Abstract

The plate description of a typical, thin, compact plant leaf, introduced previously, has been generalized to the noncompact case and applied to experimental data including average reflectance and transmittance measurements on 200 mature, field-cotton leaves. A compact leaf has few and a noncompact leaf has many intercellular air spaces in the mesophyll. No statistically significant difference was found between the average leaf thickness and the mean effective water thickness of the leaves. The Kubelka-Munk scattering coefficient <i>s</i> for a typical leaf, measured at the 1-µ spectral region, is approximated by the relation <i>s</i> = <i>r</i>/<i>t</i>, where <i>r</i> and <i>t</i>, respectively, are the reflectance and transmittance of the leaf. The approximate equality of <i>r</i> and <i>t</i>, noted by previous investigators, is explained on the basis of the scattering of diffuse light within the leaf by critical internal reflections. Predictions from the plate (P) model for cotton leaves compare favorably with those of the Kubelka-Munk (K-M) and Melamed (M) theories. Applied to vegetation, all three theories predict a characteristic linear dimension related to the cellular structure of the leaf.

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  1. W. A. Allen and A. J. Richardson, J. Opt. Soc. Am. 58, 1023 (1968).
  2. P. Kubelka and F. Munk, Z. Tech. Physik 12, 593 (1931).
  3. W. A. Allen, H. W. Gausman, A. J. Richardson, and J. R. Thomas, J. Opt. Soc. Am. 59, 1376 (1969).
  4. N. T. Melamed, J. Appl. Phys. 34, 560 (1963).
  5. W. W. Wendlandt and H. G. Hecht, Reflectance Spectroscopy (Interscience Publ., John Wiley & Sons, Inc., New York, 1966), p. 62.
  6. A. C. Hardy and F. H. Perrin, The Principles of Optics (McGraw—Hill Book Co., New York, 1932), p. 24.
  7. Seishi Isobe, Bull. Natl. Inst. Agricultural Sci. (Japan) Ser. A, No. 16 (March 1969).
  8. D. M. Gates, H. J. Keegan, J. C. Schleter, and V. R. Weidner, Appl. Opt. 4, 11 (1965).
  9. E. I. Rabinowitch, Photosynthesis and Related Processes (Interscience Publ., John Wiley & Sons, Inc., New York, 1961), Vol. II, Part 1.
  10. R. A. Moss and W. E. Loomis, Plant Physiol. 27, 370 (1952).
  11. H. W. Gausman, W. A. Allen, V. I. Myers, and R. Cardenas, Agron. J. 61, 374 (1969).
  12. V. I. Myers and W. A. Allen, Appl. Opt. 7, 1819 (1968).
  13. Trade names are included for information only and do not constitute endorsement by the U. S. Department of Agriculture.
  14. C. T. de Wit, Agr. Res. Rep. 663. Inst. Biol. Chem. Res. on Field Crops and Herbage, Wageningen, Netherlands (1965).
  15. G. Kortüm, W. Braun, and G. Herzog, Angew. Chem. 2, 333 (1963).
  16. G. G. Stokes, Proc. Roy. Soc. (London) 11, 545 (1862).
  17. G. W. Ingle. Note on coincidence of equations for the reflectance of translucent films. American Society for Testing and Materials Bulletin 116, 32 (1942).
  18. F. Stern, Appl. Opt. 3, 111 (1964).
  19. P. Kubelka, J. Opt. Soc. Am. 38, 448 (1948).
  20. M. Centeno, J. Opt. Soc. Am. 31, 245 (1941).
  21. R. Willstätter and A. Stoll, Untersuchungen über die Assimilation der Kohlensäure (Springer-Verlag, Berlin, 1913).
  22. M. D. Heilman, C. L. Gonzalez, W. A. Swanson, and W. J. Rippert, Agron. J. 60, 578 (1968).

Allen, W. A.

