Abstract

The transmission and absorption properties of turbid media have been examined with Kubelka and Munk’s theory of the optics of intensely scattering material. The equation for the optical density of such material as a function of thickness has been derived and examined experimentally. It is shown that the reflectivity and scattering coefficient can be determined absolutely without reference to a standard material from the optical-density measurements. The absorption spectra of pigments in scattering media and in clear solution have been compared. It is shown that light in passing through a turbid sample may traverse an optical path which is many times the sample thickness. The practical consequence of this increased path length is an intensification of the absorption bands of pigments in light-scattering media. The theoretical expression for this intensification has been derived and tested experimentally. Spectral effects due to the physical binding of pigment molecules to the scattering particles have also been examined.

© 1962 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. L. Butler and K. H. Norris, Arch. Biochem. Biophys. 87;31 (1960).
    [Crossref] [PubMed]
  2. K. H. Norris and W. L. Butler, IRE Trans. Bio-Medical Electronics BME-8, 153 (1961).
    [Crossref]
  3. W. L. Butler and K. H. Norris, Modern Methods of Plant Analysis, edited by H. F. Linskens and M. V. Tracey (Springer-Verlag, Berlin, to be published).
  4. H. J. Channon and F. F. Renwick, B. V. Storr. Proc. Roy. Soc. (London) A94, 222 (1918).
    [Crossref]
  5. P. Kubelka and F. Munk, Z. tech. Physik 12, 593 (1931).
  6. S. Q. Duntley, J. Opt. Soc. Am. 32, 61 (1942).
    [Crossref]
  7. D. B. Judd, J. Research Nat’l. Bur. Standards 19, 287 (1937).
    [Crossref]
  8. J. L. Saunderson, J. Opt. Soc. Am. 32, 727 (1942).
    [Crossref]
  9. The mention of specific names or trade names is for the purpose of identification and does not imply any endorsement by the United States Government.
  10. P. Kubelka, J. Opt. Soc. Am. 38, 448 (1947).
    [Crossref]
  11. J. A. Van den Akker, Tappi 32, 498 (1949).
  12. P. Latimer, Plant Physiol. 34, 193 (1959).
  13. E. Charney (personal communication).
  14. H. Meistre, Cold Spring Harbor Symposia Quart. Biol. 3, 191 (1935).
    [Crossref]
  15. D. Keilin and E. F. Hartree, Nature 164, 254 (1949).
    [Crossref] [PubMed]
  16. L. M. M. Duysens, Biochim. et Biophys. Acta 19, 1 (1956).
    [Crossref]

1961 (1)

K. H. Norris and W. L. Butler, IRE Trans. Bio-Medical Electronics BME-8, 153 (1961).
[Crossref]

1960 (1)

W. L. Butler and K. H. Norris, Arch. Biochem. Biophys. 87;31 (1960).
[Crossref] [PubMed]

1959 (1)

P. Latimer, Plant Physiol. 34, 193 (1959).

1956 (1)

L. M. M. Duysens, Biochim. et Biophys. Acta 19, 1 (1956).
[Crossref]

1949 (2)

J. A. Van den Akker, Tappi 32, 498 (1949).

D. Keilin and E. F. Hartree, Nature 164, 254 (1949).
[Crossref] [PubMed]

1947 (1)

1942 (2)

1937 (1)

D. B. Judd, J. Research Nat’l. Bur. Standards 19, 287 (1937).
[Crossref]

1935 (1)

H. Meistre, Cold Spring Harbor Symposia Quart. Biol. 3, 191 (1935).
[Crossref]

1931 (1)

P. Kubelka and F. Munk, Z. tech. Physik 12, 593 (1931).

1918 (1)

H. J. Channon and F. F. Renwick, B. V. Storr. Proc. Roy. Soc. (London) A94, 222 (1918).
[Crossref]

Butler, W. L.

