Abstract

The Kubelka-Munk theory of light propagation in intensely scattering materials is extended for application to fluorescing media. As an example, the extended theory is applied to the plant sensory pigment system phytochrome that is masked by chlorophyll.

© 1980 Optical Society of America

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  1. A. Schuster, "Radiation through a foggy atmosphere," Astrophys. J. 21, 1–22 (1905).
  2. P. Kubelka, "New contributions to the optics of intensely light-scattering materials," J. Opt. Soc. Am. 38, 448–456 (1948).
  3. P. Kubelka and F. Munk, "Ein Beitrag zur Optik der Farbanstriche," Z. Techn. Physik 11, 593–601 (1931).
  4. G. Kortüm, Reflectance Spectroscopy: Principles, Methods, Applications (Springer-Verlag, New York, 1969).
  5. S. Q. Duntley, "The optical properties of Diffusing Materials," J. Opt. Soc. Am. 32, 61–70 (1942).
  6. J. L. Saunderson, "Reflectance Spectrophotometry of Pigment Materials: Color Matching Calculations" in Organic Protective Coatings, edited by W. von Fischer and E. G. Bobalek (Reinholt, New York, 1953).
  7. W. R. Butler, "Absorption of Light by Turbid Materials," J. Opt. Soc. Am. 52, 292–299 (1962).
  8. W. R. Blevin and W. J. Brown, "Total Reflectances of Opaque Diffusers," J. Opt. Soc. Am. 52, 1250–1255 (1962).
  9. W. R. Butler, "Absorption Spectroscopy in vivo: theory and application," Ann. Rev. Plant. Physiol. 15, 451–470 (1964).
  10. E. Allen, "Fluorescent White Dyes: Calculation of Fluorescence from Reflectivity Values," J. Opt. Soc. Am. 54, 506–515 (1964).
  11. R. N. Wolfe and J. J. De Palma, "Constance of the Schuster scatter and Absorption Coefficients," J. Opt. Soc. Am. 55, 1580 (A) (1965).
  12. W. A. Allen and A. J. Richardson, "Interaction of Light with a Plant Canopy," J. Opt. Soc. Am. 58, 1023–1028 (1968).
  13. K. Klier, "Absorption and Scattering in Plane Parallel Turbid Media," J. Opt. Soc. Am. 62, 882–885 (1962).
  14. W. A. Allen, T. V. Gayle, and A. J. Richardson, "Plant-Canopy Irradiance Specified by the Duntley Equations," J. Opt. Soc. Am. 60, 372–376 (1970).
  15. K. M. Hartmann and I. Cohnen Unser, "Analytical Action Spectroscopy with Living Systems: Photochemical Aspects and Attenuance," Ber. Deutsch. Bot. Ges. 85, 481–555 (1972).
  16. E. D. Lipson and D. Presti, "Light-induced absorbance changes in Phycomyces photomutants," Photochem. Photobiol. 25, 203–208 (1977).
  17. M. G. Holmes and L. Fukshansky, "Phytochrome photoequilibria in green leaves under polychromatic radiation: a theoretical approach," Plant, Cell, Environment 2, 59–65 (1979).
  18. R. H. Harding, B. Golding, and R. A. Morgen, "Optics of light-scattering films. Study of effects of pigment size and concentration," J. Opt. Soc. Am. 50, 446–455 (1960)
  19. The entire following treatment is relevant for any secondary irradiation that can be characterized by known quantum yield and spectral composition; another particular case is Raman scattering.
  20. Th. Förster, "Energiewanderung und Fluoreszenz," Naturwissenschaften 33, 166–172 (1946).
  21. This has no influence on the process of derivation; in order to get the solution for a reflecting backing one must only substitute T(1 + Rg) for T and [-νT(1 - Rg)] for (-νT) in the right-hand side of Eqs. (13a), (17), (18), and (19).
  22. H. Mohr, Lectures on Photomorphogenesis (Springer-Verlag, Berlin, 1972).
  23. M. Delbrück, A. Katzir, and D. Presti, "Responses of phycomyces indicating optical excitation of the lowest triplet state of riboflavin," Proc. Natl. Acad. Sci. USA 73, 1969–1973 (1976).
  24. O. Wartburg, Über die katalytischen Wirkungen der lebendigen Substanz (Springer-Verlag, Berlin, 1928).
  25. R. B. Setlow and E. C. Polard, "Action spectra and quantum yields," in Molecular Biophysics (Pergamon, Oxford, London, New York, Paris, 1962), pp. 267–305.
  26. V. Muňoz and W. L. Butler, "Photoreceptor pigment for blue light in Neurespora crassa," Plant Physiol. 55, 421–426 (1975).
  27. K. L. Poff and W. L. Butler, "Absorbance changes induced by blue light in Phycomyces blakesleeanus and Dictyostelium discoideum," Nature 248, 799–801 (1974).
