Abstract

Aerosols affect climate, health and aviation. Currently, their retrieval assumes a plane-parallel atmosphere and solely vertical radiative transfer. We propose a principle to estimate the aerosol distribution as it really is: a three dimensional (3D) volume. The principle is a type of tomography. The process involves wide angle integral imaging of the sky on a very large scale. The imaging can use an array of cameras in visible light. We formulate an image formation model based on 3D radiative transfer. Model inversion is done using optimization methods, exploiting a closed-form gradient which we derive for the model-fit cost function. The tomography model is distinct, as the radiation source is unidirectional and uncontrolled, while off-axis scattering dominates the images.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proceedings of the IEEE94.3 (2006).
  2. J. Kim, D. Lanman, Y. Mukaigawa, and R. Raskar, “Descattering transmission via angular filtering,” in Proc. ECCV’ 10, (Springer-Verlag, Berlin, Heidelberg, 2010), pp. 86–99.
  3. M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Transactions on Graphics (TOG)25, 924–934 (2006).
    [CrossRef]
  4. U. Dayan, B. Ziv, T. Shoob, and Y. Enzel, “Suspended dust over southeastern Mediterranean and its relation to atmospheric circulations,” International Journal of Climatology924, 915–924 (2008).
    [CrossRef]
  5. O. V. Kalashnikova, M. J. Garay, A. B. Davis, D. J. Diner, and J. V. Martonchik, “Sensitivity of multi-angle photo-polarimetry to vertical layering and mixing of absorbing aerosols: Quantifying measurement uncertainties,” Journal of Quantitative Spectroscopy and Radiative Transfer112, 2149–2163 (2011).
    [CrossRef]
  6. M. I. Mishchenko and I. V. Geogdzhayev, “Satellite remote sensing reveals regional tropospheric aerosol trends,” Opt. Express15, 7423–38 (2007).
    [CrossRef] [PubMed]
  7. J. Martonchik, D. D. J. Diner, J. M. David, R. Kahn, T. P. Ackerman, M. M. Verstraete, B. Pinty, and H. R. Gordon, “Techniques for the Retrieval of Aerosol Properties over Land and Ocean Using Multi-angle Imaging,” IEEE Trans. on Geoscience and Remote Sensing36, 1212–1227 (1998).
    [CrossRef]
  8. E. Namer, S. Shwartz, and Y. Y. Schechner, “Skyless polarimetric calibration and visibility enhancement,” Opt. Express17, 472–93 (2009).
    [CrossRef] [PubMed]
  9. A. Bluestone, G. Abdoulaev, C. Schmitz, R. Barbour, and A. Hielscher, “Three-dimensional optical tomography of hemodynamics in the human head,” Opt. Express9, 272–86 (2001).
    [CrossRef] [PubMed]
  10. I. Ihrke, K. N. Kutulakos, H. P. Lensch, M. Magnor, and W. Heidrich, “State of the art in transparent and specular object reconstruction,” in EUROGRAPHICS 2008 STAR–STATE OF THE ART REPORT, (2008).
  11. D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” Sig.Proc. Magazine18, 57–75 (2001).
    [CrossRef]
  12. H. Messer, A. Zinevich, and P. Alpert, “Environmental sensor networks using existing wireless communication systems for rainfall and wind velocity measurements,” IEEE Instrumentation & Measurement Magazine15, 32–38 (2012).
    [CrossRef]
  13. J. Gregson, M. Krimerman, M. B. Hullin, and W. Heidrich, “Stochastic tomography and its applications in 3D imaging of mixing fluids,” ACM Trans. Graph.31, 52:1–52 (2012).
    [CrossRef]
  14. B. R. Cosofret, D. Konno, A. Faghfouri, H. S. Kindle, C. M. Gittins, M. L. Finson, T. E. Janov, M. J. Levreault, R. K. Miyashiro, and W. J. Marinelli, “Imaging sensor constellation for tomographic chemical cloud mapping,” Appl. Opt.48, 1837–52 (2009).
    [CrossRef] [PubMed]
  15. J. A. Aviles, “The Development and Validation of a First Generation X-Ray Scatter Computed Tomography Algorithm for the Reconstruction of Electron Density Breast Images Using Monte Carlo Simulation,” Ph.D. thesis (2011).
  16. W. M. Cornette and J. G. Shanks, “Physically reasonable analytic expression for the single-scattering phase function,” Appl. Opt.31, 3152–3160 (1992).
    [CrossRef] [PubMed]
  17. L. Levi, Applied Optics (John Wiley & Sons, Inc., 1980).
  18. L. Devroye, “Sample-based non-uniform random variate generation,” in Proceedings of the 18th conference on Winter simulation, (ACM, 1986), pp. 260–265.
    [CrossRef]
  19. S.-H. Hong, J.-S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Opt. Express12, 483–491 (2004).
    [CrossRef] [PubMed]
  20. M. Charity, “Blackbody color datafile,” (2001), http://www.vendian.org/mncharity/dir3/blackbody/UnstableURLs/bbr\_color.html .
  21. Wikipedia, “Sunlight — Wikipedia, The Free Encyclopedia,” (2012), http://en.wikipedia.org/w/index.php?title=Sunlight\&oldid=502554571 .
  22. J. V. Martonchik, R. A. Kahn, and D. J. Diner, “Retrieval of aerosol properties over land using MISR observations,” in Satellite Aerosol Remote Sensing over Land,, A. A. Kokhanovsky and G. Leeuw, eds. (Springer BerlinHeidelberg, 2009), pp. 267–293.
    [CrossRef]
  23. H. Iwabuchi, “Efficient Monte Carlo Methods for Radiative Transfer Modeling,” Journal of the Atmospheric Sciences63, 2324–2339 (2006).
    [CrossRef]
  24. A. Marshak and A. Davis, 3D Radiative Transfer in Cloudy Atmospheres, Physics of Earth and Space Environments (Springer, 2005).
    [CrossRef]
  25. C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization,” ACM Trans. Math. Softw.23, 550–560 (1997).
    [CrossRef]
  26. N. J. Pust, A. R. Dahlberg, M. J. Thomas, and J. a. Shaw, “Comparison of full-sky polarization and radiance observations to radiative transfer simulations which employ AERONET products,” Opt. Express19, 18602–18613 (2011).
    [CrossRef] [PubMed]