K. H. Norris and W. L. Butler, IRE Trans. Bio-Medical Electronics BME-8, 153 (1961).
[Crossref]

W. L. Butler and K. H. Norris, Arch. Biochem. Biophys. 87;31 (1960).
[Crossref] [PubMed]

W. L. Butler and K. H. Norris, Modern Methods of Plant Analysis, edited by H. F. Linskens and M. V. Tracey (Springer-Verlag, Berlin, to be published).

Channon, H. J.

H. J. Channon and F. F. Renwick, B. V. Storr. Proc. Roy. Soc. (London) A94, 222 (1918).
[Crossref]

Charney, E.

E. Charney (personal communication).

Duntley, S. Q.

Duysens, L. M. M.

L. M. M. Duysens, Biochim. et Biophys. Acta 19, 1 (1956).
[Crossref]

Hartree, E. F.

D. Keilin and E. F. Hartree, Nature 164, 254 (1949).
[Crossref] [PubMed]

Judd, D. B.

D. B. Judd, J. Research Nat’l. Bur. Standards 19, 287 (1937).
[Crossref]

Keilin, D.

D. Keilin and E. F. Hartree, Nature 164, 254 (1949).
[Crossref] [PubMed]

Kubelka, P.

P. Kubelka, J. Opt. Soc. Am. 38, 448 (1947).
[Crossref]

P. Kubelka and F. Munk, Z. tech. Physik 12, 593 (1931).

Latimer, P.

P. Latimer, Plant Physiol. 34, 193 (1959).

Meistre, H.

H. Meistre, Cold Spring Harbor Symposia Quart. Biol. 3, 191 (1935).
[Crossref]

Munk, F.

P. Kubelka and F. Munk, Z. tech. Physik 12, 593 (1931).

Norris, K. H.

K. H. Norris and W. L. Butler, IRE Trans. Bio-Medical Electronics BME-8, 153 (1961).
[Crossref]

W. L. Butler and K. H. Norris, Arch. Biochem. Biophys. 87;31 (1960).
[Crossref] [PubMed]

W. L. Butler and K. H. Norris, Modern Methods of Plant Analysis, edited by H. F. Linskens and M. V. Tracey (Springer-Verlag, Berlin, to be published).

Renwick, F. F.

H. J. Channon and F. F. Renwick, B. V. Storr. Proc. Roy. Soc. (London) A94, 222 (1918).
[Crossref]

Saunderson, J. L.

Van den Akker, J. A.

J. A. Van den Akker, Tappi 32, 498 (1949).

Arch. Biochem. Biophys. (1)

W. L. Butler and K. H. Norris, Arch. Biochem. Biophys. 87;31 (1960).
[Crossref] [PubMed]

B. V. Storr. Proc. Roy. Soc. (London) (1)

H. J. Channon and F. F. Renwick, B. V. Storr. Proc. Roy. Soc. (London) A94, 222 (1918).
[Crossref]

Biochim. et Biophys. Acta (1)

L. M. M. Duysens, Biochim. et Biophys. Acta 19, 1 (1956).
[Crossref]

Cold Spring Harbor Symposia Quart. Biol. (1)

H. Meistre, Cold Spring Harbor Symposia Quart. Biol. 3, 191 (1935).
[Crossref]

IRE Trans. Bio-Medical Electronics (1)

K. H. Norris and W. L. Butler, IRE Trans. Bio-Medical Electronics BME-8, 153 (1961).
[Crossref]

J. Opt. Soc. Am. (3)

J. Research Nat’l. Bur. Standards (1)

D. B. Judd, J. Research Nat’l. Bur. Standards 19, 287 (1937).
[Crossref]

Nature (1)

D. Keilin and E. F. Hartree, Nature 164, 254 (1949).
[Crossref] [PubMed]

Plant Physiol. (1)

P. Latimer, Plant Physiol. 34, 193 (1959).

Tappi (1)

J. A. Van den Akker, Tappi 32, 498 (1949).

Z. tech. Physik (1)

P. Kubelka and F. Munk, Z. tech. Physik 12, 593 (1931).

Other (3)

W. L. Butler and K. H. Norris, Modern Methods of Plant Analysis, edited by H. F. Linskens and M. V. Tracey (Springer-Verlag, Berlin, to be published).

