Abstract

We investigate the accuracy in retrieving the real refractive index of submicron aerosol particles, at a visible wavelength, from near critical angle reflectance measurements of a dilute suspension of the aerosol. A coherent scattering model (CSM) is used to model the coherent reflectance from the colloidal suspension. We use an extension of the model for polydisperse particles to properly account for the modified size distribution close to the incident medium to colloid interface. We perform a rigorous sensitivity analysis, for both the monodisperse and polydisperse models, to determine how experimental uncertainties propagate into uncertainty in the retrieval of real refractive index. The effect of non-spherical scattering was included in the sensitivity analysis by using T-matrix methods. Experimental reflectance data, at a wavelength of 635 nm, were obtained for monodisperse spherical latex particles, a polydisperse sand sample and a polydisperse volcanic ash sample. We show that the retrieved real refractive index for these particles is consistent with values obtained using other techniques.

© 2016 Optical Society of America

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Retrieving radius, concentration, optical depth, and mass of different types of aerosols from high-resolution infrared nadir spectra

Lieven Clarisse, Daniel Hurtmans, Alfred J. Prata, Federico Karagulian, Cathy Clerbaux, Martine De Mazière, and Pierre-François Coheur
Appl. Opt. 49(19) 3713-3722 (2010)

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    [Crossref]
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    [Crossref]
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  21. J. Keller, W. B. F. Ryan, D. Ninkovich, and R. Altherr, “Explosive volcanic activity in the Mediterranean over the past 200,000 yr as recorded in deep-sea sediments,” Geol. Soc. Am. Bull. 89, 591–604 (1978).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  26. R. G. Barrera and A. García-Valenzuela, “Coherent reflectance in a system of random mie scatters and its relation to the effective-medium approach,” J. Opt. Soc. Am. A 20, 296–311 (2003).
    [Crossref]
  27. E. Gutiérrez-Reyes, A. García-Valenzuela, and R. G. Barrera, “Overview of an effective-medium approach to the reflection and refraction of light at a turbid colloidal half-space,” Phys. Status Solidi B 249, 1140–1147 (2012).
    [Crossref]
  28. R. G. Barrera, A. Reyes-Coronado, and A. García-Valenzuela, “Nonlocal nature of the electrodynamic response of colloidal systems,” Phys. Rev. B 75, 184202 (2007).
    [Crossref]
  29. R. G. Barrera, A. García-Valenzuela, C. Sánchez-Pérez, A. Reyes-Coronado, and E. R. Mendez, “Coherent reflection of light from a turbid suspension of particles in an internal reflection configuration: Theory versus experiment,” Opt. Express 18, 6724 (2005).
  30. A. García-Valenzuela, R. G. Barrera, and E. Gutiérrez-Reyes, “Rigorous theoretical framework for particle sizing in turbid colloids using light refraction,” Opt. Express 16, 19741–19756 (2008).
    [Crossref] [PubMed]
  31. A. García-Valenzuela, C. Sánchez-Pérez, and E. Gutiérrez-Reyes, “On the retrieval of particle size from the effective optical properties of colloids,” Physica B 405, 3016–3021 (2010).
    [Crossref]
  32. C. Sánchez-Pérez, A. García-Valenzuela, R. Y. Sato-Berrú, J. O. Flores-Flores, and R. G. Barrera, “Sizing colloidal particles from their contribution to the effective refractive index: Experimental results,” J. Phys. Conf. Ser.274 (2011).
    [Crossref]
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  34. 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. Transfer 60, 309–324 (1998).
    [Crossref]
  35. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983).
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  37. P. Grossel, J. M. Vigoureux, and F. Baïda, “Nonlocal approach to scattering in a one-dimensional problem,” Phys. Rev. A 50, 3627–3637 (1994).
    [Crossref] [PubMed]
  38. J. M. Vigoureux, “Use of Einstein’s addition law in studies of reflection by stratified planar structures,” J. Opt. Soc. Am. A 9, 1313–1319 (1992).
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  40. M. Xiaoyan, Q. L. Jun, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
    [Crossref]
  41. S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater. 29, 1481–1490 (2007).
    [Crossref]

2015 (1)

J. G. C. Ball, B. E. Reed, R. G. Grainger, D. M. Peters, T. A. Mather, and D. M. Pyle, “Measurements of the complex refractive index of volcanic ash at 450, 546.7 and 650 nm,” J. Geophys. Res. Atmos. 120, 7747–7757 (2015).
[Crossref]

2014 (1)

S. K. Ebmeier, A. M. Sayer, R. G. Grainger, T. A. Mather, and E. Carboni, “Systematic satellite observations of the impact of aerosols from passive volcanic degassing on local cloud properties,” Atmos. Chem. Phys. 14, 10601–10618 (2014).
[Crossref]

2013 (1)

I. Niskanen and J. R. K. Erik Peiponen, “Determination of the refractive index of microparticles by utilizing light dispersion properties of the particle and an immersion liquid,” Talanta 115, 68–73 (2013).
[Crossref] [PubMed]

2012 (2)

E. Gutiérrez-Reyes, A. García-Valenzuela, and R. G. Barrera, “Overview of an effective-medium approach to the reflection and refraction of light at a turbid colloidal half-space,” Phys. Status Solidi B 249, 1140–1147 (2012).
[Crossref]

K. Turnbull, B. Johnson, F. Marenco, J. Haywood, A. Minikin, B. Weinzierl, H. Schlager, U. Schumann, S. Leadbetter, and A. Woolley, “A case study of observations of volcanic ash from the Eyjafjallajökull eruption: 1. In situ airborne observations,” J. Geophys. Res. 117, D20 (2012).

