Abstract

An integrating sphere for determining spectral reflectance and transmittance as a function of angle of incidence and wavelength in the 0.33- to 2.5-μ region is described. Geometrical arrangement of sample, entrance port, and detector as well as directional characteristics of detector and sphere wall coating permit absolute or relative measurements to be made for a sample with an arbitrary reflection-distribution function.

© 1961 Optical Society of America

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References

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  1. The ending “ance” is used to denote the radiation characteristic of a surface system that may be composed of many layers or particles and may be characterized by its geometry such as a surface roughness. The ending “ivity” is reserved for the characteristic of a perfectly plane interface between media of different indices of refraction.
  2. H. J. McNicholas, Natl. Bur. Standards, J. Research 1, 29 (1928).
    [Crossref]
  3. C. v. Fragstein, Optik 12, 60 (1955).
  4. R. V. Dunkle, “Spectral reflectance measurements,” in Surface Effects on Spacecraft Materials, edited by F. J. Clauss (John Wiley & Sons, Inc., New York, 1960).
  5. B. P. Kozyrev and O. E. Vershinin, Optics and Spectroscopy 6, 345 (1959).
  6. A. H. Karrer, Bur. Standards, Sci. Papers 17, 203 (1922).
    [Crossref]
  7. A. H. Taylor, J. Opt. Soc. Am. 25, 51 (1935).
    [Crossref]
  8. F. Benford, J. Opt. Soc. Am. 24, 165 (1934).
    [Crossref]
  9. J. A. Jacquez and H. R. Kuppenheim, J. Opt. Soc. Am. 45, 460 (1955).
    [Crossref]
  10. A. C. Hardy and J. Pineo, J. Opt. Soc. Am. 21, 502 (1931).
    [Crossref]
  11. C. P. Tingwaldt, Optik 9, 323 (1952).
  12. A. S. Toporets, Optics and Spectroscopy 7, 471 (1959).
  13. P. Moon, The Scientific Basis of Illuminating Engineering (McGraw-Hill Book Company, Inc., New York, 1936), pp. 254, 291.
  14. W. Budde, J. Opt. Soc. Am. 50, 217 (1960).
    [Crossref]
  15. P. A. Tellex and J. P. Waldron, J. Opt. Soc. Am. 45, 19 (1955).
    [Crossref]
  16. G. Coolures, Master of Engineering thesis, University of California, Berkeley, California, 1959.
  17. All equations are written for monochromatic energy. All therefore require integration over the monochromator slit function, but for convenience this integration is not shown explicitly.
  18. O. H. Olson and D. A. Pontarelli, J. Opt. Soc. Am. 47, 119 (1957).
  19. K. Forsterling and V. Freedericksz, Ann. Physik 40, 201 (1913).
    [Crossref]
  20. J. T. Gier, R. V. Dunkle, and J. T. Bevans, J. Opt. Soc. Am. 44, 558 (1954).
    [Crossref]
  21. W. E. K. Middleton and C. L. Sanders, J. Opt. Soc. Am. 41, 419 (1951).
    [Crossref] [PubMed]

1960 (1)

1959 (2)

A. S. Toporets, Optics and Spectroscopy 7, 471 (1959).

B. P. Kozyrev and O. E. Vershinin, Optics and Spectroscopy 6, 345 (1959).

1957 (1)

O. H. Olson and D. A. Pontarelli, J. Opt. Soc. Am. 47, 119 (1957).

1955 (3)

1954 (1)

1952 (1)

C. P. Tingwaldt, Optik 9, 323 (1952).

1951 (1)

1935 (1)

1934 (1)

1931 (1)

1928 (1)

H. J. McNicholas, Natl. Bur. Standards, J. Research 1, 29 (1928).
[Crossref]

1922 (1)

A. H. Karrer, Bur. Standards, Sci. Papers 17, 203 (1922).
[Crossref]

1913 (1)

K. Forsterling and V. Freedericksz, Ann. Physik 40, 201 (1913).
[Crossref]

Benford, F.

Bevans, J. T.

Budde, W.

Coolures, G.

G. Coolures, Master of Engineering thesis, University of California, Berkeley, California, 1959.

Dunkle, R. V.

