Abstract

We present our investigations into the optical scattering properties of both sugar maple (Acer saccarum) and eastern cottonwood (Populus deltoides) leaves in the near-IR wavelength regime. The bidirectional scattering distribution function (BSDF) describes the fractions of light reflected by and transmitted through a leaf for a given set of illumination and observation angles. Experiments were performed to measure the BSDF of each species at a discrete set of illumination and observation angles. We then modeled the BSDFs in such a way that other researchers may interpolate their values for scattering in any direction under illumination at any angle.

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  1. H. T. Breece III and R. A. Holmes, "Bidirectional scattering characteristics of healthy green soybean and corn leaves in vivo," Appl. Opt. 10, 119-127 (1971).
    [CrossRef]
  2. T. T. Lei, R. Tabuchi, and T. Koike, "Functional relationship between chlorophyll content and leaf reflectance, and light-capturing efficiency of Japanese forest species," Physiol. Plant. 96, 411-418 (1996).
    [CrossRef]
  3. S. Jacquemoud and F. Baret, "PROSPECT: a model of leaf optical properties spectra," Remote Sens. Environ. 34, 75-91 (1990).
    [CrossRef]
  4. J. Ross and T. Nilson, "A mathematical model of radiation regime of plant cover," in Actinometry and Atmospheric Optics (Valgus, 1968), pp. 263-281 (in Russian).
  5. J. K. Shultis and R. B. Myneni, "Radiative transfer in vegetation canopies with anisotropic scattering," J. Quant. Spectrosc. Radiat. Transfer 39, 115-129 (1988).
    [CrossRef]
  6. T. W. Brakke, "Goniometric measurements of light scattered in the principle plane from leaves," in 1992 International Geoscience and Remote Sensing Symposium (IEEE, 1992), Vol. 2, pp. 508-510.
    [CrossRef]
  7. J. T. Woolley, "Reflectance and transmittance of light by leaves," Plant Physiol. 47, 656-662 (1971).
    [CrossRef] [PubMed]
  8. T. W. Brakke, J. A. Smith, and J. M Harnden, "Bidirectional scattering of light from tree leaves," Remote Sens. Environ. 29, 175-183 (1989).
    [CrossRef]
  9. S. Jacquemond and S. Ustin, "Leaf optical properties: a state of the art," in Proceedings of the 8th International Symposium on Physical Measurements and Signatures in Remote Sensing, Aussois, France, 8-12 January 2001, pp. 223-232.

1996 (1)

T. T. Lei, R. Tabuchi, and T. Koike, "Functional relationship between chlorophyll content and leaf reflectance, and light-capturing efficiency of Japanese forest species," Physiol. Plant. 96, 411-418 (1996).
[CrossRef]

1992 (1)

T. W. Brakke, "Goniometric measurements of light scattered in the principle plane from leaves," in 1992 International Geoscience and Remote Sensing Symposium (IEEE, 1992), Vol. 2, pp. 508-510.
[CrossRef]

1990 (1)

S. Jacquemoud and F. Baret, "PROSPECT: a model of leaf optical properties spectra," Remote Sens. Environ. 34, 75-91 (1990).
[CrossRef]

1989 (1)

T. W. Brakke, J. A. Smith, and J. M Harnden, "Bidirectional scattering of light from tree leaves," Remote Sens. Environ. 29, 175-183 (1989).
[CrossRef]

1988 (1)

J. K. Shultis and R. B. Myneni, "Radiative transfer in vegetation canopies with anisotropic scattering," J. Quant. Spectrosc. Radiat. Transfer 39, 115-129 (1988).
[CrossRef]

1971 (2)

1968 (1)

J. Ross and T. Nilson, "A mathematical model of radiation regime of plant cover," in Actinometry and Atmospheric Optics (Valgus, 1968), pp. 263-281 (in Russian).

Baret, F.

S. Jacquemoud and F. Baret, "PROSPECT: a model of leaf optical properties spectra," Remote Sens. Environ. 34, 75-91 (1990).
[CrossRef]

Brakke, T. W.

T. W. Brakke, "Goniometric measurements of light scattered in the principle plane from leaves," in 1992 International Geoscience and Remote Sensing Symposium (IEEE, 1992), Vol. 2, pp. 508-510.
[CrossRef]

T. W. Brakke, J. A. Smith, and J. M Harnden, "Bidirectional scattering of light from tree leaves," Remote Sens. Environ. 29, 175-183 (1989).
[CrossRef]

Breece, H. T.

Harnden, J. M

T. W. Brakke, J. A. Smith, and J. M Harnden, "Bidirectional scattering of light from tree leaves," Remote Sens. Environ. 29, 175-183 (1989).
[CrossRef]

Holmes, R. A.

Jacquemond, S.

S. Jacquemond and S. Ustin, "Leaf optical properties: a state of the art," in Proceedings of the 8th International Symposium on Physical Measurements and Signatures in Remote Sensing, Aussois, France, 8-12 January 2001, pp. 223-232.

Jacquemoud, S.

