Abstract

Here we use the state-of-the-art invariant imbedding T-matrix method to theoretically assess the backscattering linear depolarization ratio (LDR) of nonspherical particles in a super-ellipsoidal shape space. Super-ellipsoids have inherent flexibility to model the particle aspect ratio, roundness, and concavity, these being salient characteristics of most atmospheric particles (e.g., sea salt and dust aerosols). The complex refractive index of super-ellipsoids was set up with the real part ranging from 1.1 to 2.0 and the imaginary part from 10−7 to 0.5. To constrain the computational burden, the maximum size parameters for spheroids and super-ellipsoids were set as 100 and 50, respectively. From the LDRs of spheroids, we found that enhanced LDRs (>~60%) are common for optically soft particles. However, as the real part of the refractive index increases (larger than ~1.33), the enhanced LDRs (>~60%) are in high probability observed for nearly-spherical particles, and then disappear as the refractive index exceeds 1.7. To produce the enhanced LDRs, the imaginary part of the refractive index should also be less than ~0.01 such that the backscattered waves from particle-to-air transmission have sizable contributions, as the external reflection of spheroids produces no depolarization. This finding has particular relevance to LiDAR observations of atmospheric particles because the refractive index of most aerosols and hydrometeors at the LiDAR wavelength (e.g., 0.532μm) locates in this region, and aerosols and hydrometeors could have nearly-spherical morphologies. From the LDRs for general super-ellipsoids, we found that the enhanced LDRs (>~60%) exist for nearly-spherical particles with the aspect ratio close to unity, but disappear for super-ellipsoids with an aspect ratio at unity. In addition, the LDRs trend to decrease as the real part of the refractive index increases for convex super-ellipsoids, but show different features for concave super-ellipsoids. Furthermore, super-ellipsoids with different roundness parameters have a distinct dependence on the aspect ratio, which is significantly different from spheroids. The results presented here provide comprehensive references for understanding the LDR change of atmospheric aerosols as the particle shape and refractive index for interpreting LiDAR backscattering signals.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (1)

M. Haarig, A. Ansmann, D. Althausen, A. Klepel, S. Groß, V. Freudenthaler, C. Toledano, R.-E. Mamouri, D. A. Farrell, D. A. Prescod, E. Marinou, S. P. Burton, J. Gasteiger, R. Engelmann, and H. Baars, “Triple-wavelength depolarization-ratio profiling of Saharan dust over Barbados during SALTRACE in 2013 and 2014,” Atmos. Chem. Phys. 17(17), 10767–10794 (2017).
[Crossref]

2016 (5)

E. Järvinen, O. Kemppinen, T. Nousiainen, T. Kociok, O. Möhler, T. Leisner, and M. Schnaiter, “Laboratory investigations of mineral dust near-backscattering depolarization ratios,” J. Quant. Spectrosc. Radiat. Transf. 178, 192–208 (2016).
[Crossref]

H. R. Smith, P. J. Connolly, A. R. Webb, and A. J. Baran, “Exact and near backscattering measurements of the linear depolarization ratio of various ice crystal habits generated in a laboratory cloud chamber,” J. Quant. Spectrosc. Radiat. Transf. 178(2), 361–378 (2016).
[Crossref]

A. Miffre, T. Mehri, M. Francis, and P. Rairoux, “UV-VIS depolarization from Arizona Test Dust particles at exact backscattering angle,” J. Quant. Spectrosc. Radiat. Transf. 169, 79–90 (2016).
[Crossref]

M. I. Mishchenko, J. M. Dlugach, and L. Liu, “Linear depolarization of lidar returns by aged smoke particles,” Appl. Opt. 55(35), 9968–9973 (2016).
[Crossref] [PubMed]

M. I. Mishchenko, J. M. Dlugach, M. A. Yurkin, L. Bi, B. Cairns, L. Liu, R. L. Panetta, L. D. Travis, P. Yang, and N. T. Zakharova, “First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media,” Phys. Rep. 632, 1–75 (2016).
[Crossref]

2015 (3)

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Optical tunneling by arbitrary macroscopic three-dimensional objects,” Phys. Rev. A 92(1), 013814 (2015).
[Crossref]

L. Bi and P. Yang, “Impact of calcification state on the inherent optical properties of Emiliania huxleyi coccoliths and coccolithophores,” J. Quant. Spectrosc. Radiat. Transf. 155, 10–21 (2015).
[Crossref]

D. Liu, Y. Yang, Y. Zhang, Z. Cheng, Z. Wang, J. Luo, L. Su, L. Yang, Y. Shen, J. Bai, and K. Wang, “Pattern recognition model for aerosol classification with atmospheric backscatter lidars: principles and simulations,” J. Appl. Remote Sens. 9(1), 096006 (2015).
[Crossref]

2014 (2)

H. Lindqvist, O. Jokinen, K. Kandler, D. Scheuvens, and T. Nousiainen, “Single scattering by realistic, inhomogeneous mineral dust particles with stereogrammetric shapes,” Atmos. Chem. Phys. 14(1), 143–157 (2014).
[Crossref]

L. Bi and P. Yang, “Accurate simulation of the optical properties of atmospheric ice crystals with invariant imbedding T-matrix method,” J. Quant. Spectrosc. Radiat. Transf. 138, 17–35 (2014).
[Crossref]

2013 (5)

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 116(2), 169–183 (2013).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “A numerical combination of extended boundary condition method and invariant imbedding method to light scattering by large spheroids and cylinders,” J. Quant. Spectrosc. Radiat. Transf. 123, 17–22 (2013).
[Crossref]

L. Bi and P. Yang, “Modeling of light scattering by biconcave and deformed red blood cells with the invariant imbedding T-matrix method,” J. Biomed. Opt. 18(5), 055001 (2013).
[Crossref] [PubMed]

S. P. Burton, R. A. Ferrare, M. A. Vaughan, A. H. Omar, R. R. Rogers, C. A. Hostetler, and J. W. Hair, “Aerosol classification from airborne HSRL and comparisons with the CALIPSO vertical feature mask,” Atmos. Meas. Tech. 6(5), 1397–1412 (2013).
[Crossref]

M. I. Mishchenko, L. Liu, and D. W. Mackowski, “T-matrix modeling of linear depolarization by morphologically complex soot and soot-containing aerosols,” J. Quant. Spectrosc. Radiat. Transf. 123(4), 135–144 (2013).
[Crossref]

2012 (2)

C. Zhou, P. Yang, A. E. Dessler, Y. Hu, and B. A. Baum, “Study of horizontally oriented ice crystals with CALIPSO observations and comparison with Monte Carlo radiative transfer Simulations,” J. Appl. Meteorol. Climatol. 51(7), 1426–1439 (2012).
[Crossref]

M. I. Mishchenko and J. M. Dlugach, “Adhesion of mineral and soot aerosols can strongly affect their scattering and absorption properties,” Opt. Lett. 37(4), 704–706 (2012).
[Crossref] [PubMed]

