Abstract

A dual-photoelastic-modulator- (PEM-) based spectropolarimetric camera concept is presented as an approach for global aerosol monitoring from space. The most challenging performance objective is to measure degree of linear polarization (DOLP) with an uncertainty of less than 0.5% in multiple spectral bands, at moderately high spatial resolution, over a wide field of view, and for the duration of a multiyear mission. To achieve this, the tandem PEMs are operated as an electro-optic circular retardance modulator within a high-performance reflective imaging system. Operating the PEMs at slightly different resonant frequencies generates a beat signal that modulates the polarized component of the incident light at a much lower heterodyne frequency. The Stokes parameter ratio q=Q/I is obtained from measurements acquired from each pixel during a single frame, providing insensitivity to pixel responsivity drift and minimizing polarization artifacts that conventionally arise when this quantity is derived from differences in the signals from separate detectors. Similarly, u=U/I is obtained from a different pixel; q and u are then combined to form the DOLP. A detailed accuracy and tolerance analysis for this polarimeter is presented.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
    [CrossRef]
  2. L. A. Remer, D. Tanré, Y. J. Kaufman, C. Ichoku, S. Mattoo, R. Levy, D. A. Chu, B. N. Holben, O. Dubovik, A. Smirnov, J. V. Martins, R. R. Li, and Z. Ahmad, "Validation of MODIS aerosol retrieval over ocean," Geophys. Res. Lett. 29, 1-4 (2002).
    [CrossRef]
  3. D. A. Chu, Y. J. Kaufman, C. Ichoku, L. A. Remer, D. Tanré, and B. N. Holben, "Validation of MODIS aerosol optical depth retrieval over land," Geophys. Res. Lett. 29, 5-8 (2002).
    [CrossRef]
  4. O. Torres, P. K. Bhartia, J. R. Herman, A. Syniuk, P. Ginoux, and B. Holben, "A long term record of aerosol optical depth from TOMS observations and comparison to AERONET measurements," J. Atmos. Sci. 59, 398-413 (2002).
    [CrossRef]
  5. O. Torres, R. Decae, P. Veefkind, and G. de Leeuw, "OMI aerosol retrieval algorithm," in OMI Algorithm Theoretical Basis Document: Clouds, Aerosols, and Surface UV Irradiance, P. Stammes and R. Noordhoek, eds. (NASA, 2002), Vol. III, pp. 46-71.
  6. J. P. Veefkind, G. de Leeuw, and P. A. Durkee, "Retrieval of aerosol optical depth over land using two-angle view satellite radiometry during TARFOX," Geophys. Res. Lett. 25, 3135-3138 (1998).
    [CrossRef]
  7. P. R. J. North, S. A. Briggs, S. E. Plummer, and J. J. Settle, "Retrieval of land surface bidirectional reflectance and aerosol opacity from ATSR-2 multi-angle imagery," IEEE Trans. Geosci. Remote Sens. 37, 526-537 (1999).
    [CrossRef]
  8. J. V. Martonchik, D. J. Diner, K. A. Crean, and M. A. Bull, "Regional aerosol retrieval results from MISR," IEEE Trans. Geosci. Remote Sens. 40, 1520-1531 (2002).
    [CrossRef]
  9. R. A. Kahn, B. J. Gaitley, J. V. Martonchik, D. J. Diner, K. A. Crean, and B. Holben, "Multiangle Imaging Spectroradiometer (MISR) global aerosol optical depth validation based on 2 years of coincident Aerosol Robotic Network (AERONET) observations," J. Geophys. Res. 110, D10S04 (2005).
    [CrossRef]
  10. R. Kahn, P. Banerjee, and D. McDonald, "The sensitivity of multiangle imaging to natural mixtures of aerosols over ocean," J. Geophys. Res. 106, 18219-18238 (2001).
    [CrossRef]
  11. O. Kalashnikova, R. Kahn, I. N. Sokolik, and W.-H. Li, "Ability of multiangle remote sensing observations to identify and distinguish mineral dust types: optical models and retrievals of optically thick plumes," J. Geophys. Res. 110, 18S14 (2005).
    [CrossRef]
  12. R. Kahn, W.-H. Li, C. Moroney, D. J. Diner, J. V. Martonchik, and E. Fishbein, "Aerosol source characterization from space-based multi-angle imaging," J. Geophys. Res. 112, D11205 (2007).
    [CrossRef]
  13. J. Chowdhary, B. Cairns, M. Mishchenko, and L. Travis, "Retrieval of aerosol properties over the ocean using multispectral and multiangle photopolarimetric measurements from the Research Scanning Polarimeter," Geophys. Res. Lett. 28, 243-246 (2001).
    [CrossRef]
  14. J. Chowdhary, B. Cairns, and L. D. Travis, "Case studies of aerosol retrievals over the ocean from multiangle, multispectral photopolarimetric remote sensing data," J. Atmos. Sci. 59, 383-397 (2002).
    [CrossRef]
  15. M. I. Mishchenko and L. D. Travis, "Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight," J. Geophys. Res. 102, 16989-17014 (1997).
    [CrossRef]
  16. J. L. Deuzé, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanré, "Estimate of the aerosol properties over the ocean with POLDER," J. Geophys. Res. 105, 15329-15346 (2000).
    [CrossRef]
  17. O. Hagolle, P. Goloub, P. Y. Deschamps, H. Cosnefroy, X. Briottet, T. Bailleul, J. M. Nicolas, F. Parol, B. Lafrance, and M. Herman, "Results of POLDER in-flight calibration," IEEE Trans. Geosci. Remote Sens. 37, 1550-1566 (1999).
    [CrossRef]
  18. M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueller, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, "Precise and accurate monitoring of terrestrial aerosols and total solar irradiance: introducing the Glory mission," Bull. Am. Meteorol. Soc. 88, 677-691 (2007).
    [CrossRef]
  19. O. P. Hasekamp and J. Landgraf, "Retrieval of aerosol properties over land surfaces: capabilities of multiple-viewing-angle intensity and polarization measurements," Appl. Opt. 46, 3332-3344 (2007).
    [CrossRef] [PubMed]
  20. National Research Council, Committee on Earth Science and Applications from Space, Earth Science and Applications from Space: National Imperatives for the Next Decade and Beyond (The National Academies Press, 2007).
  21. D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
    [CrossRef]
  22. V. M. Jovanovic, M. A. Bull, M. M. Smyth, and J. Zong, "MISR in-flight camera geometric model calibration and georectification performance," IEEE Trans. Geosci. Remote Sens. 40, 1512-1519 (2002).
    [CrossRef]
  23. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, "Review of passive imaging polarimetry for remote sensing applications," Appl. Opt. 45, 5453-5469 (2006).
    [CrossRef] [PubMed]
  24. M. Descour and E. Dereniak, "Computed-tomography imaging spectrometer: experimental calibration and reconstruction results," Appl. Opt. 34, 4817-4826 (1995).
    [CrossRef] [PubMed]
  25. A. M. Locke, D. S. Sabatke, E. L. Dereniak, M. R. Descour, J. P. Garcia, T. K. Hamilton, and R. W. McMillan, "Snapshot imaging spectropolarimeter," Proc. SPIE 4481, 64-72 (2002).
    [CrossRef]
  26. J. S. Van Delden, "Ortho-Babinet polarization-interrogating filter: an interferometric approach to polarization measurement," Opt. Lett. 28, 1173-1175 (2003).
    [CrossRef] [PubMed]
  27. K. Oka and T. Kato, "Spectroscopic polarimetry with a channeled spectrum," Opt. Lett. 24, 1475-1477 (1999).
    [CrossRef]
  28. F. J. Iannarilli, S. H. Jones, H. E. Scott, and P. Kebabian, "Polarimetric-spectral intensity modulation (P-SIM): Enabling simultaneous hyperspectral and polarimetric imaging," Proc. SPIE 3698, 474-481 (1999).
    [CrossRef]
  29. C. J. Bruegge, N. L. Chrien, R. R. Ando, D. J. Diner, W. A. Abdou, M. C. Helmlinger, S. H. Pilorz, and K. J. Thome, "Early validation of the Multi-angle Imaging SpectroRadiometer (MISR) radiometric scale," IEEE Trans. Geosci. Remote Sens. 40, 1477-1492 (2002).
    [CrossRef]
  30. Boulder Nonlinear Systems, "Ferroelectric liquid crystal based polarization filters," http://dev.bouldernonlinear.com/papers/FerroPolarFilters.pdf.
  31. C. U. Keller, "Instrumentation for astrophysical spectropolarimetry," in Astrophysical Spectropolarimetry, J. Trujillo-Bueno, F. Moreno-Insertis, and F. Sánchez, eds. (Cambridge U. Press, 2002), pp. 303-354.
  32. J. O. Stenflo and H. Povel, "Astronomical polarimeter with 2-D detector arrays," Appl. Opt. 24, 3893-3898 (1985).
    [CrossRef] [PubMed]
  33. H. Povel, H. Aebersold, and J. O. Stenflo, "Charge-coupled device image sensor as a demodulator in a 2-D polarimeter with a piezoelastic modulator," Appl. Opt. 29, 1186-1190 (1990).
    [CrossRef] [PubMed]
  34. H. Povel, C. U. Keller, and I.-A. Yadigaroglu, "Two-dimensional polarimeter with a charge-coupled-device image sensor and a piezoelastic modulator," Appl. Opt. 33, 4254-4260 (1994).
    [CrossRef] [PubMed]
  35. A. M. Gandorfer and H. P. Povel, "First observations with a new imaging polarimeter," Astron. Astrophys. 328, 381-389 (1997).
  36. L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Vol. 7 of Course of Theoretical Physics, second English ed. (Pergamon, 1970).
  37. R. A. Chipman, "Polarimetry," in Handbook of Optics: Devices, Measurements and Properties, 2nd ed. M. Bass, ed. (McGraw-Hill, 1994), Vol. II, pp. 1-37.
  38. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).
  39. J. O. Stenflo, "Solar magnetic and velocity-field measurements: new instrument concepts," Appl. Opt. 23, 1267-1278 (1984).
    [CrossRef] [PubMed]
  40. J. Bland-Hawthorn and D. H. Jones, "Taurus tunable filter: a flexible approach to narrowband imaging," Publ.-Astron. Soc. Aust. 15, 44-49 (1998).
    [CrossRef]
  41. C. U. Keller, "Charge-caching CMOS detector for polarimetry (C3Po)," Proc. SPIE 5171, 239-246 (2004).
    [CrossRef]
  42. A. M. Gandorfer, "Ferroelectric retarders as an alternative to piezoelastic modulators for use in solar Stokes vector polarimetry," Opt. Eng. 38, 1402-1408 (1999).
    [CrossRef]