S. Jacquemoud and F. Baret, "PROSPECT: a model of leaf optical properties spectra," Remote Sens. Environ. 34, 75-91 (1990).
[CrossRef]

Koike, T.

T. T. Lei, R. Tabuchi, and T. Koike, "Functional relationship between chlorophyll content and leaf reflectance, and light-capturing efficiency of Japanese forest species," Physiol. Plant. 96, 411-418 (1996).
[CrossRef]

Lei, T. T.

T. T. Lei, R. Tabuchi, and T. Koike, "Functional relationship between chlorophyll content and leaf reflectance, and light-capturing efficiency of Japanese forest species," Physiol. Plant. 96, 411-418 (1996).
[CrossRef]

Myneni, R. B.

J. K. Shultis and R. B. Myneni, "Radiative transfer in vegetation canopies with anisotropic scattering," J. Quant. Spectrosc. Radiat. Transfer 39, 115-129 (1988).
[CrossRef]

Nilson, T.

J. Ross and T. Nilson, "A mathematical model of radiation regime of plant cover," in Actinometry and Atmospheric Optics (Valgus, 1968), pp. 263-281 (in Russian).

Ross, J.

J. Ross and T. Nilson, "A mathematical model of radiation regime of plant cover," in Actinometry and Atmospheric Optics (Valgus, 1968), pp. 263-281 (in Russian).

Shultis, J. K.

J. K. Shultis and R. B. Myneni, "Radiative transfer in vegetation canopies with anisotropic scattering," J. Quant. Spectrosc. Radiat. Transfer 39, 115-129 (1988).
[CrossRef]

Smith, J. A.

T. W. Brakke, J. A. Smith, and J. M Harnden, "Bidirectional scattering of light from tree leaves," Remote Sens. Environ. 29, 175-183 (1989).
[CrossRef]

Tabuchi, R.

T. T. Lei, R. Tabuchi, and T. Koike, "Functional relationship between chlorophyll content and leaf reflectance, and light-capturing efficiency of Japanese forest species," Physiol. Plant. 96, 411-418 (1996).
[CrossRef]

Ustin, S.

S. Jacquemond and S. Ustin, "Leaf optical properties: a state of the art," in Proceedings of the 8th International Symposium on Physical Measurements and Signatures in Remote Sensing, Aussois, France, 8-12 January 2001, pp. 223-232.

Woolley, J. T.

J. T. Woolley, "Reflectance and transmittance of light by leaves," Plant Physiol. 47, 656-662 (1971).
[CrossRef] [PubMed]

Appl. Opt. (1)

J. Quant. Spectrosc. Radiat. Transfer (1)

J. K. Shultis and R. B. Myneni, "Radiative transfer in vegetation canopies with anisotropic scattering," J. Quant. Spectrosc. Radiat. Transfer 39, 115-129 (1988).
[CrossRef]

Physiol. Plant. (1)

T. T. Lei, R. Tabuchi, and T. Koike, "Functional relationship between chlorophyll content and leaf reflectance, and light-capturing efficiency of Japanese forest species," Physiol. Plant. 96, 411-418 (1996).
[CrossRef]

Plant Physiol. (1)

J. T. Woolley, "Reflectance and transmittance of light by leaves," Plant Physiol. 47, 656-662 (1971).
[CrossRef] [PubMed]

Remote Sens. Environ. (2)

T. W. Brakke, J. A. Smith, and J. M Harnden, "Bidirectional scattering of light from tree leaves," Remote Sens. Environ. 29, 175-183 (1989).
[CrossRef]

S. Jacquemoud and F. Baret, "PROSPECT: a model of leaf optical properties spectra," Remote Sens. Environ. 34, 75-91 (1990).
[CrossRef]

Other (3)

J. Ross and T. Nilson, "A mathematical model of radiation regime of plant cover," in Actinometry and Atmospheric Optics (Valgus, 1968), pp. 263-281 (in Russian).

T. W. Brakke, "Goniometric measurements of light scattered in the principle plane from leaves," in 1992 International Geoscience and Remote Sensing Symposium (IEEE, 1992), Vol. 2, pp. 508-510.
[CrossRef]

S. Jacquemond and S. Ustin, "Leaf optical properties: a state of the art," in Proceedings of the 8th International Symposium on Physical Measurements and Signatures in Remote Sensing, Aussois, France, 8-12 January 2001, pp. 223-232.

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Figures (17)

Fig. 1
Fig. 1

Reflectance and transmittance spectra of fresh poplar (Populus canadensis) leaves [9].

Fig. 2
Fig. 2

Photograph of the BSDF measurement apparatus.

Fig. 3
Fig. 3

Schematic of the BSDF measurement apparatus.

Fig. 4
Fig. 4

BSDF of (a) a fresh sugar maple leaf, and (b) the same appreciably dried maple leaf. Light, depicted by the arrow, is incident from the left and illuminates the leaf, portrayed by the solid line, at normal incidence.

