Abstract

Bidirectional reflection and transmission distribution functions are measured for healthy green soybean and corn leaves in vivo, for nineteen narrow wavelength bands from 375 nm to 1000 nm. Off-normal incidence reflection distribution functions show considerable specular contributions at wavelengths of strong absorption, while transmission distribution functions show a near-lambertian shape for all wavelengths employed. An empirical m-layer leaf model affords a reasonable qualitative understanding of these scattering distributions.

© 1971 Optical Society of America

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References

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  1. Remote Multispectral Sensing in Agriculture (The Laboratory for Agricultural Remote Sensing, Purdue U., 1968), Vol. 3.
  2. J. E. Dinger, “The Absorption of Radiant Energy in Plants,” Unpublished Ph.D. Thesis, Iowa State College, 1941.
  3. A. Seybold, Planta—Arch. Wissenschaft. Botan. 20, 577 (1933).
  4. I. A. Shulgin, V. S. Khazanov, A. F. Kleshnin, Dokl. Botan. Sci. Sec.—Plant Morphol. 134, 197 (1960).
  5. I. A. Shulgin, V. S. Khazanov, Dokl. Botan. Sci. Sec.—Plant Ecol. 141, 210 (1961).
  6. D. M. Gates, H. J. Keegan, J. C. Schleter, V. R. Weidner, Appl. Opt. 4, 11 (1965).
    [CrossRef]
  7. F. E. Nicodemus, Appl. Opt. 7, 1359 (1968).
    [CrossRef] [PubMed]
  8. W. W. Wendlandt, H. G. Hecht, Reflectance Spectroscopy (Interscience, New York, 1966).
  9. F. Kottler, “The Elements of Radiative Transfer,” in Progress in Optics (Wiley, New York, 1964), Vol. 3.
    [CrossRef]
  10. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  11. V. I. Myers, W. A. Allen, Appl. Opt. 7, 1819 (1968).
    [CrossRef] [PubMed]
  12. G. G. Stokes, Proc. Roy. Soc. (London) 11, 545 (1860–1862).
  13. N. T. Melamed, J. Appl. Phys. 34, 560 (1963).
    [CrossRef]

1968

1965

1963

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

1961

I. A. Shulgin, V. S. Khazanov, Dokl. Botan. Sci. Sec.—Plant Ecol. 141, 210 (1961).

1960

I. A. Shulgin, V. S. Khazanov, A. F. Kleshnin, Dokl. Botan. Sci. Sec.—Plant Morphol. 134, 197 (1960).

1933

A. Seybold, Planta—Arch. Wissenschaft. Botan. 20, 577 (1933).

Allen, W. A.

Chandrasekhar, S.

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

Dinger, J. E.

J. E. Dinger, “The Absorption of Radiant Energy in Plants,” Unpublished Ph.D. Thesis, Iowa State College, 1941.

Gates, D. M.

Hecht, H. G.

W. W. Wendlandt, H. G. Hecht, Reflectance Spectroscopy (Interscience, New York, 1966).

Keegan, H. J.

Khazanov, V. S.

I. A. Shulgin, V. S. Khazanov, Dokl. Botan. Sci. Sec.—Plant Ecol. 141, 210 (1961).

I. A. Shulgin, V. S. Khazanov, A. F. Kleshnin, Dokl. Botan. Sci. Sec.—Plant Morphol. 134, 197 (1960).

Kleshnin, A. F.

I. A. Shulgin, V. S. Khazanov, A. F. Kleshnin, Dokl. Botan. Sci. Sec.—Plant Morphol. 134, 197 (1960).

Kottler, F.

F. Kottler, “The Elements of Radiative Transfer,” in Progress in Optics (Wiley, New York, 1964), Vol. 3.
[CrossRef]

Melamed, N. T.

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

Myers, V. I.

Nicodemus, F. E.

Schleter, J. C.

Seybold, A.

A. Seybold, Planta—Arch. Wissenschaft. Botan. 20, 577 (1933).

Shulgin, I. A.

I. A. Shulgin, V. S. Khazanov, Dokl. Botan. Sci. Sec.—Plant Ecol. 141, 210 (1961).

I. A. Shulgin, V. S. Khazanov, A. F. Kleshnin, Dokl. Botan. Sci. Sec.—Plant Morphol. 134, 197 (1960).

Stokes, G. G.

G. G. Stokes, Proc. Roy. Soc. (London) 11, 545 (1860–1862).

Weidner, V. R.

Wendlandt, W. W.

W. W. Wendlandt, H. G. Hecht, Reflectance Spectroscopy (Interscience, New York, 1966).

Appl. Opt.

Dokl. Botan. Sci. Sec.—Plant Ecol.

I. A. Shulgin, V. S. Khazanov, Dokl. Botan. Sci. Sec.—Plant Ecol. 141, 210 (1961).

Dokl. Botan. Sci. Sec.—Plant Morphol.

I. A. Shulgin, V. S. Khazanov, A. F. Kleshnin, Dokl. Botan. Sci. Sec.—Plant Morphol. 134, 197 (1960).

J. Appl. Phys.

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

Planta—Arch. Wissenschaft. Botan.

A. Seybold, Planta—Arch. Wissenschaft. Botan. 20, 577 (1933).

Proc. Roy. Soc. (London)

G. G. Stokes, Proc. Roy. Soc. (London) 11, 545 (1860–1862).

Other

Remote Multispectral Sensing in Agriculture (The Laboratory for Agricultural Remote Sensing, Purdue U., 1968), Vol. 3.