The mention of specific names or trade names is for the purpose of identification and does not imply any endorsement by the United States Government.

E. Charney (personal communication).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Schematic diagram of monochromator, L, tungsten lamp; S1 and S2, entrance and exit slits; P, multiplier-type phototube; M, motor; H, two-position cell holder; G1, wavelength potentiometer; G2, compensation potentiometer. End view of monochromator and phototube housing. m, mirror; C, sample cell; 1, lens.

Fig. 2
Fig. 2

Optical density of CaCO3 at 546 mμ versus thickness. 1 g gives 0.075 cm-thick layer. Solid line: 0.865 intercept and 2.16/cm slope. Dashed line: 0.930 intercept 1.83 slope.

Fig. 3
Fig. 3

Spectra of different amounts of rose bengale. Solid curves: in CaCO3 scattering medium 0.6 cm thick. Dashed curves: in water.

Fig. 4
Fig. 4

Optical-density difference between 546 and 570 mμ versus amount of rose bengale in CaCO3 scattering medium (1 through 6 μg) and in water (50 and 100 μg).

Fig. 5
Fig. 5

Absorption spectra of rose bengale corrected for baselines.

Fig. 6
Fig. 6

Absorption spectra of different amounts of NaCu chlorophyllin. Solid curves: in CaCO3 scattering medium 0.6 cm thick. Dashed curves: in water.

Fig. 7
Fig. 7

Optical-density difference between 633 and 660 mμ versus amount of chlorophyllin in CaCO3 scattering medium. In clear solution 1000 μg gave an optical-density difference of 0.44 between the peak at 630 mμ and the reference at 660 mμ.

Fig. 8
Fig. 8

Optical density of CaCO3 at 633 mμ versus thickness. 1 g gives 0.075 cm-thick layer. Solid line: 0.975 intercept and 1.62/cm slope. Dashed line: 1.00 intercept and 1.58/cm slope.

Fig. 9
Fig. 9

Optical-density difference between absorption maximum and 570 mμ versus amount of rose bengale in Al2O3 scattering media. In clear solution the optical-density difference between 546 and 570 mμ of 100 μg of rose bengale was 0.45.

Fig. 10
Fig. 10

Optical density of 1.0-μ Al2O3 at 546 mμ versus thickness. 1 gm gives 0.10-cm thick layer. Solid line: 1.28 intercept and 4.37/cm slope. Dashed line: 1.34 intercept and 4.06/cm slope.

Fig. 11
Fig. 11

Optical density of polystyrene latexes of various particle sizes at 630 mμ versus thickness.

Tables (1)

Tables Icon

Table I Calculated and measured values of β for polystyrene latexes at different particle sizes.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

T = b ( a sinh b S X + b cosh b S X ) - 1 ;
T = ( 1 - R 2 ) e - b S X 1 - R 2 e - 2 b S X .
O . D . = log T - 1 = log [ ( 1 - R 2 ) - 1 ] + 0.434 b S X + log ( 1 - R 2 e - 2 b S X ) .
O . D . = log [ ( 1 - R 2 ) - 1 ] + 0.434 b S X .
O . D . - log ( 1 - R 2 e - 2 b S X ) = log [ ( 1 - R 2 ) - 1 ] + 0.434 b S X .
O . D . sol = k X ,
O . D . sus = β k X .
R = 1 + ( K / S ) - ( K 2 / S 2 ) + [ ( 2 K / S ) 1 2 ]
b = [ ( K 2 / S 2 ) + ( 2 K / S ) 1 2 ] .
K = 2 ( 2.3 k ) .
d ( O . D . ) d k X = β = 2 [ - 4 R 3 ( 1 - R 2 ) 2 S X + 1 + R 2 1 - R 2 ] .
β = O . D . sus / O . D . sol .