2012 (2)

H. Messer, A. Zinevich, and P. Alpert, “Environmental sensor networks using existing wireless communication systems for rainfall and wind velocity measurements,” IEEE Instrumentation & Measurement Magazine15, 32–38 (2012).
[CrossRef]

J. Gregson, M. Krimerman, M. B. Hullin, and W. Heidrich, “Stochastic tomography and its applications in 3D imaging of mixing fluids,” ACM Trans. Graph.31, 52:1–52 (2012).
[CrossRef]

2011 (2)

O. V. Kalashnikova, M. J. Garay, A. B. Davis, D. J. Diner, and J. V. Martonchik, “Sensitivity of multi-angle photo-polarimetry to vertical layering and mixing of absorbing aerosols: Quantifying measurement uncertainties,” Journal of Quantitative Spectroscopy and Radiative Transfer112, 2149–2163 (2011).
[CrossRef]

N. J. Pust, A. R. Dahlberg, M. J. Thomas, and J. a. Shaw, “Comparison of full-sky polarization and radiance observations to radiative transfer simulations which employ AERONET products,” Opt. Express19, 18602–18613 (2011).
[CrossRef] [PubMed]

2009 (2)

2008 (2)

U. Dayan, B. Ziv, T. Shoob, and Y. Enzel, “Suspended dust over southeastern Mediterranean and its relation to atmospheric circulations,” International Journal of Climatology924, 915–924 (2008).
[CrossRef]

I. Ihrke, K. N. Kutulakos, H. P. Lensch, M. Magnor, and W. Heidrich, “State of the art in transparent and specular object reconstruction,” in EUROGRAPHICS 2008 STAR–STATE OF THE ART REPORT, (2008).

2007 (1)

2006 (3)

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proceedings of the IEEE94.3 (2006).

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Transactions on Graphics (TOG)25, 924–934 (2006).
[CrossRef]

H. Iwabuchi, “Efficient Monte Carlo Methods for Radiative Transfer Modeling,” Journal of the Atmospheric Sciences63, 2324–2339 (2006).
[CrossRef]

2004 (1)

2001 (2)

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” Sig.Proc. Magazine18, 57–75 (2001).
[CrossRef]

A. Bluestone, G. Abdoulaev, C. Schmitz, R. Barbour, and A. Hielscher, “Three-dimensional optical tomography of hemodynamics in the human head,” Opt. Express9, 272–86 (2001).
[CrossRef] [PubMed]

1998 (1)

J. Martonchik, D. D. J. Diner, J. M. David, R. Kahn, T. P. Ackerman, M. M. Verstraete, B. Pinty, and H. R. Gordon, “Techniques for the Retrieval of Aerosol Properties over Land and Ocean Using Multi-angle Imaging,” IEEE Trans. on Geoscience and Remote Sensing36, 1212–1227 (1998).
[CrossRef]

1997 (1)

C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization,” ACM Trans. Math. Softw.23, 550–560 (1997).
[CrossRef]

1992 (1)

1986 (1)

L. Devroye, “Sample-based non-uniform random variate generation,” in Proceedings of the 18th conference on Winter simulation, (ACM, 1986), pp. 260–265.
[CrossRef]

Abdoulaev, G.