2007 (4)

R. Kahn, W.-H. Li, C. Moroney, D. J. Diner, J. V. Martonchik, and E. Fishbein, "Aerosol source characterization from space-based multi-angle imaging," J. Geophys. Res. 112, D11205 (2007).
[CrossRef]

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueller, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, "Precise and accurate monitoring of terrestrial aerosols and total solar irradiance: introducing the Glory mission," Bull. Am. Meteorol. Soc. 88, 677-691 (2007).
[CrossRef]

O. P. Hasekamp and J. Landgraf, "Retrieval of aerosol properties over land surfaces: capabilities of multiple-viewing-angle intensity and polarization measurements," Appl. Opt. 46, 3332-3344 (2007).
[CrossRef] [PubMed]

National Research Council, Committee on Earth Science and Applications from Space, Earth Science and Applications from Space: National Imperatives for the Next Decade and Beyond (The National Academies Press, 2007).

2006 (2)

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, "Review of passive imaging polarimetry for remote sensing applications," Appl. Opt. 45, 5453-5469 (2006).
[CrossRef] [PubMed]

2005 (2)

O. Kalashnikova, R. Kahn, I. N. Sokolik, and W.-H. Li, "Ability of multiangle remote sensing observations to identify and distinguish mineral dust types: optical models and retrievals of optically thick plumes," J. Geophys. Res. 110, 18S14 (2005).
[CrossRef]

R. A. Kahn, B. J. Gaitley, J. V. Martonchik, D. J. Diner, K. A. Crean, and B. Holben, "Multiangle Imaging Spectroradiometer (MISR) global aerosol optical depth validation based on 2 years of coincident Aerosol Robotic Network (AERONET) observations," J. Geophys. Res. 110, D10S04 (2005).
[CrossRef]

2004 (1)

C. U. Keller, "Charge-caching CMOS detector for polarimetry (C3Po)," Proc. SPIE 5171, 239-246 (2004).
[CrossRef]

2003 (1)

2002 (10)

V. M. Jovanovic, M. A. Bull, M. M. Smyth, and J. Zong, "MISR in-flight camera geometric model calibration and georectification performance," IEEE Trans. Geosci. Remote Sens. 40, 1512-1519 (2002).
[CrossRef]

C. J. Bruegge, N. L. Chrien, R. R. Ando, D. J. Diner, W. A. Abdou, M. C. Helmlinger, S. H. Pilorz, and K. J. Thome, "Early validation of the Multi-angle Imaging SpectroRadiometer (MISR) radiometric scale," IEEE Trans. Geosci. Remote Sens. 40, 1477-1492 (2002).
[CrossRef]

C. U. Keller, "Instrumentation for astrophysical spectropolarimetry," in Astrophysical Spectropolarimetry, J. Trujillo-Bueno, F. Moreno-Insertis, and F. Sánchez, eds. (Cambridge U. Press, 2002), pp. 303-354.

A. M. Locke, D. S. Sabatke, E. L. Dereniak, M. R. Descour, J. P. Garcia, T. K. Hamilton, and R. W. McMillan, "Snapshot imaging spectropolarimeter," Proc. SPIE 4481, 64-72 (2002).
[CrossRef]

J. V. Martonchik, D. J. Diner, K. A. Crean, and M. A. Bull, "Regional aerosol retrieval results from MISR," IEEE Trans. Geosci. Remote Sens. 40, 1520-1531 (2002).
[CrossRef]

L. A. Remer, D. Tanré, Y. J. Kaufman, C. Ichoku, S. Mattoo, R. Levy, D. A. Chu, B. N. Holben, O. Dubovik, A. Smirnov, J. V. Martins, R. R. Li, and Z. Ahmad, "Validation of MODIS aerosol retrieval over ocean," Geophys. Res. Lett. 29, 1-4 (2002).
[CrossRef]

D. A. Chu, Y. J. Kaufman, C. Ichoku, L. A. Remer, D. Tanré, and B. N. Holben, "Validation of MODIS aerosol optical depth retrieval over land," Geophys. Res. Lett. 29, 5-8 (2002).
[CrossRef]

O. Torres, P. K. Bhartia, J. R. Herman, A. Syniuk, P. Ginoux, and B. Holben, "A long term record of aerosol optical depth from TOMS observations and comparison to AERONET measurements," J. Atmos. Sci. 59, 398-413 (2002).
[CrossRef]

O. Torres, R. Decae, P. Veefkind, and G. de Leeuw, "OMI aerosol retrieval algorithm," in OMI Algorithm Theoretical Basis Document: Clouds, Aerosols, and Surface UV Irradiance, P. Stammes and R. Noordhoek, eds. (NASA, 2002), Vol. III, pp. 46-71.

J. Chowdhary, B. Cairns, and L. D. Travis, "Case studies of aerosol retrievals over the ocean from multiangle, multispectral photopolarimetric remote sensing data," J. Atmos. Sci. 59, 383-397 (2002).
[CrossRef]

2001 (2)

J. Chowdhary, B. Cairns, M. Mishchenko, and L. Travis, "Retrieval of aerosol properties over the ocean using multispectral and multiangle photopolarimetric measurements from the Research Scanning Polarimeter," Geophys. Res. Lett. 28, 243-246 (2001).
[CrossRef]

R. Kahn, P. Banerjee, and D. McDonald, "The sensitivity of multiangle imaging to natural mixtures of aerosols over ocean," J. Geophys. Res. 106, 18219-18238 (2001).
[CrossRef]

2000 (1)

J. L. Deuzé, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanré, "Estimate of the aerosol properties over the ocean with POLDER," J. Geophys. Res. 105, 15329-15346 (2000).
[CrossRef]

1999 (5)

O. Hagolle, P. Goloub, P. Y. Deschamps, H. Cosnefroy, X. Briottet, T. Bailleul, J. M. Nicolas, F. Parol, B. Lafrance, and M. Herman, "Results of POLDER in-flight calibration," IEEE Trans. Geosci. Remote Sens. 37, 1550-1566 (1999).
[CrossRef]

K. Oka and T. Kato, "Spectroscopic polarimetry with a channeled spectrum," Opt. Lett. 24, 1475-1477 (1999).
[CrossRef]

F. J. Iannarilli, S. H. Jones, H. E. Scott, and P. Kebabian, "Polarimetric-spectral intensity modulation (P-SIM): Enabling simultaneous hyperspectral and polarimetric imaging," Proc. SPIE 3698, 474-481 (1999).
[CrossRef]

P. R. J. North, S. A. Briggs, S. E. Plummer, and J. J. Settle, "Retrieval of land surface bidirectional reflectance and aerosol opacity from ATSR-2 multi-angle imagery," IEEE Trans. Geosci. Remote Sens. 37, 526-537 (1999).
[CrossRef]

A. M. Gandorfer, "Ferroelectric retarders as an alternative to piezoelastic modulators for use in solar Stokes vector polarimetry," Opt. Eng. 38, 1402-1408 (1999).
[CrossRef]

1998 (3)

J. Bland-Hawthorn and D. H. Jones, "Taurus tunable filter: a flexible approach to narrowband imaging," Publ.-Astron. Soc. Aust. 15, 44-49 (1998).
[CrossRef]

J. P. Veefkind, G. de Leeuw, and P. A. Durkee, "Retrieval of aerosol optical depth over land using two-angle view satellite radiometry during TARFOX," Geophys. Res. Lett. 25, 3135-3138 (1998).
[CrossRef]

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

1997 (2)

M. I. Mishchenko and L. D. Travis, "Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight," J. Geophys. Res. 102, 16989-17014 (1997).
[CrossRef]

A. M. Gandorfer and H. P. Povel, "First observations with a new imaging polarimeter," Astron. Astrophys. 328, 381-389 (1997).

1995 (1)

1994 (2)

R. A. Chipman, "Polarimetry," in Handbook of Optics: Devices, Measurements and Properties, 2nd ed. M. Bass, ed. (McGraw-Hill, 1994), Vol. II, pp. 1-37.

H. Povel, C. U. Keller, and I.-A. Yadigaroglu, "Two-dimensional polarimeter with a charge-coupled-device image sensor and a piezoelastic modulator," Appl. Opt. 33, 4254-4260 (1994).
[CrossRef] [PubMed]

1990 (1)

1985 (1)

1984 (1)

1970 (1)

L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Vol. 7 of Course of Theoretical Physics, second English ed. (Pergamon, 1970).

1965 (1)

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

Abdou, W. A.

C. J. Bruegge, N. L. Chrien, R. R. Ando, D. J. Diner, W. A. Abdou, M. C. Helmlinger, S. H. Pilorz, and K. J. Thome, "Early validation of the Multi-angle Imaging SpectroRadiometer (MISR) radiometric scale," IEEE Trans. Geosci. Remote Sens. 40, 1477-1492 (2002).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

Ackerman, T. P.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

Aebersold, H.

Ahmad, Z.

L. A. Remer, D. Tanré, Y. J. Kaufman, C. Ichoku, S. Mattoo, R. Levy, D. A. Chu, B. N. Holben, O. Dubovik, A. Smirnov, J. V. Martins, R. R. Li, and Z. Ahmad, "Validation of MODIS aerosol retrieval over ocean," Geophys. Res. Lett. 29, 1-4 (2002).
[CrossRef]

Anderson, T. L.

