Abstract

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.

© 1966 Optical Society of America

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References

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  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).
  2. Also referred to as the comparison mode, and the substitution mode, respectively.
  3. J. A. Jacques and H. F. Kuppenheim, J. Opt. Soc. Am. 45, 460 (1955).
    [Crossref]
  4. D. C. Baird, Experimentation: An Introduction to Measurement Theory and Experiment Design (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962).
  5. “Tentative Recommended Practice for Preparation of Reference White Reflectance Standards,” ASTM Designation E 259-65T, Book of ASTM Standards, Part 30 (1966).
  6. W. J. Dixon and F. J. Massey, Introduction to Statistical Analysis (McGraw-Hill Book Co., Inc., New York, 1957), 2nd ed.
  7. 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).

1955 (1)

Baird, D. C.

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

Dearth, L. R.

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).

Dixon, W. J.

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

Jacques, J. A.

Kuppenheim, H. F.

Massey, F. J.

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).

J. A. Jacques and H. F. Kuppenheim, J. Opt. Soc. Am. 45, 460 (1955).
[Crossref]

Other (4)

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

Also referred to as the comparison mode, and the substitution mode, respectively.

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).

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Figures (6)

F. 1
F. 1

Schematic diagram of double-beam spectrophotometer with integrating sphere and auxiliary sphere attached.

F. 2
F. 2

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.

F. 3
F. 3

Curves showing the percentage error in reflectance 100 ΔρFF for various percentage errors in f, QF, and Qs, computed from Eq. (7) for values of Φ equal to 0.5, 1, 2, 4, and 6% and for f=0.01.

F. 4
F. 4

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

F. 5
F. 5

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.

F. 6
F. 6

Tracing of the near-infrared spectrum, 0.73 to 1.08 μm, for the same specimens as Fig. 5.

Tables (3)

Tables Icon

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.

Tables Icon

Table II Absolute reflectance values 0.4 to 0.75 μm.

Tables Icon

Table III Absolute reflectance values 0.73 to 1.08 μm.

Equations (20)

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ρ s = ρ F f / ( 1 ρ F ) ( 1 f ) .
Q s = K ( ρ s / ρ c ) .
Q F = K ( ρ F / ρ c ) .
Q s / Q F = f / ( 1 ρ F ) ( 1 f ) .
ρ F = ( 1 f ) ( Q F / Q s ) / ( 1 f ) .
f = A P / A s = 1 / 2 [ 1 ( 1 ( r / R ) 2 ) 1 2 ] ,
A P = 2 π R h A s = 4 π R 2 ,
Q s = K ( ρ F / ρ c ) f / ( 1 ρ F ) ( 1 f ) .
( Δ Z ) 2 = i ( Z X i Δ X i ) 2 .
( Δ ρ F ) 2 = ( 1 Q F / Q s ( 1 f ) 2 Δ f ) 2 + ( f Δ Q F Q s ( 1 f ) ) 2 + ( f Q F Δ Q s Q s 2 ( 1 f ) ) 2 .
( Δ ρ F ) 2 = 4.3 × 10 8 + 0.32 × 10 8 + 5.0 × 10 8 Δ ρ F = 0.00031 .
( Δ ρ F ) 2 = 1.1 × 10 6 + 5.5 × 10 8 + 13.8 × 10 6 ,
Δ ρ F = 0.0039 .
( Δ ρ F ) 2 = ( 1 ρ F 1 f Δ f f ) 2 + ( 1 ρ F ( 1 f ) ( 1 f ) Δ Q F Q F ) 2 + ( 1 ρ F ( 1 f ) ( 1 f ) Δ Q s Q s ) 2 ( 1 ρ F ( 1 f ) 1 f ) 2 [ ( Δ f f ) 2 + ( Δ Q F Q F ) 2 + ( Δ Q s Q s ) 2 ] , for f < 0.04 .
Δ ρ F ρ F ( 1 ρ F ) ( 1 f ) ρ F ( 1 f ) Φ ,
Φ = [ ( Δ f f ) 2 + ( Δ Q F Q F ) 2 + ( Δ Q s Q s ) 2 ] 1 2 .
Δ ρ F / ρ F = [ ( 1 ρ F ) ( 1 0.01 ) / ρ F ( 1 0.01 ) ] Φ .
Δ ρ F / ρ F [ ( 1 ρ F ) ( 1 0.01 ) / ρ F ( 1 0.01 ) + ] Φ [ ( 1 ρ F ) ( 1 0.01 ) / ρ F ( 1 0.01 ) ] Φ + Φ ,
Δ f / f 2 [ ( Δ r / r ) 2 + ( Δ R / R ) 2 ] 1 2 .
ρ υ = ( ρ F / Q F ) Q υ .