  28. L. H. Pratt, "Molecular properties of phytochrome" (Review article), Photochem. Photobiol. 27, 81–105 (1978).
  29. D. Oelkrug and G. Kortüdm, "Zur Berechnung der Lumineszenzre-absorption bei pulverförmigen Substanzen," Z. Phys. Chem. N.F. 58, 181–188 (1968).
  30. G. G. Stokes, "On the intensity of the light reflected from or transmitted through a pile of plates," Proc. R. Soc. London 11, 545–557 (1860/1862).
  31. B. Schrader and G. Bergmann, "Die Intersität des Ramanspektrums polykristalliner Substanzen. I. Strahlungsbilanz von Substanz und Probenanordnung," Z. Anal. Chem. 225, 230–247 (1967).
  32. L. D. Landau, and E. M. Lifshitz, Electrodynamics of Continuous Media (in Russian) (VINITI, Moscow, 1959).
  33. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  34. P. S. Mudgett, and L. W. Richards, "Multiple scattering calculations for technology," Appl. Opt. 10, 1485–1502 (1971).
  35. R. G. Giovanelli, "Reflection by semi-infinite diffusers," Opt. Acta (Paris) 2, 153–162 (1955).
  36. Yu. A. Tsirlin, L. E. Pargamanik, and A. R. Daich, "Diffusion of light in scattering media," Opt. Spectrosc. 12, 165–168 (1962).
  37. Yu. Ya. Bobyrenko, "Diffusion theory of the passage of light through scattering media," Opt. Spectrosc. 24, 365–366 (1968).
  38. L. F. Gate, "The determination of light absorption in diffusing materials by a photon diffusion model," J. Phys. D. 4, 1049–1056 (1971).
  39. B. J. Brinkworth, "On the theory of reflection by scattering and absorbing media," J. Phys. D. 4, 1105–1106 (1971).
  40. B. J. Brinkworth, "Interpretation of the Kubelka-Munk coefficients in reflection theory," Appl. Opt. 11, 1434–1435 (1972).
  41. J. W. Ryde, "The scattering of light by turbid media—Part I," Proc. R. Soc. London Ser. A 131, 451–464 (1931).
  42. J. W. Ryde and B. S. Cooper, "The scattering of light by turbid media—Part II," Proc. R. Soc. London Ser. A 131, 464–475 (1931).
  43. K. Shibata, "Simple absolute method for measuring diffuse reflectance spectra," J. Opt. Soc. Am. 47, 172–178 (1957).
  44. P. Kubelka, "New contributions to the optics of intensely light-scattering materials. Part II: Nonhomogeneous layers," J. Opt. Soc. Am. 44, 330–335 (1954).
  45. Å. S:son Stenius, "Reflectance and transmittance of inhomogeneous diffusing layers," J. Opt. Soc. Am. 44, 804–805 (1954).
  46. Tung-Po Lin and H. K. A. Kan, "Calculation of reflectance of a light diffuser with nonuniform absorption," J. Opt. Soc. Am. 60, 1252–1256 (1970).
  47. E. I. Rabinowitch, in Photosynthesis and Related Processes (Wiley-Interscience, New York, 1951), Vol. II(1), p. 672.
  48. L. N. M. Duysens, "The Flattening of the Absorption Spectrum of Suspensions as Compared to that of Solutions," Biochim. Biophys. Acta 19, 1–12 (1956).
  49. L. Fukshansky, "On the Theory of Light Absorption in Non-Homogeneous Objects: the Sieve Effect in One-Component Suspensions," J. Math. Biol, 6, 177–196 (1978).
  50. G. Duyckaerts, "The infrared analysis of solid substances" (A review) Analyst 84, 201–214 (1959).
  51. R. J. Gledhill and D. B. Julian, "Light absorption in heterogeneous systems with application to photographic dye images," J. Opt. Soc. Am. 53, 239–246 (1963).
  52. B. Felder, "Über die Teilchengrössenabhäǹgigkeit der Lichtabsorption in heterogeneous Systemen. I. Theoretische Betrachtungen,"Helv. Chim. Acta 47, 488-497 (1964).
  53. W. L. Butler, K. H. Norris, H. W. Siegelman, and S. B. Heǹdricks, "Detection, Assay and Preliminary Purification of the Pigment Controlling Photoresponsive Development of Plants," Proc. Natl. Acad. Sci. USA 45, 1703–1708 (1959).
  54. L. H. Pratt, "Photochemistry of High Molecular Weight Phytochrome in vitro," Photochem. Photobiol. 22, 33–36 (1975).
  55. H. W. Gausman, W. A. Allen, C. L. Wiegand, D. E. Escobar, and R. R. Rodriques, Texas Agricultural Experimental Station, Technical Bulletin No. 1465, 1973 (unpublished).
  56. R. A. Moss and W. E. Loomis, "Absorption Spectra of Leaves," Plant Physiol. 27, 370–391 (1952).
  57. E. Rabinowitch and Govindjee, Photosynthesis (Wiley, New York, 1969).