J. E. Dinger, “The Absorption of Radiant Energy in Plants,” Unpublished Ph.D. Thesis, Iowa State College, 1941.

W. W. Wendlandt, H. G. Hecht, Reflectance Spectroscopy (Interscience, New York, 1966).

F. Kottler, “The Elements of Radiative Transfer,” in Progress in Optics (Wiley, New York, 1964), Vol. 3.
[CrossRef]

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

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Figures (18)

Fig. 1
Fig. 1

Goniometry of the incident and scattered radiation beam elements.

Fig. 2
Fig. 2

The scattering measurement chamber showing the sample mounting and photomultiplier mount.

Fig. 3
Fig. 3

A soybean plant positioned under the measurement chamber sample holder.

Fig. 4
Fig. 4

Polar plots of soybean leaf ρ′cosθcoll and τ′cos(πθcoll) for top incidence at θinc = 0°.

Fig. 5
Fig. 5

Polar plots for soybean similar to those of Fig. 4, with identical wavelength code but for top incidence at θinc = 30°.

Fig. 6
Fig. 6

Polar plots for soybean similar to those of Fig. 4, with identical wavelength code but for top incidence at θinc = 60°.

Fig. 7
Fig. 7

Soybean leaf bidirectional reflection and transmission distribution functions ρ′ at θcoll = 45° (—), θcoll = 0° (……), and τ′ at θcoll = 180° (---) vs wavelength for top incidence at θinc = 45°.

Fig. 8
Fig. 8

Polar plots of corn leaf ρ′cosθcoll and τ′cos(πθcoll) for top incidence at θinc = 0° and vertical midvein orientation. The wavelength code is identical to that of Fig. 4.

Fig. 9
Fig. 9

Polar plots for corn similar to those of Fig. 8, but for top incidence at θinc = 30°; vertical midvein orientation.

Fig. 10
Fig. 10

Polar plots for corn similar to those of Fig. 8, but for top incidence at θinc = 60°; vertical midvein orientation.

Fig. 11
Fig. 11

Corn leaf bidirectional reflection and transmission distribution functions ρ′ at θcoll = 45° (—), θcoll = 0° (……), and τ′ at θcoll = 180° (----) vs wavelength for top incidence at θinc = 45° and vertical midvein orientation.

Fig. 12
Fig. 12

Polar plots of corn leaf ρ′cosθcoll and τ′cos(πθcoll) for top incidence at θinc = 0° and horizontal midvein orientation. The wavelength code is identical to that of Fig. 4.

Fig. 13
Fig. 13

Polar plots for corn similar to those of Fig. 12 but for top incidence at θinc = 30°; horizontal midvein orientation.

Fig. 14
Fig. 14

Polar plots for corn similar to those of Fig. 12 but for top incidence at θinc = 60°; horizontal midvein orientation.

Fig. 15
Fig. 15

Corn leaf bidirectional reflection and transmission distribution functions ρ′ at θcoll = 45° (—), θcoll = 0° (……), and τ′ at θcoll = 180° (----) vs wavelength for top incidence at θinc = 45° and horizontal midvein orientation.

Fig. 16
Fig. 16

Soybean and corn leaf sections. (a), (b) Soybean. (c), (d) Corn.

Fig. 17
Fig. 17

Nomenclature for an m-layer model of a leaf.

Fig. 18
Fig. 18

Rm and Tm vs m for three values of kl.

Equations (20)

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δ P i = δ H i δ A δ λ ,
δ P τ ( θ coll ) = δ N τ ( θ coll ) cos θ coll δ A δ Ω r δ λ ,
δ P r / δ P i = ρ cos θ coll δ Ω r
δ P t / δ P i = τ cos ( π - θ coll ) δ Ω t .
ρ cos ( π / 4 ) = 40 × 0.88 × 10 - 3 × 0.707 sr - 1
ρ = 0.035 sr - 1 .
τ cos ( - π / 8 ) = 80 × 0.65 × 10 - 3 × 0.924 sr - 1
τ = 0.052 sr - 1 .
R = r 0 + ( 1 - r 0 ) 2 r 0 e - 2 k l / ( 1 - r 0 2 e - 2 k l ) ,
T = ( 1 - r 0 ) 2 e - k l / ( 1 - r 0 2 e - 2 k l ) ,
R i , j = R i + T i 2 R j / ( 1 - R i R j ) ,
T i , j = T i T j / ( 1 - R i R j ) ,
R m + 1 = R m + T m 2 R / ( 1 - R m R )
T m + 1 = T m T / ( 1 - R m R ) .
( R m + 1 - R m ) / 1 = T m 2 R / ( 1 - R m R ) d R m / d m ,
T m + 1 - T m 1 = T m ( T 1 - R m R - 1 ) d T m d m ,
T m 2 = T 2 - R 2 + 2 ( 1 - T ) - [ ( 2 / R ) ( 1 - T ) R m ] + R m 2
m = 1 + T R ( - q ) 1 2 ln 2 R m - 2 ( 1 - T ) / R - ( - q ) 1 2 2 R m - 2 ( 1 - T ) / R + ( - q ) 1 2 · 2 R - 2 ( 1 - T ) / R + ( - q ) 1 2 2 R - 2 ( 1 - T ) / R - ( - q ) 1 2 + ln ( T / T m ) ,
( - q ) 1 2 2 ( 1 - T ) R { 1 - [ T 2 - R 2 + 2 ( 1 - T ) ] R 2 ( 1 - T ) 2 } 1 2 .
m = R m ( 1 - R ) / [ R ( 1 - R m ) ] + ln [ ( 1 - R ) / ( 1 - R m ) ] .

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