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

Ando, R. R.

C. J. Bruegge, N. L. Chrien, R. R. Ando, D. J. Diner, W. A. Abdou, M. C. Helmlinger, S. H. Pilorz, and K. J. Thome, "Early validation of the Multi-angle Imaging SpectroRadiometer (MISR) radiometric scale," IEEE Trans. Geosci. Remote Sens. 40, 1477-1492 (2002).
[CrossRef]

Bailleul, T.

O. Hagolle, P. Goloub, P. Y. Deschamps, H. Cosnefroy, X. Briottet, T. Bailleul, J. M. Nicolas, F. Parol, B. Lafrance, and M. Herman, "Results of POLDER in-flight calibration," IEEE Trans. Geosci. Remote Sens. 37, 1550-1566 (1999).
[CrossRef]

Balkanski, Y.

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

Banerjee, P.

R. Kahn, P. Banerjee, and D. McDonald, "The sensitivity of multiangle imaging to natural mixtures of aerosols over ocean," J. Geophys. Res. 106, 18219-18238 (2001).
[CrossRef]

Beckert, J. C.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

Bellouin, N.

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

Bhartia, P. K.

O. Torres, P. K. Bhartia, J. R. Herman, A. Syniuk, P. Ginoux, and B. Holben, "A long term record of aerosol optical depth from TOMS observations and comparison to AERONET measurements," J. Atmos. Sci. 59, 398-413 (2002).
[CrossRef]

Bland-Hawthorn, J.

J. Bland-Hawthorn and D. H. Jones, "Taurus tunable filter: a flexible approach to narrowband imaging," Publ.-Astron. Soc. Aust. 15, 44-49 (1998).
[CrossRef]

Boucher, O.

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

Briggs, S. A.

P. R. J. North, S. A. Briggs, S. E. Plummer, and J. J. Settle, "Retrieval of land surface bidirectional reflectance and aerosol opacity from ATSR-2 multi-angle imagery," IEEE Trans. Geosci. Remote Sens. 37, 526-537 (1999).
[CrossRef]

Briottet, X.

O. Hagolle, P. Goloub, P. Y. Deschamps, H. Cosnefroy, X. Briottet, T. Bailleul, J. M. Nicolas, F. Parol, B. Lafrance, and M. Herman, "Results of POLDER in-flight calibration," IEEE Trans. Geosci. Remote Sens. 37, 1550-1566 (1999).
[CrossRef]

Bruegge, C. J.

C. J. Bruegge, N. L. Chrien, R. R. Ando, D. J. Diner, W. A. Abdou, M. C. Helmlinger, S. H. Pilorz, and K. J. Thome, "Early validation of the Multi-angle Imaging SpectroRadiometer (MISR) radiometric scale," IEEE Trans. Geosci. Remote Sens. 40, 1477-1492 (2002).
[CrossRef]

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

Bull, M. A.

V. M. Jovanovic, M. A. Bull, M. M. Smyth, and J. Zong, "MISR in-flight camera geometric model calibration and georectification performance," IEEE Trans. Geosci. Remote Sens. 40, 1512-1519 (2002).
[CrossRef]

J. V. Martonchik, D. J. Diner, K. A. Crean, and M. A. Bull, "Regional aerosol retrieval results from MISR," IEEE Trans. Geosci. Remote Sens. 40, 1520-1531 (2002).
[CrossRef]

Cairns, B.

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueller, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, "Precise and accurate monitoring of terrestrial aerosols and total solar irradiance: introducing the Glory mission," Bull. Am. Meteorol. Soc. 88, 677-691 (2007).
[CrossRef]

J. Chowdhary, B. Cairns, and L. D. Travis, "Case studies of aerosol retrievals over the ocean from multiangle, multispectral photopolarimetric remote sensing data," J. Atmos. Sci. 59, 383-397 (2002).
[CrossRef]

J. Chowdhary, B. Cairns, M. Mishchenko, and L. Travis, "Retrieval of aerosol properties over the ocean using multispectral and multiangle photopolarimetric measurements from the Research Scanning Polarimeter," Geophys. Res. Lett. 28, 243-246 (2001).
[CrossRef]

Chenault, D. B.

Chin, M.

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

Chipman, R. A.

R. A. Chipman, "Polarimetry," in Handbook of Optics: Devices, Measurements and Properties, 2nd ed. M. Bass, ed. (McGraw-Hill, 1994), Vol. II, pp. 1-37.

Chowdhary, J.

J. Chowdhary, B. Cairns, and L. D. Travis, "Case studies of aerosol retrievals over the ocean from multiangle, multispectral photopolarimetric remote sensing data," J. Atmos. Sci. 59, 383-397 (2002).
[CrossRef]

J. Chowdhary, B. Cairns, M. Mishchenko, and L. Travis, "Retrieval of aerosol properties over the ocean using multispectral and multiangle photopolarimetric measurements from the Research Scanning Polarimeter," Geophys. Res. Lett. 28, 243-246 (2001).
[CrossRef]

Chrien, N. L.

C. J. Bruegge, N. L. Chrien, R. R. Ando, D. J. Diner, W. A. Abdou, M. C. Helmlinger, S. H. Pilorz, and K. J. Thome, "Early validation of the Multi-angle Imaging SpectroRadiometer (MISR) radiometric scale," IEEE Trans. Geosci. Remote Sens. 40, 1477-1492 (2002).
[CrossRef]

Christopher, S.

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

Chu, D. A.

D. A. Chu, Y. J. Kaufman, C. Ichoku, L. A. Remer, D. Tanré, and B. N. Holben, "Validation of MODIS aerosol optical depth retrieval over land," Geophys. Res. Lett. 29, 5-8 (2002).
[CrossRef]

L. A. Remer, D. Tanré, Y. J. Kaufman, C. Ichoku, S. Mattoo, R. Levy, D. A. Chu, B. N. Holben, O. Dubovik, A. Smirnov, J. V. Martins, R. R. Li, and Z. Ahmad, "Validation of MODIS aerosol retrieval over ocean," Geophys. Res. Lett. 29, 1-4 (2002).
[CrossRef]

Conel, J. E.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

Cosnefroy, H.

O. Hagolle, P. Goloub, P. Y. Deschamps, H. Cosnefroy, X. Briottet, T. Bailleul, J. M. Nicolas, F. Parol, B. Lafrance, and M. Herman, "Results of POLDER in-flight calibration," IEEE Trans. Geosci. Remote Sens. 37, 1550-1566 (1999).
[CrossRef]

Crean, K. A.

R. A. Kahn, B. J. Gaitley, J. V. Martonchik, D. J. Diner, K. A. Crean, and B. Holben, "Multiangle Imaging Spectroradiometer (MISR) global aerosol optical depth validation based on 2 years of coincident Aerosol Robotic Network (AERONET) observations," J. Geophys. Res. 110, D10S04 (2005).
[CrossRef]

J. V. Martonchik, D. J. Diner, K. A. Crean, and M. A. Bull, "Regional aerosol retrieval results from MISR," IEEE Trans. Geosci. Remote Sens. 40, 1520-1531 (2002).
[CrossRef]

Davies, R.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

de Leeuw, G.

O. Torres, R. Decae, P. Veefkind, and G. de Leeuw, "OMI aerosol retrieval algorithm," in OMI Algorithm Theoretical Basis Document: Clouds, Aerosols, and Surface UV Irradiance, P. Stammes and R. Noordhoek, eds. (NASA, 2002), Vol. III, pp. 46-71.

J. P. Veefkind, G. de Leeuw, and P. A. Durkee, "Retrieval of aerosol optical depth over land using two-angle view satellite radiometry during TARFOX," Geophys. Res. Lett. 25, 3135-3138 (1998).
[CrossRef]

Decae, R.

O. Torres, R. Decae, P. Veefkind, and G. de Leeuw, "OMI aerosol retrieval algorithm," in OMI Algorithm Theoretical Basis Document: Clouds, Aerosols, and Surface UV Irradiance, P. Stammes and R. Noordhoek, eds. (NASA, 2002), Vol. III, pp. 46-71.

DeCola, P.

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

Dereniak, E.

Dereniak, E. L.

A. M. Locke, D. S. Sabatke, E. L. Dereniak, M. R. Descour, J. P. Garcia, T. K. Hamilton, and R. W. McMillan, "Snapshot imaging spectropolarimeter," Proc. SPIE 4481, 64-72 (2002).
[CrossRef]

Deschamps, P. Y.

O. Hagolle, P. Goloub, P. Y. Deschamps, H. Cosnefroy, X. Briottet, T. Bailleul, J. M. Nicolas, F. Parol, B. Lafrance, and M. Herman, "Results of POLDER in-flight calibration," IEEE Trans. Geosci. Remote Sens. 37, 1550-1566 (1999).
[CrossRef]

Descour, M.

Descour, M. R.

A. M. Locke, D. S. Sabatke, E. L. Dereniak, M. R. Descour, J. P. Garcia, T. K. Hamilton, and R. W. McMillan, "Snapshot imaging spectropolarimeter," Proc. SPIE 4481, 64-72 (2002).
[CrossRef]

Deuzé, J. L.

J. L. Deuzé, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanré, "Estimate of the aerosol properties over the ocean with POLDER," J. Geophys. Res. 105, 15329-15346 (2000).
[CrossRef]

Diner, D. J.

