Abstract

Using polarization measurements, the reflectance factor R(θi,ϕi,θr,ϕr) of two wheat canopies is divided into components due to specularly and diffusely reflected light. The data show that two key angles may be predicted, the angle of the polarizer for minimum flux and the angle of incidence of sunlight specularly reflected by a leaf to a sensor. The results show that specular reflection is a key aspect to radiation transfer by two canopies. Results suggest that the advent of heading in wheat may be remotely sensed from polarization measurements of the canopy reflectance.

© 1985 Optical Society of America

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References

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  1. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations, and Nomenclature for Reflectance,” Nat. Bur. Stand. U.S. Monogr. 160 (1977).
  2. T. R. Sinclair, “Pathway of Solar Radiation through Leaves,” Master’s Thesis, Purdue U. (1968).
  3. J. T. Martin, B. E. Juniper, The Cuticles of Plants (St. Martin’s, New York, 1970).
  4. B. E. Juniper, C. E. Jeffree, Plant Surfaces (Edward Arnold, London, 1983).
  5. R. Kumar, L. F. Silva “Light Ray Tracing Through a Leaf Cross Section,” Appl. Opt. 12, 2950 (1973).
    [CrossRef] [PubMed]
  6. T. P. O’Brien, M. E. McCully, Plant Structure and Development (Macmillan, New York, 1969).
  7. V. A. Greulach, Plant Function and Structure (Macmillan, New York, 1973).
  8. W. G. Egan, “Optical Stokes Parameters for Farm Crop Identification,” Remote Sensing Environ. 1, 165 (1970).
    [CrossRef]
  9. W. G. Egan, H. B. Hallock, “Coherence Polarization Phenomena in Remote Sensing,” Proc. IEEE 57, 621 (1969).
    [CrossRef]
  10. W. G. Egan, J. Grusauskas, H. B. Hallock, “Optical Depolarization Properties of Surfaces Illuminated by Coherent Light,” Appl. Opt. 7, 1529 (1968).
    [CrossRef] [PubMed]
  11. P. J. Curran, “A Photographic Method for Recording of Polarized Visible Light for Soil Surface Moisture Indications,” Remote Sensing Environ. 7, 305 (1978).
    [CrossRef]
  12. P. J. Curran, “The Use of Polarized Panchromatic and False Color Infrared Film in the Monitoring of Soil Surface Moisture,” Remote Sensing Environ. 8, 249 (1979).
    [CrossRef]
  13. W. G. Egan, Photometry and Polarization in Remote Sensing (Elsevier, New York, 1985).
  14. R. B. MacDonald, F. G. Hall, “Global Crop Forecasting,” Science 208, 670 (1980).
    [CrossRef] [PubMed]
  15. R. W. Leamer, V. I. Myers, L. F. Silva, “A Spectroradiometer for Field Use,” Rev. Sci. Instrum. 44, 611 (1973).
    [CrossRef]
  16. R. C. Weast, Ed., Handbook of Chemistry and Physics (CRC Press, Cleveland, 1973).
  17. P. J. Holloway, “Structure and Histochemistry of Plant Cuticular Membranes: An Overview,” in The Plant Cuticle, D. F. Cutler, K. L. Alvin, C. E. Price, Eds. (Academic, New York, 1982), pp. 1–32.
  18. H. W. Gausman, W. A. Allen, C. L. Wiegand, D. E. Escobar, R. R. Rodriguez, A. J. Richardson, “The Leaf Mesophylls of Twenty Crops, Their light Spectra, and Optical and Geometrical Parameters,” U.S. Dep. Agric. Tech. Bull. 1465, (1973), 59 pp.
  19. V. C. Vanderbilt, “A Model of Plant Canopy Polarization Response,” in Proceedings, Machine Processing of Remotely Sensed Data, IEEE CH1533-9/80/0000-0098 (1980), p. 98.
  20. E. C. Large, “Growth Stages in Cereals,” Plant Pathol. 3, 129 (1954).