2010 (3)

L. Clarisse, D. Hurtmans, A. J. Prata, F. Karagulian, C. Clerbaux, M. De Maziere, and P.-F. Coheur, “Retrieving radius, concentration, optical depth, and mass of different types of aerosols from high-resolution infrared nadir spectra,” Appl. Optics 49, 3713–3722 (2010).
[Crossref]

G. Gangale, A. J. Prata, and L. Clarisse, “The infrared spectral signature of volcanic ash determined from high-spectral resolution satellite measurements,” Remote Sens. Environ. 114, 414–425 (2010).
[Crossref]

A. García-Valenzuela, C. Sánchez-Pérez, and E. Gutiérrez-Reyes, “On the retrieval of particle size from the effective optical properties of colloids,” Physica B 405, 3016–3021 (2010).
[Crossref]

2008 (1)

2007 (3)

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater. 29, 1481–1490 (2007).
[Crossref]

R. G. Barrera, A. Reyes-Coronado, and A. García-Valenzuela, “Nonlocal nature of the electrodynamic response of colloidal systems,” Phys. Rev. B 75, 184202 (2007).
[Crossref]

I. Niskanen, J. Räty, and K. Erik Peiponen, “Measurement of refractive index of isotropic particles by incorporating a multifunction spectrophotometer and immersion liquid method,” Appl. Opt. 46, 5404–5407 (2007).
[Crossref] [PubMed]

2006 (1)

C. J. Horwell and P. J. Baxter, “The respiratory health hazards of volcanic ash: a review for volcanic risk mitigation,” Bull. Volcanol. 69, 1–24 (2006).
[Crossref]

2005 (2)

G. E. Thomas, S. F. Bass, R. G. Grainger, and A. Lambert, “Retrieval of aerosol refractive index from extinction spectra with a damped harmonic-oscillator band model,” Appl. Opt. 44, 1332–1341 (2005).
[Crossref] [PubMed]

R. G. Barrera, A. García-Valenzuela, C. Sánchez-Pérez, A. Reyes-Coronado, and E. R. Mendez, “Coherent reflection of light from a turbid suspension of particles in an internal reflection configuration: Theory versus experiment,” Opt. Express 18, 6724 (2005).

2003 (2)

R. G. Barrera and A. García-Valenzuela, “Coherent reflectance in a system of random mie scatters and its relation to the effective-medium approach,” J. Opt. Soc. Am. A 20, 296–311 (2003).
[Crossref]

M. Xiaoyan, Q. L. Jun, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[Crossref]

1999 (1)

N. A. Krotkov, D. E. Flittner, A. J. Krueger, A. Kostinski, C. Riley, W. Rose, and O. Torres, “Effect of particle non-sphericity on satellite monitoring of drifting volcanic ash clouds,” J. Quant. Spectrosc. Radiat. Transfer 63, 613–630 (1999).
[Crossref]

1998 (1)

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. Transfer 60, 309–324 (1998).
[Crossref]

1994 (1)

P. Grossel, J. M. Vigoureux, and F. Baïda, “Nonlocal approach to scattering in a one-dimensional problem,” Phys. Rev. A 50, 3627–3637 (1994).
[Crossref] [PubMed]

1992 (1)

1983 (1)

E. M. Patterson, C. O. Pollard, and I. Galindo, “Optical-properties of the ashes from El-Chichon volcano,” Geophys. Res. Lett. 10, 317–320 (1983).
[Crossref]

1981 (1)

E. M. Patterson, “Measurements of the imaginary part of the refractive index between 300 and 700 nanometers for Mount St. Helens ash,” Science 211, 836–838 (1981).
[Crossref] [PubMed]

1978 (1)

J. Keller, W. B. F. Ryan, D. Ninkovich, and R. Altherr, “Explosive volcanic activity in the Mediterranean over the past 200,000 yr as recorded in deep-sea sediments,” Geol. Soc. Am. Bull. 89, 591–604 (1978).
[Crossref]

1977 (1)

O. B. Toon, J. B. Pollack, and C. Sagan, “Physical properties of the particles composing the Martian dust storm of 1971–1972,” Icarus 30, 663–696 (1977).
[Crossref]

1975 (1)

W. Egan, T. Hilgeman, and K. Pang, “Ultraviolet complex refractive-index of Martian dust — Laboratory measurements of terrestrial analogs,” Icarus 25, 344–355 (1975).
[Crossref]

1973 (2)

F. E. Volz, “Infrared optical constants of ammonium sulfate, Sahara dust, volcanic pumice and flyash,” Appl. Optics 12, 564–568 (1973).
[Crossref]

J. B. Pollack, O. B. Toon, and B. N. Khare, “Optical properties of some terrestrial rocks and glasses,” Icarus 19, 372–389 (1973).
[Crossref]

1963 (1)

L. Kittleman, “Glass-bead silica determination for a suite of volcanic rocks from the Owyee Plateau, Oregon,” Geol. Soc. Am. Bull. 73, 1405 (1963).

Altherr, R.

J. Keller, W. B. F. Ryan, D. Ninkovich, and R. Altherr, “Explosive volcanic activity in the Mediterranean over the past 200,000 yr as recorded in deep-sea sediments,” Geol. Soc. Am. Bull. 89, 591–604 (1978).
[Crossref]

Artaxo, P.

P. Forster, V. Ramaswamy, P. Artaxo, T. Bernsten, R. Betts, D. Fahey, J. Haywood, J. Lean, D. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. V. Dorland, “Changes in atmospheric consituents and in radiative forcing,” in Climate Change 2007: The Physical Science Basis. Contribution of Working Group 1 to the Fourth assesment report of Intergovernmental Panel on Climate Change, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miler, eds. (Cambridge University Press, 2007).

Baïda, F.

P. Grossel, J. M. Vigoureux, and F. Baïda, “Nonlocal approach to scattering in a one-dimensional problem,” Phys. Rev. A 50, 3627–3637 (1994).
[Crossref] [PubMed]

Ball, J. G. C.

J. G. C. Ball, B. E. Reed, R. G. Grainger, D. M. Peters, T. A. Mather, and D. M. Pyle, “Measurements of the complex refractive index of volcanic ash at 450, 546.7 and 650 nm,” J. Geophys. Res. Atmos. 120, 7747–7757 (2015).
[Crossref]

Barrera, R. G.

E. Gutiérrez-Reyes, A. García-Valenzuela, and R. G. Barrera, “Overview of an effective-medium approach to the reflection and refraction of light at a turbid colloidal half-space,” Phys. Status Solidi B 249, 1140–1147 (2012).
[Crossref]

A. García-Valenzuela, R. G. Barrera, and E. Gutiérrez-Reyes, “Rigorous theoretical framework for particle sizing in turbid colloids using light refraction,” Opt. Express 16, 19741–19756 (2008).
[Crossref] [PubMed]

R. G. Barrera, A. Reyes-Coronado, and A. García-Valenzuela, “Nonlocal nature of the electrodynamic response of colloidal systems,” Phys. Rev. B 75, 184202 (2007).
[Crossref]

R. G. Barrera, A. García-Valenzuela, C. Sánchez-Pérez, A. Reyes-Coronado, and E. R. Mendez, “Coherent reflection of light from a turbid suspension of particles in an internal reflection configuration: Theory versus experiment,” Opt. Express 18, 6724 (2005).