1979 (1)

M. G. Holmes and L. Fukshansky, "Phytochrome photoequilibria in green leaves under polychromatic radiation: a theoretical approach," Plant, Cell, Environment 2, 59–65 (1979).

1978 (2)

L. H. Pratt, "Molecular properties of phytochrome" (Review article), Photochem. Photobiol. 27, 81–105 (1978).

L. Fukshansky, "On the Theory of Light Absorption in Non-Homogeneous Objects: the Sieve Effect in One-Component Suspensions," J. Math. Biol, 6, 177–196 (1978).

1977 (1)

E. D. Lipson and D. Presti, "Light-induced absorbance changes in Phycomyces photomutants," Photochem. Photobiol. 25, 203–208 (1977).

1976 (1)

M. Delbrück, A. Katzir, and D. Presti, "Responses of phycomyces indicating optical excitation of the lowest triplet state of riboflavin," Proc. Natl. Acad. Sci. USA 73, 1969–1973 (1976).

1975 (2)

V. Muňoz and W. L. Butler, "Photoreceptor pigment for blue light in Neurespora crassa," Plant Physiol. 55, 421–426 (1975).

L. H. Pratt, "Photochemistry of High Molecular Weight Phytochrome in vitro," Photochem. Photobiol. 22, 33–36 (1975).

1974 (1)

K. L. Poff and W. L. Butler, "Absorbance changes induced by blue light in Phycomyces blakesleeanus and Dictyostelium discoideum," Nature 248, 799–801 (1974).

1972 (2)

B. J. Brinkworth, "Interpretation of the Kubelka-Munk coefficients in reflection theory," Appl. Opt. 11, 1434–1435 (1972).

K. M. Hartmann and I. Cohnen Unser, "Analytical Action Spectroscopy with Living Systems: Photochemical Aspects and Attenuance," Ber. Deutsch. Bot. Ges. 85, 481–555 (1972).

1971 (3)

L. F. Gate, "The determination of light absorption in diffusing materials by a photon diffusion model," J. Phys. D. 4, 1049–1056 (1971).

B. J. Brinkworth, "On the theory of reflection by scattering and absorbing media," J. Phys. D. 4, 1105–1106 (1971).

P. S. Mudgett, and L. W. Richards, "Multiple scattering calculations for technology," Appl. Opt. 10, 1485–1502 (1971).

1970 (2)

1968 (3)

W. A. Allen and A. J. Richardson, "Interaction of Light with a Plant Canopy," J. Opt. Soc. Am. 58, 1023–1028 (1968).

Yu. Ya. Bobyrenko, "Diffusion theory of the passage of light through scattering media," Opt. Spectrosc. 24, 365–366 (1968).

D. Oelkrug and G. Kortüdm, "Zur Berechnung der Lumineszenzre-absorption bei pulverförmigen Substanzen," Z. Phys. Chem. N.F. 58, 181–188 (1968).

1967 (1)

B. Schrader and G. Bergmann, "Die Intersität des Ramanspektrums polykristalliner Substanzen. I. Strahlungsbilanz von Substanz und Probenanordnung," Z. Anal. Chem. 225, 230–247 (1967).

1965 (1)

R. N. Wolfe and J. J. De Palma, "Constance of the Schuster scatter and Absorption Coefficients," J. Opt. Soc. Am. 55, 1580 (A) (1965).

1964 (3)

W. R. Butler, "Absorption Spectroscopy in vivo: theory and application," Ann. Rev. Plant. Physiol. 15, 451–470 (1964).

E. Allen, "Fluorescent White Dyes: Calculation of Fluorescence from Reflectivity Values," J. Opt. Soc. Am. 54, 506–515 (1964).

