Abstract

The directional–hemispherical reflectance is obtained for Spectralon, the material chosen for onboard radiometric calibration of the multiangle imaging spectroradiometer, at laser wavelengths of 442, 632.8, and 859.9 nm. With p- and s-polarized incident light and for an angle of incidence of 45°, the bidirectional reflectance distribution function was measured over a polar angle range of 1–85° and a range of azimuthal angles of 0–180° in 10° increments. The resultant directional–hemispherical reflectance is found by integration to be 1.00 ± 0.01 at 442 nm, 0.953 ± 0.01 at 632.8 nm, and 0.956 ± 0.01 at 859.9 nm. The experimental methodology and the data analysis are presented together with a full discussion of the primary experimental errors.

© 1998 Optical Society of America

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References

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  1. C. J. Bruegge, V. G. Duval, N. L. Chrien, D. J. Diner, “Calibration plans for the multi-angle imaging spectroradiometer (MISR),” Metrologia. 30, 213–221 (1993).
    [CrossRef]
  2. B. T. McGuckin, D. A. Haner, R. T. Menzies, C. Esproles, A. M. Brothers, “Directional reflectance characterization facility and measurement methodology,” Appl. Opt. 35, 4827–4834 (1996).
    [CrossRef] [PubMed]
  3. B. T. McGuckin, D. A. Haner, R. T. Menzies, “Multi-angle imaging spectroradiometer: optical characterization of calibration panels,” Appl. Opt. 36, 7016–7022 (1997).
    [CrossRef]
  4. D. A. Haner, B. T. McGuckin, “Measurement of depolarization of reflected light from Spectralon,” submitted for publication, Applied Optics.
  5. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160, (1977).
  6. F. E. Nicodemus, eds., “Self-study manual on optical radiation measurements: Part I. Concepts,” Natl. Bur. Stand. (U.S.) Tech. Note 910-1 (1976), Chaps. 1–3.
  7. G. E. Forsythe, M. A. Malcolm, C. B. Maler, Computer Methods For Mathematical Computation (Prentice-Hall, Englewood Cliffs, N.J., 1977).
  8. F. B. Hildebrand, Introduction to Numerical Analysis (McGraw-Hill, New York, 1956).
  9. J. M. McCormick, M. G. Salvadori, Numerical Methods in FORTRAN (Prentice-Hall, Englewood Cliffs, N.J., 1964).
  10. A. M. Brothers, Jet Propulsion Laboratory.His reference, W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1986).
  11. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).
  12. V. R. Weidner, J. J. Hsia, B. Adams, “Laboratory intercomparison study of pressed polytetrafluoroethylene powder reflectance standards,” Appl. Opt. 24, 2225–2230 (1985).
    [CrossRef] [PubMed]

1997 (1)

1996 (1)

1993 (1)

C. J. Bruegge, V. G. Duval, N. L. Chrien, D. J. Diner, “Calibration plans for the multi-angle imaging spectroradiometer (MISR),” Metrologia. 30, 213–221 (1993).
[CrossRef]

1985 (1)

1977 (1)

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160, (1977).

Adams, B.

Bevington, P. R.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

Brothers, A. M.

B. T. McGuckin, D. A. Haner, R. T. Menzies, C. Esproles, A. M. Brothers, “Directional reflectance characterization facility and measurement methodology,” Appl. Opt. 35, 4827–4834 (1996).
[CrossRef] [PubMed]

A. M. Brothers, Jet Propulsion Laboratory.His reference, W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1986).

Bruegge, C. J.

C. J. Bruegge, V. G. Duval, N. L. Chrien, D. J. Diner, “Calibration plans for the multi-angle imaging spectroradiometer (MISR),” Metrologia. 30, 213–221 (1993).
[CrossRef]

Chrien, N. L.

C. J. Bruegge, V. G. Duval, N. L. Chrien, D. J. Diner, “Calibration plans for the multi-angle imaging spectroradiometer (MISR),” Metrologia. 30, 213–221 (1993).
[CrossRef]

Diner, D. J.

C. J. Bruegge, V. G. Duval, N. L. Chrien, D. J. Diner, “Calibration plans for the multi-angle imaging spectroradiometer (MISR),” Metrologia. 30, 213–221 (1993).
[CrossRef]

Duval, V. G.

C. J. Bruegge, V. G. Duval, N. L. Chrien, D. J. Diner, “Calibration plans for the multi-angle imaging spectroradiometer (MISR),” Metrologia. 30, 213–221 (1993).
[CrossRef]

Esproles, C.

Forsythe, G. E.

G. E. Forsythe, M. A. Malcolm, C. B. Maler, Computer Methods For Mathematical Computation (Prentice-Hall, Englewood Cliffs, N.J., 1977).