R. Kahn, W.-H. Li, C. Moroney, D. J. Diner, J. V. Martonchik, and E. Fishbein, "Aerosol source characterization from space-based multi-angle imaging," J. Geophys. Res. 112, D11205 (2007).
[CrossRef]

R. A. Kahn, B. J. Gaitley, J. V. Martonchik, D. J. Diner, K. A. Crean, and B. Holben, "Multiangle Imaging Spectroradiometer (MISR) global aerosol optical depth validation based on 2 years of coincident Aerosol Robotic Network (AERONET) observations," J. Geophys. Res. 110, D10S04 (2005).
[CrossRef]

J. V. Martonchik, D. J. Diner, K. A. Crean, and M. A. Bull, "Regional aerosol retrieval results from MISR," IEEE Trans. Geosci. Remote Sens. 40, 1520-1531 (2002).
[CrossRef]

C. J. Bruegge, N. L. Chrien, R. R. Ando, D. J. Diner, W. A. Abdou, M. C. Helmlinger, S. H. Pilorz, and K. J. Thome, "Early validation of the Multi-angle Imaging SpectroRadiometer (MISR) radiometric scale," IEEE Trans. Geosci. Remote Sens. 40, 1477-1492 (2002).
[CrossRef]

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

Dubovik, O.

L. A. Remer, D. Tanré, Y. J. Kaufman, C. Ichoku, S. Mattoo, R. Levy, D. A. Chu, B. N. Holben, O. Dubovik, A. Smirnov, J. V. Martins, R. R. Li, and Z. Ahmad, "Validation of MODIS aerosol retrieval over ocean," Geophys. Res. Lett. 29, 1-4 (2002).
[CrossRef]

Durkee, P. A.

J. P. Veefkind, G. de Leeuw, and P. A. Durkee, "Retrieval of aerosol optical depth over land using two-angle view satellite radiometry during TARFOX," Geophys. Res. Lett. 25, 3135-3138 (1998).
[CrossRef]

Fafaul, B. A.

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueller, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, "Precise and accurate monitoring of terrestrial aerosols and total solar irradiance: introducing the Glory mission," Bull. Am. Meteorol. Soc. 88, 677-691 (2007).
[CrossRef]

Feingold, G.

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

Fishbein, E.

R. Kahn, W.-H. Li, C. Moroney, D. J. Diner, J. V. Martonchik, and E. Fishbein, "Aerosol source characterization from space-based multi-angle imaging," J. Geophys. Res. 112, D11205 (2007).
[CrossRef]

Gaitley, B. J.

R. A. Kahn, B. J. Gaitley, J. V. Martonchik, D. J. Diner, K. A. Crean, and B. Holben, "Multiangle Imaging Spectroradiometer (MISR) global aerosol optical depth validation based on 2 years of coincident Aerosol Robotic Network (AERONET) observations," J. Geophys. Res. 110, D10S04 (2005).
[CrossRef]

Gandorfer, A. M.

A. M. Gandorfer, "Ferroelectric retarders as an alternative to piezoelastic modulators for use in solar Stokes vector polarimetry," Opt. Eng. 38, 1402-1408 (1999).
[CrossRef]

A. M. Gandorfer and H. P. Povel, "First observations with a new imaging polarimeter," Astron. Astrophys. 328, 381-389 (1997).

Garcia, J. P.

A. M. Locke, D. S. Sabatke, E. L. Dereniak, M. R. Descour, J. P. Garcia, T. K. Hamilton, and R. W. McMillan, "Snapshot imaging spectropolarimeter," Proc. SPIE 4481, 64-72 (2002).
[CrossRef]

Gerstl, S. A. W.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

Ginoux, P.

O. Torres, P. K. Bhartia, J. R. Herman, A. Syniuk, P. Ginoux, and B. Holben, "A long term record of aerosol optical depth from TOMS observations and comparison to AERONET measurements," J. Atmos. Sci. 59, 398-413 (2002).
[CrossRef]

Goldstein, D. L.

Goloub, P.

J. L. Deuzé, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanré, "Estimate of the aerosol properties over the ocean with POLDER," J. Geophys. Res. 105, 15329-15346 (2000).
[CrossRef]

O. Hagolle, P. Goloub, P. Y. Deschamps, H. Cosnefroy, X. Briottet, T. Bailleul, J. M. Nicolas, F. Parol, B. Lafrance, and M. Herman, "Results of POLDER in-flight calibration," IEEE Trans. Geosci. Remote Sens. 37, 1550-1566 (1999).
[CrossRef]

Gordon, H. R.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

Hagolle, O.

O. Hagolle, P. Goloub, P. Y. Deschamps, H. Cosnefroy, X. Briottet, T. Bailleul, J. M. Nicolas, F. Parol, B. Lafrance, and M. Herman, "Results of POLDER in-flight calibration," IEEE Trans. Geosci. Remote Sens. 37, 1550-1566 (1999).
[CrossRef]

Hamilton, T. K.

A. M. Locke, D. S. Sabatke, E. L. Dereniak, M. R. Descour, J. P. Garcia, T. K. Hamilton, and R. W. McMillan, "Snapshot imaging spectropolarimeter," Proc. SPIE 4481, 64-72 (2002).
[CrossRef]

Hansen, J. E.

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueller, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, "Precise and accurate monitoring of terrestrial aerosols and total solar irradiance: introducing the Glory mission," Bull. Am. Meteorol. Soc. 88, 677-691 (2007).
[CrossRef]

Hasekamp, O. P.

Helmlinger, M. C.

C. J. Bruegge, N. L. Chrien, R. R. Ando, D. J. Diner, W. A. Abdou, M. C. Helmlinger, S. H. Pilorz, and K. J. Thome, "Early validation of the Multi-angle Imaging SpectroRadiometer (MISR) radiometric scale," IEEE Trans. Geosci. Remote Sens. 40, 1477-1492 (2002).
[CrossRef]

Herman, J. R.

O. Torres, P. K. Bhartia, J. R. Herman, A. Syniuk, P. Ginoux, and B. Holben, "A long term record of aerosol optical depth from TOMS observations and comparison to AERONET measurements," J. Atmos. Sci. 59, 398-413 (2002).
[CrossRef]

Herman, M.

J. L. Deuzé, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanré, "Estimate of the aerosol properties over the ocean with POLDER," J. Geophys. Res. 105, 15329-15346 (2000).
[CrossRef]

O. Hagolle, P. Goloub, P. Y. Deschamps, H. Cosnefroy, X. Briottet, T. Bailleul, J. M. Nicolas, F. Parol, B. Lafrance, and M. Herman, "Results of POLDER in-flight calibration," IEEE Trans. Geosci. Remote Sens. 37, 1550-1566 (1999).
[CrossRef]

Holben, B.

R. A. Kahn, B. J. Gaitley, J. V. Martonchik, D. J. Diner, K. A. Crean, and B. Holben, "Multiangle Imaging Spectroradiometer (MISR) global aerosol optical depth validation based on 2 years of coincident Aerosol Robotic Network (AERONET) observations," J. Geophys. Res. 110, D10S04 (2005).
[CrossRef]

O. Torres, P. K. Bhartia, J. R. Herman, A. Syniuk, P. Ginoux, and B. Holben, "A long term record of aerosol optical depth from TOMS observations and comparison to AERONET measurements," J. Atmos. Sci. 59, 398-413 (2002).
[CrossRef]

Holben, B. N.

D. A. Chu, Y. J. Kaufman, C. Ichoku, L. A. Remer, D. Tanré, and B. N. Holben, "Validation of MODIS aerosol optical depth retrieval over land," Geophys. Res. Lett. 29, 5-8 (2002).
[CrossRef]

L. A. Remer, D. Tanré, Y. J. Kaufman, C. Ichoku, S. Mattoo, R. Levy, D. A. Chu, B. N. Holben, O. Dubovik, A. Smirnov, J. V. Martins, R. R. Li, and Z. Ahmad, "Validation of MODIS aerosol retrieval over ocean," Geophys. Res. Lett. 29, 1-4 (2002).
[CrossRef]

Hooker, R. J.

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueller, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, "Precise and accurate monitoring of terrestrial aerosols and total solar irradiance: introducing the Glory mission," Bull. Am. Meteorol. Soc. 88, 677-691 (2007).
[CrossRef]

Iannarilli, F. J.

F. J. Iannarilli, S. H. Jones, H. E. Scott, and P. Kebabian, "Polarimetric-spectral intensity modulation (P-SIM): Enabling simultaneous hyperspectral and polarimetric imaging," Proc. SPIE 3698, 474-481 (1999).
[CrossRef]

Ichoku, C.

D. A. Chu, Y. J. Kaufman, C. Ichoku, L. A. Remer, D. Tanré, and B. N. Holben, "Validation of MODIS aerosol optical depth retrieval over land," Geophys. Res. Lett. 29, 5-8 (2002).
[CrossRef]

L. A. Remer, D. Tanré, Y. J. Kaufman, C. Ichoku, S. Mattoo, R. Levy, D. A. Chu, B. N. Holben, O. Dubovik, A. Smirnov, J. V. Martins, R. R. Li, and Z. Ahmad, "Validation of MODIS aerosol retrieval over ocean," Geophys. Res. Lett. 29, 1-4 (2002).
[CrossRef]

Itchkawich, T.

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueller, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, "Precise and accurate monitoring of terrestrial aerosols and total solar irradiance: introducing the Glory mission," Bull. Am. Meteorol. Soc. 88, 677-691 (2007).
[CrossRef]

Jones, D. H.

J. Bland-Hawthorn and D. H. Jones, "Taurus tunable filter: a flexible approach to narrowband imaging," Publ.-Astron. Soc. Aust. 15, 44-49 (1998).
[CrossRef]

Jones, S. H.

F. J. Iannarilli, S. H. Jones, H. E. Scott, and P. Kebabian, "Polarimetric-spectral intensity modulation (P-SIM): Enabling simultaneous hyperspectral and polarimetric imaging," Proc. SPIE 3698, 474-481 (1999).
[CrossRef]

Jovanovic, V. M.

V. M. Jovanovic, M. A. Bull, M. M. Smyth, and J. Zong, "MISR in-flight camera geometric model calibration and georectification performance," IEEE Trans. Geosci. Remote Sens. 40, 1512-1519 (2002).
[CrossRef]

Kahn, R.