1980 (1)

R. B. MacDonald, F. G. Hall, “Global Crop Forecasting,” Science 208, 670 (1980).
[CrossRef] [PubMed]

1979 (1)

P. J. Curran, “The Use of Polarized Panchromatic and False Color Infrared Film in the Monitoring of Soil Surface Moisture,” Remote Sensing Environ. 8, 249 (1979).
[CrossRef]

1978 (1)

P. J. Curran, “A Photographic Method for Recording of Polarized Visible Light for Soil Surface Moisture Indications,” Remote Sensing Environ. 7, 305 (1978).
[CrossRef]

1973 (2)

R. W. Leamer, V. I. Myers, L. F. Silva, “A Spectroradiometer for Field Use,” Rev. Sci. Instrum. 44, 611 (1973).
[CrossRef]

R. Kumar, L. F. Silva “Light Ray Tracing Through a Leaf Cross Section,” Appl. Opt. 12, 2950 (1973).
[CrossRef] [PubMed]

1970 (1)

W. G. Egan, “Optical Stokes Parameters for Farm Crop Identification,” Remote Sensing Environ. 1, 165 (1970).
[CrossRef]

1969 (1)

W. G. Egan, H. B. Hallock, “Coherence Polarization Phenomena in Remote Sensing,” Proc. IEEE 57, 621 (1969).
[CrossRef]

1968 (1)

1954 (1)

E. C. Large, “Growth Stages in Cereals,” Plant Pathol. 3, 129 (1954).

Allen, W. A.

H. W. Gausman, W. A. Allen, C. L. Wiegand, D. E. Escobar, R. R. Rodriguez, A. J. Richardson, “The Leaf Mesophylls of Twenty Crops, Their light Spectra, and Optical and Geometrical Parameters,” U.S. Dep. Agric. Tech. Bull. 1465, (1973), 59 pp.

Curran, P. J.

P. J. Curran, “The Use of Polarized Panchromatic and False Color Infrared Film in the Monitoring of Soil Surface Moisture,” Remote Sensing Environ. 8, 249 (1979).
[CrossRef]

P. J. Curran, “A Photographic Method for Recording of Polarized Visible Light for Soil Surface Moisture Indications,” Remote Sensing Environ. 7, 305 (1978).
[CrossRef]

Egan, W. G.

W. G. Egan, “Optical Stokes Parameters for Farm Crop Identification,” Remote Sensing Environ. 1, 165 (1970).
[CrossRef]

W. G. Egan, H. B. Hallock, “Coherence Polarization Phenomena in Remote Sensing,” Proc. IEEE 57, 621 (1969).
[CrossRef]

W. G. Egan, J. Grusauskas, H. B. Hallock, “Optical Depolarization Properties of Surfaces Illuminated by Coherent Light,” Appl. Opt. 7, 1529 (1968).
[CrossRef] [PubMed]

W. G. Egan, Photometry and Polarization in Remote Sensing (Elsevier, New York, 1985).

Escobar, D. E.

H. W. Gausman, W. A. Allen, C. L. Wiegand, D. E. Escobar, R. R. Rodriguez, A. J. Richardson, “The Leaf Mesophylls of Twenty Crops, Their light Spectra, and Optical and Geometrical Parameters,” U.S. Dep. Agric. Tech. Bull. 1465, (1973), 59 pp.

Gausman, H. W.

H. W. Gausman, W. A. Allen, C. L. Wiegand, D. E. Escobar, R. R. Rodriguez, A. J. Richardson, “The Leaf Mesophylls of Twenty Crops, Their light Spectra, and Optical and Geometrical Parameters,” U.S. Dep. Agric. Tech. Bull. 1465, (1973), 59 pp.

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations, and Nomenclature for Reflectance,” Nat. Bur. Stand. U.S. Monogr. 160 (1977).

Greulach, V. A.

V. A. Greulach, Plant Function and Structure (Macmillan, New York, 1973).

Grusauskas, J.

Hall, F. G.