Ackerman, T. P.

J. Martonchik, D. D. J. Diner, J. M. David, R. Kahn, T. P. Ackerman, M. M. Verstraete, B. Pinty, and H. R. Gordon, “Techniques for the Retrieval of Aerosol Properties over Land and Ocean Using Multi-angle Imaging,” IEEE Trans. on Geoscience and Remote Sensing36, 1212–1227 (1998).
[CrossRef]

Adams, A.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Transactions on Graphics (TOG)25, 924–934 (2006).
[CrossRef]

Alpert, P.

H. Messer, A. Zinevich, and P. Alpert, “Environmental sensor networks using existing wireless communication systems for rainfall and wind velocity measurements,” IEEE Instrumentation & Measurement Magazine15, 32–38 (2012).
[CrossRef]

Aviles, J. A.

J. A. Aviles, “The Development and Validation of a First Generation X-Ray Scatter Computed Tomography Algorithm for the Reconstruction of Electron Density Breast Images Using Monte Carlo Simulation,” Ph.D. thesis (2011).

Barbour, R.

Bluestone, A.

Boas, D. A.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” Sig.Proc. Magazine18, 57–75 (2001).
[CrossRef]

Brooks, D. H.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” Sig.Proc. Magazine18, 57–75 (2001).
[CrossRef]

Byrd, R. H.

C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization,” ACM Trans. Math. Softw.23, 550–560 (1997).
[CrossRef]

Cornette, W. M.

Cosofret, B. R.

Dahlberg, A. R.

David, J. M.

J. Martonchik, D. D. J. Diner, J. M. David, R. Kahn, T. P. Ackerman, M. M. Verstraete, B. Pinty, and H. R. Gordon, “Techniques for the Retrieval of Aerosol Properties over Land and Ocean Using Multi-angle Imaging,” IEEE Trans. on Geoscience and Remote Sensing36, 1212–1227 (1998).
[CrossRef]

Davis, A.

A. Marshak and A. Davis, 3D Radiative Transfer in Cloudy Atmospheres, Physics of Earth and Space Environments (Springer, 2005).
[CrossRef]

Davis, A. B.

O. V. Kalashnikova, M. J. Garay, A. B. Davis, D. J. Diner, and J. V. Martonchik, “Sensitivity of multi-angle photo-polarimetry to vertical layering and mixing of absorbing aerosols: Quantifying measurement uncertainties,” Journal of Quantitative Spectroscopy and Radiative Transfer112, 2149–2163 (2011).
[CrossRef]

Dayan, U.

U. Dayan, B. Ziv, T. Shoob, and Y. Enzel, “Suspended dust over southeastern Mediterranean and its relation to atmospheric circulations,” International Journal of Climatology924, 915–924 (2008).
[CrossRef]

Devroye, L.

L. Devroye, “Sample-based non-uniform random variate generation,” in Proceedings of the 18th conference on Winter simulation, (ACM, 1986), pp. 260–265.
[CrossRef]

DiMarzio, C. A.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” Sig.Proc. Magazine18, 57–75 (2001).
[CrossRef]

Diner, D. D. J.

J. Martonchik, D. D. J. Diner, J. M. David, R. Kahn, T. P. Ackerman, M. M. Verstraete, B. Pinty, and H. R. Gordon, “Techniques for the Retrieval of Aerosol Properties over Land and Ocean Using Multi-angle Imaging,” IEEE Trans. on Geoscience and Remote Sensing36, 1212–1227 (1998).
[CrossRef]

Diner, D. J.

O. V. Kalashnikova, M. J. Garay, A. B. Davis, D. J. Diner, and J. V. Martonchik, “Sensitivity of multi-angle photo-polarimetry to vertical layering and mixing of absorbing aerosols: Quantifying measurement uncertainties,” Journal of Quantitative Spectroscopy and Radiative Transfer112, 2149–2163 (2011).
[CrossRef]

J. V. Martonchik, R. A. Kahn, and D. J. Diner, “Retrieval of aerosol properties over land using MISR observations,” in Satellite Aerosol Remote Sensing over Land,, A. A. Kokhanovsky and G. Leeuw, eds. (Springer BerlinHeidelberg, 2009), pp. 267–293.
[CrossRef]

Enzel, Y.