R. Kahn, W.-H. Li, C. Moroney, D. J. Diner, J. V. Martonchik, and E. Fishbein, "Aerosol source characterization from space-based multi-angle imaging," J. Geophys. Res. 112, D11205 (2007).
[CrossRef]

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

O. Kalashnikova, R. Kahn, I. N. Sokolik, and W.-H. Li, "Ability of multiangle remote sensing observations to identify and distinguish mineral dust types: optical models and retrievals of optically thick plumes," J. Geophys. Res. 110, 18S14 (2005).
[CrossRef]

R. Kahn, P. Banerjee, and D. McDonald, "The sensitivity of multiangle imaging to natural mixtures of aerosols over ocean," J. Geophys. Res. 106, 18219-18238 (2001).
[CrossRef]

Kahn, R. A.

R. A. Kahn, B. J. Gaitley, J. V. Martonchik, D. J. Diner, K. A. Crean, and B. Holben, "Multiangle Imaging Spectroradiometer (MISR) global aerosol optical depth validation based on 2 years of coincident Aerosol Robotic Network (AERONET) observations," J. Geophys. Res. 110, D10S04 (2005).
[CrossRef]

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

Kalashnikova, O.

O. Kalashnikova, R. Kahn, I. N. Sokolik, and W.-H. Li, "Ability of multiangle remote sensing observations to identify and distinguish mineral dust types: optical models and retrievals of optically thick plumes," J. Geophys. Res. 110, 18S14 (2005).
[CrossRef]

Kato, T.

Kaufman, Y. J.

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

D. A. Chu, Y. J. Kaufman, C. Ichoku, L. A. Remer, D. Tanré, and B. N. Holben, "Validation of MODIS aerosol optical depth retrieval over land," Geophys. Res. Lett. 29, 5-8 (2002).
[CrossRef]

L. A. Remer, D. Tanré, Y. J. Kaufman, C. Ichoku, S. Mattoo, R. Levy, D. A. Chu, B. N. Holben, O. Dubovik, A. Smirnov, J. V. Martins, R. R. Li, and Z. Ahmad, "Validation of MODIS aerosol retrieval over ocean," Geophys. Res. Lett. 29, 1-4 (2002).
[CrossRef]

Kebabian, P.

F. J. Iannarilli, S. H. Jones, H. E. Scott, and P. Kebabian, "Polarimetric-spectral intensity modulation (P-SIM): Enabling simultaneous hyperspectral and polarimetric imaging," Proc. SPIE 3698, 474-481 (1999).
[CrossRef]

Keller, C. U.

C. U. Keller, "Charge-caching CMOS detector for polarimetry (C3Po)," Proc. SPIE 5171, 239-246 (2004).
[CrossRef]

C. U. Keller, "Instrumentation for astrophysical spectropolarimetry," in Astrophysical Spectropolarimetry, J. Trujillo-Bueno, F. Moreno-Insertis, and F. Sánchez, eds. (Cambridge U. Press, 2002), pp. 303-354.

H. Povel, C. U. Keller, and I.-A. Yadigaroglu, "Two-dimensional polarimeter with a charge-coupled-device image sensor and a piezoelastic modulator," Appl. Opt. 33, 4254-4260 (1994).
[CrossRef] [PubMed]

Koch, D.

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

Kopp, G.

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueller, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, "Precise and accurate monitoring of terrestrial aerosols and total solar irradiance: introducing the Glory mission," Bull. Am. Meteorol. Soc. 88, 677-691 (2007).
[CrossRef]

Lafrance, B.

O. Hagolle, P. Goloub, P. Y. Deschamps, H. Cosnefroy, X. Briottet, T. Bailleul, J. M. Nicolas, F. Parol, B. Lafrance, and M. Herman, "Results of POLDER in-flight calibration," IEEE Trans. Geosci. Remote Sens. 37, 1550-1566 (1999).
[CrossRef]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Vol. 7 of Course of Theoretical Physics, second English ed. (Pergamon, 1970).

Landgraf, J.

Levy, R.

L. A. Remer, D. Tanré, Y. J. Kaufman, C. Ichoku, S. Mattoo, R. Levy, D. A. Chu, B. N. Holben, O. Dubovik, A. Smirnov, J. V. Martins, R. R. Li, and Z. Ahmad, "Validation of MODIS aerosol retrieval over ocean," Geophys. Res. Lett. 29, 1-4 (2002).
[CrossRef]

Li, R. R.

L. A. Remer, D. Tanré, Y. J. Kaufman, C. Ichoku, S. Mattoo, R. Levy, D. A. Chu, B. N. Holben, O. Dubovik, A. Smirnov, J. V. Martins, R. R. Li, and Z. Ahmad, "Validation of MODIS aerosol retrieval over ocean," Geophys. Res. Lett. 29, 1-4 (2002).
[CrossRef]

Li, W.-H.

R. Kahn, W.-H. Li, C. Moroney, D. J. Diner, J. V. Martonchik, and E. Fishbein, "Aerosol source characterization from space-based multi-angle imaging," J. Geophys. Res. 112, D11205 (2007).
[CrossRef]

O. Kalashnikova, R. Kahn, I. N. Sokolik, and W.-H. Li, "Ability of multiangle remote sensing observations to identify and distinguish mineral dust types: optical models and retrievals of optically thick plumes," J. Geophys. Res. 110, 18S14 (2005).
[CrossRef]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Vol. 7 of Course of Theoretical Physics, second English ed. (Pergamon, 1970).

Locke, A. M.

A. M. Locke, D. S. Sabatke, E. L. Dereniak, M. R. Descour, J. P. Garcia, T. K. Hamilton, and R. W. McMillan, "Snapshot imaging spectropolarimeter," Proc. SPIE 4481, 64-72 (2002).
[CrossRef]

Loeb, N.

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

Marchand, A.

J. L. Deuzé, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanré, "Estimate of the aerosol properties over the ocean with POLDER," J. Geophys. Res. 105, 15329-15346 (2000).
[CrossRef]

Maring, H. B.

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueller, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, "Precise and accurate monitoring of terrestrial aerosols and total solar irradiance: introducing the Glory mission," Bull. Am. Meteorol. Soc. 88, 677-691 (2007).
[CrossRef]

Martins, J. V.

L. A. Remer, D. Tanré, Y. J. Kaufman, C. Ichoku, S. Mattoo, R. Levy, D. A. Chu, B. N. Holben, O. Dubovik, A. Smirnov, J. V. Martins, R. R. Li, and Z. Ahmad, "Validation of MODIS aerosol retrieval over ocean," Geophys. Res. Lett. 29, 1-4 (2002).
[CrossRef]

Martonchik, J. V.

R. Kahn, W.-H. Li, C. Moroney, D. J. Diner, J. V. Martonchik, and E. Fishbein, "Aerosol source characterization from space-based multi-angle imaging," J. Geophys. Res. 112, D11205 (2007).
[CrossRef]

R. A. Kahn, B. J. Gaitley, J. V. Martonchik, D. J. Diner, K. A. Crean, and B. Holben, "Multiangle Imaging Spectroradiometer (MISR) global aerosol optical depth validation based on 2 years of coincident Aerosol Robotic Network (AERONET) observations," J. Geophys. Res. 110, D10S04 (2005).
[CrossRef]

J. V. Martonchik, D. J. Diner, K. A. Crean, and M. A. Bull, "Regional aerosol retrieval results from MISR," IEEE Trans. Geosci. Remote Sens. 40, 1520-1531 (2002).
[CrossRef]

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

Mattoo, S.

L. A. Remer, D. Tanré, Y. J. Kaufman, C. Ichoku, S. Mattoo, R. Levy, D. A. Chu, B. N. Holben, O. Dubovik, A. Smirnov, J. V. Martins, R. R. Li, and Z. Ahmad, "Validation of MODIS aerosol retrieval over ocean," Geophys. Res. Lett. 29, 1-4 (2002).
[CrossRef]

McDonald, D.

R. Kahn, P. Banerjee, and D. McDonald, "The sensitivity of multiangle imaging to natural mixtures of aerosols over ocean," J. Geophys. Res. 106, 18219-18238 (2001).
[CrossRef]

McMillan, R. W.

A. M. Locke, D. S. Sabatke, E. L. Dereniak, M. R. Descour, J. P. Garcia, T. K. Hamilton, and R. W. McMillan, "Snapshot imaging spectropolarimeter," Proc. SPIE 4481, 64-72 (2002).
[CrossRef]

Mishchenko, M.

J. Chowdhary, B. Cairns, M. Mishchenko, and L. Travis, "Retrieval of aerosol properties over the ocean using multispectral and multiangle photopolarimetric measurements from the Research Scanning Polarimeter," Geophys. Res. Lett. 28, 243-246 (2001).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueller, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, "Precise and accurate monitoring of terrestrial aerosols and total solar irradiance: introducing the Glory mission," Bull. Am. Meteorol. Soc. 88, 677-691 (2007).
[CrossRef]

M. I. Mishchenko and L. D. Travis, "Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight," J. Geophys. Res. 102, 16989-17014 (1997).
[CrossRef]

Moroney, C.

R. Kahn, W.-H. Li, C. Moroney, D. J. Diner, J. V. Martonchik, and E. Fishbein, "Aerosol source characterization from space-based multi-angle imaging," J. Geophys. Res. 112, D11205 (2007).
[CrossRef]

Muller, J.-P.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

Myneni, R. B.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

Nicolas, J. M.

O. Hagolle, P. Goloub, P. Y. Deschamps, H. Cosnefroy, X. Briottet, T. Bailleul, J. M. Nicolas, F. Parol, B. Lafrance, and M. Herman, "Results of POLDER in-flight calibration," IEEE Trans. Geosci. Remote Sens. 37, 1550-1566 (1999).
[CrossRef]

North, P. R. J.

P. R. J. North, S. A. Briggs, S. E. Plummer, and J. J. Settle, "Retrieval of land surface bidirectional reflectance and aerosol opacity from ATSR-2 multi-angle imagery," IEEE Trans. Geosci. Remote Sens. 37, 526-537 (1999).
[CrossRef]

Oka, K.