R. B. MacDonald, F. G. Hall, “Global Crop Forecasting,” Science 208, 670 (1980).
[CrossRef] [PubMed]

Hallock, H. B.

Holloway, P. J.

P. J. Holloway, “Structure and Histochemistry of Plant Cuticular Membranes: An Overview,” in The Plant Cuticle, D. F. Cutler, K. L. Alvin, C. E. Price, Eds. (Academic, New York, 1982), pp. 1–32.

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations, and Nomenclature for Reflectance,” Nat. Bur. Stand. U.S. Monogr. 160 (1977).

Jeffree, C. E.

B. E. Juniper, C. E. Jeffree, Plant Surfaces (Edward Arnold, London, 1983).

Juniper, B. E.

B. E. Juniper, C. E. Jeffree, Plant Surfaces (Edward Arnold, London, 1983).

J. T. Martin, B. E. Juniper, The Cuticles of Plants (St. Martin’s, New York, 1970).

Kumar, R.

Large, E. C.

E. C. Large, “Growth Stages in Cereals,” Plant Pathol. 3, 129 (1954).

Leamer, R. W.

R. W. Leamer, V. I. Myers, L. F. Silva, “A Spectroradiometer for Field Use,” Rev. Sci. Instrum. 44, 611 (1973).
[CrossRef]

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations, and Nomenclature for Reflectance,” Nat. Bur. Stand. U.S. Monogr. 160 (1977).

MacDonald, R. B.

R. B. MacDonald, F. G. Hall, “Global Crop Forecasting,” Science 208, 670 (1980).
[CrossRef] [PubMed]

Martin, J. T.

J. T. Martin, B. E. Juniper, The Cuticles of Plants (St. Martin’s, New York, 1970).

McCully, M. E.

T. P. O’Brien, M. E. McCully, Plant Structure and Development (Macmillan, New York, 1969).

Myers, V. I.

R. W. Leamer, V. I. Myers, L. F. Silva, “A Spectroradiometer for Field Use,” Rev. Sci. Instrum. 44, 611 (1973).
[CrossRef]

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations, and Nomenclature for Reflectance,” Nat. Bur. Stand. U.S. Monogr. 160 (1977).

O’Brien, T. P.

T. P. O’Brien, M. E. McCully, Plant Structure and Development (Macmillan, New York, 1969).

Richardson, A. J.

H. W. Gausman, W. A. Allen, C. L. Wiegand, D. E. Escobar, R. R. Rodriguez, A. J. Richardson, “The Leaf Mesophylls of Twenty Crops, Their light Spectra, and Optical and Geometrical Parameters,” U.S. Dep. Agric. Tech. Bull. 1465, (1973), 59 pp.

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations, and Nomenclature for Reflectance,” Nat. Bur. Stand. U.S. Monogr. 160 (1977).

Rodriguez, R. R.

H. W. Gausman, W. A. Allen, C. L. Wiegand, D. E. Escobar, R. R. Rodriguez, A. J. Richardson, “The Leaf Mesophylls of Twenty Crops, Their light Spectra, and Optical and Geometrical Parameters,” U.S. Dep. Agric. Tech. Bull. 1465, (1973), 59 pp.

Silva, L. F.

R. W. Leamer, V. I. Myers, L. F. Silva, “A Spectroradiometer for Field Use,” Rev. Sci. Instrum. 44, 611 (1973).
[CrossRef]

R. Kumar, L. F. Silva “Light Ray Tracing Through a Leaf Cross Section,” Appl. Opt. 12, 2950 (1973).
[CrossRef] [PubMed]

Sinclair, T. R.

T. R. Sinclair, “Pathway of Solar Radiation through Leaves,” Master’s Thesis, Purdue U. (1968).

Vanderbilt, V. C.

V. C. Vanderbilt, “A Model of Plant Canopy Polarization Response,” in Proceedings, Machine Processing of Remotely Sensed Data, IEEE CH1533-9/80/0000-0098 (1980), p. 98.

