Abstract

It is shown experimentally that the reflectance of a semi-infinite suspension of particles in a nonabsorbing matrix is independent of particle concentration, except at high concentrations where the reflectance usually falls.

© 1961 Optical Society of America

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References

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  1. G. V. Rozenberg, Bull. Acad. Sci. U.S.S.R., Phys. Ser. (English translation)  21, 1465 (1957).
  2. The coefficients used by different authors vary somewhat in definition, but this is of no importance in the present context.
  3. P. Kubelka and F. Munk, Z. tech. Physik 12, 593 (1931).
  4. S. Chandrasekhar, Radiative Transfer (Oxford University Press, New York, 1950).
  5. R. G. Giovanelli, Optica Acta (Paris) 2, 153 (1955).
    [Crossref]
  6. R. G. Giovanelli, Australian J. Phys. 10, 227 (1957).
    [Crossref]
  7. L. Amy, Compt. rend. 207, 329 (1938).
  8. Smithsonian Physical Tables (Smithsonian Institution, Washington, D. C., 1956), p. 536.
  9. S. G. Tinsley and B. A. Bowman, J. Oil and Colour Chemists’ Assoc. 32, 233 (1949).

1957 (2)

G. V. Rozenberg, Bull. Acad. Sci. U.S.S.R., Phys. Ser. (English translation)  21, 1465 (1957).

R. G. Giovanelli, Australian J. Phys. 10, 227 (1957).
[Crossref]

1955 (1)

R. G. Giovanelli, Optica Acta (Paris) 2, 153 (1955).
[Crossref]

1949 (1)

S. G. Tinsley and B. A. Bowman, J. Oil and Colour Chemists’ Assoc. 32, 233 (1949).

1938 (1)

L. Amy, Compt. rend. 207, 329 (1938).

1931 (1)

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

Amy, L.

L. Amy, Compt. rend. 207, 329 (1938).

Bowman, B. A.

S. G. Tinsley and B. A. Bowman, J. Oil and Colour Chemists’ Assoc. 32, 233 (1949).

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Oxford University Press, New York, 1950).

Giovanelli, R. G.

R. G. Giovanelli, Australian J. Phys. 10, 227 (1957).
[Crossref]

R. G. Giovanelli, Optica Acta (Paris) 2, 153 (1955).
[Crossref]

Kubelka, P.

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

Munk, F.

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

Rozenberg, G. V.

G. V. Rozenberg, Bull. Acad. Sci. U.S.S.R., Phys. Ser. (English translation)  21, 1465 (1957).

Tinsley, S. G.

S. G. Tinsley and B. A. Bowman, J. Oil and Colour Chemists’ Assoc. 32, 233 (1949).

Australian J. Phys. (1)

R. G. Giovanelli, Australian J. Phys. 10, 227 (1957).
[Crossref]

Bull. Acad. Sci. U.S.S.R., Phys. Ser. (1)

G. V. Rozenberg, Bull. Acad. Sci. U.S.S.R., Phys. Ser. (English translation)  21, 1465 (1957).

Compt. rend. (1)

L. Amy, Compt. rend. 207, 329 (1938).

J. Oil and Colour Chemists’ Assoc. (1)

S. G. Tinsley and B. A. Bowman, J. Oil and Colour Chemists’ Assoc. 32, 233 (1949).

Optica Acta (Paris) (1)

R. G. Giovanelli, Optica Acta (Paris) 2, 153 (1955).
[Crossref]

Z. tech. Physik (1)

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

Other (3)

S. Chandrasekhar, Radiative Transfer (Oxford University Press, New York, 1950).

The coefficients used by different authors vary somewhat in definition, but this is of no importance in the present context.

Smithsonian Physical Tables (Smithsonian Institution, Washington, D. C., 1956), p. 536.

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of the spectrophotometer used for reflectance measurements. The diffusing window is shielded from the pigment surface by a screen, and from the top surface of the reference plate by slight tilting of the plate.

Fig. 2
Fig. 2

Photomicrograph of a well-dispersed suspension of barium sulfate in water, taken with an objective of N.A. 0.75.

Fig. 3
Fig. 3

The total spectral reflectance at four wavelengths of a semi-infinite diffuser consisting of well-dispersed titanium dioxide (anatase) particles in a water matrix, plotted against titanium dioxide concentration.

Fig. 4
Fig. 4

The total spectral reflectance at four wavelengths of a semi-infinite diffuser consisting of magnesium carbonate particles in an air matrix, plotted against magnesium carbonate concentration.

Tables (3)

Tables Icon

Table I Total spectral reflectances of four well-dispersed aqueous pigment suspensions, tabulated against pigment concentration.

Tables Icon

Table II Total spectral reflectances of four commercially supplied well-dispersed pigment suspensions, tabulated against pigment concentration.

Tables Icon

Table III Total spectral reflectances of four pigments in an air matrix, tabulated against pigment concentration.

Equations (3)

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α = c α 0             and             σ = c σ 0 ,
R = R ( α / σ ) .
R = R ( α 0 / σ 0 ) ,