2011 (2)

M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2234–2247 (2011).
[Crossref]

D. W. Mackowski and M. I. Mishchenko, “A multiple sphere T-matrix Fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2182–2192 (2011).
[Crossref]

2010 (1)

F. Xu, J. A. Lock, and G. Gouesbet, “Debye series for light scattering by a nonspherical particle,” Phys. Rev. A 81(4), 043824 (2010).
[Crossref]

2009 (2)

D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO mission and CALIOP data processing algorithms,” J. Atmos. Ocean. Technol. 26(11), 2310–2323 (2009).
[Crossref]

S. D. Druger, J. Czege, Z. Li, and B. V. Bronk, “Light scattering calculations exploring sensitivity of depolarization ratio to shape changes. I. Single spores in air,” Appl. Opt. 48(4), 716–724 (2009).
[Crossref] [PubMed]

2007 (1)

2002 (1)

T. Wriedt, “Using the T-matrix method for light scattering computations by non-axisymmetric particles: superellipsoids and realistically shaped particles,” Part. Part. Syst. Charact. 19(4), 256–268 (2002).
[Crossref]

1999 (1)

T. Murayama, H. Okamoto, N. Kaneyasu, H. Kamataki, and K. Miura, “Application of lidar depolarization measurement in the atmospheric boundary layer: Effects of dust and sea-salt particles,” J. Geophys. Res. 104(D24), 31781–31792 (1999).
[Crossref]

1998 (2)

M. I. Mishchenko and K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25(3), 309–312 (1998).
[Crossref]

M. I. Mishchenko and L. D. Travis, “Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transf. 60(3), 309–324 (1998).
[Crossref]

1995 (1)

1991 (1)

K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72(12), 1848–1866 (1991).
[Crossref]

Althausen, D.

M. Haarig, A. Ansmann, D. Althausen, A. Klepel, S. Groß, V. Freudenthaler, C. Toledano, R.-E. Mamouri, D. A. Farrell, D. A. Prescod, E. Marinou, S. P. Burton, J. Gasteiger, R. Engelmann, and H. Baars, “Triple-wavelength depolarization-ratio profiling of Saharan dust over Barbados during SALTRACE in 2013 and 2014,” Atmos. Chem. Phys. 17(17), 10767–10794 (2017).
[Crossref]

Ansmann, A.

M. Haarig, A. Ansmann, D. Althausen, A. Klepel, S. Groß, V. Freudenthaler, C. Toledano, R.-E. Mamouri, D. A. Farrell, D. A. Prescod, E. Marinou, S. P. Burton, J. Gasteiger, R. Engelmann, and H. Baars, “Triple-wavelength depolarization-ratio profiling of Saharan dust over Barbados during SALTRACE in 2013 and 2014,” Atmos. Chem. Phys. 17(17), 10767–10794 (2017).
[Crossref]

Baars, H.

M. Haarig, A. Ansmann, D. Althausen, A. Klepel, S. Groß, V. Freudenthaler, C. Toledano, R.-E. Mamouri, D. A. Farrell, D. A. Prescod, E. Marinou, S. P. Burton, J. Gasteiger, R. Engelmann, and H. Baars, “Triple-wavelength depolarization-ratio profiling of Saharan dust over Barbados during SALTRACE in 2013 and 2014,” Atmos. Chem. Phys. 17(17), 10767–10794 (2017).
[Crossref]

Bai, J.

D. Liu, Y. Yang, Y. Zhang, Z. Cheng, Z. Wang, J. Luo, L. Su, L. Yang, Y. Shen, J. Bai, and K. Wang, “Pattern recognition model for aerosol classification with atmospheric backscatter lidars: principles and simulations,” J. Appl. Remote Sens. 9(1), 096006 (2015).
[Crossref]

Baran, A. J.

H. R. Smith, P. J. Connolly, A. R. Webb, and A. J. Baran, “Exact and near backscattering measurements of the linear depolarization ratio of various ice crystal habits generated in a laboratory cloud chamber,” J. Quant. Spectrosc. Radiat. Transf. 178(2), 361–378 (2016).
[Crossref]

Baum, B. A.

C. Zhou, P. Yang, A. E. Dessler, Y. Hu, and B. A. Baum, “Study of horizontally oriented ice crystals with CALIPSO observations and comparison with Monte Carlo radiative transfer Simulations,” J. Appl. Meteorol. Climatol. 51(7), 1426–1439 (2012).
[Crossref]

Bi, L.

M. I. Mishchenko, J. M. Dlugach, M. A. Yurkin, L. Bi, B. Cairns, L. Liu, R. L. Panetta, L. D. Travis, P. Yang, and N. T. Zakharova, “First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media,” Phys. Rep. 632, 1–75 (2016).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Optical tunneling by arbitrary macroscopic three-dimensional objects,” Phys. Rev. A 92(1), 013814 (2015).
[Crossref]

L. Bi and P. Yang, “Impact of calcification state on the inherent optical properties of Emiliania huxleyi coccoliths and coccolithophores,” J. Quant. Spectrosc. Radiat. Transf. 155, 10–21 (2015).
[Crossref]

L. Bi and P. Yang, “Accurate simulation of the optical properties of atmospheric ice crystals with invariant imbedding T-matrix method,” J. Quant. Spectrosc. Radiat. Transf. 138, 17–35 (2014).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “A numerical combination of extended boundary condition method and invariant imbedding method to light scattering by large spheroids and cylinders,” J. Quant. Spectrosc. Radiat. Transf. 123, 17–22 (2013).
[Crossref]

L. Bi and P. Yang, “Modeling of light scattering by biconcave and deformed red blood cells with the invariant imbedding T-matrix method,” J. Biomed. Opt. 18(5), 055001 (2013).
[Crossref] [PubMed]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 116(2), 169–183 (2013).
[Crossref]

Bronk, B. V.

Burton, S. P.

M. Haarig, A. Ansmann, D. Althausen, A. Klepel, S. Groß, V. Freudenthaler, C. Toledano, R.-E. Mamouri, D. A. Farrell, D. A. Prescod, E. Marinou, S. P. Burton, J. Gasteiger, R. Engelmann, and H. Baars, “Triple-wavelength depolarization-ratio profiling of Saharan dust over Barbados during SALTRACE in 2013 and 2014,” Atmos. Chem. Phys. 17(17), 10767–10794 (2017).
[Crossref]

S. P. Burton, R. A. Ferrare, M. A. Vaughan, A. H. Omar, R. R. Rogers, C. A. Hostetler, and J. W. Hair, “Aerosol classification from airborne HSRL and comparisons with the CALIPSO vertical feature mask,” Atmos. Meas. Tech. 6(5), 1397–1412 (2013).
[Crossref]

Cairns, B.

M. I. Mishchenko, J. M. Dlugach, M. A. Yurkin, L. Bi, B. Cairns, L. Liu, R. L. Panetta, L. D. Travis, P. Yang, and N. T. Zakharova, “First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media,” Phys. Rep. 632, 1–75 (2016).
[Crossref]

Cheng, Z.