U. Dayan, B. Ziv, T. Shoob, and Y. Enzel, “Suspended dust over southeastern Mediterranean and its relation to atmospheric circulations,” International Journal of Climatology924, 915–924 (2008).
[CrossRef]

Faghfouri, A.

Finson, M. L.

Footer, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Transactions on Graphics (TOG)25, 924–934 (2006).
[CrossRef]

Garay, M. J.

O. V. Kalashnikova, M. J. Garay, A. B. Davis, D. J. Diner, and J. V. Martonchik, “Sensitivity of multi-angle photo-polarimetry to vertical layering and mixing of absorbing aerosols: Quantifying measurement uncertainties,” Journal of Quantitative Spectroscopy and Radiative Transfer112, 2149–2163 (2011).
[CrossRef]

Gaudette, R. J.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” Sig.Proc. Magazine18, 57–75 (2001).
[CrossRef]

Geogdzhayev, I. V.

Gittins, C. M.

Gordon, H. R.

J. Martonchik, D. D. J. Diner, J. M. David, R. Kahn, T. P. Ackerman, M. M. Verstraete, B. Pinty, and H. R. Gordon, “Techniques for the Retrieval of Aerosol Properties over Land and Ocean Using Multi-angle Imaging,” IEEE Trans. on Geoscience and Remote Sensing36, 1212–1227 (1998).
[CrossRef]

Gregson, J.

J. Gregson, M. Krimerman, M. B. Hullin, and W. Heidrich, “Stochastic tomography and its applications in 3D imaging of mixing fluids,” ACM Trans. Graph.31, 52:1–52 (2012).
[CrossRef]

Heidrich, W.

J. Gregson, M. Krimerman, M. B. Hullin, and W. Heidrich, “Stochastic tomography and its applications in 3D imaging of mixing fluids,” ACM Trans. Graph.31, 52:1–52 (2012).
[CrossRef]

I. Ihrke, K. N. Kutulakos, H. P. Lensch, M. Magnor, and W. Heidrich, “State of the art in transparent and specular object reconstruction,” in EUROGRAPHICS 2008 STAR–STATE OF THE ART REPORT, (2008).

Hielscher, A.

Hong, S.-H.

Horowitz, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Transactions on Graphics (TOG)25, 924–934 (2006).
[CrossRef]

Hullin, M. B.

J. Gregson, M. Krimerman, M. B. Hullin, and W. Heidrich, “Stochastic tomography and its applications in 3D imaging of mixing fluids,” ACM Trans. Graph.31, 52:1–52 (2012).
[CrossRef]

Ihrke, I.

I. Ihrke, K. N. Kutulakos, H. P. Lensch, M. Magnor, and W. Heidrich, “State of the art in transparent and specular object reconstruction,” in EUROGRAPHICS 2008 STAR–STATE OF THE ART REPORT, (2008).

Iwabuchi, H.

H. Iwabuchi, “Efficient Monte Carlo Methods for Radiative Transfer Modeling,” Journal of the Atmospheric Sciences63, 2324–2339 (2006).
[CrossRef]

Jang, J.-S.

Janov, T. E.

Javidi, B.

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proceedings of the IEEE94.3 (2006).

S.-H. Hong, J.-S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Opt. Express12, 483–491 (2004).
[CrossRef] [PubMed]

Kahn, R.

J. Martonchik, D. D. J. Diner, J. M. David, R. Kahn, T. P. Ackerman, M. M. Verstraete, B. Pinty, and H. R. Gordon, “Techniques for the Retrieval of Aerosol Properties over Land and Ocean Using Multi-angle Imaging,” IEEE Trans. on Geoscience and Remote Sensing36, 1212–1227 (1998).
[CrossRef]

Kahn, R. A.

J. V. Martonchik, R. A. Kahn, and D. J. Diner, “Retrieval of aerosol properties over land using MISR observations,” in Satellite Aerosol Remote Sensing over Land,, A. A. Kokhanovsky and G. Leeuw, eds. (Springer BerlinHeidelberg, 2009), pp. 267–293.
[CrossRef]

Kalashnikova, O. V.