Wiegand, C. L.

H. W. Gausman, W. A. Allen, C. L. Wiegand, D. E. Escobar, R. R. Rodriguez, A. J. Richardson, “The Leaf Mesophylls of Twenty Crops, Their light Spectra, and Optical and Geometrical Parameters,” U.S. Dep. Agric. Tech. Bull. 1465, (1973), 59 pp.

Appl. Opt. (2)

Plant Pathol. (1)

E. C. Large, “Growth Stages in Cereals,” Plant Pathol. 3, 129 (1954).

Proc. IEEE (1)

W. G. Egan, H. B. Hallock, “Coherence Polarization Phenomena in Remote Sensing,” Proc. IEEE 57, 621 (1969).
[CrossRef]

Remote Sensing Environ. (3)

P. J. Curran, “A Photographic Method for Recording of Polarized Visible Light for Soil Surface Moisture Indications,” Remote Sensing Environ. 7, 305 (1978).
[CrossRef]

P. J. Curran, “The Use of Polarized Panchromatic and False Color Infrared Film in the Monitoring of Soil Surface Moisture,” Remote Sensing Environ. 8, 249 (1979).
[CrossRef]

W. G. Egan, “Optical Stokes Parameters for Farm Crop Identification,” Remote Sensing Environ. 1, 165 (1970).
[CrossRef]

Rev. Sci. Instrum. (1)

R. W. Leamer, V. I. Myers, L. F. Silva, “A Spectroradiometer for Field Use,” Rev. Sci. Instrum. 44, 611 (1973).
[CrossRef]

Science (1)

R. B. MacDonald, F. G. Hall, “Global Crop Forecasting,” Science 208, 670 (1980).
[CrossRef] [PubMed]

Other (11)

R. C. Weast, Ed., Handbook of Chemistry and Physics (CRC Press, Cleveland, 1973).

P. J. Holloway, “Structure and Histochemistry of Plant Cuticular Membranes: An Overview,” in The Plant Cuticle, D. F. Cutler, K. L. Alvin, C. E. Price, Eds. (Academic, New York, 1982), pp. 1–32.

H. W. Gausman, W. A. Allen, C. L. Wiegand, D. E. Escobar, R. R. Rodriguez, A. J. Richardson, “The Leaf Mesophylls of Twenty Crops, Their light Spectra, and Optical and Geometrical Parameters,” U.S. Dep. Agric. Tech. Bull. 1465, (1973), 59 pp.

V. C. Vanderbilt, “A Model of Plant Canopy Polarization Response,” in Proceedings, Machine Processing of Remotely Sensed Data, IEEE CH1533-9/80/0000-0098 (1980), p. 98.

W. G. Egan, Photometry and Polarization in Remote Sensing (Elsevier, New York, 1985).

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations, and Nomenclature for Reflectance,” Nat. Bur. Stand. U.S. Monogr. 160 (1977).

T. R. Sinclair, “Pathway of Solar Radiation through Leaves,” Master’s Thesis, Purdue U. (1968).

J. T. Martin, B. E. Juniper, The Cuticles of Plants (St. Martin’s, New York, 1970).

B. E. Juniper, C. E. Jeffree, Plant Surfaces (Edward Arnold, London, 1983).

T. P. O’Brien, M. E. McCully, Plant Structure and Development (Macmillan, New York, 1969).

V. A. Greulach, Plant Function and Structure (Macmillan, New York, 1973).

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Figures (15)

Fig. 1
Fig. 1

During acquisition of spectra in multiple-view directions, the vehicle transporting the aerial tower was parked in the middle of a wheat field with uniform properties. The spectroradiometer was attached to a pan head mounted to a boom of the tower and elevated over the canopy.

Fig. 2
Fig. 2

From the data (Rmax,Rmin) measured on the wheat canopy on 19 June 1976 at 60° view zenith angle toward the solar azimuth, the polarized RQ, specular RS, and diffuse RD parts of the reflectance factor R and the degrees of specularity, diffuseness, and polarization are determined. The ratio is shown in Fie. 4.