R. G. Barrera and A. García-Valenzuela, “Coherent reflectance in a system of random mie scatters and its relation to the effective-medium approach,” J. Opt. Soc. Am. A 20, 296–311 (2003).
[Crossref]

C. Sánchez-Pérez, A. García-Valenzuela, R. Y. Sato-Berrú, J. O. Flores-Flores, and R. G. Barrera, “Sizing colloidal particles from their contribution to the effective refractive index: Experimental results,” J. Phys. Conf. Ser.274 (2011).
[Crossref]

A. García-Valenzuela, C. Sánchez-Pérez, R. G. Barrera, and A. Reyes-Coronado, “Surface Effects on the Coherent Reflection of Light from a Polydisperse Colloid,” in Progress in Electromagnetics Research Symposium 2005 (PIERS Online, 2005), pp. 650–653.

Bass, S. F.

Baxter, P. J.

C. J. Horwell and P. J. Baxter, “The respiratory health hazards of volcanic ash: a review for volcanic risk mitigation,” Bull. Volcanol. 69, 1–24 (2006).
[Crossref]

Becke, F. J. K.

F. J. K. Becke, “Beziehungen zwischen Dynamometamorphose und Moldkularcolumen,” Neues Jahrbuch für Mineralogie pp. 182–183 (1896).

Bernsten, T.

P. Forster, V. Ramaswamy, P. Artaxo, T. Bernsten, R. Betts, D. Fahey, J. Haywood, J. Lean, D. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. V. Dorland, “Changes in atmospheric consituents and in radiative forcing,” in Climate Change 2007: The Physical Science Basis. Contribution of Working Group 1 to the Fourth assesment report of Intergovernmental Panel on Climate Change, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miler, eds. (Cambridge University Press, 2007).

Betts, R.

P. Forster, V. Ramaswamy, P. Artaxo, T. Bernsten, R. Betts, D. Fahey, J. Haywood, J. Lean, D. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. V. Dorland, “Changes in atmospheric consituents and in radiative forcing,” in Climate Change 2007: The Physical Science Basis. Contribution of Working Group 1 to the Fourth assesment report of Intergovernmental Panel on Climate Change, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miler, eds. (Cambridge University Press, 2007).

Blong, R.

R. Blong, Volcanic Hazards: A Sourcebook on the Effects of Eruptions (Academic Press, 1984).

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983).

Brock, R. S.

M. Xiaoyan, Q. L. Jun, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[Crossref]

Carboni, E.

S. K. Ebmeier, A. M. Sayer, R. G. Grainger, T. A. Mather, and E. Carboni, “Systematic satellite observations of the impact of aerosols from passive volcanic degassing on local cloud properties,” Atmos. Chem. Phys. 14, 10601–10618 (2014).
[Crossref]

R. G. Grainger, D. M. Peters, G. E. Thomas, A. J. A. Smith, R. Siddans, E. Carboni, and A. Dudhia, Remote Sensing of Volcanoes and Volcanic Processes: Integrating Observation and Modelling (Geol. Soc. London Spec. Publ., 2013), vol. 380, chap. Measuring volcanic plume and ash properties from space, pp. 293–320.

Clarisse, L.

L. Clarisse, D. Hurtmans, A. J. Prata, F. Karagulian, C. Clerbaux, M. De Maziere, and P.-F. Coheur, “Retrieving radius, concentration, optical depth, and mass of different types of aerosols from high-resolution infrared nadir spectra,” Appl. Optics 49, 3713–3722 (2010).
[Crossref]

G. Gangale, A. J. Prata, and L. Clarisse, “The infrared spectral signature of volcanic ash determined from high-spectral resolution satellite measurements,” Remote Sens. Environ. 114, 414–425 (2010).
[Crossref]

Clerbaux, C.

L. Clarisse, D. Hurtmans, A. J. Prata, F. Karagulian, C. Clerbaux, M. De Maziere, and P.-F. Coheur, “Retrieving radius, concentration, optical depth, and mass of different types of aerosols from high-resolution infrared nadir spectra,” Appl. Optics 49, 3713–3722 (2010).
[Crossref]

Coheur, P.-F.

L. Clarisse, D. Hurtmans, A. J. Prata, F. Karagulian, C. Clerbaux, M. De Maziere, and P.-F. Coheur, “Retrieving radius, concentration, optical depth, and mass of different types of aerosols from high-resolution infrared nadir spectra,” Appl. Optics 49, 3713–3722 (2010).
[Crossref]

De Maziere, M.

L. Clarisse, D. Hurtmans, A. J. Prata, F. Karagulian, C. Clerbaux, M. De Maziere, and P.-F. Coheur, “Retrieving radius, concentration, optical depth, and mass of different types of aerosols from high-resolution infrared nadir spectra,” Appl. Optics 49, 3713–3722 (2010).
[Crossref]

Dorland, R. V.

P. Forster, V. Ramaswamy, P. Artaxo, T. Bernsten, R. Betts, D. Fahey, J. Haywood, J. Lean, D. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. V. Dorland, “Changes in atmospheric consituents and in radiative forcing,” in Climate Change 2007: The Physical Science Basis. Contribution of Working Group 1 to the Fourth assesment report of Intergovernmental Panel on Climate Change, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miler, eds. (Cambridge University Press, 2007).

Dudhia, A.

R. G. Grainger, D. M. Peters, G. E. Thomas, A. J. A. Smith, R. Siddans, E. Carboni, and A. Dudhia, Remote Sensing of Volcanoes and Volcanic Processes: Integrating Observation and Modelling (Geol. Soc. London Spec. Publ., 2013), vol. 380, chap. Measuring volcanic plume and ash properties from space, pp. 293–320.

Ebmeier, S. K.

S. K. Ebmeier, A. M. Sayer, R. G. Grainger, T. A. Mather, and E. Carboni, “Systematic satellite observations of the impact of aerosols from passive volcanic degassing on local cloud properties,” Atmos. Chem. Phys. 14, 10601–10618 (2014).
[Crossref]

Egan, W.