Fig. 5
Fig. 5

Measured BSDF data for sugar maple leaves at θ I illumination angles of (a) 0°, (b) 10°, (c) 20°, (d) 30°, (e) 40°, (f) 50°, (g) 60°, (h) 70°, and (i) 78°.

Fig. 6
Fig. 6

Measured BSDF data for eastern cottonwood leaves for θ I illumination angles of (a) 0°, (b) 10°, (c) 20°, (d) 30°, (e) 40°, (f) 50°, (g) 60°, (h) 70°, and (i) 78°.

Fig. 7
Fig. 7

Comparison of the sugar maple leaf BSDF and Spectralon BRDF for normal illumination. For clarity, the detector angles have been adjusted so that the two curves overlap.

Fig. 8
Fig. 8

Absorption coefficient for maple leaves as a function of illumination angle. The measured data (circles) is fit with the second-order polynomial described in Eq. (5).

Fig. 9
Fig. 9

Lambertian fit to the BRDF (left) and BTDF (right) for (a) normal illumination and (b) illumination at 70°.

Fig. 10
Fig. 10

Separation of the sugar maple leaf diffuse and specular reflection components for 70° illumination. The nonseparated BRDF data is depicted by the stars and circles, which represent the diffuse and overlapping regions, respectively. A fourth-order polynomial is fitted to the diffuse data and represented by the solid curve.

Fig. 11
Fig. 11

Normalized, reverse Rayleigh fits of the specular reflection data for illumination angles of (a) 50°, (b) 60°, (c) 70°, and (d) 78°.

Fig. 12
Fig. 12

Fractional specular reflection for maple leaves as a function of incident angle. The measured data, depicted by the circles, is fit with a polynomial.

Fig. 13
Fig. 13

Fitted sugar maple leaf BSDF curves for illumination at 70°. (a) The diffuse reflection data is fit with a fourth-order polynomial while (b) the transmission data is fit with a second-order polynomial.

Fig. 14
Fig. 14

Sugar maple leaf BRDF models created by adding the diffuse and specular components at (a) 50°, (b) 60°, (c) 70°, and (d) 78° illumination.

Fig. 15
Fig. 15

Polynomial fits of the (a) zeroth-, (b) first-, and (c) second-order p coefficients describing the BTDF data for sugar maple leaves.

Fig. 16
Fig. 16

Two-dimensional BRDF surface fit for sugar maple leaves.

Fig. 17
Fig. 17

Two-dimensional BTDF surface fit for sugar maple leaves.

Tables (6)

Tables Icon

Table 1 Sugar Maple Leaf Reflection, Transmission, and Absorption Coefficients as a Function of Illumination Angle

Tables Icon

Table 2 Eastern Cottonwood Leaf Reflection, Transmission, and Absorption Coefficients as a Function of Illumination Angle

Tables Icon

Table 3 Sugar Maple Leaf BTDF q Coefficients

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Table 4 Sugar Maple Leaf BRDF q Coefficients

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Table 5 Eastern Cottonwood Leaf BTDF q Coefficients

Tables Icon

Table 6 Eastern Cottonwood Leaf BRDF q Coefficients

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

A R ( θ I ) = + 90 + 270 r L ( θ I , θ D ) d θ D ,
A T ( θ I ) = 90 + 90 t L ( θ I , θ D ) d θ D ,
R L ( θ I ) 0.60 = A R ( θ I ) A S ,
T L ( θ I ) 0.60 = A T ( θ I ) A S .
A L ( θ I ) = 1 R L ( θ I ) T L ( θ I ) .
A L ( θ I ) = 4.5156 × 10 6 θ I 2 + 1.0373 × 10 3 θ I + 25.415 × 10 3 ,
A L ( θ I ) = 1.1885 × 10 6 θ I 2 67.238 × 10 6 θ I + 32.7 × 10 3 .
r s ( θ D ) = F S ( θ I ) ( 90 θ D ) ( 90 θ P ) 2 exp [ ( 90 θ D ) 2 2 ( 90 θ P ) 2 ] ,
F S ( θ I ) = A R S ( θ I ) A R ( θ I ) .
F S = { 0 θ I < 50 12.7 × 10 6 θ I 3 1.7 × 10 3 θ I 2 + 77.2 × 10 3 θ I 1.19 θ I 50 ,
F S = { 0 θ I < 50 1.65 × 10 6 θ I 3 + 922 × 10 6 θ I 2 79.2 × 10 3 θ I + 1.89 θ I 50 .
t ( θ D , θ I ) = p 1 t θ D 2 + p 2 t θ D + p 3 t ,
  r d ( θ D , θ I ) = p 1 r θ D 4 + p 2 r θ D 3 + p 3 r θ D 2 + p 4 r θ D + p 5 r ,
p i x ( θ I ) = q 1 θ I 4 + q 2 θ I 3 + q 3 θ I 2 + q 4 θ I + q 5 ,
r L ( θ D , θ I ) = r d ( θ D , θ I ) + r s ( θ D , θ I ) .
1 = 90 90 t ( θ D , θ I ) d θ D + 90 270 r L ( θ D , θ I ) d θ D + A L ( θ I ) .

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