W. A. Allen, H. W. Gausman, A. J. Richardson, and J. R. Thomas, J. Opt. Soc. Am. 59, 1376 (1969).

V. I. Myers and W. A. Allen, Appl. Opt. 7, 1819 (1968).

W. A. Allen and A. J. Richardson, J. Opt. Soc. Am. 58, 1023 (1968).

H. W. Gausman, W. A. Allen, V. I. Myers, and R. Cardenas, Agron. J. 61, 374 (1969).

Braun, W.

G. Kortüm, W. Braun, and G. Herzog, Angew. Chem. 2, 333 (1963).

Cardenas, R.

H. W. Gausman, W. A. Allen, V. I. Myers, and R. Cardenas, Agron. J. 61, 374 (1969).

Centeno, M.

M. Centeno, J. Opt. Soc. Am. 31, 245 (1941).

de Wit, C. T.

C. T. de Wit, Agr. Res. Rep. 663. Inst. Biol. Chem. Res. on Field Crops and Herbage, Wageningen, Netherlands (1965).

Gates, D. M.

D. M. Gates, H. J. Keegan, J. C. Schleter, and V. R. Weidner, Appl. Opt. 4, 11 (1965).

Gausman, H. W.

H. W. Gausman, W. A. Allen, V. I. Myers, and R. Cardenas, Agron. J. 61, 374 (1969).

W. A. Allen, H. W. Gausman, A. J. Richardson, and J. R. Thomas, J. Opt. Soc. Am. 59, 1376 (1969).

Gonzalez, C. L.

M. D. Heilman, C. L. Gonzalez, W. A. Swanson, and W. J. Rippert, Agron. J. 60, 578 (1968).

Hardy, A. C.

A. C. Hardy and F. H. Perrin, The Principles of Optics (McGraw—Hill Book Co., New York, 1932), p. 24.

Hecht, H. G.

W. W. Wendlandt and H. G. Hecht, Reflectance Spectroscopy (Interscience Publ., John Wiley & Sons, Inc., New York, 1966), p. 62.

Heilman, M. D.

M. D. Heilman, C. L. Gonzalez, W. A. Swanson, and W. J. Rippert, Agron. J. 60, 578 (1968).

Herzog, G.

G. Kortüm, W. Braun, and G. Herzog, Angew. Chem. 2, 333 (1963).

Ingle, G. W.

G. W. Ingle. Note on coincidence of equations for the reflectance of translucent films. American Society for Testing and Materials Bulletin 116, 32 (1942).

Isobe, Seishi

Seishi Isobe, Bull. Natl. Inst. Agricultural Sci. (Japan) Ser. A, No. 16 (March 1969).

Keegan, H. J.

D. M. Gates, H. J. Keegan, J. C. Schleter, and V. R. Weidner, Appl. Opt. 4, 11 (1965).

Kortüm, G.

G. Kortüm, W. Braun, and G. Herzog, Angew. Chem. 2, 333 (1963).

Kubelka, P.

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

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

Loomis, W. E.

R. A. Moss and W. E. Loomis, Plant Physiol. 27, 370 (1952).

Melamed, N. T.

N. T. Melamed, J. Appl. Phys. 34, 560 (1963).

Moss, R. A.

R. A. Moss and W. E. Loomis, Plant Physiol. 27, 370 (1952).

Munk, F.

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

Myers, V. I.

V. I. Myers and W. A. Allen, Appl. Opt. 7, 1819 (1968).

H. W. Gausman, W. A. Allen, V. I. Myers, and R. Cardenas, Agron. J. 61, 374 (1969).

Perrin, F. H.

A. C. Hardy and F. H. Perrin, The Principles of Optics (McGraw—Hill Book Co., New York, 1932), p. 24.

Rabinowitch, E. I.

E. I. Rabinowitch, Photosynthesis and Related Processes (Interscience Publ., John Wiley & Sons, Inc., New York, 1961), Vol. II, Part 1.

Richardson, A. J.

W. A. Allen and A. J. Richardson, J. Opt. Soc. Am. 58, 1023 (1968).

W. A. Allen, H. W. Gausman, A. J. Richardson, and J. R. Thomas, J. Opt. Soc. Am. 59, 1376 (1969).

Rippert, W. J.

