David G. Goebel, B. Patrick Caldwell, and Harry K. Hammond, "Use of an Auxiliary Sphere with a Spectroreflectometer to Obtain Absolute Reflectance," J. Opt. Soc. Am. 56, 783-788 (1966)

Reflectance measurements that are made on a scale that is not relative to an arbitrary standard are often called “absolute” measurements. The method presented here uses an auxiliary sphere with a double-beam integrating-sphere spectrophotometer to make measurements on an absolute basis. The basic requirements are: (1) The auxiliary sphere must be uniformly coated with a highly-reflecting, highly-diffusing material; (2) a flat plate must be coated in an identical manner to provide a measure of reflectance of the coating; (3) the interior-surface area of the sphere and the area of the entrance port must be measured.

The theory of the method is discussed and an error analysis is made. Reflectance data are reported for specimens of smoked MgO and pressed powders of MgO and BaSO_{4}.

The precision of repeatability has been evaluated from measurements of a Vitrolite reference standard. More than a dozen measurements at each of eight wavelengths made over a 3-year period exhibited a standard deviation of 0.003 for the spectral reflectance.

D. C. Baird, Experimentation: An Introduction to Measurement Theory and Experiment Design (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962).

“Tentative Recommended Practice for Preparation of Reference White Reflectance Standards,” ASTM Designation E 259-65T, Book of ASTM Standards, Part 30 (1966).

W. J. Dixon and F. J. Massey, Introduction to Statistical Analysis (McGraw-Hill Book Co., Inc., New York, 1957), 2nd ed.

Calibration of the Reflectance Standard for the Elrepho (Carl Zeiss, Oberkochen, Germany and New York, 1963).

1966 (1)

“Tentative Recommended Practice for Preparation of Reference White Reflectance Standards,” ASTM Designation E 259-65T, Book of ASTM Standards, Part 30 (1966).

1956 (1)

J. A. Van den Akker, L. R. Dearth, and W. M. Shillcox, J. Opt. Soc. Am. 46, 378A (1956);J. Opt. Soc. Am. 56, 250 (1966).

W. J. Dixon and F. J. Massey, Introduction to Statistical Analysis (McGraw-Hill Book Co., Inc., New York, 1957), 2nd ed.

Shillcox, W. M.

J. A. Van den Akker, L. R. Dearth, and W. M. Shillcox, J. Opt. Soc. Am. 46, 378A (1956);J. Opt. Soc. Am. 56, 250 (1966).

Van den Akker, J. A.

J. A. Van den Akker, L. R. Dearth, and W. M. Shillcox, J. Opt. Soc. Am. 46, 378A (1956);J. Opt. Soc. Am. 56, 250 (1966).

ASTM Designation E 259-65T, Book of ASTM Standards (1)

“Tentative Recommended Practice for Preparation of Reference White Reflectance Standards,” ASTM Designation E 259-65T, Book of ASTM Standards, Part 30 (1966).

J. Opt. Soc. Am. (2)

J. A. Van den Akker, L. R. Dearth, and W. M. Shillcox, J. Opt. Soc. Am. 46, 378A (1956);J. Opt. Soc. Am. 56, 250 (1966).

Auxiliary-sphere reflectance as a function of coating reflectance for three values of f, the ratio of the area of the port to the area of the entire sphere.

Curves showing the percentage error in reflectance 100 Δρ_{F}/ρ_{F} for various percentage errors in f, Q_{F}, and Q_{s}, computed from Eq. (7) for values of Φ equal to 0.5, 1, 2, 4, and 6% and for f=0.01.

Photograph of the disassembled precision-auxiliary sphere with jig used to provide accurately dimensioned interior. coating for pressed-power specimens.

Tracing of the curve sheet from a General Electric recording spectrophotometer used to compute absolute-reflectance data for the visible spectrum, 0.40 to 0.75 μm. All of the specimens were measured relative to the same comparison specimen, a specimen pressed from powder removed from the sphere: Curve (1) is the 100% curve obtained with the two pressed-powder specimens; Curve (2) was obtained with the Vitrolite-reference standard V1-G3; Curve (3) was obtained for a 15-cm auxiliary sphere with a pressed-MgO coating and a 2.54-cm port.

Average values of reflectance ρ and the standard deviation of a single measurement computed from 12 measurements.
Average values of reflectance ρ computed from 20 measurements and the estimated standard deviation of a single measurement as determined by multiplying the range of values by 0.307 as shown in Ref. 6, Table 8b(1), p. 404.
Reflectance ρ of a smoked-MgO specimen (1.0 mm thick) prepared in an argon–oxygen atmosphere to eliminate the possibility of the formation of magnesium nitride.
Average values of reflectance ρ and the standard deviation of a single measurement computed from 30 specimens of reagent-grade MgO (5 mm thick); powder from four different suppliers.
Average values of reflectance ρ and the standard deviation of a single measurement computed from 21 specimens of reagent-grade BaSO_{4} (5 mm thick); powder from four different suppliers.
The accuracy of specimens measured relative to Vitrolite involves the uncertainty of both determinations; δ is computed as
${[{({S}_{p\upsilon})}^{2}+{{S}_{p}}^{2}]}^{\frac{1}{2}}$.

Average values of reflectance ρ and range for two determinations.
Average values of reflectance ρ and estimated standard deviation S for 18 specimens.
Reflectance values ρ for one specimen. Note that this specimen has values higher than the average values reported for pressed specimens in Table II.
Average values of reflectance ρ for two specimens; powder from two suppliers.

Tables (3)

Table I

Effect of sphere-coating reflectance on instrument reading calculated by use of Eq. (5) for an auxiliary sphere with an f value of 0.01.

Average values of reflectance ρ and the standard deviation of a single measurement computed from 12 measurements.
Average values of reflectance ρ computed from 20 measurements and the estimated standard deviation of a single measurement as determined by multiplying the range of values by 0.307 as shown in Ref. 6, Table 8b(1), p. 404.
Reflectance ρ of a smoked-MgO specimen (1.0 mm thick) prepared in an argon–oxygen atmosphere to eliminate the possibility of the formation of magnesium nitride.
Average values of reflectance ρ and the standard deviation of a single measurement computed from 30 specimens of reagent-grade MgO (5 mm thick); powder from four different suppliers.
Average values of reflectance ρ and the standard deviation of a single measurement computed from 21 specimens of reagent-grade BaSO_{4} (5 mm thick); powder from four different suppliers.
The accuracy of specimens measured relative to Vitrolite involves the uncertainty of both determinations; δ is computed as
${[{({S}_{p\upsilon})}^{2}+{{S}_{p}}^{2}]}^{\frac{1}{2}}$.

Average values of reflectance ρ and range for two determinations.
Average values of reflectance ρ and estimated standard deviation S for 18 specimens.
Reflectance values ρ for one specimen. Note that this specimen has values higher than the average values reported for pressed specimens in Table II.
Average values of reflectance ρ for two specimens; powder from two suppliers.