O. V. Kalashnikova, M. J. Garay, A. B. Davis, D. J. Diner, and J. V. Martonchik, “Sensitivity of multi-angle photo-polarimetry to vertical layering and mixing of absorbing aerosols: Quantifying measurement uncertainties,” Journal of Quantitative Spectroscopy and Radiative Transfer112, 2149–2163 (2011).
[CrossRef]

Kilmer, M.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” Sig.Proc. Magazine18, 57–75 (2001).
[CrossRef]

Kim, J.

J. Kim, D. Lanman, Y. Mukaigawa, and R. Raskar, “Descattering transmission via angular filtering,” in Proc. ECCV’ 10, (Springer-Verlag, Berlin, Heidelberg, 2010), pp. 86–99.

Kindle, H. S.

Konno, D.

Krimerman, M.

J. Gregson, M. Krimerman, M. B. Hullin, and W. Heidrich, “Stochastic tomography and its applications in 3D imaging of mixing fluids,” ACM Trans. Graph.31, 52:1–52 (2012).
[CrossRef]

Kutulakos, K. N.

I. Ihrke, K. N. Kutulakos, H. P. Lensch, M. Magnor, and W. Heidrich, “State of the art in transparent and specular object reconstruction,” in EUROGRAPHICS 2008 STAR–STATE OF THE ART REPORT, (2008).

Lanman, D.

J. Kim, D. Lanman, Y. Mukaigawa, and R. Raskar, “Descattering transmission via angular filtering,” in Proc. ECCV’ 10, (Springer-Verlag, Berlin, Heidelberg, 2010), pp. 86–99.

Lensch, H. P.

I. Ihrke, K. N. Kutulakos, H. P. Lensch, M. Magnor, and W. Heidrich, “State of the art in transparent and specular object reconstruction,” in EUROGRAPHICS 2008 STAR–STATE OF THE ART REPORT, (2008).

Levi, L.

L. Levi, Applied Optics (John Wiley & Sons, Inc., 1980).

Levoy, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Transactions on Graphics (TOG)25, 924–934 (2006).
[CrossRef]

Levreault, M. J.

Lu, P.

C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization,” ACM Trans. Math. Softw.23, 550–560 (1997).
[CrossRef]

Magnor, M.

I. Ihrke, K. N. Kutulakos, H. P. Lensch, M. Magnor, and W. Heidrich, “State of the art in transparent and specular object reconstruction,” in EUROGRAPHICS 2008 STAR–STATE OF THE ART REPORT, (2008).

Marinelli, W. J.

Marshak, A.

A. Marshak and A. Davis, 3D Radiative Transfer in Cloudy Atmospheres, Physics of Earth and Space Environments (Springer, 2005).
[CrossRef]

Martonchik, J.

J. Martonchik, D. D. J. Diner, J. M. David, R. Kahn, T. P. Ackerman, M. M. Verstraete, B. Pinty, and H. R. Gordon, “Techniques for the Retrieval of Aerosol Properties over Land and Ocean Using Multi-angle Imaging,” IEEE Trans. on Geoscience and Remote Sensing36, 1212–1227 (1998).
[CrossRef]

Martonchik, J. V.

O. V. Kalashnikova, M. J. Garay, A. B. Davis, D. J. Diner, and J. V. Martonchik, “Sensitivity of multi-angle photo-polarimetry to vertical layering and mixing of absorbing aerosols: Quantifying measurement uncertainties,” Journal of Quantitative Spectroscopy and Radiative Transfer112, 2149–2163 (2011).
[CrossRef]

J. V. Martonchik, R. A. Kahn, and D. J. Diner, “Retrieval of aerosol properties over land using MISR observations,” in Satellite Aerosol Remote Sensing over Land,, A. A. Kokhanovsky and G. Leeuw, eds. (Springer BerlinHeidelberg, 2009), pp. 267–293.
[CrossRef]

Messer, H.

H. Messer, A. Zinevich, and P. Alpert, “Environmental sensor networks using existing wireless communication systems for rainfall and wind velocity measurements,” IEEE Instrumentation & Measurement Magazine15, 32–38 (2012).
[CrossRef]

Miller, E. L.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” Sig.Proc. Magazine18, 57–75 (2001).
[CrossRef]

Mishchenko, M. I.

Miyashiro, R. K.

Mukaigawa, Y.

J. Kim, D. Lanman, Y. Mukaigawa, and R. Raskar, “Descattering transmission via angular filtering,” in Proc. ECCV’ 10, (Springer-Verlag, Berlin, Heidelberg, 2010), pp. 86–99.

Namer, E.

