Abstract

<p>The derived laws apply to layers whose scattering coefficient <i>S</i> and absorption coefficient <i>K</i> vary vertically to the surface of the layer. In the general case the differential equations of the preceding paper [P. Kubelka, J. Opt. Soc. Am. <b>38</b>, 448 (1948)] must be used; the coefficients, however, hitherto constant, now are functions of the distance <i>x</i> from the surface. In the practically important case in which <i>K/S</i> is constant, one may introduce the variable <i>p</i>, such that <i>p</i> ∫<sub>0</sub><sup><i>x</i></sup><i>S</i>(<i>x</i>)<i>dx</i>. One reduces thereby the nonhomogeneous to the previously treated homogeneous case.</p><p>Transmittance <i>T</i><sub>1,2</sub> and reflectance <i>R</i><sub>1,2</sub> of two nonhomogeneous sheets can be calculated by the following equations: [Equations] where <i>T</i><sub>1</sub><i>T</i><sub>2</sub><i>R</i><sub>1</sub>, <i>R</i><sub>2</sub> are the transmittances and reflectances of the single sheets, and R<sub>1</sub> represents the reflectance of the first sheet when illuminated in the inverse direction. Analogous formulas for more sheets and formulas relating transmittance, reflectance for specimens upon black, gray or white backing surfaces, and contrast ratio, are derived.</p><p>It is shown by theory and experiment that reflectance and absorption of a nonhomogeneous specimen depend on the direction of illumination, whereas transmittance does not.</p>

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  1. Paul Kubelka and Franz Munk, Z. tech. Phys. 12, 593 (1931). See also abstracts in English given by F. A. Steele, reference 5; Deane B. Judd, reference 6; H. A. Gardner, Physical and Chemical Examination of Paints, Varnishes, Laquers and Colors (Inst. Paints Varnishes Research, Washington, D. C., 1939), ninth edition, p. 10ƒƒ.
  2. Paul Kubelka, J. Opt. Soc. Am. 38, 448 (1948).
  3. Åke S :son Stenius, Svensk Papperstidn. 56, 607 (1953).
  4. F. A. Steele, Paper Trade J. 100, 37 (1935).
  5. Deane B. Judd, (with collaboration of Harrison, Sweo, Hickson, Eickjoff, Show, and Pfaffenbarger) J. Research Natl. Bur. Standards 39, 287 (1937). Deane B. Judd, Paper Trade J. (1938), January 6.
  6. Åke S:son Stenius, Svensk Papperstidn. 54, 663 (1951); (reference 6) 54, 701 (1951).
  7. Gurevic, Physik. Z. 31, 753 (1930).
  8. Hans Zocher, Kolloidchemisches Taschenbuch, (1948) third edition, p. 83.
  9. Deane B. Judd, J. Research Natl. Bur. Standards 12, 345 (1934) (reference 9); 13, 281 (1934).

1953 (1)

Åke S :son Stenius, Svensk Papperstidn. 56, 607 (1953).

1951 (1)

Åke S:son Stenius, Svensk Papperstidn. 54, 663 (1951); (reference 6) 54, 701 (1951).

1948 (2)

Hans Zocher, Kolloidchemisches Taschenbuch, (1948) third edition, p. 83.

Paul Kubelka, J. Opt. Soc. Am. 38, 448 (1948).

1937 (1)

Deane B. Judd, (with collaboration of Harrison, Sweo, Hickson, Eickjoff, Show, and Pfaffenbarger) J. Research Natl. Bur. Standards 39, 287 (1937). Deane B. Judd, Paper Trade J. (1938), January 6.

1935 (1)

F. A. Steele, Paper Trade J. 100, 37 (1935).

1934 (1)

Deane B. Judd, J. Research Natl. Bur. Standards 12, 345 (1934) (reference 9); 13, 281 (1934).

1931 (1)

Paul Kubelka and Franz Munk, Z. tech. Phys. 12, 593 (1931). See also abstracts in English given by F. A. Steele, reference 5; Deane B. Judd, reference 6; H. A. Gardner, Physical and Chemical Examination of Paints, Varnishes, Laquers and Colors (Inst. Paints Varnishes Research, Washington, D. C., 1939), ninth edition, p. 10ƒƒ.

1930 (1)

Gurevic, Physik. Z. 31, 753 (1930).

Judd, Deane B.

Deane B. Judd, (with collaboration of Harrison, Sweo, Hickson, Eickjoff, Show, and Pfaffenbarger) J. Research Natl. Bur. Standards 39, 287 (1937). Deane B. Judd, Paper Trade J. (1938), January 6.

Deane B. Judd, J. Research Natl. Bur. Standards 12, 345 (1934) (reference 9); 13, 281 (1934).

Kubelka, Paul

Paul Kubelka, J. Opt. Soc. Am. 38, 448 (1948).

Paul Kubelka and Franz Munk, Z. tech. Phys. 12, 593 (1931). See also abstracts in English given by F. A. Steele, reference 5; Deane B. Judd, reference 6; H. A. Gardner, Physical and Chemical Examination of Paints, Varnishes, Laquers and Colors (Inst. Paints Varnishes Research, Washington, D. C., 1939), ninth edition, p. 10ƒƒ.

Munk, Franz

Paul Kubelka and Franz Munk, Z. tech. Phys. 12, 593 (1931). See also abstracts in English given by F. A. Steele, reference 5; Deane B. Judd, reference 6; H. A. Gardner, Physical and Chemical Examination of Paints, Varnishes, Laquers and Colors (Inst. Paints Varnishes Research, Washington, D. C., 1939), ninth edition, p. 10ƒƒ.

Steele, F. A.

F. A. Steele, Paper Trade J. 100, 37 (1935).

Stenius, Åke S:son

Åke S :son Stenius, Svensk Papperstidn. 56, 607 (1953).

Åke S:son Stenius, Svensk Papperstidn. 54, 663 (1951); (reference 6) 54, 701 (1951).

Zocher, Hans

Hans Zocher, Kolloidchemisches Taschenbuch, (1948) third edition, p. 83.

Other (9)

Paul Kubelka and Franz Munk, Z. tech. Phys. 12, 593 (1931). See also abstracts in English given by F. A. Steele, reference 5; Deane B. Judd, reference 6; H. A. Gardner, Physical and Chemical Examination of Paints, Varnishes, Laquers and Colors (Inst. Paints Varnishes Research, Washington, D. C., 1939), ninth edition, p. 10ƒƒ.

Paul Kubelka, J. Opt. Soc. Am. 38, 448 (1948).

Åke S :son Stenius, Svensk Papperstidn. 56, 607 (1953).

F. A. Steele, Paper Trade J. 100, 37 (1935).

Deane B. Judd, (with collaboration of Harrison, Sweo, Hickson, Eickjoff, Show, and Pfaffenbarger) J. Research Natl. Bur. Standards 39, 287 (1937). Deane B. Judd, Paper Trade J. (1938), January 6.

Åke S:son Stenius, Svensk Papperstidn. 54, 663 (1951); (reference 6) 54, 701 (1951).

Gurevic, Physik. Z. 31, 753 (1930).

Hans Zocher, Kolloidchemisches Taschenbuch, (1948) third edition, p. 83.

Deane B. Judd, J. Research Natl. Bur. Standards 12, 345 (1934) (reference 9); 13, 281 (1934).

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