D. Liu, Y. Yang, Y. Zhang, Z. Cheng, Z. Wang, J. Luo, L. Su, L. Yang, Y. Shen, J. Bai, and K. Wang, “Pattern recognition model for aerosol classification with atmospheric backscatter lidars: principles and simulations,” J. Appl. Remote Sens. 9(1), 096006 (2015).
[Crossref]

Connolly, P. J.

H. R. Smith, P. J. Connolly, A. R. Webb, and A. J. Baran, “Exact and near backscattering measurements of the linear depolarization ratio of various ice crystal habits generated in a laboratory cloud chamber,” J. Quant. Spectrosc. Radiat. Transf. 178(2), 361–378 (2016).
[Crossref]

Czege, J.

Dessler, A. E.

C. Zhou, P. Yang, A. E. Dessler, Y. Hu, and B. A. Baum, “Study of horizontally oriented ice crystals with CALIPSO observations and comparison with Monte Carlo radiative transfer Simulations,” J. Appl. Meteorol. Climatol. 51(7), 1426–1439 (2012).
[Crossref]

Dlugach, J. M.

M. I. Mishchenko, J. M. Dlugach, and L. Liu, “Linear depolarization of lidar returns by aged smoke particles,” Appl. Opt. 55(35), 9968–9973 (2016).
[Crossref] [PubMed]

M. I. Mishchenko, J. M. Dlugach, M. A. Yurkin, L. Bi, B. Cairns, L. Liu, R. L. Panetta, L. D. Travis, P. Yang, and N. T. Zakharova, “First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media,” Phys. Rep. 632, 1–75 (2016).
[Crossref]

M. I. Mishchenko and J. M. Dlugach, “Adhesion of mineral and soot aerosols can strongly affect their scattering and absorption properties,” Opt. Lett. 37(4), 704–706 (2012).
[Crossref] [PubMed]

Druger, S. D.

Engelmann, R.

M. Haarig, A. Ansmann, D. Althausen, A. Klepel, S. Groß, V. Freudenthaler, C. Toledano, R.-E. Mamouri, D. A. Farrell, D. A. Prescod, E. Marinou, S. P. Burton, J. Gasteiger, R. Engelmann, and H. Baars, “Triple-wavelength depolarization-ratio profiling of Saharan dust over Barbados during SALTRACE in 2013 and 2014,” Atmos. Chem. Phys. 17(17), 10767–10794 (2017).
[Crossref]

Farrell, D. A.

M. Haarig, A. Ansmann, D. Althausen, A. Klepel, S. Groß, V. Freudenthaler, C. Toledano, R.-E. Mamouri, D. A. Farrell, D. A. Prescod, E. Marinou, S. P. Burton, J. Gasteiger, R. Engelmann, and H. Baars, “Triple-wavelength depolarization-ratio profiling of Saharan dust over Barbados during SALTRACE in 2013 and 2014,” Atmos. Chem. Phys. 17(17), 10767–10794 (2017).
[Crossref]

Ferrare, R. A.

S. P. Burton, R. A. Ferrare, M. A. Vaughan, A. H. Omar, R. R. Rogers, C. A. Hostetler, and J. W. Hair, “Aerosol classification from airborne HSRL and comparisons with the CALIPSO vertical feature mask,” Atmos. Meas. Tech. 6(5), 1397–1412 (2013).
[Crossref]

Flittner, D.

Francis, M.

A. Miffre, T. Mehri, M. Francis, and P. Rairoux, “UV-VIS depolarization from Arizona Test Dust particles at exact backscattering angle,” J. Quant. Spectrosc. Radiat. Transf. 169, 79–90 (2016).
[Crossref]

Freudenthaler, V.

M. Haarig, A. Ansmann, D. Althausen, A. Klepel, S. Groß, V. Freudenthaler, C. Toledano, R.-E. Mamouri, D. A. Farrell, D. A. Prescod, E. Marinou, S. P. Burton, J. Gasteiger, R. Engelmann, and H. Baars, “Triple-wavelength depolarization-ratio profiling of Saharan dust over Barbados during SALTRACE in 2013 and 2014,” Atmos. Chem. Phys. 17(17), 10767–10794 (2017).
[Crossref]

Gasteiger, J.

M. Haarig, A. Ansmann, D. Althausen, A. Klepel, S. Groß, V. Freudenthaler, C. Toledano, R.-E. Mamouri, D. A. Farrell, D. A. Prescod, E. Marinou, S. P. Burton, J. Gasteiger, R. Engelmann, and H. Baars, “Triple-wavelength depolarization-ratio profiling of Saharan dust over Barbados during SALTRACE in 2013 and 2014,” Atmos. Chem. Phys. 17(17), 10767–10794 (2017).
[Crossref]

Gouesbet, G.

F. Xu, J. A. Lock, and G. Gouesbet, “Debye series for light scattering by a nonspherical particle,” Phys. Rev. A 81(4), 043824 (2010).
[Crossref]

Groß, S.

M. Haarig, A. Ansmann, D. Althausen, A. Klepel, S. Groß, V. Freudenthaler, C. Toledano, R.-E. Mamouri, D. A. Farrell, D. A. Prescod, E. Marinou, S. P. Burton, J. Gasteiger, R. Engelmann, and H. Baars, “Triple-wavelength depolarization-ratio profiling of Saharan dust over Barbados during SALTRACE in 2013 and 2014,” Atmos. Chem. Phys. 17(17), 10767–10794 (2017).
[Crossref]

Haarig, M.

M. Haarig, A. Ansmann, D. Althausen, A. Klepel, S. Groß, V. Freudenthaler, C. Toledano, R.-E. Mamouri, D. A. Farrell, D. A. Prescod, E. Marinou, S. P. Burton, J. Gasteiger, R. Engelmann, and H. Baars, “Triple-wavelength depolarization-ratio profiling of Saharan dust over Barbados during SALTRACE in 2013 and 2014,” Atmos. Chem. Phys. 17(17), 10767–10794 (2017).
[Crossref]

Hair, J. W.

S. P. Burton, R. A. Ferrare, M. A. Vaughan, A. H. Omar, R. R. Rogers, C. A. Hostetler, and J. W. Hair, “Aerosol classification from airborne HSRL and comparisons with the CALIPSO vertical feature mask,” Atmos. Meas. Tech. 6(5), 1397–1412 (2013).
[Crossref]

Hoekstra, A. G.

M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2234–2247 (2011).
[Crossref]

Hostetler, C. A.

S. P. Burton, R. A. Ferrare, M. A. Vaughan, A. H. Omar, R. R. Rogers, C. A. Hostetler, and J. W. Hair, “Aerosol classification from airborne HSRL and comparisons with the CALIPSO vertical feature mask,” Atmos. Meas. Tech. 6(5), 1397–1412 (2013).
[Crossref]

Hovenier, J. W.