Ng, R.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Transactions on Graphics (TOG)25, 924–934 (2006).
[CrossRef]

Nocedal, J.

C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization,” ACM Trans. Math. Softw.23, 550–560 (1997).
[CrossRef]

Pinty, B.

J. Martonchik, D. D. J. Diner, J. M. David, R. Kahn, T. P. Ackerman, M. M. Verstraete, B. Pinty, and H. R. Gordon, “Techniques for the Retrieval of Aerosol Properties over Land and Ocean Using Multi-angle Imaging,” IEEE Trans. on Geoscience and Remote Sensing36, 1212–1227 (1998).
[CrossRef]

Pust, N. J.

Raskar, R.

J. Kim, D. Lanman, Y. Mukaigawa, and R. Raskar, “Descattering transmission via angular filtering,” in Proc. ECCV’ 10, (Springer-Verlag, Berlin, Heidelberg, 2010), pp. 86–99.

Schechner, Y. Y.

Schmitz, C.

Shanks, J. G.

Shaw, J. a.

Shoob, T.

U. Dayan, B. Ziv, T. Shoob, and Y. Enzel, “Suspended dust over southeastern Mediterranean and its relation to atmospheric circulations,” International Journal of Climatology924, 915–924 (2008).
[CrossRef]

Shwartz, S.

Stern, A.

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proceedings of the IEEE94.3 (2006).

Thomas, M. J.

Verstraete, M. M.

J. Martonchik, D. D. J. Diner, J. M. David, R. Kahn, T. P. Ackerman, M. M. Verstraete, B. Pinty, and H. R. Gordon, “Techniques for the Retrieval of Aerosol Properties over Land and Ocean Using Multi-angle Imaging,” IEEE Trans. on Geoscience and Remote Sensing36, 1212–1227 (1998).
[CrossRef]

Zhang, Q.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” Sig.Proc. Magazine18, 57–75 (2001).
[CrossRef]

Zhu, C.

C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization,” ACM Trans. Math. Softw.23, 550–560 (1997).
[CrossRef]

Zinevich, A.

H. Messer, A. Zinevich, and P. Alpert, “Environmental sensor networks using existing wireless communication systems for rainfall and wind velocity measurements,” IEEE Instrumentation & Measurement Magazine15, 32–38 (2012).
[CrossRef]

Ziv, B.

U. Dayan, B. Ziv, T. Shoob, and Y. Enzel, “Suspended dust over southeastern Mediterranean and its relation to atmospheric circulations,” International Journal of Climatology924, 915–924 (2008).
[CrossRef]

ACM Trans. Graph. (1)

J. Gregson, M. Krimerman, M. B. Hullin, and W. Heidrich, “Stochastic tomography and its applications in 3D imaging of mixing fluids,” ACM Trans. Graph.31, 52:1–52 (2012).
[CrossRef]

ACM Trans. Math. Softw. (1)

C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization,” ACM Trans. Math. Softw.23, 550–560 (1997).
[CrossRef]

ACM Transactions on Graphics (TOG) (1)

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Transactions on Graphics (TOG)25, 924–934 (2006).
[CrossRef]

Appl. Opt. (2)

EUROGRAPHICS 2008 STAR–STATE OF THE ART REPORT (1)

I. Ihrke, K. N. Kutulakos, H. P. Lensch, M. Magnor, and W. Heidrich, “State of the art in transparent and specular object reconstruction,” in EUROGRAPHICS 2008 STAR–STATE OF THE ART REPORT, (2008).

IEEE Instrumentation & Measurement Magazine (1)

H. Messer, A. Zinevich, and P. Alpert, “Environmental sensor networks using existing wireless communication systems for rainfall and wind velocity measurements,” IEEE Instrumentation & Measurement Magazine15, 32–38 (2012).
[CrossRef]

IEEE Trans. on Geoscience and Remote Sensing (1)

J. Martonchik, D. D. J. Diner, J. M. David, R. Kahn, T. P. Ackerman, M. M. Verstraete, B. Pinty, and H. R. Gordon, “Techniques for the Retrieval of Aerosol Properties over Land and Ocean Using Multi-angle Imaging,” IEEE Trans. on Geoscience and Remote Sensing36, 1212–1227 (1998).
[CrossRef]

International Journal of Climatology (1)

U. Dayan, B. Ziv, T. Shoob, and Y. Enzel, “Suspended dust over southeastern Mediterranean and its relation to atmospheric circulations,” International Journal of Climatology924, 915–924 (2008).
[CrossRef]

