assumed to be zero.

Table 2.

Average DHR and Diffuse Reflectance and Percent Change Between
PNNL and NIST Measurement of the Five NIST Standards^{a}

Averages calculated between $1000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$7000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$. The values in
parenthesis after the reflectances are the two standard
deviation ($k=2$ coverage factor) expanded
uncertainties.
Percent change, $\%\mathrm{\Delta}\rho =\{({\rho}_{\mathrm{PNNL}}-{\rho}_{\mathrm{NIST}})/{\rho}_{\mathrm{NIST}}\}\times 100\%$.
The diffuseness spectrum is defined as
$D={\rho}_{d}/\rho $ and measured by the
Bruker sphere. $D$ is averaged between
$1000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$7000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ to give the values
shown.

Table 3.

Average Scaled DHR and Diffuse Reflectance Values for
Infragold, Bruker Diffuse Gold, Spectralon 99% Reflectance
Standard, Hand-Loaded Sulfur, Hand-Loaded Talc, and Water^{a}

Average DHR values for calibration spectra, where
available, and percent change with the PNNL results are
given. Calculated diffuseness values are also given. The
values in parenthesis after the reflectances are the two
standard deviation ($k=2$ coverage factor) expanded
uncertainties.
Percent change, $\%\mathrm{\Delta}\rho =\{({\rho}_{\mathrm{PNNL}}-{\rho}_{\text{calib}})/{\rho}_{\text{calib}}\}\times 100\%$.
The diffuseness spectrum is defined as
$D={\rho}_{d}/\rho $ and measured by the
Bruker sphere. $D$ is averaged over the
wavenumber ranges noted to give the values shown.
Averaged between $1000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$7000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$.
Averaged between $5000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$9000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$.
Averaged between $4000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$7000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$.
Averaged between $1500\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$7000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$.
Averaged between $5000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$7500\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$.
Averaged between $5000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$7000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$.
Averaged between $1000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and
$5000\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$.