Hu, Y.

C. Zhou, P. Yang, A. E. Dessler, Y. Hu, and B. A. Baum, “Study of horizontally oriented ice crystals with CALIPSO observations and comparison with Monte Carlo radiative transfer Simulations,” J. Appl. Meteorol. Climatol. 51(7), 1426–1439 (2012).
[Crossref]

D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO mission and CALIOP data processing algorithms,” J. Atmos. Ocean. Technol. 26(11), 2310–2323 (2009).
[Crossref]

Y. Hu, M. Vaughan, Z. Liu, B. Lin, P. Yang, D. Flittner, B. Hunt, R. Kuehn, J. Huang, D. Wu, S. Rodier, K. Powell, C. Trepte, and D. Winker, “The depolarization - attenuated backscatter relation: CALIPSO lidar measurements vs. theory,” Opt. Express 15(9), 5327–5332 (2007).
[Crossref] [PubMed]

Huang, J.

Hunt, B.

Hunt, W. H.

D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO mission and CALIOP data processing algorithms,” J. Atmos. Ocean. Technol. 26(11), 2310–2323 (2009).
[Crossref]

Järvinen, E.

E. Järvinen, O. Kemppinen, T. Nousiainen, T. Kociok, O. Möhler, T. Leisner, and M. Schnaiter, “Laboratory investigations of mineral dust near-backscattering depolarization ratios,” J. Quant. Spectrosc. Radiat. Transf. 178, 192–208 (2016).
[Crossref]

Jokinen, O.

H. Lindqvist, O. Jokinen, K. Kandler, D. Scheuvens, and T. Nousiainen, “Single scattering by realistic, inhomogeneous mineral dust particles with stereogrammetric shapes,” Atmos. Chem. Phys. 14(1), 143–157 (2014).
[Crossref]

Kamataki, H.

T. Murayama, H. Okamoto, N. Kaneyasu, H. Kamataki, and K. Miura, “Application of lidar depolarization measurement in the atmospheric boundary layer: Effects of dust and sea-salt particles,” J. Geophys. Res. 104(D24), 31781–31792 (1999).
[Crossref]

Kandler, K.

H. Lindqvist, O. Jokinen, K. Kandler, D. Scheuvens, and T. Nousiainen, “Single scattering by realistic, inhomogeneous mineral dust particles with stereogrammetric shapes,” Atmos. Chem. Phys. 14(1), 143–157 (2014).
[Crossref]

Kaneyasu, N.

T. Murayama, H. Okamoto, N. Kaneyasu, H. Kamataki, and K. Miura, “Application of lidar depolarization measurement in the atmospheric boundary layer: Effects of dust and sea-salt particles,” J. Geophys. Res. 104(D24), 31781–31792 (1999).
[Crossref]

Kattawar, G. W.

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Optical tunneling by arbitrary macroscopic three-dimensional objects,” Phys. Rev. A 92(1), 013814 (2015).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 116(2), 169–183 (2013).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “A numerical combination of extended boundary condition method and invariant imbedding method to light scattering by large spheroids and cylinders,” J. Quant. Spectrosc. Radiat. Transf. 123, 17–22 (2013).
[Crossref]

Kemppinen, O.

E. Järvinen, O. Kemppinen, T. Nousiainen, T. Kociok, O. Möhler, T. Leisner, and M. Schnaiter, “Laboratory investigations of mineral dust near-backscattering depolarization ratios,” J. Quant. Spectrosc. Radiat. Transf. 178, 192–208 (2016).
[Crossref]

Klepel, A.

M. Haarig, A. Ansmann, D. Althausen, A. Klepel, S. Groß, V. Freudenthaler, C. Toledano, R.-E. Mamouri, D. A. Farrell, D. A. Prescod, E. Marinou, S. P. Burton, J. Gasteiger, R. Engelmann, and H. Baars, “Triple-wavelength depolarization-ratio profiling of Saharan dust over Barbados during SALTRACE in 2013 and 2014,” Atmos. Chem. Phys. 17(17), 10767–10794 (2017).
[Crossref]

Kociok, T.

E. Järvinen, O. Kemppinen, T. Nousiainen, T. Kociok, O. Möhler, T. Leisner, and M. Schnaiter, “Laboratory investigations of mineral dust near-backscattering depolarization ratios,” J. Quant. Spectrosc. Radiat. Transf. 178, 192–208 (2016).
[Crossref]

Kuehn, R.

Leisner, T.

E. Järvinen, O. Kemppinen, T. Nousiainen, T. Kociok, O. Möhler, T. Leisner, and M. Schnaiter, “Laboratory investigations of mineral dust near-backscattering depolarization ratios,” J. Quant. Spectrosc. Radiat. Transf. 178, 192–208 (2016).
[Crossref]

Li, Z.

Lin, B.

Lindqvist, H.

H. Lindqvist, O. Jokinen, K. Kandler, D. Scheuvens, and T. Nousiainen, “Single scattering by realistic, inhomogeneous mineral dust particles with stereogrammetric shapes,” Atmos. Chem. Phys. 14(1), 143–157 (2014).
[Crossref]

Liu, D.

D. Liu, Y. Yang, Y. Zhang, Z. Cheng, Z. Wang, J. Luo, L. Su, L. Yang, Y. Shen, J. Bai, and K. Wang, “Pattern recognition model for aerosol classification with atmospheric backscatter lidars: principles and simulations,” J. Appl. Remote Sens. 9(1), 096006 (2015).
[Crossref]

Liu, L.

M. I. Mishchenko, J. M. Dlugach, M. A. Yurkin, L. Bi, B. Cairns, L. Liu, R. L. Panetta, L. D. Travis, P. Yang, and N. T. Zakharova, “First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media,” Phys. Rep. 632, 1–75 (2016).
[Crossref]

M. I. Mishchenko, J. M. Dlugach, and L. Liu, “Linear depolarization of lidar returns by aged smoke particles,” Appl. Opt. 55(35), 9968–9973 (2016).
[Crossref] [PubMed]

M. I. Mishchenko, L. Liu, and D. W. Mackowski, “T-matrix modeling of linear depolarization by morphologically complex soot and soot-containing aerosols,” J. Quant. Spectrosc. Radiat. Transf. 123(4), 135–144 (2013).
[Crossref]

Liu, Z.

D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO mission and CALIOP data processing algorithms,” J. Atmos. Ocean. Technol. 26(11), 2310–2323 (2009).
[Crossref]

Y. Hu, M. Vaughan, Z. Liu, B. Lin, P. Yang, D. Flittner, B. Hunt, R. Kuehn, J. Huang, D. Wu, S. Rodier, K. Powell, C. Trepte, and D. Winker, “The depolarization - attenuated backscatter relation: CALIPSO lidar measurements vs. theory,” Opt. Express 15(9), 5327–5332 (2007).
[Crossref] [PubMed]

Lock, J. A.