W. Egan, T. Hilgeman, and K. Pang, “Ultraviolet complex refractive-index of Martian dust — Laboratory measurements of terrestrial analogs,” Icarus 25, 344–355 (1975).
[Crossref]

Erik Peiponen, J. R. K.

I. Niskanen and J. R. K. Erik Peiponen, “Determination of the refractive index of microparticles by utilizing light dispersion properties of the particle and an immersion liquid,” Talanta 115, 68–73 (2013).
[Crossref] [PubMed]

Erik Peiponen, K.

Fahey, D.

P. Forster, V. Ramaswamy, P. Artaxo, T. Bernsten, R. Betts, D. Fahey, J. Haywood, J. Lean, D. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. V. Dorland, “Changes in atmospheric consituents and in radiative forcing,” in Climate Change 2007: The Physical Science Basis. Contribution of Working Group 1 to the Fourth assesment report of Intergovernmental Panel on Climate Change, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miler, eds. (Cambridge University Press, 2007).

Flittner, D. E.

N. A. Krotkov, D. E. Flittner, A. J. Krueger, A. Kostinski, C. Riley, W. Rose, and O. Torres, “Effect of particle non-sphericity on satellite monitoring of drifting volcanic ash clouds,” J. Quant. Spectrosc. Radiat. Transfer 63, 613–630 (1999).
[Crossref]

Flores-Flores, J. O.

C. Sánchez-Pérez, A. García-Valenzuela, R. Y. Sato-Berrú, J. O. Flores-Flores, and R. G. Barrera, “Sizing colloidal particles from their contribution to the effective refractive index: Experimental results,” J. Phys. Conf. Ser.274 (2011).
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P. Forster, V. Ramaswamy, P. Artaxo, T. Bernsten, R. Betts, D. Fahey, J. Haywood, J. Lean, D. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. V. Dorland, “Changes in atmospheric consituents and in radiative forcing,” in Climate Change 2007: The Physical Science Basis. Contribution of Working Group 1 to the Fourth assesment report of Intergovernmental Panel on Climate Change, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miler, eds. (Cambridge University Press, 2007).

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E. M. Patterson, C. O. Pollard, and I. Galindo, “Optical-properties of the ashes from El-Chichon volcano,” Geophys. Res. Lett. 10, 317–320 (1983).
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Gangale, G.

G. Gangale, A. J. Prata, and L. Clarisse, “The infrared spectral signature of volcanic ash determined from high-spectral resolution satellite measurements,” Remote Sens. Environ. 114, 414–425 (2010).
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E. Gutiérrez-Reyes, A. García-Valenzuela, and R. G. Barrera, “Overview of an effective-medium approach to the reflection and refraction of light at a turbid colloidal half-space,” Phys. Status Solidi B 249, 1140–1147 (2012).
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A. García-Valenzuela, C. Sánchez-Pérez, and E. Gutiérrez-Reyes, “On the retrieval of particle size from the effective optical properties of colloids,” Physica B 405, 3016–3021 (2010).
[Crossref]

A. García-Valenzuela, R. G. Barrera, and E. Gutiérrez-Reyes, “Rigorous theoretical framework for particle sizing in turbid colloids using light refraction,” Opt. Express 16, 19741–19756 (2008).
[Crossref] [PubMed]

R. G. Barrera, A. Reyes-Coronado, and A. García-Valenzuela, “Nonlocal nature of the electrodynamic response of colloidal systems,” Phys. Rev. B 75, 184202 (2007).
[Crossref]

R. G. Barrera, A. García-Valenzuela, C. Sánchez-Pérez, A. Reyes-Coronado, and E. R. Mendez, “Coherent reflection of light from a turbid suspension of particles in an internal reflection configuration: Theory versus experiment,” Opt. Express 18, 6724 (2005).

R. G. Barrera and A. García-Valenzuela, “Coherent reflectance in a system of random mie scatters and its relation to the effective-medium approach,” J. Opt. Soc. Am. A 20, 296–311 (2003).
[Crossref]

C. Sánchez-Pérez, A. García-Valenzuela, R. Y. Sato-Berrú, J. O. Flores-Flores, and R. G. Barrera, “Sizing colloidal particles from their contribution to the effective refractive index: Experimental results,” J. Phys. Conf. Ser.274 (2011).
[Crossref]

A. García-Valenzuela, C. Sánchez-Pérez, R. G. Barrera, and A. Reyes-Coronado, “Surface Effects on the Coherent Reflection of Light from a Polydisperse Colloid,” in Progress in Electromagnetics Research Symposium 2005 (PIERS Online, 2005), pp. 650–653.

Grainger, R. G.

J. G. C. Ball, B. E. Reed, R. G. Grainger, D. M. Peters, T. A. Mather, and D. M. Pyle, “Measurements of the complex refractive index of volcanic ash at 450, 546.7 and 650 nm,” J. Geophys. Res. Atmos. 120, 7747–7757 (2015).
[Crossref]

S. K. Ebmeier, A. M. Sayer, R. G. Grainger, T. A. Mather, and E. Carboni, “Systematic satellite observations of the impact of aerosols from passive volcanic degassing on local cloud properties,” Atmos. Chem. Phys. 14, 10601–10618 (2014).
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G. E. Thomas, S. F. Bass, R. G. Grainger, and A. Lambert, “Retrieval of aerosol refractive index from extinction spectra with a damped harmonic-oscillator band model,” Appl. Opt. 44, 1332–1341 (2005).
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R. G. Grainger, D. M. Peters, G. E. Thomas, A. J. A. Smith, R. Siddans, E. Carboni, and A. Dudhia, Remote Sensing of Volcanoes and Volcanic Processes: Integrating Observation and Modelling (Geol. Soc. London Spec. Publ., 2013), vol. 380, chap. Measuring volcanic plume and ash properties from space, pp. 293–320.

