Abstract

We investigate the information content of the radiation measurements to be used in the retrieval of the scattering properties of the atmosphere with the perturbation technique that we previously introduced. Applying this technique to different sets of data, we obtained solutions with varying accuracy. An analysis of these solutions shows that selecting linearly independent data in directions corresponding to small values of the scattering angle increases the number of pieces of information. (This result is in accord with conclusions reached by other researchers, based on a variety of criteria.) This information content should be largely independent of the method or methods employed to perform the inversion procedure.

© 1999 Optical Society of America

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References

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  1. M. A. Box, C. Sendra, “Retrieval of the albedo and phase function from exiting radiances with radiative perturbation theory,” Appl. Opt. 38, 1636–1643 (1999).
    [CrossRef]
  2. S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, New York, 1977).
  3. R. L. Parker, Geophysical Inverse Theory (Princeton U. Press, Princeton, N.J., 1994).
  4. J. Lenoble, ed, Radiative Transfer in Scattering and Absorbing Atmospheres: Standard Computational Procedures (Deepak, Hampton, Va., 1985).
  5. L. G. Henyey, J. L. Greenstein, “Diffuse light in the galaxy,” Astrophys. J. 93, 70–83 (1941).
    [CrossRef]
  6. M. Herman, J. L. Deuze, C. Devaux, P. Goloub, F. M. Breon, D. Tanre, “Remote sensing of aerosols over land surfaces including polarization measurements and application to POLDER measurements,” J. Geophys. Res. 102, 17,039–17,049 (1997).
    [CrossRef]
  7. W. Wanner, A. H. Strahler, B. Hu, P. Lewis, J.-P. Muller, X. Li, C. L. Barker Schaaf, M. J. Barnsley, “Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: theory and algorithm,” J. Geophys. Res. 102, 17,143–17,161 (1997).
    [CrossRef]
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    [CrossRef]
  9. C. Lanczos, Linear Differential Operators (Van Nostrand, Princeton, N.J., 1961).

1999

1997

M. Herman, J. L. Deuze, C. Devaux, P. Goloub, F. M. Breon, D. Tanre, “Remote sensing of aerosols over land surfaces including polarization measurements and application to POLDER measurements,” J. Geophys. Res. 102, 17,039–17,049 (1997).
[CrossRef]

W. Wanner, A. H. Strahler, B. Hu, P. Lewis, J.-P. Muller, X. Li, C. L. Barker Schaaf, M. J. Barnsley, “Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: theory and algorithm,” J. Geophys. Res. 102, 17,143–17,161 (1997).
[CrossRef]

1972

R. A. Wiggins, “The general linear inverse problem: implication of surface waves and free oscillations for Earth structure,” Rev. Geophys. Space Phys. 10, 251–285 (1972).
[CrossRef]

1941

L. G. Henyey, J. L. Greenstein, “Diffuse light in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Barker Schaaf, C. L.

W. Wanner, A. H. Strahler, B. Hu, P. Lewis, J.-P. Muller, X. Li, C. L. Barker Schaaf, M. J. Barnsley, “Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: theory and algorithm,” J. Geophys. Res. 102, 17,143–17,161 (1997).
[CrossRef]

Barnsley, M. J.

W. Wanner, A. H. Strahler, B. Hu, P. Lewis, J.-P. Muller, X. Li, C. L. Barker Schaaf, M. J. Barnsley, “Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: theory and algorithm,” J. Geophys. Res. 102, 17,143–17,161 (1997).
[CrossRef]

Box, M. A.

Breon, F. M.

M. Herman, J. L. Deuze, C. Devaux, P. Goloub, F. M. Breon, D. Tanre, “Remote sensing of aerosols over land surfaces including polarization measurements and application to POLDER measurements,” J. Geophys. Res. 102, 17,039–17,049 (1997).
[CrossRef]

Deuze, J. L.

M. Herman, J. L. Deuze, C. Devaux, P. Goloub, F. M. Breon, D. Tanre, “Remote sensing of aerosols over land surfaces including polarization measurements and application to POLDER measurements,” J. Geophys. Res. 102, 17,039–17,049 (1997).
[CrossRef]

Devaux, C.

M. Herman, J. L. Deuze, C. Devaux, P. Goloub, F. M. Breon, D. Tanre, “Remote sensing of aerosols over land surfaces including polarization measurements and application to POLDER measurements,” J. Geophys. Res. 102, 17,039–17,049 (1997).
[CrossRef]

Goloub, P.

M. Herman, J. L. Deuze, C. Devaux, P. Goloub, F. M. Breon, D. Tanre, “Remote sensing of aerosols over land surfaces including polarization measurements and application to POLDER measurements,” J. Geophys. Res. 102, 17,039–17,049 (1997).
[CrossRef]

Greenstein, J. L.