Journal of Quantitative Spectroscopy and Radiative Transfer (1)

O. V. Kalashnikova, M. J. Garay, A. B. Davis, D. J. Diner, and J. V. Martonchik, “Sensitivity of multi-angle photo-polarimetry to vertical layering and mixing of absorbing aerosols: Quantifying measurement uncertainties,” Journal of Quantitative Spectroscopy and Radiative Transfer112, 2149–2163 (2011).
[CrossRef]

Journal of the Atmospheric Sciences (1)

H. Iwabuchi, “Efficient Monte Carlo Methods for Radiative Transfer Modeling,” Journal of the Atmospheric Sciences63, 2324–2339 (2006).
[CrossRef]

Opt. Express (5)

Proceedings of the 18th conference on Winter simulation (1)

L. Devroye, “Sample-based non-uniform random variate generation,” in Proceedings of the 18th conference on Winter simulation, (ACM, 1986), pp. 260–265.
[CrossRef]

Proceedings of the IEEE (1)

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proceedings of the IEEE94.3 (2006).

Sig.Proc. Magazine (1)

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” Sig.Proc. Magazine18, 57–75 (2001).
[CrossRef]

Other (7)

A. Marshak and A. Davis, 3D Radiative Transfer in Cloudy Atmospheres, Physics of Earth and Space Environments (Springer, 2005).
[CrossRef]

L. Levi, Applied Optics (John Wiley & Sons, Inc., 1980).

J. Kim, D. Lanman, Y. Mukaigawa, and R. Raskar, “Descattering transmission via angular filtering,” in Proc. ECCV’ 10, (Springer-Verlag, Berlin, Heidelberg, 2010), pp. 86–99.

J. A. Aviles, “The Development and Validation of a First Generation X-Ray Scatter Computed Tomography Algorithm for the Reconstruction of Electron Density Breast Images Using Monte Carlo Simulation,” Ph.D. thesis (2011).

M. Charity, “Blackbody color datafile,” (2001), http://www.vendian.org/mncharity/dir3/blackbody/UnstableURLs/bbr\_color.html .

Wikipedia, “Sunlight — Wikipedia, The Free Encyclopedia,” (2012), http://en.wikipedia.org/w/index.php?title=Sunlight\&oldid=502554571 .

J. V. Martonchik, R. A. Kahn, and D. J. Diner, “Retrieval of aerosol properties over land using MISR observations,” in Satellite Aerosol Remote Sensing over Land,, A. A. Kokhanovsky and G. Leeuw, eds. (Springer BerlinHeidelberg, 2009), pp. 267–293.
[CrossRef]

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 (10)

Fig. 1
Fig. 1

Integral (lightfield) imaging through a volumetric distribution in the atmosphere, using ground-based cameras.

Fig. 2
Fig. 2

Simulated 3D aerosol distributions: [a] Haze blobs and [b] Haze Front. Here, an aerosol density unit is 106 particles/m3. The atmopsheric domain has area of 50 × 50km2, extending from the ground up to altitude of 10km. The domain is divided into a rectilinear grid having Nvoxels voxels.

Fig. 3
Fig. 3

Different viewpoints of a sky that includes Haze Blobs. Images are rendered using the single-scattering model. A yellow dot marks the Sun location. Dashed white circles mark zenith angles.

Fig. 4
Fig. 4

[a] Multiple-scattering forward model by MC. [b] Photograph of the same sky and view point as in Fig. 3(a), rendered using MC.

Fig. 5
Fig. 5

Images simulated by MC, from the same viewpoint, but different aerosol characteristics. (a) Haze blobs, characterized in Sec. 5. (b) Partly absorbing aerosol. (c) Aerosol having an isotropic phase function. (d) High aerosol density. Details of the scenarios used in creating (b) and (c) are given in Sec. 8.

Fig. 6
Fig. 6

Separation of the image shown in Fig. 4(b) to contributions by successive orders of scattering: (a) first, (b) second, (c) third and (d) forth scattering order.

Fig. 7
Fig. 7

Cross-sections along the X-axis of photographs rendered by the single-scattering (dotted) and MC (solid line) forward models. (a) cross sections of the Haze Blobs scene (described in Sec. 5). The difference between the models is much more pronounced (b) when the scatterers are ten times denser (see Sec. 8).

Fig. 8
Fig. 8

Recoveries of scenes shown in Fig. 2. Color represents aerosol density, in units of 106 particles/m3. In (a) and (b) images simulated by single-scattering are used as input for the recovery. In (c) and (d), MC simulated images are used as input for the recovery.