B. Felder, "Über die Teilchengrössenabhäǹgigkeit der Lichtabsorption in heterogeneous Systemen. I. Theoretische Betrachtungen,"Helv. Chim. Acta 47, 488-497 (1964).

1963 (1)

1962 (4)

1960 (1)

1959 (2)

W. L. Butler, K. H. Norris, H. W. Siegelman, and S. B. Heǹdricks, "Detection, Assay and Preliminary Purification of the Pigment Controlling Photoresponsive Development of Plants," Proc. Natl. Acad. Sci. USA 45, 1703–1708 (1959).

G. Duyckaerts, "The infrared analysis of solid substances" (A review) Analyst 84, 201–214 (1959).

1957 (1)

1956 (1)

L. N. M. Duysens, "The Flattening of the Absorption Spectrum of Suspensions as Compared to that of Solutions," Biochim. Biophys. Acta 19, 1–12 (1956).

1955 (1)

R. G. Giovanelli, "Reflection by semi-infinite diffusers," Opt. Acta (Paris) 2, 153–162 (1955).

1954 (2)

1952 (1)

R. A. Moss and W. E. Loomis, "Absorption Spectra of Leaves," Plant Physiol. 27, 370–391 (1952).

1948 (1)

1946 (1)

Th. Förster, "Energiewanderung und Fluoreszenz," Naturwissenschaften 33, 166–172 (1946).

1942 (1)

1931 (3)

P. Kubelka and F. Munk, "Ein Beitrag zur Optik der Farbanstriche," Z. Techn. Physik 11, 593–601 (1931).

J. W. Ryde, "The scattering of light by turbid media—Part I," Proc. R. Soc. London Ser. A 131, 451–464 (1931).

J. W. Ryde and B. S. Cooper, "The scattering of light by turbid media—Part II," Proc. R. Soc. London Ser. A 131, 464–475 (1931).

1905 (1)

A. Schuster, "Radiation through a foggy atmosphere," Astrophys. J. 21, 1–22 (1905).

Allen, E.

Allen, W. A.

Bergmann, G.

B. Schrader and G. Bergmann, "Die Intersität des Ramanspektrums polykristalliner Substanzen. I. Strahlungsbilanz von Substanz und Probenanordnung," Z. Anal. Chem. 225, 230–247 (1967).

Blevin, W. R.

Bobyrenko, Yu. Ya.

Yu. Ya. Bobyrenko, "Diffusion theory of the passage of light through scattering media," Opt. Spectrosc. 24, 365–366 (1968).

Brinkworth, B. J.

B. J. Brinkworth, "Interpretation of the Kubelka-Munk coefficients in reflection theory," Appl. Opt. 11, 1434–1435 (1972).

B. J. Brinkworth, "On the theory of reflection by scattering and absorbing media," J. Phys. D. 4, 1105–1106 (1971).

Brown, W. J.

Butler, W. L.

V. Muňoz and W. L. Butler, "Photoreceptor pigment for blue light in Neurespora crassa," Plant Physiol. 55, 421–426 (1975).

K. L. Poff and W. L. Butler, "Absorbance changes induced by blue light in Phycomyces blakesleeanus and Dictyostelium discoideum," Nature 248, 799–801 (1974).

W. L. Butler, K. H. Norris, H. W. Siegelman, and S. B. Heǹdricks, "Detection, Assay and Preliminary Purification of the Pigment Controlling Photoresponsive Development of Plants," Proc. Natl. Acad. Sci. USA 45, 1703–1708 (1959).

Butler, W. R.

W. R. Butler, "Absorption Spectroscopy in vivo: theory and application," Ann. Rev. Plant. Physiol. 15, 451–470 (1964).

W. R. Butler, "Absorption of Light by Turbid Materials," J. Opt. Soc. Am. 52, 292–299 (1962).

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

Cooper, B. S.

J. W. Ryde and B. S. Cooper, "The scattering of light by turbid media—Part II," Proc. R. Soc. London Ser. A 131, 464–475 (1931).

Daich, A. R.

Yu. A. Tsirlin, L. E. Pargamanik, and A. R. Daich, "Diffusion of light in scattering media," Opt. Spectrosc. 12, 165–168 (1962).

De Palma, J. J.

R. N. Wolfe and J. J. De Palma, "Constance of the Schuster scatter and Absorption Coefficients," J. Opt. Soc. Am. 55, 1580 (A) (1965).

Delbrück, M.