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E. Gutiérrez-Reyes, A. García-Valenzuela, and R. G. Barrera, “Overview of an effective-medium approach to the reflection and refraction of light at a turbid colloidal half-space,” Phys. Status Solidi B 249, 1140–1147 (2012).
[Crossref]

A. García-Valenzuela, C. Sánchez-Pérez, and E. Gutiérrez-Reyes, “On the retrieval of particle size from the effective optical properties of colloids,” Physica B 405, 3016–3021 (2010).
[Crossref]

A. García-Valenzuela, R. G. Barrera, and E. Gutiérrez-Reyes, “Rigorous theoretical framework for particle sizing in turbid colloids using light refraction,” Opt. Express 16, 19741–19756 (2008).
[Crossref] [PubMed]

Haywood, J.

K. Turnbull, B. Johnson, F. Marenco, J. Haywood, A. Minikin, B. Weinzierl, H. Schlager, U. Schumann, S. Leadbetter, and A. Woolley, “A case study of observations of volcanic ash from the Eyjafjallajökull eruption: 1. In situ airborne observations,” J. Geophys. Res. 117, D20 (2012).

P. Forster, V. Ramaswamy, P. Artaxo, T. Bernsten, R. Betts, D. Fahey, J. Haywood, J. Lean, D. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. V. Dorland, “Changes in atmospheric consituents and in radiative forcing,” in Climate Change 2007: The Physical Science Basis. Contribution of Working Group 1 to the Fourth assesment report of Intergovernmental Panel on Climate Change, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miler, eds. (Cambridge University Press, 2007).

Hilgeman, T.

W. Egan, T. Hilgeman, and K. Pang, “Ultraviolet complex refractive-index of Martian dust — Laboratory measurements of terrestrial analogs,” Icarus 25, 344–355 (1975).
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C. J. Horwell and P. J. Baxter, “The respiratory health hazards of volcanic ash: a review for volcanic risk mitigation,” Bull. Volcanol. 69, 1–24 (2006).
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M. Xiaoyan, Q. L. Jun, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
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C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983).

Hurtmans, D.

L. Clarisse, D. Hurtmans, A. J. Prata, F. Karagulian, C. Clerbaux, M. De Maziere, and P.-F. Coheur, “Retrieving radius, concentration, optical depth, and mass of different types of aerosols from high-resolution infrared nadir spectra,” Appl. Optics 49, 3713–3722 (2010).
[Crossref]

Ivanov, C. D.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater. 29, 1481–1490 (2007).
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Jacobs, K. M.

M. Xiaoyan, Q. L. Jun, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[Crossref]

Johnson, B.

K. Turnbull, B. Johnson, F. Marenco, J. Haywood, A. Minikin, B. Weinzierl, H. Schlager, U. Schumann, S. Leadbetter, and A. Woolley, “A case study of observations of volcanic ash from the Eyjafjallajökull eruption: 1. In situ airborne observations,” J. Geophys. Res. 117, D20 (2012).

Jun, Q. L.

M. Xiaoyan, Q. L. Jun, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[Crossref]

Karagulian, F.

L. Clarisse, D. Hurtmans, A. J. Prata, F. Karagulian, C. Clerbaux, M. De Maziere, and P.-F. Coheur, “Retrieving radius, concentration, optical depth, and mass of different types of aerosols from high-resolution infrared nadir spectra,” Appl. Optics 49, 3713–3722 (2010).
[Crossref]

Kasarova, S. N.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater. 29, 1481–1490 (2007).
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Keller, J.

J. Keller, W. B. F. Ryan, D. Ninkovich, and R. Altherr, “Explosive volcanic activity in the Mediterranean over the past 200,000 yr as recorded in deep-sea sediments,” Geol. Soc. Am. Bull. 89, 591–604 (1978).
[Crossref]

Khare, B. N.

J. B. Pollack, O. B. Toon, and B. N. Khare, “Optical properties of some terrestrial rocks and glasses,” Icarus 19, 372–389 (1973).
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Kim, Y. J.

K. H. Lee, Z. Li, Y. J. Kim, and A. Kokhanovsky, “Atmospheric aerosol monitoring from satellite observations: A history of three decades,” in Atmospheric and Biological Environmental Monitoring (Springer, 2009).
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Kokhanovsky, A.

K. H. Lee, Z. Li, Y. J. Kim, and A. Kokhanovsky, “Atmospheric aerosol monitoring from satellite observations: A history of three decades,” in Atmospheric and Biological Environmental Monitoring (Springer, 2009).
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Kostinski, A.

N. A. Krotkov, D. E. Flittner, A. J. Krueger, A. Kostinski, C. Riley, W. Rose, and O. Torres, “Effect of particle non-sphericity on satellite monitoring of drifting volcanic ash clouds,” J. Quant. Spectrosc. Radiat. Transfer 63, 613–630 (1999).
[Crossref]

Krotkov, N. A.

N. A. Krotkov, D. E. Flittner, A. J. Krueger, A. Kostinski, C. Riley, W. Rose, and O. Torres, “Effect of particle non-sphericity on satellite monitoring of drifting volcanic ash clouds,” J. Quant. Spectrosc. Radiat. Transfer 63, 613–630 (1999).
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Krueger, A. J.

N. A. Krotkov, D. E. Flittner, A. J. Krueger, A. Kostinski, C. Riley, W. Rose, and O. Torres, “Effect of particle non-sphericity on satellite monitoring of drifting volcanic ash clouds,” J. Quant. Spectrosc. Radiat. Transfer 63, 613–630 (1999).
[Crossref]

Lambert, A.

Leadbetter, S.

K. Turnbull, B. Johnson, F. Marenco, J. Haywood, A. Minikin, B. Weinzierl, H. Schlager, U. Schumann, S. Leadbetter, and A. Woolley, “A case study of observations of volcanic ash from the Eyjafjallajökull eruption: 1. In situ airborne observations,” J. Geophys. Res. 117, D20 (2012).

Lean, J.

P. Forster, V. Ramaswamy, P. Artaxo, T. Bernsten, R. Betts, D. Fahey, J. Haywood, J. Lean, D. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. V. Dorland, “Changes in atmospheric consituents and in radiative forcing,” in Climate Change 2007: The Physical Science Basis. Contribution of Working Group 1 to the Fourth assesment report of Intergovernmental Panel on Climate Change, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miler, eds. (Cambridge University Press, 2007).

Lee, K. H.

K. H. Lee, Z. Li, Y. J. Kim, and A. Kokhanovsky, “Atmospheric aerosol monitoring from satellite observations: A history of three decades,” in Atmospheric and Biological Environmental Monitoring (Springer, 2009).
[Crossref]

Li, Z.

