Abstract

A new experimental method has been developed to determine the scattering and absorption characteristics of a turbid material. Existing methods usually require transmission and reflection measurements carried out on a thin slab of the material under study; this method is based on reflection measurements carried out on bulk material. This will be of great advantage in many applications. This paper describes the measuring system and indicates the area of application of the method. Calibration measurements have been carried out to substantiate the approach.

© 1983 Optical Society of America

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References

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  1. W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979).
  2. R. A. J. Groenhuis, H. A. Ferwerda, J. J. Ten Bosch, Appl. Opt. 22, 2456 (1983).
    [CrossRef] [PubMed]
  3. R. A. J. Groenhuis, in Technical Digest, Topical Meeting on Optical Phenomena Peculiar to Matter of Small Dimensions (Optical Society of America, Washington D.C., 1980), paper WB-6.
  4. D. Spitzer, J. J. Ten Bosch, Calcif. Tissue Res. 17, 129 (1975).
    [CrossRef] [PubMed]
  5. P. S. Mudgett, L. W. Richards, Appl. Opt. 10, 1485 (1971).
    [CrossRef] [PubMed]
  6. P. S. Mudgett, L. W. Richards, J. Colloid Interface Sci. 39, 551 (1972).
    [CrossRef]
  7. W. E. Meador, W. R. Weaver, Appl. Opt. 18, 1204 (1979).
    [CrossRef] [PubMed]
  8. M. Abramowitz, I. A. Stegun, Eds. Handbook of Mathematical Functions (Dover, New York, 1965).

1983 (1)

1979 (1)

1975 (1)

D. Spitzer, J. J. Ten Bosch, Calcif. Tissue Res. 17, 129 (1975).
[CrossRef] [PubMed]

1972 (1)

P. S. Mudgett, L. W. Richards, J. Colloid Interface Sci. 39, 551 (1972).
[CrossRef]

1971 (1)

Egan, W. G.

W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979).

Ferwerda, H. A.

Groenhuis, R. A. J.

R. A. J. Groenhuis, H. A. Ferwerda, J. J. Ten Bosch, Appl. Opt. 22, 2456 (1983).
[CrossRef] [PubMed]

R. A. J. Groenhuis, in Technical Digest, Topical Meeting on Optical Phenomena Peculiar to Matter of Small Dimensions (Optical Society of America, Washington D.C., 1980), paper WB-6.

Hilgeman, T. W.

W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979).

Meador, W. E.

Mudgett, P. S.

P. S. Mudgett, L. W. Richards, J. Colloid Interface Sci. 39, 551 (1972).
[CrossRef]

P. S. Mudgett, L. W. Richards, Appl. Opt. 10, 1485 (1971).
[CrossRef] [PubMed]

Richards, L. W.

P. S. Mudgett, L. W. Richards, J. Colloid Interface Sci. 39, 551 (1972).
[CrossRef]

P. S. Mudgett, L. W. Richards, Appl. Opt. 10, 1485 (1971).
[CrossRef] [PubMed]

Spitzer, D.

D. Spitzer, J. J. Ten Bosch, Calcif. Tissue Res. 17, 129 (1975).
[CrossRef] [PubMed]

Ten Bosch, J. J.

Weaver, W. R.

Appl. Opt. (3)

Calcif. Tissue Res. (1)

D. Spitzer, J. J. Ten Bosch, Calcif. Tissue Res. 17, 129 (1975).
[CrossRef] [PubMed]

J. Colloid Interface Sci. (1)

P. S. Mudgett, L. W. Richards, J. Colloid Interface Sci. 39, 551 (1972).
[CrossRef]

Other (3)

M. Abramowitz, I. A. Stegun, Eds. Handbook of Mathematical Functions (Dover, New York, 1965).

W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979).

R. A. J. Groenhuis, in Technical Digest, Topical Meeting on Optical Phenomena Peculiar to Matter of Small Dimensions (Optical Society of America, Washington D.C., 1980), paper WB-6.

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Figures (6)

Fig. 1
Fig. 1

Geometry to measure backscattered light as a function of the distance r from the axis of the incident beam to the center of the detection area: top top view; below cross section.

Fig. 2
Fig. 2

Experimental arrangement: the relative radiance of the sample is measured as a function of r (see Fig. 1).

Fig. 3
Fig. 3

Diagram to read the values of s(1 − g) and a from the values of C1 and C2, which fit the calculated relative radiance curves (full line, diffusion theory; dashed line, Monte Carlo method2). The applicability area at a wavelength of 400 nm is the area on the left of the indicated limit (dotted line); at wavelengths between 500 and 700 nm the whole area may be used. The diagram is valid for the geometry used and for an index of refraction of 1.62.

Fig. 4
Fig. 4

Experimental relative radiance of three samples shown as a function of r (full lines). These curves were each fitted to six theoretical points calculated for definite values of s(1 − g) and a. These values are attributed to the respective measured curve.

Fig. 5
Fig. 5

Values of s(1 − g) as determined with the new method plotted vs those determined with the calibration method. The line shows the desired equality.

Fig. 6
Fig. 6

Values of a as determined with the new method plotted vs those determined with the calibration method. The line shows the desired equality.

Equations (6)

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s ( 1 g ) = 4 / 3 S + K , a = ½ K .
R ( r ) = i = 1 C i 1 r r K 1 ( λ i r ) ,
1 x x [ x K 1 ( x ) ] = K 0 ( x ) ,
R ( r ) = i = 1 C i λ i 2 K 0 ( λ i r ) .
R ( r ) i = 1 1.253 C i λ i 3 / 2 r 1 / 2 exp ( λ i r ) .
R ( r ) C 1 r 1 / 2 exp ( C 2 r ) .

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