M. Delbrück, A. Katzir, and D. Presti, "Responses of phycomyces indicating optical excitation of the lowest triplet state of riboflavin," Proc. Natl. Acad. Sci. USA 73, 1969–1973 (1976).

Duntley, S. Q.

Duyckaerts, G.

G. Duyckaerts, "The infrared analysis of solid substances" (A review) Analyst 84, 201–214 (1959).

Duysens, L. N. M.

L. N. M. Duysens, "The Flattening of the Absorption Spectrum of Suspensions as Compared to that of Solutions," Biochim. Biophys. Acta 19, 1–12 (1956).

Escobar, D. E.

H. W. Gausman, W. A. Allen, C. L. Wiegand, D. E. Escobar, and R. R. Rodriques, Texas Agricultural Experimental Station, Technical Bulletin No. 1465, 1973 (unpublished).

Felder, B.

B. Felder, "Über die Teilchengrössenabhäǹgigkeit der Lichtabsorption in heterogeneous Systemen. I. Theoretische Betrachtungen,"Helv. Chim. Acta 47, 488-497 (1964).

Förster, Th.

Th. Förster, "Energiewanderung und Fluoreszenz," Naturwissenschaften 33, 166–172 (1946).

Fukshansky, L.

M. G. Holmes and L. Fukshansky, "Phytochrome photoequilibria in green leaves under polychromatic radiation: a theoretical approach," Plant, Cell, Environment 2, 59–65 (1979).

L. Fukshansky, "On the Theory of Light Absorption in Non-Homogeneous Objects: the Sieve Effect in One-Component Suspensions," J. Math. Biol, 6, 177–196 (1978).

Gate, L. F.

L. F. Gate, "The determination of light absorption in diffusing materials by a photon diffusion model," J. Phys. D. 4, 1049–1056 (1971).

Gausman, H. W.

H. W. Gausman, W. A. Allen, C. L. Wiegand, D. E. Escobar, and R. R. Rodriques, Texas Agricultural Experimental Station, Technical Bulletin No. 1465, 1973 (unpublished).

Gayle, T. V.

Giovanelli, R. G.

R. G. Giovanelli, "Reflection by semi-infinite diffusers," Opt. Acta (Paris) 2, 153–162 (1955).

Gledhill, R. J.

Golding, B.

Harding, R. H.

Hartmann, K. M.

K. M. Hartmann and I. Cohnen Unser, "Analytical Action Spectroscopy with Living Systems: Photochemical Aspects and Attenuance," Ber. Deutsch. Bot. Ges. 85, 481–555 (1972).

He?dricks, S. B.

W. L. Butler, K. H. Norris, H. W. Siegelman, and S. B. Heǹdricks, "Detection, Assay and Preliminary Purification of the Pigment Controlling Photoresponsive Development of Plants," Proc. Natl. Acad. Sci. USA 45, 1703–1708 (1959).

Holmes, M. G.

M. G. Holmes and L. Fukshansky, "Phytochrome photoequilibria in green leaves under polychromatic radiation: a theoretical approach," Plant, Cell, Environment 2, 59–65 (1979).

Julian, D. B.

Kan, H. K. A.

Katzir, A.

M. Delbrück, A. Katzir, and D. Presti, "Responses of phycomyces indicating optical excitation of the lowest triplet state of riboflavin," Proc. Natl. Acad. Sci. USA 73, 1969–1973 (1976).

Klier, K.

Kortüdm, G.

D. Oelkrug and G. Kortüdm, "Zur Berechnung der Lumineszenzre-absorption bei pulverförmigen Substanzen," Z. Phys. Chem. N.F. 58, 181–188 (1968).

Kortüm, G.

G. Kortüm, Reflectance Spectroscopy: Principles, Methods, Applications (Springer-Verlag, New York, 1969).

Kubelka, P.

Landau, L. D.

L. D. Landau, and E. M. Lifshitz, Electrodynamics of Continuous Media (in Russian) (VINITI, Moscow, 1959).

Lifshitz, E. M.

L. D. Landau, and E. M. Lifshitz, Electrodynamics of Continuous Media (in Russian) (VINITI, Moscow, 1959).

Lin, Tung-Po

Lipson, E. D.

E. D. Lipson and D. Presti, "Light-induced absorbance changes in Phycomyces photomutants," Photochem. Photobiol. 25, 203–208 (1977).

Loomis, W. E.

R. A. Moss and W. E. Loomis, "Absorption Spectra of Leaves," Plant Physiol. 27, 370–391 (1952).

Mohr, H.