Parol, F.

O. Hagolle, P. Goloub, P. Y. Deschamps, H. Cosnefroy, X. Briottet, T. Bailleul, J. M. Nicolas, F. Parol, B. Lafrance, and M. Herman, "Results of POLDER in-flight calibration," IEEE Trans. Geosci. Remote Sens. 37, 1550-1566 (1999).
[CrossRef]

Perry, G.

J. L. Deuzé, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanré, "Estimate of the aerosol properties over the ocean with POLDER," J. Geophys. Res. 105, 15329-15346 (2000).
[CrossRef]

Pilorz, S. H.

C. J. Bruegge, N. L. Chrien, R. R. Ando, D. J. Diner, W. A. Abdou, M. C. Helmlinger, S. H. Pilorz, and K. J. Thome, "Early validation of the Multi-angle Imaging SpectroRadiometer (MISR) radiometric scale," IEEE Trans. Geosci. Remote Sens. 40, 1477-1492 (2002).
[CrossRef]

Pinty, B.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

Plummer, S. E.

P. R. J. North, S. A. Briggs, S. E. Plummer, and J. J. Settle, "Retrieval of land surface bidirectional reflectance and aerosol opacity from ATSR-2 multi-angle imagery," IEEE Trans. Geosci. Remote Sens. 37, 526-537 (1999).
[CrossRef]

Povel, H.

Povel, H. P.

A. M. Gandorfer and H. P. Povel, "First observations with a new imaging polarimeter," Astron. Astrophys. 328, 381-389 (1997).

Reddy, M. S.

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

Reilly, T. H.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

Remer, L. A.

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

L. A. Remer, D. Tanré, Y. J. Kaufman, C. Ichoku, S. Mattoo, R. Levy, D. A. Chu, B. N. Holben, O. Dubovik, A. Smirnov, J. V. Martins, R. R. Li, and Z. Ahmad, "Validation of MODIS aerosol retrieval over ocean," Geophys. Res. Lett. 29, 1-4 (2002).
[CrossRef]

D. A. Chu, Y. J. Kaufman, C. Ichoku, L. A. Remer, D. Tanré, and B. N. Holben, "Validation of MODIS aerosol optical depth retrieval over land," Geophys. Res. Lett. 29, 5-8 (2002).
[CrossRef]

Sabatke, D. S.

A. M. Locke, D. S. Sabatke, E. L. Dereniak, M. R. Descour, J. P. Garcia, T. K. Hamilton, and R. W. McMillan, "Snapshot imaging spectropolarimeter," Proc. SPIE 4481, 64-72 (2002).
[CrossRef]

Schueller, C. F.

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueller, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, "Precise and accurate monitoring of terrestrial aerosols and total solar irradiance: introducing the Glory mission," Bull. Am. Meteorol. Soc. 88, 677-691 (2007).
[CrossRef]

Schulz, M.

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

Scott, H. E.

F. J. Iannarilli, S. H. Jones, H. E. Scott, and P. Kebabian, "Polarimetric-spectral intensity modulation (P-SIM): Enabling simultaneous hyperspectral and polarimetric imaging," Proc. SPIE 3698, 474-481 (1999).
[CrossRef]

Sellers, P. J.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

Settle, J. J.

P. R. J. North, S. A. Briggs, S. E. Plummer, and J. J. Settle, "Retrieval of land surface bidirectional reflectance and aerosol opacity from ATSR-2 multi-angle imagery," IEEE Trans. Geosci. Remote Sens. 37, 526-537 (1999).
[CrossRef]

Shaw, J. A.

Smirnov, A.

L. A. Remer, D. Tanré, Y. J. Kaufman, C. Ichoku, S. Mattoo, R. Levy, D. A. Chu, B. N. Holben, O. Dubovik, A. Smirnov, J. V. Martins, R. R. Li, and Z. Ahmad, "Validation of MODIS aerosol retrieval over ocean," Geophys. Res. Lett. 29, 1-4 (2002).
[CrossRef]

Smyth, M. M.

V. M. Jovanovic, M. A. Bull, M. M. Smyth, and J. Zong, "MISR in-flight camera geometric model calibration and georectification performance," IEEE Trans. Geosci. Remote Sens. 40, 1512-1519 (2002).
[CrossRef]

Sokolik, I. N.

O. Kalashnikova, R. Kahn, I. N. Sokolik, and W.-H. Li, "Ability of multiangle remote sensing observations to identify and distinguish mineral dust types: optical models and retrievals of optically thick plumes," J. Geophys. Res. 110, 18S14 (2005).
[CrossRef]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

Stenflo, J. O.

Susana, S.

J. L. Deuzé, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanré, "Estimate of the aerosol properties over the ocean with POLDER," J. Geophys. Res. 105, 15329-15346 (2000).
[CrossRef]

Syniuk, A.

O. Torres, P. K. Bhartia, J. R. Herman, A. Syniuk, P. Ginoux, and B. Holben, "A long term record of aerosol optical depth from TOMS observations and comparison to AERONET measurements," J. Atmos. Sci. 59, 398-413 (2002).
[CrossRef]

Takemura, T.

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

Tanré, D.

L. A. Remer, D. Tanré, Y. J. Kaufman, C. Ichoku, S. Mattoo, R. Levy, D. A. Chu, B. N. Holben, O. Dubovik, A. Smirnov, J. V. Martins, R. R. Li, and Z. Ahmad, "Validation of MODIS aerosol retrieval over ocean," Geophys. Res. Lett. 29, 1-4 (2002).
[CrossRef]

D. A. Chu, Y. J. Kaufman, C. Ichoku, L. A. Remer, D. Tanré, and B. N. Holben, "Validation of MODIS aerosol optical depth retrieval over land," Geophys. Res. Lett. 29, 5-8 (2002).
[CrossRef]

J. L. Deuzé, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanré, "Estimate of the aerosol properties over the ocean with POLDER," J. Geophys. Res. 105, 15329-15346 (2000).
[CrossRef]

Thome, K. J.

C. J. Bruegge, N. L. Chrien, R. R. Ando, D. J. Diner, W. A. Abdou, M. C. Helmlinger, S. H. Pilorz, and K. J. Thome, "Early validation of the Multi-angle Imaging SpectroRadiometer (MISR) radiometric scale," IEEE Trans. Geosci. Remote Sens. 40, 1477-1492 (2002).
[CrossRef]

Torres, O.

O. Torres, P. K. Bhartia, J. R. Herman, A. Syniuk, P. Ginoux, and B. Holben, "A long term record of aerosol optical depth from TOMS observations and comparison to AERONET measurements," J. Atmos. Sci. 59, 398-413 (2002).
[CrossRef]

O. Torres, R. Decae, P. Veefkind, and G. de Leeuw, "OMI aerosol retrieval algorithm," in OMI Algorithm Theoretical Basis Document: Clouds, Aerosols, and Surface UV Irradiance, P. Stammes and R. Noordhoek, eds. (NASA, 2002), Vol. III, pp. 46-71.

Travis, L.

J. Chowdhary, B. Cairns, M. Mishchenko, and L. Travis, "Retrieval of aerosol properties over the ocean using multispectral and multiangle photopolarimetric measurements from the Research Scanning Polarimeter," Geophys. Res. Lett. 28, 243-246 (2001).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueller, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, "Precise and accurate monitoring of terrestrial aerosols and total solar irradiance: introducing the Glory mission," Bull. Am. Meteorol. Soc. 88, 677-691 (2007).
[CrossRef]

J. Chowdhary, B. Cairns, and L. D. Travis, "Case studies of aerosol retrievals over the ocean from multiangle, multispectral photopolarimetric remote sensing data," J. Atmos. Sci. 59, 383-397 (2002).
[CrossRef]

M. I. Mishchenko and L. D. Travis, "Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight," J. Geophys. Res. 102, 16989-17014 (1997).
[CrossRef]

Tyo, J. S.

Van Delden, J. S.

Veefkind, J. P.

J. P. Veefkind, G. de Leeuw, and P. A. Durkee, "Retrieval of aerosol optical depth over land using two-angle view satellite radiometry during TARFOX," Geophys. Res. Lett. 25, 3135-3138 (1998).
[CrossRef]

Veefkind, P.

O. Torres, R. Decae, P. Veefkind, and G. de Leeuw, "OMI aerosol retrieval algorithm," in OMI Algorithm Theoretical Basis Document: Clouds, Aerosols, and Surface UV Irradiance, P. Stammes and R. Noordhoek, eds. (NASA, 2002), Vol. III, pp. 46-71.

Verstraete, M.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

Yadigaroglu, I.-A.

Yu, H.

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

Zhou, M.

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

Zong, J.

V. M. Jovanovic, M. A. Bull, M. M. Smyth, and J. Zong, "MISR in-flight camera geometric model calibration and georectification performance," IEEE Trans. Geosci. Remote Sens. 40, 1512-1519 (2002).
[CrossRef]

Appl. Opt. (7)

Astron. Astrophys. (1)

A. M. Gandorfer and H. P. Povel, "First observations with a new imaging polarimeter," Astron. Astrophys. 328, 381-389 (1997).