Fig. 3
Fig. 3

Angle of incidence is computed for a solar zenith angle of 30° as a function of view direction (as shown in Fig. 6) noting that if an observer sees specularly reflected sunlight, the direction of the normal to the surface of the specular reflector is unique.

Fig. 4
Fig. 4

For a specularly reflecting leaf facet, the ratio of the polarized part of the specularly reflected light and the specularly reflected light equals the ratio (shown here) of the first and second components of the Stokes vector of a nondiffuse purely specular reflector. The ratio depends on the angle of incidence and on the index of refraction of the cuticle of the wheat leaf—assumed here to be 1.5 for purposes of calculating the properties of the canopy.

Fig. 5
Fig. 5

If the index of refraction of the cuticle is other than 1.5, ratio n is proportionately larger or smaller than ratio 1.5.

Fig. 6
Fig. 6

This subset of the spectra acquired 19 June 1976 illustrates the variation of reflectance factor R with view direction.

Fig. 7
Fig. 7

Spectra of the polarized part RQ of the reflectance factor correspond to the spectra of R in Fig. 6.

Fig. 8
Fig. 8

Polarized part RQ of the reflectance factor for a wavelength of 0.60 μm varies for preheaded (19 July 1976) and headed (17 July 1976) wheat measured in view directions toward (1) and away from (2) the solar azimuth.

Fig. 9
Fig. 9

Degree of polarization at 0.66-μm wavelength varies for view directions on 19 June 1976 and 17 July 1976.

Fig. 10
Fig. 10

Specular, diffuse, and polarized light scattering properties of two wheat canopies depend on wavelength and view directions.

Fig. 11
Fig. 11

Degree of polarization at 0.66 μm for the two wheat canopies varied with angle of incidence.

Fig. 12
Fig. 12

For the wheat canopies measured 19 June and 17 July 1976, comparison of the actual and predicted angles of the axis of the polarization analyzer is made with the aid of a 1:1 line.

Fig. 13
Fig. 13

Specular part of the reflectance factor averaged over the visible wavelength region for the wheat canopies.

Fig. 14
Fig. 14

Specular reflectance of the canopy at a wavelength of 0.66 μm normalized by the specular reflectance of a hypothetical piece of glass at the same angle of incidence provides a measure of the efficiency of the wheat canopies as specular reflectors.

Fig. 15
Fig. 15

With the aid of the polarization measurements, the reflectance factor of the wheat canopies was split into its specular and diffuse components at 0.66-μm wavelength and 60° view zenith angle.

Tables (1)

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Table I Ancillary Meteorologie and Agronomic Data

Equations (5)

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γ = 0 . 5 arccos [ sin θ r cos ( ϕ i ϕ r ) sin θ i + cos θ i cos θ r ] ,
cos 2 γ = i ˆ · r ˆ .
β = arccos [ [ r ˆ x ( r ˆ x υ ˆ ) ] · i ˆ ( [ ( r ˆ x υ ˆ ) · i ˆ ] 2 + [ r ˆ x ( r ˆ x υ ˆ ) · i ˆ ] 2 ) 1 / 2 ] , β = arccos ( cos θ i sin θ r + c o s ( ϕ i ϕ Q r ) sin θ i cos θ r { sin 2 ( ϕ i ϕ r ) sin 2 θ i + [ cos θ i sin θ r + c o s ( ϕ i ϕ r ) s i n θ i cos θ r ] 2 } 1 / 2 ) ,
R glass = π w r w i 2 δ ( sin 2 γ i sin 2 γ r ) δ ( ϕ i ϕ r ) p ( γ i ) sin γ i cos γ i d γ i d ϕ i sin γ r cos γ r d γ r d ϕ r w r w i cos γ i cos γ r sin γ i sin γ r d γ i d γ r d ϕ r .
R glass = π p ( γ ) cos γ Δ w i ,

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