Fig. 9
Fig. 9

The relative error ε measure decreases with the number of cameras. Bars represent the standard deviation of ε, over our random tests.

Fig. 10
Fig. 10

Recovered distributions when the aerosol is either party absorbing (a), has isotropic phase function (b) or has high density (c).

Tables (1)

Tables Icon

Table 1 Relative errors in various simulations. Here �� denotes order of magnitude.

Equations (33)

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

τ = d τ = ( β aerosol + β air ) d l = ( σ aerosol n + β air ) d l = τ air + σ aerosol n d l ,
t = exp ( τ ) .
α aerosol = ϖ aerosol β aerosol = ϖ aerosol σ aerosol n .
α ˜ aerosol ( Φ scatter ) = α aerosol P aerosol ( Φ scatter ) = ϖ aerosol σ aerosol n P aerosol ( Φ scatter ) .
P g aerosol ( Φ scatter ) 3 8 π ( 1 g 2 ) [ 1 + ( cos Φ scatter ) 2 ] ( 2 + g 2 ) ( 1 + g 2 2 g cos Φ scatter ) 3 2
P air ( Φ scatter ) 3 16 π ( 1 + cos 2 Φ scatter )
α air ( h , λ ) = β air ( h , λ ) 1.09 × 10 3 λ 4 exp ( h / H air ) ,
F ( τ ) = 0 τ exp ( τ ) d τ = 1 exp ( τ ) .
τ random = F 1 ( u ) = ln ( 1 u ) .
l random = ( β aerosol + β air ) 1 τ random = ( β aerosol + β air ) 1 ln ( 1 u ) ,
D Sun voxel ( k , q ) = { l SR ( q ) if q [ SR , k ] 0 otherwise
D c voxel cam ( k , m ) = { l LOS c ( m ) if m [ LOS c , k ] 0 otherwise .
τ SR ( k ) = q [ SR , k ] l SR ( q ) [ β air ( q ) + σ aerosol n ( q ) ] τ LOS c ( k ) = m [ SR , k ] l LOS c ( m ) [ β air ( m ) + σ aerosol n ( m ) ] .
τ SR = D Sun voxel β air + σ aerosol D Sun voxel n τ LOS c = D c voxel cam β air + σ aerosol D c voxel cam n .
τ c = τ c air + σ aerosol D c n ,
α ˜ c air = β air P air ( Φ c scatter ) , α ˜ c aerosol = ϖ aerosol σ aerosol n P g aerosol ( Φ c scatter ) .
p c ( k ) = L TOA [ α ˜ c air ( k ) + α ˜ c aerosol ( k ) ] exp [ τ c ( k ) ] ,
p c = L TOA ( α ˜ c air + α ˜ c aerosol ) exp ( τ c ) .
i c = Π c p c ,
i c = L TOA Π c { [ α ˜ c air + ϖ aerosol σ aerosol P g aerosol ( Φ c scatter ) n ] exp [ ( τ c air + σ aerosol D c n ) ] } .
f 1 [ h ( k ) ] = n sealevel exp [ h ( k ) / H aerosol ] ,
f 2 ( k ) = { 1 if k any blob cluster 0 otherwise .
0 l random ( σ aerosol n + β air ) d l = τ random
n ^ = arg min n 𝒞 E ( n )
E ( n ) = c = 1 N views [ i c measured i c ( n ) ] 2 2 + η Ψ ( n ) .
Ψ ( n ) = W n 2 2
n E = 2 c = 1 N views [ J i c ( n ) ] [ i c measured i c ( n ) ] + 2 η W W n .
C ( a u ) n = [ a n 𝔻 { u } + u n 𝔻 { a } ] C .
a n = C 𝔻 { exp ( Cn ) } .
exp [ ( τ c air + σ aerosol D c n ) ] n = σ aerosol D c 𝔻 { exp [ ( τ c air + σ aerosol D c n ) ] } ,
[ ϖ aerosol σ aerosol P g aerosol ( Φ c scatter ) n ] n = ϖ aerosol σ aerosol 𝔻 { P g aerosol ( Φ c scatter ) } .
J i c ( n ) = L TOA σ aerosol ( A B ) 𝔻 { exp [ ( τ c air + σ aerosol D c n ) ] } Π c ,
A = ϖ aerosol 𝔻 { P g aerosol ( Φ c scatter ) } , B = D c 𝔻 { [ α ˜ c air + ϖ aerosol σ aerosol P g aerosol ( Φ c scatter ) n ] }

Metrics