F. Xu, J. A. Lock, and G. Gouesbet, “Debye series for light scattering by a nonspherical particle,” Phys. Rev. A 81(4), 043824 (2010).
[Crossref]

Luo, J.

D. Liu, Y. Yang, Y. Zhang, Z. Cheng, Z. Wang, J. Luo, L. Su, L. Yang, Y. Shen, J. Bai, and K. Wang, “Pattern recognition model for aerosol classification with atmospheric backscatter lidars: principles and simulations,” J. Appl. Remote Sens. 9(1), 096006 (2015).
[Crossref]

Mackowski, D. W.

M. I. Mishchenko, L. Liu, and D. W. Mackowski, “T-matrix modeling of linear depolarization by morphologically complex soot and soot-containing aerosols,” J. Quant. Spectrosc. Radiat. Transf. 123(4), 135–144 (2013).
[Crossref]

D. W. Mackowski and M. I. Mishchenko, “A multiple sphere T-matrix Fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2182–2192 (2011).
[Crossref]

Mamouri, R.-E.

M. Haarig, A. Ansmann, D. Althausen, A. Klepel, S. Groß, V. Freudenthaler, C. Toledano, R.-E. Mamouri, D. A. Farrell, D. A. Prescod, E. Marinou, S. P. Burton, J. Gasteiger, R. Engelmann, and H. Baars, “Triple-wavelength depolarization-ratio profiling of Saharan dust over Barbados during SALTRACE in 2013 and 2014,” Atmos. Chem. Phys. 17(17), 10767–10794 (2017).
[Crossref]

Marinou, E.

M. Haarig, A. Ansmann, D. Althausen, A. Klepel, S. Groß, V. Freudenthaler, C. Toledano, R.-E. Mamouri, D. A. Farrell, D. A. Prescod, E. Marinou, S. P. Burton, J. Gasteiger, R. Engelmann, and H. Baars, “Triple-wavelength depolarization-ratio profiling of Saharan dust over Barbados during SALTRACE in 2013 and 2014,” Atmos. Chem. Phys. 17(17), 10767–10794 (2017).
[Crossref]

Mehri, T.

A. Miffre, T. Mehri, M. Francis, and P. Rairoux, “UV-VIS depolarization from Arizona Test Dust particles at exact backscattering angle,” J. Quant. Spectrosc. Radiat. Transf. 169, 79–90 (2016).
[Crossref]

Miffre, A.

A. Miffre, T. Mehri, M. Francis, and P. Rairoux, “UV-VIS depolarization from Arizona Test Dust particles at exact backscattering angle,” J. Quant. Spectrosc. Radiat. Transf. 169, 79–90 (2016).
[Crossref]

Mishchenko, M. I.

M. I. Mishchenko, J. M. Dlugach, M. A. Yurkin, L. Bi, B. Cairns, L. Liu, R. L. Panetta, L. D. Travis, P. Yang, and N. T. Zakharova, “First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media,” Phys. Rep. 632, 1–75 (2016).
[Crossref]

M. I. Mishchenko, J. M. Dlugach, and L. Liu, “Linear depolarization of lidar returns by aged smoke particles,” Appl. Opt. 55(35), 9968–9973 (2016).
[Crossref] [PubMed]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Optical tunneling by arbitrary macroscopic three-dimensional objects,” Phys. Rev. A 92(1), 013814 (2015).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 116(2), 169–183 (2013).
[Crossref]

M. I. Mishchenko, L. Liu, and D. W. Mackowski, “T-matrix modeling of linear depolarization by morphologically complex soot and soot-containing aerosols,” J. Quant. Spectrosc. Radiat. Transf. 123(4), 135–144 (2013).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “A numerical combination of extended boundary condition method and invariant imbedding method to light scattering by large spheroids and cylinders,” J. Quant. Spectrosc. Radiat. Transf. 123, 17–22 (2013).
[Crossref]

M. I. Mishchenko and J. M. Dlugach, “Adhesion of mineral and soot aerosols can strongly affect their scattering and absorption properties,” Opt. Lett. 37(4), 704–706 (2012).
[Crossref] [PubMed]

D. W. Mackowski and M. I. Mishchenko, “A multiple sphere T-matrix Fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2182–2192 (2011).
[Crossref]

M. I. Mishchenko and K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25(3), 309–312 (1998).
[Crossref]

M. I. Mishchenko and L. D. Travis, “Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transf. 60(3), 309–324 (1998).
[Crossref]

M. I. Mishchenko and J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett. 20(12), 1356–1358 (1995).
[Crossref] [PubMed]

Miura, K.

T. Murayama, H. Okamoto, N. Kaneyasu, H. Kamataki, and K. Miura, “Application of lidar depolarization measurement in the atmospheric boundary layer: Effects of dust and sea-salt particles,” J. Geophys. Res. 104(D24), 31781–31792 (1999).
[Crossref]

Möhler, O.

E. Järvinen, O. Kemppinen, T. Nousiainen, T. Kociok, O. Möhler, T. Leisner, and M. Schnaiter, “Laboratory investigations of mineral dust near-backscattering depolarization ratios,” J. Quant. Spectrosc. Radiat. Transf. 178, 192–208 (2016).
[Crossref]

Murayama, T.

T. Murayama, H. Okamoto, N. Kaneyasu, H. Kamataki, and K. Miura, “Application of lidar depolarization measurement in the atmospheric boundary layer: Effects of dust and sea-salt particles,” J. Geophys. Res. 104(D24), 31781–31792 (1999).
[Crossref]

Nousiainen, T.

E. Järvinen, O. Kemppinen, T. Nousiainen, T. Kociok, O. Möhler, T. Leisner, and M. Schnaiter, “Laboratory investigations of mineral dust near-backscattering depolarization ratios,” J. Quant. Spectrosc. Radiat. Transf. 178, 192–208 (2016).
[Crossref]

H. Lindqvist, O. Jokinen, K. Kandler, D. Scheuvens, and T. Nousiainen, “Single scattering by realistic, inhomogeneous mineral dust particles with stereogrammetric shapes,” Atmos. Chem. Phys. 14(1), 143–157 (2014).
[Crossref]

Okamoto, H.

T. Murayama, H. Okamoto, N. Kaneyasu, H. Kamataki, and K. Miura, “Application of lidar depolarization measurement in the atmospheric boundary layer: Effects of dust and sea-salt particles,” J. Geophys. Res. 104(D24), 31781–31792 (1999).
[Crossref]

Omar, A.

D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO mission and CALIOP data processing algorithms,” J. Atmos. Ocean. Technol. 26(11), 2310–2323 (2009).
[Crossref]

Omar, A. H.

S. P. Burton, R. A. Ferrare, M. A. Vaughan, A. H. Omar, R. R. Rogers, C. A. Hostetler, and J. W. Hair, “Aerosol classification from airborne HSRL and comparisons with the CALIPSO vertical feature mask,” Atmos. Meas. Tech. 6(5), 1397–1412 (2013).
[Crossref]

Panetta, R. L.