H. Mohr, Lectures on Photomorphogenesis (Springer-Verlag, Berlin, 1972).

Morgen, R. A.

Moss, R. A.

R. A. Moss and W. E. Loomis, "Absorption Spectra of Leaves," Plant Physiol. 27, 370–391 (1952).

Mudgett, P. S.

Munk, F.

P. Kubelka and F. Munk, "Ein Beitrag zur Optik der Farbanstriche," Z. Techn. Physik 11, 593–601 (1931).

Munoz, V.

V. Muňoz and W. L. Butler, "Photoreceptor pigment for blue light in Neurespora crassa," Plant Physiol. 55, 421–426 (1975).

Norris, K. H.

W. L. Butler, K. H. Norris, H. W. Siegelman, and S. B. Heǹdricks, "Detection, Assay and Preliminary Purification of the Pigment Controlling Photoresponsive Development of Plants," Proc. Natl. Acad. Sci. USA 45, 1703–1708 (1959).

Oelkrug, D.

D. Oelkrug and G. Kortüdm, "Zur Berechnung der Lumineszenzre-absorption bei pulverförmigen Substanzen," Z. Phys. Chem. N.F. 58, 181–188 (1968).

Pargamanik, L. E.

Yu. A. Tsirlin, L. E. Pargamanik, and A. R. Daich, "Diffusion of light in scattering media," Opt. Spectrosc. 12, 165–168 (1962).

Poff, K. L.

K. L. Poff and W. L. Butler, "Absorbance changes induced by blue light in Phycomyces blakesleeanus and Dictyostelium discoideum," Nature 248, 799–801 (1974).

Polard, E. C.

R. B. Setlow and E. C. Polard, "Action spectra and quantum yields," in Molecular Biophysics (Pergamon, Oxford, London, New York, Paris, 1962), pp. 267–305.

Pratt, L. H.

L. H. Pratt, "Molecular properties of phytochrome" (Review article), Photochem. Photobiol. 27, 81–105 (1978).

L. H. Pratt, "Photochemistry of High Molecular Weight Phytochrome in vitro," Photochem. Photobiol. 22, 33–36 (1975).

Presti, D.

E. D. Lipson and D. Presti, "Light-induced absorbance changes in Phycomyces photomutants," Photochem. Photobiol. 25, 203–208 (1977).

M. Delbrück, A. Katzir, and D. Presti, "Responses of phycomyces indicating optical excitation of the lowest triplet state of riboflavin," Proc. Natl. Acad. Sci. USA 73, 1969–1973 (1976).

Rabinowitch, E.

E. Rabinowitch and Govindjee, Photosynthesis (Wiley, New York, 1969).

Rabinowitch, E. I.

E. I. Rabinowitch, in Photosynthesis and Related Processes (Wiley-Interscience, New York, 1951), Vol. II(1), p. 672.

Richards, L. W.

Richardson, A. J.

Rodriques, R. R.

H. W. Gausman, W. A. Allen, C. L. Wiegand, D. E. Escobar, and R. R. Rodriques, Texas Agricultural Experimental Station, Technical Bulletin No. 1465, 1973 (unpublished).

Ryde, J. W.

J. W. Ryde, "The scattering of light by turbid media—Part I," Proc. R. Soc. London Ser. A 131, 451–464 (1931).

J. W. Ryde and B. S. Cooper, "The scattering of light by turbid media—Part II," Proc. R. Soc. London Ser. A 131, 464–475 (1931).

Saunderson, J. L.

J. L. Saunderson, "Reflectance Spectrophotometry of Pigment Materials: Color Matching Calculations" in Organic Protective Coatings, edited by W. von Fischer and E. G. Bobalek (Reinholt, New York, 1953).

Schrader, B.

B. Schrader and G. Bergmann, "Die Intersität des Ramanspektrums polykristalliner Substanzen. I. Strahlungsbilanz von Substanz und Probenanordnung," Z. Anal. Chem. 225, 230–247 (1967).

Schuster, A.

A. Schuster, "Radiation through a foggy atmosphere," Astrophys. J. 21, 1–22 (1905).

Setlow, R. B.

R. B. Setlow and E. C. Polard, "Action spectra and quantum yields," in Molecular Biophysics (Pergamon, Oxford, London, New York, Paris, 1962), pp. 267–305.

Shibata, K.

Siegelman, H. W.