K. H. Lee, Z. Li, Y. J. Kim, and A. Kokhanovsky, “Atmospheric aerosol monitoring from satellite observations: A history of three decades,” in Atmospheric and Biological Environmental Monitoring (Springer, 2009).
[Crossref]

Lowe, D.

P. Forster, V. Ramaswamy, P. Artaxo, T. Bernsten, R. Betts, D. Fahey, J. Haywood, J. Lean, D. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. V. Dorland, “Changes in atmospheric consituents and in radiative forcing,” in Climate Change 2007: The Physical Science Basis. Contribution of Working Group 1 to the Fourth assesment report of Intergovernmental Panel on Climate Change, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miler, eds. (Cambridge University Press, 2007).

Marenco, F.

K. Turnbull, B. Johnson, F. Marenco, J. Haywood, A. Minikin, B. Weinzierl, H. Schlager, U. Schumann, S. Leadbetter, and A. Woolley, “A case study of observations of volcanic ash from the Eyjafjallajökull eruption: 1. In situ airborne observations,” J. Geophys. Res. 117, D20 (2012).

Mather, T. A.

J. G. C. Ball, B. E. Reed, R. G. Grainger, D. M. Peters, T. A. Mather, and D. M. Pyle, “Measurements of the complex refractive index of volcanic ash at 450, 546.7 and 650 nm,” J. Geophys. Res. Atmos. 120, 7747–7757 (2015).
[Crossref]

S. K. Ebmeier, A. M. Sayer, R. G. Grainger, T. A. Mather, and E. Carboni, “Systematic satellite observations of the impact of aerosols from passive volcanic degassing on local cloud properties,” Atmos. Chem. Phys. 14, 10601–10618 (2014).
[Crossref]

Mendez, E. R.

R. G. Barrera, A. García-Valenzuela, C. Sánchez-Pérez, A. Reyes-Coronado, and E. R. Mendez, “Coherent reflection of light from a turbid suspension of particles in an internal reflection configuration: Theory versus experiment,” Opt. Express 18, 6724 (2005).

Minikin, A.

K. Turnbull, B. Johnson, F. Marenco, J. Haywood, A. Minikin, B. Weinzierl, H. Schlager, U. Schumann, S. Leadbetter, and A. Woolley, “A case study of observations of volcanic ash from the Eyjafjallajökull eruption: 1. In situ airborne observations,” J. Geophys. Res. 117, D20 (2012).

Mishchenko, M. I.

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. Transfer 60, 309–324 (1998).
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Myhre, G.

P. Forster, V. Ramaswamy, P. Artaxo, T. Bernsten, R. Betts, D. Fahey, J. Haywood, J. Lean, D. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. V. Dorland, “Changes in atmospheric consituents and in radiative forcing,” in Climate Change 2007: The Physical Science Basis. Contribution of Working Group 1 to the Fourth assesment report of Intergovernmental Panel on Climate Change, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miler, eds. (Cambridge University Press, 2007).

Nganga, J.

P. Forster, V. Ramaswamy, P. Artaxo, T. Bernsten, R. Betts, D. Fahey, J. Haywood, J. Lean, D. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. V. Dorland, “Changes in atmospheric consituents and in radiative forcing,” in Climate Change 2007: The Physical Science Basis. Contribution of Working Group 1 to the Fourth assesment report of Intergovernmental Panel on Climate Change, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miler, eds. (Cambridge University Press, 2007).

Nikolov, I. D.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater. 29, 1481–1490 (2007).
[Crossref]

Ninkovich, D.

J. Keller, W. B. F. Ryan, D. Ninkovich, and R. Altherr, “Explosive volcanic activity in the Mediterranean over the past 200,000 yr as recorded in deep-sea sediments,” Geol. Soc. Am. Bull. 89, 591–604 (1978).
[Crossref]

Niskanen, I.

I. Niskanen and J. R. K. Erik Peiponen, “Determination of the refractive index of microparticles by utilizing light dispersion properties of the particle and an immersion liquid,” Talanta 115, 68–73 (2013).
[Crossref] [PubMed]

I. Niskanen, J. Räty, and K. Erik Peiponen, “Measurement of refractive index of isotropic particles by incorporating a multifunction spectrophotometer and immersion liquid method,” Appl. Opt. 46, 5404–5407 (2007).
[Crossref] [PubMed]

Pang, K.

W. Egan, T. Hilgeman, and K. Pang, “Ultraviolet complex refractive-index of Martian dust — Laboratory measurements of terrestrial analogs,” Icarus 25, 344–355 (1975).
[Crossref]

Patterson, E. M.

E. M. Patterson, C. O. Pollard, and I. Galindo, “Optical-properties of the ashes from El-Chichon volcano,” Geophys. Res. Lett. 10, 317–320 (1983).
[Crossref]

E. M. Patterson, “Measurements of the imaginary part of the refractive index between 300 and 700 nanometers for Mount St. Helens ash,” Science 211, 836–838 (1981).
[Crossref] [PubMed]

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Peters, D. M.

J. G. C. Ball, B. E. Reed, R. G. Grainger, D. M. Peters, T. A. Mather, and D. M. Pyle, “Measurements of the complex refractive index of volcanic ash at 450, 546.7 and 650 nm,” J. Geophys. Res. Atmos. 120, 7747–7757 (2015).
[Crossref]

R. G. Grainger, D. M. Peters, G. E. Thomas, A. J. A. Smith, R. Siddans, E. Carboni, and A. Dudhia, Remote Sensing of Volcanoes and Volcanic Processes: Integrating Observation and Modelling (Geol. Soc. London Spec. Publ., 2013), vol. 380, chap. Measuring volcanic plume and ash properties from space, pp. 293–320.

Pollack, J. B.

O. B. Toon, J. B. Pollack, and C. Sagan, “Physical properties of the particles composing the Martian dust storm of 1971–1972,” Icarus 30, 663–696 (1977).
[Crossref]

J. B. Pollack, O. B. Toon, and B. N. Khare, “Optical properties of some terrestrial rocks and glasses,” Icarus 19, 372–389 (1973).
[Crossref]

Pollard, C. O.

E. M. Patterson, C. O. Pollard, and I. Galindo, “Optical-properties of the ashes from El-Chichon volcano,” Geophys. Res. Lett. 10, 317–320 (1983).
[Crossref]

Prata, A. J.