M. I. Mishchenko, J. M. Dlugach, M. A. Yurkin, L. Bi, B. Cairns, L. Liu, R. L. Panetta, L. D. Travis, P. Yang, and N. T. Zakharova, “First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media,” Phys. Rep. 632, 1–75 (2016).
[Crossref]

Powell, K.

Powell, K. A.

D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO mission and CALIOP data processing algorithms,” J. Atmos. Ocean. Technol. 26(11), 2310–2323 (2009).
[Crossref]

Prescod, D. A.

M. Haarig, A. Ansmann, D. Althausen, A. Klepel, S. Groß, V. Freudenthaler, C. Toledano, R.-E. Mamouri, D. A. Farrell, D. A. Prescod, E. Marinou, S. P. Burton, J. Gasteiger, R. Engelmann, and H. Baars, “Triple-wavelength depolarization-ratio profiling of Saharan dust over Barbados during SALTRACE in 2013 and 2014,” Atmos. Chem. Phys. 17(17), 10767–10794 (2017).
[Crossref]

Rairoux, P.

A. Miffre, T. Mehri, M. Francis, and P. Rairoux, “UV-VIS depolarization from Arizona Test Dust particles at exact backscattering angle,” J. Quant. Spectrosc. Radiat. Transf. 169, 79–90 (2016).
[Crossref]

Rodier, S.

Rogers, R. R.

S. P. Burton, R. A. Ferrare, M. A. Vaughan, A. H. Omar, R. R. Rogers, C. A. Hostetler, and J. W. Hair, “Aerosol classification from airborne HSRL and comparisons with the CALIPSO vertical feature mask,” Atmos. Meas. Tech. 6(5), 1397–1412 (2013).
[Crossref]

Sassen, K.

M. I. Mishchenko and K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25(3), 309–312 (1998).
[Crossref]

K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72(12), 1848–1866 (1991).
[Crossref]

Scheuvens, D.

H. Lindqvist, O. Jokinen, K. Kandler, D. Scheuvens, and T. Nousiainen, “Single scattering by realistic, inhomogeneous mineral dust particles with stereogrammetric shapes,” Atmos. Chem. Phys. 14(1), 143–157 (2014).
[Crossref]

Schnaiter, M.

E. Järvinen, O. Kemppinen, T. Nousiainen, T. Kociok, O. Möhler, T. Leisner, and M. Schnaiter, “Laboratory investigations of mineral dust near-backscattering depolarization ratios,” J. Quant. Spectrosc. Radiat. Transf. 178, 192–208 (2016).
[Crossref]

Shen, Y.

D. Liu, Y. Yang, Y. Zhang, Z. Cheng, Z. Wang, J. Luo, L. Su, L. Yang, Y. Shen, J. Bai, and K. Wang, “Pattern recognition model for aerosol classification with atmospheric backscatter lidars: principles and simulations,” J. Appl. Remote Sens. 9(1), 096006 (2015).
[Crossref]

Smith, H. R.

H. R. Smith, P. J. Connolly, A. R. Webb, and A. J. Baran, “Exact and near backscattering measurements of the linear depolarization ratio of various ice crystal habits generated in a laboratory cloud chamber,” J. Quant. Spectrosc. Radiat. Transf. 178(2), 361–378 (2016).
[Crossref]

Su, L.

D. Liu, Y. Yang, Y. Zhang, Z. Cheng, Z. Wang, J. Luo, L. Su, L. Yang, Y. Shen, J. Bai, and K. Wang, “Pattern recognition model for aerosol classification with atmospheric backscatter lidars: principles and simulations,” J. Appl. Remote Sens. 9(1), 096006 (2015).
[Crossref]

Toledano, C.

M. Haarig, A. Ansmann, D. Althausen, A. Klepel, S. Groß, V. Freudenthaler, C. Toledano, R.-E. Mamouri, D. A. Farrell, D. A. Prescod, E. Marinou, S. P. Burton, J. Gasteiger, R. Engelmann, and H. Baars, “Triple-wavelength depolarization-ratio profiling of Saharan dust over Barbados during SALTRACE in 2013 and 2014,” Atmos. Chem. Phys. 17(17), 10767–10794 (2017).
[Crossref]

Travis, L. D.

M. I. Mishchenko, J. M. Dlugach, M. A. Yurkin, L. Bi, B. Cairns, L. Liu, R. L. Panetta, L. D. Travis, P. Yang, and N. T. Zakharova, “First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media,” Phys. Rep. 632, 1–75 (2016).
[Crossref]

M. I. Mishchenko and L. D. Travis, “Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transf. 60(3), 309–324 (1998).
[Crossref]

Trepte, C.

Vaughan, M.

Vaughan, M. A.

S. P. Burton, R. A. Ferrare, M. A. Vaughan, A. H. Omar, R. R. Rogers, C. A. Hostetler, and J. W. Hair, “Aerosol classification from airborne HSRL and comparisons with the CALIPSO vertical feature mask,” Atmos. Meas. Tech. 6(5), 1397–1412 (2013).
[Crossref]

D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO mission and CALIOP data processing algorithms,” J. Atmos. Ocean. Technol. 26(11), 2310–2323 (2009).
[Crossref]

Wang, K.

D. Liu, Y. Yang, Y. Zhang, Z. Cheng, Z. Wang, J. Luo, L. Su, L. Yang, Y. Shen, J. Bai, and K. Wang, “Pattern recognition model for aerosol classification with atmospheric backscatter lidars: principles and simulations,” J. Appl. Remote Sens. 9(1), 096006 (2015).
[Crossref]

Wang, Z.

D. Liu, Y. Yang, Y. Zhang, Z. Cheng, Z. Wang, J. Luo, L. Su, L. Yang, Y. Shen, J. Bai, and K. Wang, “Pattern recognition model for aerosol classification with atmospheric backscatter lidars: principles and simulations,” J. Appl. Remote Sens. 9(1), 096006 (2015).
[Crossref]

Webb, A. R.

H. R. Smith, P. J. Connolly, A. R. Webb, and A. J. Baran, “Exact and near backscattering measurements of the linear depolarization ratio of various ice crystal habits generated in a laboratory cloud chamber,” J. Quant. Spectrosc. Radiat. Transf. 178(2), 361–378 (2016).
[Crossref]

Winker, D.

Winker, D. M.

D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO mission and CALIOP data processing algorithms,” J. Atmos. Ocean. Technol. 26(11), 2310–2323 (2009).
[Crossref]

Wriedt, T.

T. Wriedt, “Using the T-matrix method for light scattering computations by non-axisymmetric particles: superellipsoids and realistically shaped particles,” Part. Part. Syst. Charact. 19(4), 256–268 (2002).
[Crossref]

Wu, D.

Xu, F.

F. Xu, J. A. Lock, and G. Gouesbet, “Debye series for light scattering by a nonspherical particle,” Phys. Rev. A 81(4), 043824 (2010).
[Crossref]

Yang, L.