L. G. Henyey, J. L. Greenstein, “Diffuse light in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Henyey, L. G.

L. G. Henyey, J. L. Greenstein, “Diffuse light in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Herman, M.

M. Herman, J. L. Deuze, C. Devaux, P. Goloub, F. M. Breon, D. Tanre, “Remote sensing of aerosols over land surfaces including polarization measurements and application to POLDER measurements,” J. Geophys. Res. 102, 17,039–17,049 (1997).
[CrossRef]

Hu, B.

W. Wanner, A. H. Strahler, B. Hu, P. Lewis, J.-P. Muller, X. Li, C. L. Barker Schaaf, M. J. Barnsley, “Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: theory and algorithm,” J. Geophys. Res. 102, 17,143–17,161 (1997).
[CrossRef]

Lanczos, C.

C. Lanczos, Linear Differential Operators (Van Nostrand, Princeton, N.J., 1961).

Lewis, P.

W. Wanner, A. H. Strahler, B. Hu, P. Lewis, J.-P. Muller, X. Li, C. L. Barker Schaaf, M. J. Barnsley, “Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: theory and algorithm,” J. Geophys. Res. 102, 17,143–17,161 (1997).
[CrossRef]

Li, X.

W. Wanner, A. H. Strahler, B. Hu, P. Lewis, J.-P. Muller, X. Li, C. L. Barker Schaaf, M. J. Barnsley, “Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: theory and algorithm,” J. Geophys. Res. 102, 17,143–17,161 (1997).
[CrossRef]

Muller, J.-P.

W. Wanner, A. H. Strahler, B. Hu, P. Lewis, J.-P. Muller, X. Li, C. L. Barker Schaaf, M. J. Barnsley, “Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: theory and algorithm,” J. Geophys. Res. 102, 17,143–17,161 (1997).
[CrossRef]

Parker, R. L.

R. L. Parker, Geophysical Inverse Theory (Princeton U. Press, Princeton, N.J., 1994).

Sendra, C.

Strahler, A. H.

W. Wanner, A. H. Strahler, B. Hu, P. Lewis, J.-P. Muller, X. Li, C. L. Barker Schaaf, M. J. Barnsley, “Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: theory and algorithm,” J. Geophys. Res. 102, 17,143–17,161 (1997).
[CrossRef]

Tanre, D.

M. Herman, J. L. Deuze, C. Devaux, P. Goloub, F. M. Breon, D. Tanre, “Remote sensing of aerosols over land surfaces including polarization measurements and application to POLDER measurements,” J. Geophys. Res. 102, 17,039–17,049 (1997).
[CrossRef]

Twomey, S.

S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, New York, 1977).

Wanner, W.

W. Wanner, A. H. Strahler, B. Hu, P. Lewis, J.-P. Muller, X. Li, C. L. Barker Schaaf, M. J. Barnsley, “Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: theory and algorithm,” J. Geophys. Res. 102, 17,143–17,161 (1997).
[CrossRef]

Wiggins, R. A.

R. A. Wiggins, “The general linear inverse problem: implication of surface waves and free oscillations for Earth structure,” Rev. Geophys. Space Phys. 10, 251–285 (1972).
[CrossRef]

Appl. Opt.

Astrophys. J.

L. G. Henyey, J. L. Greenstein, “Diffuse light in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

J. Geophys. Res.

M. Herman, J. L. Deuze, C. Devaux, P. Goloub, F. M. Breon, D. Tanre, “Remote sensing of aerosols over land surfaces including polarization measurements and application to POLDER measurements,” J. Geophys. Res. 102, 17,039–17,049 (1997).
[CrossRef]

W. Wanner, A. H. Strahler, B. Hu, P. Lewis, J.-P. Muller, X. Li, C. L. Barker Schaaf, M. J. Barnsley, “Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: theory and algorithm,” J. Geophys. Res. 102, 17,143–17,161 (1997).
[CrossRef]

Rev. Geophys. Space Phys.

R. A. Wiggins, “The general linear inverse problem: implication of surface waves and free oscillations for Earth structure,” Rev. Geophys. Space Phys. 10, 251–285 (1972).
[CrossRef]

Other

C. Lanczos, Linear Differential Operators (Van Nostrand, Princeton, N.J., 1961).

S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, New York, 1977).

R. L. Parker, Geophysical Inverse Theory (Princeton U. Press, Princeton, N.J., 1994).

J. Lenoble, ed, Radiative Transfer in Scattering and Absorbing Atmospheres: Standard Computational Procedures (Deepak, Hampton, Va., 1985).

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Tables (3)

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Table 1 Observational Directions (θobs, φobs) and Corresponding Scattering Angles Θscatt for the Different Data Sets

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Table 2 Retrieved Coefficients from Different Data Distributions

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Table 3 Singular Values for the Normalized Kernel Matrix Computed for Different Observational Data Sets

Equations (1)

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ηretr=BΔE+ηbc.

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