G. Gangale, A. J. Prata, and L. Clarisse, “The infrared spectral signature of volcanic ash determined from high-spectral resolution satellite measurements,” Remote Sens. Environ. 114, 414–425 (2010).
[Crossref]

L. Clarisse, D. Hurtmans, A. J. Prata, F. Karagulian, C. Clerbaux, M. De Maziere, and P.-F. Coheur, “Retrieving radius, concentration, optical depth, and mass of different types of aerosols from high-resolution infrared nadir spectra,” Appl. Optics 49, 3713–3722 (2010).
[Crossref]

Prinn, R.

P. Forster, V. Ramaswamy, P. Artaxo, T. Bernsten, R. Betts, D. Fahey, J. Haywood, J. Lean, D. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. V. Dorland, “Changes in atmospheric consituents and in radiative forcing,” in Climate Change 2007: The Physical Science Basis. Contribution of Working Group 1 to the Fourth assesment report of Intergovernmental Panel on Climate Change, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miler, eds. (Cambridge University Press, 2007).

Pyle, D. M.

J. G. C. Ball, B. E. Reed, R. G. Grainger, D. M. Peters, T. A. Mather, and D. M. Pyle, “Measurements of the complex refractive index of volcanic ash at 450, 546.7 and 650 nm,” J. Geophys. Res. Atmos. 120, 7747–7757 (2015).
[Crossref]

Raga, G.

P. Forster, V. Ramaswamy, P. Artaxo, T. Bernsten, R. Betts, D. Fahey, J. Haywood, J. Lean, D. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. V. Dorland, “Changes in atmospheric consituents and in radiative forcing,” in Climate Change 2007: The Physical Science Basis. Contribution of Working Group 1 to the Fourth assesment report of Intergovernmental Panel on Climate Change, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miler, eds. (Cambridge University Press, 2007).

Ramaswamy, V.

P. Forster, V. Ramaswamy, P. Artaxo, T. Bernsten, R. Betts, D. Fahey, J. Haywood, J. Lean, D. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. V. Dorland, “Changes in atmospheric consituents and in radiative forcing,” in Climate Change 2007: The Physical Science Basis. Contribution of Working Group 1 to the Fourth assesment report of Intergovernmental Panel on Climate Change, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miler, eds. (Cambridge University Press, 2007).

Räty, J.

Reed, B. E.

J. G. C. Ball, B. E. Reed, R. G. Grainger, D. M. Peters, T. A. Mather, and D. M. Pyle, “Measurements of the complex refractive index of volcanic ash at 450, 546.7 and 650 nm,” J. Geophys. Res. Atmos. 120, 7747–7757 (2015).
[Crossref]

Reyes-Coronado, A.

R. G. Barrera, A. Reyes-Coronado, and A. García-Valenzuela, “Nonlocal nature of the electrodynamic response of colloidal systems,” Phys. Rev. B 75, 184202 (2007).
[Crossref]

R. G. Barrera, A. García-Valenzuela, C. Sánchez-Pérez, A. Reyes-Coronado, and E. R. Mendez, “Coherent reflection of light from a turbid suspension of particles in an internal reflection configuration: Theory versus experiment,” Opt. Express 18, 6724 (2005).

A. García-Valenzuela, C. Sánchez-Pérez, R. G. Barrera, and A. Reyes-Coronado, “Surface Effects on the Coherent Reflection of Light from a Polydisperse Colloid,” in Progress in Electromagnetics Research Symposium 2005 (PIERS Online, 2005), pp. 650–653.

Riley, C.

N. A. Krotkov, D. E. Flittner, A. J. Krueger, A. Kostinski, C. Riley, W. Rose, and O. Torres, “Effect of particle non-sphericity on satellite monitoring of drifting volcanic ash clouds,” J. Quant. Spectrosc. Radiat. Transfer 63, 613–630 (1999).
[Crossref]

Rodgers, C. D.

C. D. Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Practice (World Scientific, 2000).

Rose, W.

N. A. Krotkov, D. E. Flittner, A. J. Krueger, A. Kostinski, C. Riley, W. Rose, and O. Torres, “Effect of particle non-sphericity on satellite monitoring of drifting volcanic ash clouds,” J. Quant. Spectrosc. Radiat. Transfer 63, 613–630 (1999).
[Crossref]

Ryan, W. B. F.

J. Keller, W. B. F. Ryan, D. Ninkovich, and R. Altherr, “Explosive volcanic activity in the Mediterranean over the past 200,000 yr as recorded in deep-sea sediments,” Geol. Soc. Am. Bull. 89, 591–604 (1978).
[Crossref]

Sagan, C.

O. B. Toon, J. B. Pollack, and C. Sagan, “Physical properties of the particles composing the Martian dust storm of 1971–1972,” Icarus 30, 663–696 (1977).
[Crossref]

Sánchez-Pérez, C.

A. García-Valenzuela, C. Sánchez-Pérez, and E. Gutiérrez-Reyes, “On the retrieval of particle size from the effective optical properties of colloids,” Physica B 405, 3016–3021 (2010).
[Crossref]

R. G. Barrera, A. García-Valenzuela, C. Sánchez-Pérez, A. Reyes-Coronado, and E. R. Mendez, “Coherent reflection of light from a turbid suspension of particles in an internal reflection configuration: Theory versus experiment,” Opt. Express 18, 6724 (2005).

C. Sánchez-Pérez, A. García-Valenzuela, R. Y. Sato-Berrú, J. O. Flores-Flores, and R. G. Barrera, “Sizing colloidal particles from their contribution to the effective refractive index: Experimental results,” J. Phys. Conf. Ser.274 (2011).
[Crossref]

A. García-Valenzuela, C. Sánchez-Pérez, R. G. Barrera, and A. Reyes-Coronado, “Surface Effects on the Coherent Reflection of Light from a Polydisperse Colloid,” in Progress in Electromagnetics Research Symposium 2005 (PIERS Online, 2005), pp. 650–653.

Sato-Berrú, R. Y.

C. Sánchez-Pérez, A. García-Valenzuela, R. Y. Sato-Berrú, J. O. Flores-Flores, and R. G. Barrera, “Sizing colloidal particles from their contribution to the effective refractive index: Experimental results,” J. Phys. Conf. Ser.274 (2011).
[Crossref]

Sayer, A. M.