Ginsburg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160, (1977).

Haner, D. A.

Hildebrand, F. B.

F. B. Hildebrand, Introduction to Numerical Analysis (McGraw-Hill, New York, 1956).

Hsia, J. J.

V. R. Weidner, J. J. Hsia, B. Adams, “Laboratory intercomparison study of pressed polytetrafluoroethylene powder reflectance standards,” Appl. Opt. 24, 2225–2230 (1985).
[CrossRef] [PubMed]

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160, (1977).

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160, (1977).

Malcolm, M. A.

G. E. Forsythe, M. A. Malcolm, C. B. Maler, Computer Methods For Mathematical Computation (Prentice-Hall, Englewood Cliffs, N.J., 1977).

Maler, C. B.

G. E. Forsythe, M. A. Malcolm, C. B. Maler, Computer Methods For Mathematical Computation (Prentice-Hall, Englewood Cliffs, N.J., 1977).

McCormick, J. M.

J. M. McCormick, M. G. Salvadori, Numerical Methods in FORTRAN (Prentice-Hall, Englewood Cliffs, N.J., 1964).

McGuckin, B. T.

Menzies, R. T.

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160, (1977).

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160, (1977).

Salvadori, M. G.

J. M. McCormick, M. G. Salvadori, Numerical Methods in FORTRAN (Prentice-Hall, Englewood Cliffs, N.J., 1964).

Weidner, V. R.

Appl. Opt. (3)

Metrologia. (1)

C. J. Bruegge, V. G. Duval, N. L. Chrien, D. J. Diner, “Calibration plans for the multi-angle imaging spectroradiometer (MISR),” Metrologia. 30, 213–221 (1993).
[CrossRef]

Natl. Bur. Stand. (U.S.) Monogr. (1)

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160, (1977).

Other (7)

F. E. Nicodemus, eds., “Self-study manual on optical radiation measurements: Part I. Concepts,” Natl. Bur. Stand. (U.S.) Tech. Note 910-1 (1976), Chaps. 1–3.

G. E. Forsythe, M. A. Malcolm, C. B. Maler, Computer Methods For Mathematical Computation (Prentice-Hall, Englewood Cliffs, N.J., 1977).

F. B. Hildebrand, Introduction to Numerical Analysis (McGraw-Hill, New York, 1956).

J. M. McCormick, M. G. Salvadori, Numerical Methods in FORTRAN (Prentice-Hall, Englewood Cliffs, N.J., 1964).

A. M. Brothers, Jet Propulsion Laboratory.His reference, W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1986).

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

D. A. Haner, B. T. McGuckin, “Measurement of depolarization of reflected light from Spectralon,” submitted for publication, Applied Optics.

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Figures (1)

Fig. 1
Fig. 1

Polar plot of the normalized experimental data for the BRF from Spectralon at 632 nm, s polarization, 45° incidence (open circles), and the hemispherical grid representing the ideal diffuse reflector.

Tables (1)

Tables Icon

Table 1 Measured Directional-Hemispherical Reflectance for p - and s -polarized Light Incident at an Angle of 45° with a Polarization-Insensitive Detector

Equations (8)

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f θ i ,   φ i   :   θ r ,   φ r   :   λ ,   ξ = d L θ i ,   φ i   :   θ r ,   φ r   :   λ ,   ξ d E θ i ,   φ i   :   λ ,   ξ sr - 1 ,
L θ i ,   φ i   :   θ r ,   φ r   :   λ ,   ξ = d 2 Φ r d A r cos   θ r d ω r ,
f r θ i ,   φ i   :   θ r ,   φ r   :   λ ,   ξ = d 2 Φ r d A r cos   θ r d ω r d Φ i d A i .
f r θ i ,   φ i   :   θ r ,   φ r   :   λ ,   ξ = d 2 Φ r d Φ i cos   θ r d ω r .
f r θ i ,   φ i   :   θ r ,   φ r   :   λ ,   ξ = S r θ i ,   φ i   :   θ r ,   φ r   :   λ ,   ξ S i θ i ,   φ i   :   λ ,   ξ   cos   θ r d ω r ,
R θ i ,   φ i   :   2 π   :   λ ,   ξ = 2 π   f r θ i ,   φ i   :   θ r ,   φ r   :   λ ,   ξ d Ω r ,
R θ i ,   φ i   :   2 π :   λ ,   ξ = 1 S i π / 2 ,   π :   λ ,   ξ ω D 2 π   S r θ i ,   φ i   :   θ r ,   φ r   :   λ ,   ξ sin   θ d θ d φ ,
d R R = d S i S i + d ω D ω D + d I I ,

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