W. L. Butler, K. H. Norris, H. W. Siegelman, and S. B. Heǹdricks, "Detection, Assay and Preliminary Purification of the Pigment Controlling Photoresponsive Development of Plants," Proc. Natl. Acad. Sci. USA 45, 1703–1708 (1959).

Stenius, Å. S:son

Stokes, G. G.

G. G. Stokes, "On the intensity of the light reflected from or transmitted through a pile of plates," Proc. R. Soc. London 11, 545–557 (1860/1862).

Tsirlin, Yu. A.

Yu. A. Tsirlin, L. E. Pargamanik, and A. R. Daich, "Diffusion of light in scattering media," Opt. Spectrosc. 12, 165–168 (1962).

Unser, I. Cohnen

K. M. Hartmann and I. Cohnen Unser, "Analytical Action Spectroscopy with Living Systems: Photochemical Aspects and Attenuance," Ber. Deutsch. Bot. Ges. 85, 481–555 (1972).

Wartburg, O.

O. Wartburg, Über die katalytischen Wirkungen der lebendigen Substanz (Springer-Verlag, Berlin, 1928).

Wiegand, C. L.

H. W. Gausman, W. A. Allen, C. L. Wiegand, D. E. Escobar, and R. R. Rodriques, Texas Agricultural Experimental Station, Technical Bulletin No. 1465, 1973 (unpublished).

Wolfe, R. N.

R. N. Wolfe and J. J. De Palma, "Constance of the Schuster scatter and Absorption Coefficients," J. Opt. Soc. Am. 55, 1580 (A) (1965).

Analyst (1)

G. Duyckaerts, "The infrared analysis of solid substances" (A review) Analyst 84, 201–214 (1959).

Ann. Rev. Plant. Physiol. (1)

W. R. Butler, "Absorption Spectroscopy in vivo: theory and application," Ann. Rev. Plant. Physiol. 15, 451–470 (1964).

Appl. Opt. (2)

Astrophys. J. (1)

A. Schuster, "Radiation through a foggy atmosphere," Astrophys. J. 21, 1–22 (1905).

Ber. Deutsch. Bot. Ges. (1)

K. M. Hartmann and I. Cohnen Unser, "Analytical Action Spectroscopy with Living Systems: Photochemical Aspects and Attenuance," Ber. Deutsch. Bot. Ges. 85, 481–555 (1972).

Biochim. Biophys. Acta (1)

L. N. M. Duysens, "The Flattening of the Absorption Spectrum of Suspensions as Compared to that of Solutions," Biochim. Biophys. Acta 19, 1–12 (1956).

Helv. Chim. Acta (1)

B. Felder, "Über die Teilchengrössenabhäǹgigkeit der Lichtabsorption in heterogeneous Systemen. I. Theoretische Betrachtungen,"Helv. Chim. Acta 47, 488-497 (1964).

J. Math. Biol (1)

L. Fukshansky, "On the Theory of Light Absorption in Non-Homogeneous Objects: the Sieve Effect in One-Component Suspensions," J. Math. Biol, 6, 177–196 (1978).

J. Opt. Soc. Am. (15)

K. Shibata, "Simple absolute method for measuring diffuse reflectance spectra," J. Opt. Soc. Am. 47, 172–178 (1957).

P. Kubelka, "New contributions to the optics of intensely light-scattering materials. Part II: Nonhomogeneous layers," J. Opt. Soc. Am. 44, 330–335 (1954).

Å. S:son Stenius, "Reflectance and transmittance of inhomogeneous diffusing layers," J. Opt. Soc. Am. 44, 804–805 (1954).

Tung-Po Lin and H. K. A. Kan, "Calculation of reflectance of a light diffuser with nonuniform absorption," J. Opt. Soc. Am. 60, 1252–1256 (1970).

R. J. Gledhill and D. B. Julian, "Light absorption in heterogeneous systems with application to photographic dye images," J. Opt. Soc. Am. 53, 239–246 (1963).

R. H. Harding, B. Golding, and R. A. Morgen, "Optics of light-scattering films. Study of effects of pigment size and concentration," J. Opt. Soc. Am. 50, 446–455 (1960)

E. Allen, "Fluorescent White Dyes: Calculation of Fluorescence from Reflectivity Values," J. Opt. Soc. Am. 54, 506–515 (1964).

R. N. Wolfe and J. J. De Palma, "Constance of the Schuster scatter and Absorption Coefficients," J. Opt. Soc. Am. 55, 1580 (A) (1965).