Atmos. Chem. Phys. (1)

H. Yu, Y. J. Kaufman, M. Chin, G. Feingold, L. A. Remer, T. L. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. S. Reddy, M. Schulz, T. Takemura, and M. Zhou, "A review of measurement-based assessments of the aerosol direct radiative effect and forcing," Atmos. Chem. Phys. 6, 613-666 (2006).
[CrossRef]

Bull. Am. Meteorol. Soc. (1)

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueller, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, "Precise and accurate monitoring of terrestrial aerosols and total solar irradiance: introducing the Glory mission," Bull. Am. Meteorol. Soc. 88, 677-691 (2007).
[CrossRef]

Geophys. Res. Lett. (4)

J. Chowdhary, B. Cairns, M. Mishchenko, and L. Travis, "Retrieval of aerosol properties over the ocean using multispectral and multiangle photopolarimetric measurements from the Research Scanning Polarimeter," Geophys. Res. Lett. 28, 243-246 (2001).
[CrossRef]

L. A. Remer, D. Tanré, Y. J. Kaufman, C. Ichoku, S. Mattoo, R. Levy, D. A. Chu, B. N. Holben, O. Dubovik, A. Smirnov, J. V. Martins, R. R. Li, and Z. Ahmad, "Validation of MODIS aerosol retrieval over ocean," Geophys. Res. Lett. 29, 1-4 (2002).
[CrossRef]

D. A. Chu, Y. J. Kaufman, C. Ichoku, L. A. Remer, D. Tanré, and B. N. Holben, "Validation of MODIS aerosol optical depth retrieval over land," Geophys. Res. Lett. 29, 5-8 (2002).
[CrossRef]

J. P. Veefkind, G. de Leeuw, and P. A. Durkee, "Retrieval of aerosol optical depth over land using two-angle view satellite radiometry during TARFOX," Geophys. Res. Lett. 25, 3135-3138 (1998).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (6)

P. R. J. North, S. A. Briggs, S. E. Plummer, and J. J. Settle, "Retrieval of land surface bidirectional reflectance and aerosol opacity from ATSR-2 multi-angle imagery," IEEE Trans. Geosci. Remote Sens. 37, 526-537 (1999).
[CrossRef]

J. V. Martonchik, D. J. Diner, K. A. Crean, and M. A. Bull, "Regional aerosol retrieval results from MISR," IEEE Trans. Geosci. Remote Sens. 40, 1520-1531 (2002).
[CrossRef]

O. Hagolle, P. Goloub, P. Y. Deschamps, H. Cosnefroy, X. Briottet, T. Bailleul, J. M. Nicolas, F. Parol, B. Lafrance, and M. Herman, "Results of POLDER in-flight calibration," IEEE Trans. Geosci. Remote Sens. 37, 1550-1566 (1999).
[CrossRef]

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. Verstraete, "Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview," IEEE Trans. Geosci. Remote Sens. 36, 1072-1087 (1998).
[CrossRef]

V. M. Jovanovic, M. A. Bull, M. M. Smyth, and J. Zong, "MISR in-flight camera geometric model calibration and georectification performance," IEEE Trans. Geosci. Remote Sens. 40, 1512-1519 (2002).
[CrossRef]

C. J. Bruegge, N. L. Chrien, R. R. Ando, D. J. Diner, W. A. Abdou, M. C. Helmlinger, S. H. Pilorz, and K. J. Thome, "Early validation of the Multi-angle Imaging SpectroRadiometer (MISR) radiometric scale," IEEE Trans. Geosci. Remote Sens. 40, 1477-1492 (2002).
[CrossRef]

J. Atmos. Sci. (2)

J. Chowdhary, B. Cairns, and L. D. Travis, "Case studies of aerosol retrievals over the ocean from multiangle, multispectral photopolarimetric remote sensing data," J. Atmos. Sci. 59, 383-397 (2002).
[CrossRef]

O. Torres, P. K. Bhartia, J. R. Herman, A. Syniuk, P. Ginoux, and B. Holben, "A long term record of aerosol optical depth from TOMS observations and comparison to AERONET measurements," J. Atmos. Sci. 59, 398-413 (2002).
[CrossRef]

J. Geophys. Res. (6)

R. A. Kahn, B. J. Gaitley, J. V. Martonchik, D. J. Diner, K. A. Crean, and B. Holben, "Multiangle Imaging Spectroradiometer (MISR) global aerosol optical depth validation based on 2 years of coincident Aerosol Robotic Network (AERONET) observations," J. Geophys. Res. 110, D10S04 (2005).
[CrossRef]

R. Kahn, P. Banerjee, and D. McDonald, "The sensitivity of multiangle imaging to natural mixtures of aerosols over ocean," J. Geophys. Res. 106, 18219-18238 (2001).
[CrossRef]

O. Kalashnikova, R. Kahn, I. N. Sokolik, and W.-H. Li, "Ability of multiangle remote sensing observations to identify and distinguish mineral dust types: optical models and retrievals of optically thick plumes," J. Geophys. Res. 110, 18S14 (2005).
[CrossRef]

R. Kahn, W.-H. Li, C. Moroney, D. J. Diner, J. V. Martonchik, and E. Fishbein, "Aerosol source characterization from space-based multi-angle imaging," J. Geophys. Res. 112, D11205 (2007).
[CrossRef]

M. I. Mishchenko and L. D. Travis, "Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight," J. Geophys. Res. 102, 16989-17014 (1997).
[CrossRef]

J. L. Deuzé, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanré, "Estimate of the aerosol properties over the ocean with POLDER," J. Geophys. Res. 105, 15329-15346 (2000).
[CrossRef]

Opt. Eng. (1)

A. M. Gandorfer, "Ferroelectric retarders as an alternative to piezoelastic modulators for use in solar Stokes vector polarimetry," Opt. Eng. 38, 1402-1408 (1999).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (3)

F. J. Iannarilli, S. H. Jones, H. E. Scott, and P. Kebabian, "Polarimetric-spectral intensity modulation (P-SIM): Enabling simultaneous hyperspectral and polarimetric imaging," Proc. SPIE 3698, 474-481 (1999).
[CrossRef]

A. M. Locke, D. S. Sabatke, E. L. Dereniak, M. R. Descour, J. P. Garcia, T. K. Hamilton, and R. W. McMillan, "Snapshot imaging spectropolarimeter," Proc. SPIE 4481, 64-72 (2002).
[CrossRef]

C. U. Keller, "Charge-caching CMOS detector for polarimetry (C3Po)," Proc. SPIE 5171, 239-246 (2004).
[CrossRef]

Publ.-Astron. Soc. Aust. (1)

J. Bland-Hawthorn and D. H. Jones, "Taurus tunable filter: a flexible approach to narrowband imaging," Publ.-Astron. Soc. Aust. 15, 44-49 (1998).
[CrossRef]

Other (7)

L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Vol. 7 of Course of Theoretical Physics, second English ed. (Pergamon, 1970).

R. A. Chipman, "Polarimetry," in Handbook of Optics: Devices, Measurements and Properties, 2nd ed. M. Bass, ed. (McGraw-Hill, 1994), Vol. II, pp. 1-37.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

Boulder Nonlinear Systems, "Ferroelectric liquid crystal based polarization filters," http://dev.bouldernonlinear.com/papers/FerroPolarFilters.pdf.

C. U. Keller, "Instrumentation for astrophysical spectropolarimetry," in Astrophysical Spectropolarimetry, J. Trujillo-Bueno, F. Moreno-Insertis, and F. Sánchez, eds. (Cambridge U. Press, 2002), pp. 303-354.

National Research Council, Committee on Earth Science and Applications from Space, Earth Science and Applications from Space: National Imperatives for the Next Decade and Beyond (The National Academies Press, 2007).

O. Torres, R. Decae, P. Veefkind, and G. de Leeuw, "OMI aerosol retrieval algorithm," in OMI Algorithm Theoretical Basis Document: Clouds, Aerosols, and Surface UV Irradiance, P. Stammes and R. Noordhoek, eds. (NASA, 2002), Vol. III, pp. 46-71.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1
Fig. 1

Combined retardance of two PEMs with a small frequency difference as a function of time (over two 40   ms frame intervals). The right-hand plots show instantaneous cosine of retardance (gray) and the approximate sampled signals obtained by averaging over 1.25   ms intervals (black), thus filtering out the high frequency. The top plots are for δ 0 = 2 and the bottom plots are for δ 0 = 5   rad .

Fig. 2
Fig. 2

Left, PEM test setup on an optical bench at JPL. Right, Schematic of the optical system.

Fig. 3
Fig. 3

Oscilloscope traces of measured signal as a function of time (left) compared with theoretical modulation curves (right) for a dual-PEM system as a function of the maximum amplitude in each PEM. From top to bottom, the curves are for a maximum retardance amplitude of 1 / 4 wave, 1 / 2 wave, and 1 wave.

Fig. 4
Fig. 4

Side view (left) and top view (right) of a three-mirror camera design with an integrated dual-PEM circular retarder. The PEMs have a small wedge angle between them to minimize ghosting.

Fig. 5
Fig. 5

Timing of sample and integration intervals during a frame.

Fig. 6
Fig. 6

Relative magnitudes of the low-frequency terms modulating the Stokes components for the set of parameters described in the text. The low-frequency terms are the zeroth- ( J 0 ) and second-order components of the expression F ( t ˜ ) in Eq. (23). The second-order term has been multiplied by 10 to make its magnitude and shape more apparent. The four plots are for different values of the peak retardance δ0: upper left, 2; upper right, 3; lower left, 4; lower right, 5 rad.

Fig. 7
Fig. 7

Curves labeled “Q noise” correspond to the sum of high-frequency residual terms 2 and 3 in Eq. (22) and the curves labeled “U noise” are the sum of terms 4 and 5. The upper left-hand plot is for α = 49.00 ; upper right, α = 49.25 ; lower left, α = 49.50 ; lower right, α = 49.75 . For these plots, δ 0 = 5   rad and φ 0 = 1   rad . The other parameters are as in Fig. 6. Note the magnified scale of the y axis.

Fig. 8
Fig. 8

Weighting functions W 1 and W 2 , the first and second rows of the polarimetric data reduction matrix, derived from the two basis functions 0.5 and 0.5 J 0 . The left-hand plot is for δ 0 = 2 and the right-hand plot is for δ 0 = 5   rad .

Fig. 9
Fig. 9

Left, Error in q resulting from a 1% error in δ 0 , as a function of δ 0 and q, using the weighting functions in Fig. 8. Right, Error in q resulting from a 1% error in δ0, using weighting functions that have been orthogonalized to first-order errors in δ 0 (Fig. 10). Note the change in the y-axis scale by a factor of 10.