J. T. Gier, R. V. Dunkle, and J. T. Bevans, J. Opt. Soc. Am. 44, 558 (1954).
[Crossref]

R. V. Dunkle, “Spectral reflectance measurements,” in Surface Effects on Spacecraft Materials, edited by F. J. Clauss (John Wiley & Sons, Inc., New York, 1960).

Forsterling, K.

K. Forsterling and V. Freedericksz, Ann. Physik 40, 201 (1913).
[Crossref]

Fragstein, C. v.

C. v. Fragstein, Optik 12, 60 (1955).

Freedericksz, V.

K. Forsterling and V. Freedericksz, Ann. Physik 40, 201 (1913).
[Crossref]

Gier, J. T.

Hardy, A. C.

Jacquez, J. A.

Karrer, A. H.

A. H. Karrer, Bur. Standards, Sci. Papers 17, 203 (1922).
[Crossref]

Kozyrev, B. P.

B. P. Kozyrev and O. E. Vershinin, Optics and Spectroscopy 6, 345 (1959).

Kuppenheim, H. R.

McNicholas, H. J.

H. J. McNicholas, Natl. Bur. Standards, J. Research 1, 29 (1928).
[Crossref]

Middleton, W. E. K.

Moon, P.

P. Moon, The Scientific Basis of Illuminating Engineering (McGraw-Hill Book Company, Inc., New York, 1936), pp. 254, 291.

Olson, O. H.

O. H. Olson and D. A. Pontarelli, J. Opt. Soc. Am. 47, 119 (1957).

Pineo, J.

Pontarelli, D. A.

O. H. Olson and D. A. Pontarelli, J. Opt. Soc. Am. 47, 119 (1957).

Sanders, C. L.

Taylor, A. H.

Tellex, P. A.

Tingwaldt, C. P.

C. P. Tingwaldt, Optik 9, 323 (1952).

Toporets, A. S.

A. S. Toporets, Optics and Spectroscopy 7, 471 (1959).

Vershinin, O. E.

B. P. Kozyrev and O. E. Vershinin, Optics and Spectroscopy 6, 345 (1959).

Waldron, J. P.

Ann. Physik (1)

K. Forsterling and V. Freedericksz, Ann. Physik 40, 201 (1913).
[Crossref]

Bur. Standards, Sci. Papers (1)

A. H. Karrer, Bur. Standards, Sci. Papers 17, 203 (1922).
[Crossref]

J. Opt. Soc. Am. (9)

Natl. Bur. Standards, J. Research (1)

H. J. McNicholas, Natl. Bur. Standards, J. Research 1, 29 (1928).
[Crossref]

Optics and Spectroscopy (2)

B. P. Kozyrev and O. E. Vershinin, Optics and Spectroscopy 6, 345 (1959).

A. S. Toporets, Optics and Spectroscopy 7, 471 (1959).

Optik (2)

C. v. Fragstein, Optik 12, 60 (1955).

C. P. Tingwaldt, Optik 9, 323 (1952).

Other (5)

R. V. Dunkle, “Spectral reflectance measurements,” in Surface Effects on Spacecraft Materials, edited by F. J. Clauss (John Wiley & Sons, Inc., New York, 1960).

The ending “ance” is used to denote the radiation characteristic of a surface system that may be composed of many layers or particles and may be characterized by its geometry such as a surface roughness. The ending “ivity” is reserved for the characteristic of a perfectly plane interface between media of different indices of refraction.

P. Moon, The Scientific Basis of Illuminating Engineering (McGraw-Hill Book Company, Inc., New York, 1936), pp. 254, 291.

G. Coolures, Master of Engineering thesis, University of California, Berkeley, California, 1959.

All equations are written for monochromatic energy. All therefore require integration over the monochromator slit function, but for convenience this integration is not shown explicitly.

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Figures (12)

Fig. 1
Fig. 1

Schematic of McNicholas absolute reflectometer.

Fig. 2
Fig. 2

Schematic of Tingwaldt absolute reflectometer.

Fig. 3
Fig. 3

Schematic of Toporets absolute reflectometer.

Fig. 4
Fig. 4

Integrating sphere.

Fig. 5
Fig. 5

Auxiliary optics.

Fig. 6
Fig. 6

Top view in the reference position for absolute reflectance measurements.

Fig. 7
Fig. 7

Detectors.

Fig. 8
Fig. 8

Directional response of detectors.