M. D. Heilman, C. L. Gonzalez, W. A. Swanson, and W. J. Rippert, Agron. J. 60, 578 (1968).

Schleter, J. C.

D. M. Gates, H. J. Keegan, J. C. Schleter, and V. R. Weidner, Appl. Opt. 4, 11 (1965).

Stern, F.

F. Stern, Appl. Opt. 3, 111 (1964).

Stokes, G. G.

G. G. Stokes, Proc. Roy. Soc. (London) 11, 545 (1862).

Stoll, A.

R. Willstätter and A. Stoll, Untersuchungen über die Assimilation der Kohlensäure (Springer-Verlag, Berlin, 1913).

Swanson, W. A.

M. D. Heilman, C. L. Gonzalez, W. A. Swanson, and W. J. Rippert, Agron. J. 60, 578 (1968).

Thomas, J. R.

W. A. Allen, H. W. Gausman, A. J. Richardson, and J. R. Thomas, J. Opt. Soc. Am. 59, 1376 (1969).

Weidner, V. R.

D. M. Gates, H. J. Keegan, J. C. Schleter, and V. R. Weidner, Appl. Opt. 4, 11 (1965).

Wendlandt, W. W.

W. W. Wendlandt and H. G. Hecht, Reflectance Spectroscopy (Interscience Publ., John Wiley & Sons, Inc., New York, 1966), p. 62.

Willstätter, R.

R. Willstätter and A. Stoll, Untersuchungen über die Assimilation der Kohlensäure (Springer-Verlag, Berlin, 1913).

Other (22)

W. A. Allen and A. J. Richardson, J. Opt. Soc. Am. 58, 1023 (1968).

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

W. A. Allen, H. W. Gausman, A. J. Richardson, and J. R. Thomas, J. Opt. Soc. Am. 59, 1376 (1969).

N. T. Melamed, J. Appl. Phys. 34, 560 (1963).

W. W. Wendlandt and H. G. Hecht, Reflectance Spectroscopy (Interscience Publ., John Wiley & Sons, Inc., New York, 1966), p. 62.

A. C. Hardy and F. H. Perrin, The Principles of Optics (McGraw—Hill Book Co., New York, 1932), p. 24.

Seishi Isobe, Bull. Natl. Inst. Agricultural Sci. (Japan) Ser. A, No. 16 (March 1969).

D. M. Gates, H. J. Keegan, J. C. Schleter, and V. R. Weidner, Appl. Opt. 4, 11 (1965).

E. I. Rabinowitch, Photosynthesis and Related Processes (Interscience Publ., John Wiley & Sons, Inc., New York, 1961), Vol. II, Part 1.

R. A. Moss and W. E. Loomis, Plant Physiol. 27, 370 (1952).

H. W. Gausman, W. A. Allen, V. I. Myers, and R. Cardenas, Agron. J. 61, 374 (1969).

V. I. Myers and W. A. Allen, Appl. Opt. 7, 1819 (1968).

Trade names are included for information only and do not constitute endorsement by the U. S. Department of Agriculture.

C. T. de Wit, Agr. Res. Rep. 663. Inst. Biol. Chem. Res. on Field Crops and Herbage, Wageningen, Netherlands (1965).

G. Kortüm, W. Braun, and G. Herzog, Angew. Chem. 2, 333 (1963).

G. G. Stokes, Proc. Roy. Soc. (London) 11, 545 (1862).

G. W. Ingle. Note on coincidence of equations for the reflectance of translucent films. American Society for Testing and Materials Bulletin 116, 32 (1942).

F. Stern, Appl. Opt. 3, 111 (1964).

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

M. Centeno, J. Opt. Soc. Am. 31, 245 (1941).

R. Willstätter and A. Stoll, Untersuchungen über die Assimilation der Kohlensäure (Springer-Verlag, Berlin, 1913).

M. D. Heilman, C. L. Gonzalez, W. A. Swanson, and W. J. Rippert, Agron. J. 60, 578 (1968).

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