Fig. 10
Fig. 10

Weighting functions W 1 and W 2 for δ 0 = 2 (left) and δ 0 = 5 (right) for the case in which the polarimetric data reduction matrix has been orthogonalized to first-order errors in retardance.

Fig. 11
Fig. 11

Left, Retrieval error in q as a function of δ 0 for q = 0.5 and various values of the scene gradient coefficients. The modulation signal has a phase offset of 0.002   rad , and a phase knowledge error of 0.002 rad. Right, Retrieval error in q for the same parameter values but using weighting functions that have been orthogonalized against linear gradients in I and Q. In this case there is no dependence on the magnitude of the intensity gradient, and the Q gradient introduces an error only because of the phase error.

Fig. 12
Fig. 12

Left, Relative variation in retardance across the FOV in the cross-track direction, for a system with the exact on axis ray having a retardance of 1.0   rad . Right, Relative retardance mismatch Δ between the two PEMs.

Fig. 13
Fig. 13

Left, Solid curves are the “noise sensitivity” factor s for the case where the retrieval weighting functions W 1 and W 2 are as in Fig. 8, under the simplifying assumption that noise variance is constant during a frame and dominated by photon shot noise. Right, Similar to the left-hand plot except that the weighting functions for the retrieval q are the orthogonalized forms of W 1 and W 2 , as in Fig. 10.

Tables (2)

Tables Icon

Table 1 Salient Aerosol Sensor Characteristics

Tables Icon

Table 2 Requirements on the Dual-PEM System

Equations (50)

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

D O L P = ( Q / I ) 2 + ( U / I ) 2 = q 2 + u 2 ,
q = Q / I ,
u = U / I .
ω = π L E ρ ( 1 σ 2 ) ,
δ ( x , t ) = δ   sin ( π x / L ) sin ( ω t φ ) ,
ω = π L E ρ ( 1 + σ ) ,
δ ( x , y , t ) = δ   sin ( π x / L ) sin ( π y / L ) sin ( ω t φ ) ,
δ ( t ) = δ 0   sin ( ω t φ ) ,
I 0 = 1 2 [ I + Q   cos   δ + U   sin   δ ] ,
I 45 = 1 2 [ I Q   sin   δ + U   cos   δ ] .
I 0 = 1 2 [ I + J 0 ( δ 0 ) Q ] + [ k = 1 J 2 k ( δ 0 ) cos   2 k ( ω t φ ) ] Q + [ k = 0 J 2 k + 1 ( δ 0 ) sin ( 2 k + 1 ) ( ω t φ ) ] U ,
I 45 = 1 2 [ I + J 0 ( δ 0 ) U ] + [ k = 1 J 2 k ( δ 0 ) cos   2 k ( ω t φ ) ] U [ k = 0 J 2 k + 1 ( δ 0 ) sin ( 2 k + 1 ) ( ω t φ ) ] Q ,
I 0 1 2 [ I + J 0 ( δ 0 ) Q ] ,
I 45 1 2 [ I + J 0 ( δ 0 ) U ] .
δ ( t ) = δ 0   sin ( ω 1 t φ 1 ) + δ 0   sin ( ω 2 t φ 2 ) = 2 δ 0   cos ( ω b t η ) sin ( ω ¯ t φ ¯ ) ,
δ ( t ) = z ( t ) sin ( ω ¯ t φ 0 ) ,
z ( t ) = 2 δ 0   cos ( ω b t η ) .
I 0 = 1 2 [ I + J 0 [ z ( t ) ] Q ] + [ k = 1 J 2 k [ z ( t ) ] cos   2 k ( ω ¯ t φ 0 ) ] Q + [ k = 0 J 2 k + 1 [ z ( t ) ] sin ( 2 k + 1 ) ( ω ¯ t φ 0 ) ] U ,
I 45 = 1 2 [ I + J 0 [ z ( t ) ] U ] + [ k = 1 J 2 k [ z ( t ) ] cos   2 k ( ω ¯ t φ 0 ) ] U [ k = 0 J 2 k + 1 [ z ( t ) ] sin ( 2 k + 1 ) ( ω ¯ t φ 0 ) ] Q .
I 0 1 2 [ I + J 0 [ 2 δ 0   cos ( ω b t η ) ] Q ] ,
I 45 1 2 [ I + J 0 [ 2 δ 0   cos ( ω b t η ) ] U ] .
I 0 ( t ˜ ) = 1 2 [ I + F ( t ˜ ) Q ] + [ k = 1 J 2 k [ z ( t ˜ ) ] sin   2 k π α 2 k π α   cos   2 k ( ω ¯ t ˜ φ 0 ) ] Q [ δ 0 ω b   sin ( ω b t ˜ η ) ω ¯ k = 1 A k [ z ( t ˜ ) ] × [ cos   2 k π α sin   2 k π α 2 k π α ] sin   2 k ( ω ¯ t ˜ φ 0 ) ] Q
+ [ k = 0 J 2 k + 1 [ z ( t ˜ ) ] sin ( 2 k + 1 ) π α ( 2 k + 1 ) π α × sin ( 2 k + 1 ) ( ω ¯ t ˜ φ 0 ) ] U + [ δ 0 ω b   sin ( ω b t ˜ η ) ω ¯ k = 0 B k [ z ( t ˜ ) ] × [ cos ( 2 k + 1 ) π α sin ( 2 k + 1 ) π α ( 2 k + 1 ) π α ] × cos ( 2 k + 1 ) ( ω ¯ t ˜ φ 0 ) ] U ,
F ( t ˜ ) = J 0 [ z ( t ˜ ) ] + 1 3 ( δ 0 α π ω b ω ¯ ) 2 { cos   2 ( ω b t ˜ η ) × J 0 [ z ( t ˜ ) ] + J 2 [ z ( t ˜ ) ] } ,
A k [ z ( t ˜ ) ] = 1 2 k [ J 2 k 1 [ z ( t ˜ ) ] J 2 k + 1 [ z ( t ˜ ) ] ] ,
B k [ z ( t ˜ ) ] = 1 2 k + 1 [ J 2 k [ z ( t ˜ ) ] J 2 k + 2 [ z ( t ˜ ) ] ] ,
t ˜ n = t 0 + t int 2 + ( n 1 ) t sample = [ γ + α 2 + ( n 1 ) β ] T .
ω ¯ t ˜ n φ 0 = π 2 [ 1 + 2 α + 4 ( n 1 ) β ] .
I 0 = [ I 0 , 1 I 0 , 2 I 0 , N ] = B · [ I Q ] = 1 2 [ 1 F [ z ( t ˜ 1 ) ] 1 F [ z ( t ˜ 2 ) ] 1 F [ z ( t ˜ N ) ] ] [ I Q ] ,
W = ( B T B ) 1 B T ,
[ I ^ Q ^ ] = W · I 0 .
I 0 = 1 2 [ I + F ( z ) Q ] 1 2 [ I + F ( z ^ ) Q + F δ 0 | z = z ^ ( δ 0 δ ^ 0 ) Q ] ,
I 0 1 2 [ I + J 0 ( z ^ ) Q z ^ J 0 ( z ^ ) ( δ 0 δ ^ 0 ) δ ^ 0 Q ] .
J ¯ 0 = 1 λ ¯ Δ λ λ 1 λ 2 J 0 [ 2 δ 0 r λ r   cos ( ω b t η ) / λ ] λ d λ ,
J ¯ 0 = J 0 ( z ) + 1 12 ( Δ λ λ ¯ ) 2 z J 1 ( z ) ,
I = I ¯ ( 1 + c I τ ) ,
Q = I ¯ ( q + c Q τ ) ,
τ = [ t ˜   −   t ˜ ¯ ] / [ t ˜ N   −   t ˜ 1 ] .
δ ( t ) = δ 1   sin ( ω 1 t φ 1 ) + δ 2   sin ( ω 2 t φ 2 ) , = 2 δ 0   cos ( ω b t η ) sin ( ω ¯ t φ ¯ ) + 2 Δ   sin ( ω b t η ) cos ( ω ¯ t φ ¯ ) ,
δ ( t ) = z ( t ) sin [ ω ¯ t φ 0 + ζ ( t ) ] ,
tan   ζ ( t ) = ( Δ / δ 0 ) tan ( ω b t η ) ,
z ( t ) = 2   sgn [ z ( t ) ] [ δ 0 2 cos 2 ( ω b t η ) + Δ 2 sin 2 ( ω b t η ) ] 1 / 2 .
I 0 = 1 2 [ I + J 0 [ z ( t ) ] Q ] + [ k = 1 c 2 k ( t )   cos   2 k ( ω ¯ t φ 0 ) ] Q [ k = 1 s 2 k ( t ) sin   2 k ( ω ¯ t φ 0 ) ] Q + [ k = 0 c 2 k + 1 ( t ) sin ( 2 k + 1 ) ( ω ¯ t φ 0 ) ] U + [ k = 0 s 2 k + 1 ( t ) cos ( 2 k + 1 ) ( ω ¯ t φ 0 ) ] U ,
c n ( t ) = J n [ z ( t ) ] cos   n ζ ( t ) ,
s n ( t ) = J n [ z ( t ) ] sin   n ζ ( t ) .
F ( t ˜ ) F ( t ˜ ) 2 J 1 [ z ( t ˜ ) ] z ( t ˜ ) Δ 2 sin 2 ( ω b t ˜ η ) ,
[ Δ I ^ Δ Q ^ ] = W · ε .
Δ q = Δ Q ^ q Δ I ^ I = n = 1 N ( W 2 , n q W 1, n ) ε n I .
var ( q ) = ε 2 I 2 [ n = 1 N ( W 2 , n q W 1, n ) 2 ] .
u n c ( q ) = [ N 2 n = 1 N ( W 2 , n q W 1, n ) 2 ] 1 / 2 SNR = s SNR .

Metrics