Fig. 9
Fig. 9

Fractional polarization of optical beam.

Fig. 10
Fig. 10

Absolute reflectance of platinum at 2 μ.

Fig. 11
Fig. 11

Absolute reflectance of quartz at 0.49 μ.

Fig. 12
Fig. 12

Comparison of the absolute spectral reflectance of magnesium oxide with measurements of Tellex and Waldron15 and Middleton and Sanders.21

Tables (2)

Tables Icon

Table I Explanation of symbols.

Tables Icon

Table II Errors in integrating sphere reflectometer.

Equations (28)

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ρ ( θ , ϕ ) = 0 2 π 0 π / 2 f ( θ , ϕ ; θ , ϕ ) sin θ cos θ d θ d ϕ .
V = A D A 2 K ( θ D , ϕ D ) N 2 ( θ 2 , ϕ 2 ) × [ cos θ 2 cos θ D / r D 2 2 ] d A 2 d A D ,
V = K ( π A D / A W ) A W N 2 d A W ,
π A W N W d A W = P ( ρ W + ρ W ρ ¯ W + ρ W ρ ¯ W 2 + ) π A W N W d A W = P ρ W / ( 1 - ρ ¯ W ) ,
P = A 1 0 2 π 0 π / 2 N 1 ( θ 1 , ϕ 1 ) sin θ 1 cos θ 1 d θ 1 d ϕ 1 d A 1 ,
P S = ρ S ( N E Ω E S A E ) ,
V S = ( K N E Ω E S A E ) ( A D / A W ) [ ρ W / ( 1 - ρ ¯ W ) ] ρ S .
V R = ( K N E Ω E S A E ) ( A D / A W ) [ ρ W / ( 1 - ρ ¯ W ) ] ρ R ,
P W = ( N E Ω E S A E ) .
V W = ( K N E Ω E S A E ) ( A D / A W ) [ ρ W / ( 1 - ρ ¯ W ) ] .
ρ S = ρ R ( V S / V R )
ρ S = ( V S / V W ) .
V S = K A D A W A W π N W d A W + K A D A S N S ( θ S , ϕ S ) cos θ S cos θ D r D S 2 d A S d A D .
A S N S ( θ S , ϕ S ) = N E Ω E S A E f ( θ 0 , ϕ 0 ; θ S , ϕ S )
K N E Ω E S A E ρ S p ,
p = A D f S ( θ 0 , ϕ 0 ; θ S , ϕ S ) ρ S cos θ S cos θ D r D S 2 d A D .
V S = K N E Ω E S A E A D A W ρ W 1 - ρ ¯ W × { 1 - p [ 1 - ρ ¯ W ρ W A W A D - ( 1 - ρ D ) ] } ,
V S - V S V S = p [ 1 - ρ ¯ W ρ W A W A D - ( 1 - ρ D ) ] ,
V S - V S V S = 4 sin θ 0 1 - ρ ¯ W ρ W - 4 A D A W ( 1 - ρ D ) ,
1 - ρ ¯ W = 1 4 sin θ 0 [ V S - V S V S ] .
ρ W N S ( θ S , ϕ S ) A S ( cos θ S / π r S W 2 ) ,
N S ( A S / A W ) ( ρ W ρ ¯ W / 1 - ρ ¯ W ) .
ρ W N E Ω E S A E f ( θ 0 , ϕ 0 ; θ S , ϕ S ) ( cos θ S / π r S W 2 ) ,
ρ W N E Ω E S A E ( 1 / 4 π r S W 2 ) [ ρ ¯ W / ( 1 - ρ ¯ W ) ] .
V S = K N E Ω E S A E A D A W ρ W 1 - ρ ¯ W ρ S [ ( 1 - ρ ¯ W ) q S - ρ ¯ W ] ,
K ¯ = ( 1 / A W ) A W K ( θ D , ϕ D ) d A W
q S = 4 π A W A W K ( θ D , ϕ D ) K ¯ f S ( θ 0 , ϕ 0 ; θ S , ϕ S ) ρ S ( θ 0 , ϕ 0 ) cos θ S d A W .
( V S / V R ) - ( ρ S / ρ R ) ( ρ S / ρ R ) = ( 1 - ρ ¯ W ) ( q S - q R ) ( 1 - ρ ¯ W ) q R - ρ ¯ W .