W. A. Allen and A. J. Richardson, "Interaction of Light with a Plant Canopy," J. Opt. Soc. Am. 58, 1023–1028 (1968).

K. Klier, "Absorption and Scattering in Plane Parallel Turbid Media," J. Opt. Soc. Am. 62, 882–885 (1962).

W. A. Allen, T. V. Gayle, and A. J. Richardson, "Plant-Canopy Irradiance Specified by the Duntley Equations," J. Opt. Soc. Am. 60, 372–376 (1970).

P. Kubelka, "New contributions to the optics of intensely light-scattering materials," J. Opt. Soc. Am. 38, 448–456 (1948).

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J. Phys. D. (2)

L. F. Gate, "The determination of light absorption in diffusing materials by a photon diffusion model," J. Phys. D. 4, 1049–1056 (1971).

B. J. Brinkworth, "On the theory of reflection by scattering and absorbing media," J. Phys. D. 4, 1105–1106 (1971).

Nature (1)

K. L. Poff and W. L. Butler, "Absorbance changes induced by blue light in Phycomyces blakesleeanus and Dictyostelium discoideum," Nature 248, 799–801 (1974).

Naturwissenschaften (1)

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Opt. Acta (1)

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Opt. Spectrosc. (2)

Yu. A. Tsirlin, L. E. Pargamanik, and A. R. Daich, "Diffusion of light in scattering media," Opt. Spectrosc. 12, 165–168 (1962).

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L. H. Pratt, "Photochemistry of High Molecular Weight Phytochrome in vitro," Photochem. Photobiol. 22, 33–36 (1975).

Plant Physiol. (2)

R. A. Moss and W. E. Loomis, "Absorption Spectra of Leaves," Plant Physiol. 27, 370–391 (1952).

V. Muňoz and W. L. Butler, "Photoreceptor pigment for blue light in Neurespora crassa," Plant Physiol. 55, 421–426 (1975).

Plant, Cell, Environment (1)

M. G. Holmes and L. Fukshansky, "Phytochrome photoequilibria in green leaves under polychromatic radiation: a theoretical approach," Plant, Cell, Environment 2, 59–65 (1979).

Proc. Natl. Acad. Sci. USA (2)

M. Delbrück, A. Katzir, and D. Presti, "Responses of phycomyces indicating optical excitation of the lowest triplet state of riboflavin," Proc. Natl. Acad. Sci. USA 73, 1969–1973 (1976).

W. L. Butler, K. H. Norris, H. W. Siegelman, and S. B. Heǹdricks, "Detection, Assay and Preliminary Purification of the Pigment Controlling Photoresponsive Development of Plants," Proc. Natl. Acad. Sci. USA 45, 1703–1708 (1959).

Proc. R. Soc. London (1)

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D. Oelkrug and G. Kortüdm, "Zur Berechnung der Lumineszenzre-absorption bei pulverförmigen Substanzen," Z. Phys. Chem. N.F. 58, 181–188 (1968).

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P. Kubelka and F. Munk, "Ein Beitrag zur Optik der Farbanstriche," Z. Techn. Physik 11, 593–601 (1931).

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J. L. Saunderson, "Reflectance Spectrophotometry of Pigment Materials: Color Matching Calculations" in Organic Protective Coatings, edited by W. von Fischer and E. G. Bobalek (Reinholt, New York, 1953).

The entire following treatment is relevant for any secondary irradiation that can be characterized by known quantum yield and spectral composition; another particular case is Raman scattering.

L. D. Landau, and E. M. Lifshitz, Electrodynamics of Continuous Media (in Russian) (VINITI, Moscow, 1959).

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

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R. B. Setlow and E. C. Polard, "Action spectra and quantum yields," in Molecular Biophysics (Pergamon, Oxford, London, New York, Paris, 1962), pp. 267–305.

This has no influence on the process of derivation; in order to get the solution for a reflecting backing one must only substitute T(1 + Rg) for T and [-νT(1 - Rg)] for (-νT) in the right-hand side of Eqs. (13a), (17), (18), and (19).

H. Mohr, Lectures on Photomorphogenesis (Springer-Verlag, Berlin, 1972).

E. I. Rabinowitch, in Photosynthesis and Related Processes (Wiley-Interscience, New York, 1951), Vol. II(1), p. 672.

E. Rabinowitch and Govindjee, Photosynthesis (Wiley, New York, 1969).

H. W. Gausman, W. A. Allen, C. L. Wiegand, D. E. Escobar, and R. R. Rodriques, Texas Agricultural Experimental Station, Technical Bulletin No. 1465, 1973 (unpublished).

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