D. Liu, Y. Yang, Y. Zhang, Z. Cheng, Z. Wang, J. Luo, L. Su, L. Yang, Y. Shen, J. Bai, and K. Wang, “Pattern recognition model for aerosol classification with atmospheric backscatter lidars: principles and simulations,” J. Appl. Remote Sens. 9(1), 096006 (2015).
[Crossref]

Yang, P.

M. I. Mishchenko, J. M. Dlugach, M. A. Yurkin, L. Bi, B. Cairns, L. Liu, R. L. Panetta, L. D. Travis, P. Yang, and N. T. Zakharova, “First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media,” Phys. Rep. 632, 1–75 (2016).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Optical tunneling by arbitrary macroscopic three-dimensional objects,” Phys. Rev. A 92(1), 013814 (2015).
[Crossref]

L. Bi and P. Yang, “Impact of calcification state on the inherent optical properties of Emiliania huxleyi coccoliths and coccolithophores,” J. Quant. Spectrosc. Radiat. Transf. 155, 10–21 (2015).
[Crossref]

L. Bi and P. Yang, “Accurate simulation of the optical properties of atmospheric ice crystals with invariant imbedding T-matrix method,” J. Quant. Spectrosc. Radiat. Transf. 138, 17–35 (2014).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “A numerical combination of extended boundary condition method and invariant imbedding method to light scattering by large spheroids and cylinders,” J. Quant. Spectrosc. Radiat. Transf. 123, 17–22 (2013).
[Crossref]

L. Bi and P. Yang, “Modeling of light scattering by biconcave and deformed red blood cells with the invariant imbedding T-matrix method,” J. Biomed. Opt. 18(5), 055001 (2013).
[Crossref] [PubMed]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 116(2), 169–183 (2013).
[Crossref]

C. Zhou, P. Yang, A. E. Dessler, Y. Hu, and B. A. Baum, “Study of horizontally oriented ice crystals with CALIPSO observations and comparison with Monte Carlo radiative transfer Simulations,” J. Appl. Meteorol. Climatol. 51(7), 1426–1439 (2012).
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Y. Hu, M. Vaughan, Z. Liu, B. Lin, P. Yang, D. Flittner, B. Hunt, R. Kuehn, J. Huang, D. Wu, S. Rodier, K. Powell, C. Trepte, and D. Winker, “The depolarization - attenuated backscatter relation: CALIPSO lidar measurements vs. theory,” Opt. Express 15(9), 5327–5332 (2007).
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Yang, Y.

D. Liu, Y. Yang, Y. Zhang, Z. Cheng, Z. Wang, J. Luo, L. Su, L. Yang, Y. Shen, J. Bai, and K. Wang, “Pattern recognition model for aerosol classification with atmospheric backscatter lidars: principles and simulations,” J. Appl. Remote Sens. 9(1), 096006 (2015).
[Crossref]

Young, S. A.

D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO mission and CALIOP data processing algorithms,” J. Atmos. Ocean. Technol. 26(11), 2310–2323 (2009).
[Crossref]

Yurkin, M. A.

M. I. Mishchenko, J. M. Dlugach, M. A. Yurkin, L. Bi, B. Cairns, L. Liu, R. L. Panetta, L. D. Travis, P. Yang, and N. T. Zakharova, “First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media,” Phys. Rep. 632, 1–75 (2016).
[Crossref]

M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2234–2247 (2011).
[Crossref]

Zakharova, N. T.

M. I. Mishchenko, J. M. Dlugach, M. A. Yurkin, L. Bi, B. Cairns, L. Liu, R. L. Panetta, L. D. Travis, P. Yang, and N. T. Zakharova, “First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media,” Phys. Rep. 632, 1–75 (2016).
[Crossref]

Zhang, Y.

D. Liu, Y. Yang, Y. Zhang, Z. Cheng, Z. Wang, J. Luo, L. Su, L. Yang, Y. Shen, J. Bai, and K. Wang, “Pattern recognition model for aerosol classification with atmospheric backscatter lidars: principles and simulations,” J. Appl. Remote Sens. 9(1), 096006 (2015).
[Crossref]

Zhou, C.

C. Zhou, P. Yang, A. E. Dessler, Y. Hu, and B. A. Baum, “Study of horizontally oriented ice crystals with CALIPSO observations and comparison with Monte Carlo radiative transfer Simulations,” J. Appl. Meteorol. Climatol. 51(7), 1426–1439 (2012).
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M. Haarig, A. Ansmann, D. Althausen, A. Klepel, S. Groß, V. Freudenthaler, C. Toledano, R.-E. Mamouri, D. A. Farrell, D. A. Prescod, E. Marinou, S. P. Burton, J. Gasteiger, R. Engelmann, and H. Baars, “Triple-wavelength depolarization-ratio profiling of Saharan dust over Barbados during SALTRACE in 2013 and 2014,” Atmos. Chem. Phys. 17(17), 10767–10794 (2017).
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S. P. Burton, R. A. Ferrare, M. A. Vaughan, A. H. Omar, R. R. Rogers, C. A. Hostetler, and J. W. Hair, “Aerosol classification from airborne HSRL and comparisons with the CALIPSO vertical feature mask,” Atmos. Meas. Tech. 6(5), 1397–1412 (2013).
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M. I. Mishchenko and K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25(3), 309–312 (1998).
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J. Appl. Meteorol. Climatol. (1)

C. Zhou, P. Yang, A. E. Dessler, Y. Hu, and B. A. Baum, “Study of horizontally oriented ice crystals with CALIPSO observations and comparison with Monte Carlo radiative transfer Simulations,” J. Appl. Meteorol. Climatol. 51(7), 1426–1439 (2012).
[Crossref]

J. Appl. Remote Sens. (1)

D. Liu, Y. Yang, Y. Zhang, Z. Cheng, Z. Wang, J. Luo, L. Su, L. Yang, Y. Shen, J. Bai, and K. Wang, “Pattern recognition model for aerosol classification with atmospheric backscatter lidars: principles and simulations,” J. Appl. Remote Sens. 9(1), 096006 (2015).
[Crossref]

J. Atmos. Ocean. Technol. (1)

D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO mission and CALIOP data processing algorithms,” J. Atmos. Ocean. Technol. 26(11), 2310–2323 (2009).
[Crossref]

J. Biomed. Opt. (1)

L. Bi and P. Yang, “Modeling of light scattering by biconcave and deformed red blood cells with the invariant imbedding T-matrix method,” J. Biomed. Opt. 18(5), 055001 (2013).
[Crossref] [PubMed]

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T. Murayama, H. Okamoto, N. Kaneyasu, H. Kamataki, and K. Miura, “Application of lidar depolarization measurement in the atmospheric boundary layer: Effects of dust and sea-salt particles,” J. Geophys. Res. 104(D24), 31781–31792 (1999).
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E. Järvinen, O. Kemppinen, T. Nousiainen, T. Kociok, O. Möhler, T. Leisner, and M. Schnaiter, “Laboratory investigations of mineral dust near-backscattering depolarization ratios,” J. Quant. Spectrosc. Radiat. Transf. 178, 192–208 (2016).
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A. Miffre, T. Mehri, M. Francis, and P. Rairoux, “UV-VIS depolarization from Arizona Test Dust particles at exact backscattering angle,” J. Quant. Spectrosc. Radiat. Transf. 169, 79–90 (2016).
[Crossref]

