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 BaSO4.
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.
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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 BaSO4 (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
.
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 BaSO4 (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
.
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.
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