Abstract

A simple model for transmittance measurements with an integrating sphere is presented. The scattered light is divided into three components, each resulting in its own separate contribution to the detector signal. These contributions depend on the scattering angle and mode of operation. The true specular, diffuse, and total transmittance values are obtained as functions of the signal outputs from a reference reading, a total transmittance reading, and a diffuse transmittance reading. Two different modes of operation are distinguished involving a BaSO4 plate and an Al mirror. Experimental results are presented illustrating the model for two samples with different scattering characteristics.

© 1991 Optical Society of America

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References

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    [CrossRef]
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  7. F. J. J. Clarke, J. A. Compton, “Correction Methods for Integrating Sphere Measurement of Hemispherical Reflectance,” Color Res. Appl. 11, 253–262 (1986).
    [CrossRef]
  8. A. Roos, C. G. Ribbing, M. Bergkvist, “Anomalies in Integrating Sphere Measurements on Structured Samples,” Appl. Opt. 27, 3828–3832 (1988).
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1989 (2)

1988 (2)

1986 (1)

F. J. J. Clarke, J. A. Compton, “Correction Methods for Integrating Sphere Measurement of Hemispherical Reflectance,” Color Res. Appl. 11, 253–262 (1986).
[CrossRef]

1980 (1)

1970 (1)

M. W. Finkel, “Integrating Sphere Theory,” Opt. Commun. 2, 25–28 (1970).
[CrossRef]

1967 (1)

1965 (2)

1955 (1)

Bergkvist, M.

Clarke, F. J. J.

F. J. J. Clarke, J. A. Compton, “Correction Methods for Integrating Sphere Measurement of Hemispherical Reflectance,” Color Res. Appl. 11, 253–262 (1986).
[CrossRef]

Compton, J. A.

F. J. J. Clarke, J. A. Compton, “Correction Methods for Integrating Sphere Measurement of Hemispherical Reflectance,” Color Res. Appl. 11, 253–262 (1986).
[CrossRef]

Finkel, M. W.

M. W. Finkel, “Integrating Sphere Theory,” Opt. Commun. 2, 25–28 (1970).
[CrossRef]

Goebel, D. G.

Hanssen, L. M.

Hisdal, B. J.

Hsia, J. J.

Jacquez, J. A. J.

Kuppenheim, H. F.

Lovell, D. J.

D. J. Lovell, Integrating Sphere Performance (Labsphere, North Sutton, NH, 1981).

Ribbing, C. G.

Roos, A.

Snail, K. A.

Weidner, V. R.

Appl. Opt. (6)

Color Res. Appl. (1)

F. J. J. Clarke, J. A. Compton, “Correction Methods for Integrating Sphere Measurement of Hemispherical Reflectance,” Color Res. Appl. 11, 253–262 (1986).
[CrossRef]

J. Opt. Soc. Am. (3)

Opt. Commun. (1)

M. W. Finkel, “Integrating Sphere Theory,” Opt. Commun. 2, 25–28 (1970).
[CrossRef]

Other (3)

D. J. Lovell, Integrating Sphere Performance (Labsphere, North Sutton, NH, 1981).

NBS Standard Reference Material, Lg 2019(A) and 2021.

NPL White and Black Reflectance Standards for Colorimetry and Spectrophotometry, QU h 41, National Physics Laboratory, Teddington, U.K.

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Figures (11)

Fig. 1
Fig. 1

Design of the Beckman integrating sphere: 1, entrance port–reference beam; 2, entrance port–sample beam; 3, sample port; 4, reference port; 5, specular exit port; 6, PbS detector; 7, PM detector.

Fig. 2
Fig. 2

Schematic representation of the transmitted components of radiation through a sample.

Fig. 3
Fig. 3

Integrating sphere in the BaSO4 mode set for total and diffuse measurements.

Fig. 4
Fig. 4

Integrating sphere in the Al mode set for total and diffuse measurements.

Fig. 5
Fig. 5

How transmitted laser light is scattered through three different samples: (a) clear float glass; (b) plastic pane; (c) thin diffuse plastic film.

Fig. 6
Fig. 6

Transmittance spectra of the highly scattering sample for different values of parameter B in the BaSO4 mode.

Fig. 7
Fig. 7

Transmittance spectra of the moderately scattering sample for different values of parameter B in the BaSO4 mode.

Fig. 8
Fig. 8

Transmittance spectra of the highly scattering sample for different values of parameters B1, B2, and B3 in the Al mode.

Fig. 9
Fig. 9

Transmittance spectra of the moderately scattering sample for different values of parameters B1, B2, and B3 in the Al mode.

Fig. 10
Fig. 10

Comparison of transmittance spectra using the BaSO4 mode and the Al mode with parameter values as indicated. Highly scattering sample.

Fig. 11
Fig. 11

Comparison of transmittance spectra using the BaSO4 mode and the Al mode with parameter values as indicated. Moderately scattering sample.

Equations (19)

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S 1 = A F B R B / F B R B ,
S 2 = A [ T s b F B R B + ( 1 B ) T d b F B R B + B T d b ] / F B R B ,
S 3 = A [ ( 1 B ) T d b F B R B + B T d b ] / F B R B .
T s b = ( S 2 S 3 ) / S 1 ;
T d b = S 3 / [ S 1 ( 1 B + B / F B R B ) ] ,
T t = T s b + T d b .
S 1 = A R M R B / F B R B ,
T d = T d 1 + T d 2 + T d 3 .
T d = B 1 T d + B 2 T d + B 3 T d ,
B 1 + B 2 + B 3 = 1 .
S 2 = A ( T s R M R B + T d 1 R M F M R B + T d 2 R B F B + T d 3 ) / F B R B
S 2 = A [ T s R M / F B + T d ( B 1 R M F M / F B + B 2 + B 3 / F B R B ) ] .
S 3 = A T d ( B 1 R M F M / F B + B 2 + B 3 / F B R B ) .
T s = ( S 2 S 3 ) / S 1 ,
T d = S 3 / S 1 ( B 1 F M + B 2 F B / R M + B 3 / R M R B ) ,
T t = T d + T s .
T d 1 = T s d T s .
B 1 = ( T s b T s ) / T d .
B = B 3 / ( B 2 + B 3 ) .

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