L. Bi and P. Yang, “Impact of calcification state on the inherent optical properties of Emiliania huxleyi coccoliths and coccolithophores,” J. Quant. Spectrosc. Radiat. Transf. 155, 10–21 (2015).
[Crossref]

M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2234–2247 (2011).
[Crossref]

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[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 116(2), 169–183 (2013).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “A numerical combination of extended boundary condition method and invariant imbedding method to light scattering by large spheroids and cylinders,” J. Quant. Spectrosc. Radiat. Transf. 123, 17–22 (2013).
[Crossref]

L. Bi and P. Yang, “Accurate simulation of the optical properties of atmospheric ice crystals with invariant imbedding T-matrix method,” J. Quant. Spectrosc. Radiat. Transf. 138, 17–35 (2014).
[Crossref]

M. I. Mishchenko and L. D. Travis, “Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transf. 60(3), 309–324 (1998).
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Opt. Express (1)

Opt. Lett. (2)

Part. Part. Syst. Charact. (1)

T. Wriedt, “Using the T-matrix method for light scattering computations by non-axisymmetric particles: superellipsoids and realistically shaped particles,” Part. Part. Syst. Charact. 19(4), 256–268 (2002).
[Crossref]

Phys. Rep. (1)

M. I. Mishchenko, J. M. Dlugach, M. A. Yurkin, L. Bi, B. Cairns, L. Liu, R. L. Panetta, L. D. Travis, P. Yang, and N. T. Zakharova, “First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media,” Phys. Rep. 632, 1–75 (2016).
[Crossref]

Phys. Rev. A (2)

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Optical tunneling by arbitrary macroscopic three-dimensional objects,” Phys. Rev. A 92(1), 013814 (2015).
[Crossref]

F. Xu, J. A. Lock, and G. Gouesbet, “Debye series for light scattering by a nonspherical particle,” Phys. Rev. A 81(4), 043824 (2010).
[Crossref]

Other (3)

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, 2002).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

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Figures (13)

Fig. 1
Fig. 1 The geometries of supper-ellipsoidal particles with different aspect ratios and roundness parameters: (a) shape variation from a sphere to prolate and oblate spheroids; (b) shape variation from a prolate spheroid to cube-like and octahedron-like shapes, achieved by changing the parameters n and e ; (c) and (d) are similar to (b) except that the aspect ratios are different.
Fig. 2
Fig. 2 Top: Depolarization ratio (%) as a function of the aspect ratio and the size parameter of randomly oriented spheroids. Bottom: Depolarization ratio (%) of spheroids with close-to-unity aspect ratios at three size parameters. The refractive index is 1.55 + i0.0003.
Fig. 3
Fig. 3 Depolarization ratio with respect to the incident angle for spheroids with close-to-unity aspect ratios ( a / c = 0.95 , a / c = 1.05 ).
Fig. 4
Fig. 4 Depolarization ratio (%) as a function of the aspect ratio and the size parameter of randomly oriented spheroids at five different refractive indices with the same imaginary part: (a) 1.1 + i0.001; (b) 1.3 + i0.001; (c) 1.5 + i0.001; (d) 1.7 + i0.001; (e) 2.0 + i0.001.
Fig. 5
Fig. 5 Depolarization ratio (%) as a function of the aspect ratio and the size parameter of randomly oriented spheroids at five different refractive indices with the same real part: (a) 1.5 + i10−7; (b) 1.5 + i0.001; (c) 1.5 + i0.01; (d) 1.5 + i0.1; (e) 1.5 + i0.5.
Fig. 6
Fig. 6 Similar to Fig. 4, but for an aspect ratio range from 0.8 to 1.2 with a fine resolution of refractive index.
Fig. 7
Fig. 7 Comparison of depolarization ratios for different shape variations from spheroids to cube-like and octahedron-like particles. The aspect ratios of spheroids are: 0.5 (a), 0.95 (b), 1.0 (c), 1.05 (d), and 2.0 (e). The refractive index is 1.33 + i10−7.
Fig. 8
Fig. 8 Comparison of depolarization ratios for different shape variations from spheroids to cube-like and octahedron-like particles. The aspect ratios of spheroids are: 0.5 (a), 0.95 (b), 1.0 (c), 1.05 (d), and 2.0 (e). The refractive index is 1.55 + i0.0003.
Fig. 9
Fig. 9 Comparison of depolarization ratios for shape variations from octahedral to concave particles. The aspect ratios of spheroids are: 0.5 (a), 1.0 (c), and 2.0 (c). The refractive index is 1.55 + i0.0003.
Fig. 10
Fig. 10 Comparison of depolarization ratios as a function of aspect ratio ranging from 0.5 to 2.0 for three roundness parameters (0.5, 1.8 and 2.5).
Fig. 11
Fig. 11 Comparison of depolarization ratios as a function of the refractive index for nine representative shapes with different aspect ratios and roundness parameters. The imaginary part of refractive index is fixed to be 10−7.
Fig. 12
Fig. 12 Similar to Fig. 11, except that the results are size-integration values. The wavelength is assumed to be 0.532 μ m . The geometric standard deviation is 1.5. Note, the maximum value of color bar is 60%.
Fig. 13
Fig. 13 Similar to Fig. 11, except that the results are size-integration values. The wavelength is assumed to be 0.532 μ m . The geometric standard deviation is 2.2. Note, the maximum value of color bar is 60%.

Equations (5)

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[ ( x a ) 2 / e + ( y b ) 2 / e ] e / n + [ z c ] 2 / n = 1 ,
[ I s c a ( θ ) Q s c a ( θ ) U s c a ( θ ) V s c a ( θ ) ] [ P 11 ( θ ) P 12 ( θ ) 0 0 P 21 ( θ ) P 22 ( θ ) 0 0 0 0 P 33 ( θ ) P 34 ( θ ) 0 0 P 43 ( θ ) P 44 ( θ ) ] [ I i n c Q i n c U i n c V i n c ] ,
LDR( θ )= I s c a ( θ ) Q s c a ( θ ) I s c a ( θ ) + Q s c a ( θ ) = P 11 ( θ ) P 22 ( θ ) P 11 ( θ ) + 2 P 12 ( θ ) + P 22 ( θ ) .
LDR ( 180 ° ) = 1 P 22 ( 180 ° ) / P 11 ( 180 ° ) 1 + P 22 ( 180 ° ) / P 11 ( 180 ° ) .
d N d ln r = N 0 2 π ln σ exp [ ( ln r ln r m ) 2 2 ( ln σ ) 2 ] ,

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