S. K. Ebmeier, A. M. Sayer, R. G. Grainger, T. A. Mather, and E. Carboni, “Systematic satellite observations of the impact of aerosols from passive volcanic degassing on local cloud properties,” Atmos. Chem. Phys. 14, 10601–10618 (2014).
[Crossref]

Schlager, H.

K. Turnbull, B. Johnson, F. Marenco, J. Haywood, A. Minikin, B. Weinzierl, H. Schlager, U. Schumann, S. Leadbetter, and A. Woolley, “A case study of observations of volcanic ash from the Eyjafjallajökull eruption: 1. In situ airborne observations,” J. Geophys. Res. 117, D20 (2012).

Schulz, M.

P. Forster, V. Ramaswamy, P. Artaxo, T. Bernsten, R. Betts, D. Fahey, J. Haywood, J. Lean, D. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. V. Dorland, “Changes in atmospheric consituents and in radiative forcing,” in Climate Change 2007: The Physical Science Basis. Contribution of Working Group 1 to the Fourth assesment report of Intergovernmental Panel on Climate Change, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miler, eds. (Cambridge University Press, 2007).

Schumann, U.

K. Turnbull, B. Johnson, F. Marenco, J. Haywood, A. Minikin, B. Weinzierl, H. Schlager, U. Schumann, S. Leadbetter, and A. Woolley, “A case study of observations of volcanic ash from the Eyjafjallajökull eruption: 1. In situ airborne observations,” J. Geophys. Res. 117, D20 (2012).

Siddans, R.

R. G. Grainger, D. M. Peters, G. E. Thomas, A. J. A. Smith, R. Siddans, E. Carboni, and A. Dudhia, Remote Sensing of Volcanoes and Volcanic Processes: Integrating Observation and Modelling (Geol. Soc. London Spec. Publ., 2013), vol. 380, chap. Measuring volcanic plume and ash properties from space, pp. 293–320.

Smith, A. J. A.

R. G. Grainger, D. M. Peters, G. E. Thomas, A. J. A. Smith, R. Siddans, E. Carboni, and A. Dudhia, Remote Sensing of Volcanoes and Volcanic Processes: Integrating Observation and Modelling (Geol. Soc. London Spec. Publ., 2013), vol. 380, chap. Measuring volcanic plume and ash properties from space, pp. 293–320.

Sultanova, N. G.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater. 29, 1481–1490 (2007).
[Crossref]

Thomas, G. E.

G. E. Thomas, S. F. Bass, R. G. Grainger, and A. Lambert, “Retrieval of aerosol refractive index from extinction spectra with a damped harmonic-oscillator band model,” Appl. Opt. 44, 1332–1341 (2005).
[Crossref] [PubMed]

R. G. Grainger, D. M. Peters, G. E. Thomas, A. J. A. Smith, R. Siddans, E. Carboni, and A. Dudhia, Remote Sensing of Volcanoes and Volcanic Processes: Integrating Observation and Modelling (Geol. Soc. London Spec. Publ., 2013), vol. 380, chap. Measuring volcanic plume and ash properties from space, pp. 293–320.

Toon, O. B.

O. B. Toon, J. B. Pollack, and C. Sagan, “Physical properties of the particles composing the Martian dust storm of 1971–1972,” Icarus 30, 663–696 (1977).
[Crossref]

J. B. Pollack, O. B. Toon, and B. N. Khare, “Optical properties of some terrestrial rocks and glasses,” Icarus 19, 372–389 (1973).
[Crossref]

Torres, O.

N. A. Krotkov, D. E. Flittner, A. J. Krueger, A. Kostinski, C. Riley, W. Rose, and O. Torres, “Effect of particle non-sphericity on satellite monitoring of drifting volcanic ash clouds,” J. Quant. Spectrosc. Radiat. Transfer 63, 613–630 (1999).
[Crossref]

Travis, L. D.

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. Transfer 60, 309–324 (1998).
[Crossref]

Turnbull, K.

K. Turnbull, B. Johnson, F. Marenco, J. Haywood, A. Minikin, B. Weinzierl, H. Schlager, U. Schumann, S. Leadbetter, and A. Woolley, “A case study of observations of volcanic ash from the Eyjafjallajökull eruption: 1. In situ airborne observations,” J. Geophys. Res. 117, D20 (2012).

Vigoureux, J. M.

P. Grossel, J. M. Vigoureux, and F. Baïda, “Nonlocal approach to scattering in a one-dimensional problem,” Phys. Rev. A 50, 3627–3637 (1994).
[Crossref] [PubMed]

J. M. Vigoureux, “Use of Einstein’s addition law in studies of reflection by stratified planar structures,” J. Opt. Soc. Am. A 9, 1313–1319 (1992).
[Crossref]

Volz, F. E.

F. E. Volz, “Infrared optical constants of ammonium sulfate, Sahara dust, volcanic pumice and flyash,” Appl. Optics 12, 564–568 (1973).
[Crossref]

Weinzierl, B.

K. Turnbull, B. Johnson, F. Marenco, J. Haywood, A. Minikin, B. Weinzierl, H. Schlager, U. Schumann, S. Leadbetter, and A. Woolley, “A case study of observations of volcanic ash from the Eyjafjallajökull eruption: 1. In situ airborne observations,” J. Geophys. Res. 117, D20 (2012).

Woolley, A.

K. Turnbull, B. Johnson, F. Marenco, J. Haywood, A. Minikin, B. Weinzierl, H. Schlager, U. Schumann, S. Leadbetter, and A. Woolley, “A case study of observations of volcanic ash from the Eyjafjallajökull eruption: 1. In situ airborne observations,” J. Geophys. Res. 117, D20 (2012).

Xiaoyan, M.

M. Xiaoyan, Q. L. Jun, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[Crossref]

Yang, P.

M. Xiaoyan, Q. L. Jun, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[Crossref]

Appl. Opt. (2)

Appl. Optics (2)

F. E. Volz, “Infrared optical constants of ammonium sulfate, Sahara dust, volcanic pumice and flyash,” Appl. Optics 12, 564–568 (1973).
[Crossref]

L. Clarisse, D. Hurtmans, A. J. Prata, F. Karagulian, C. Clerbaux, M. De Maziere, and P.-F. Coheur, “Retrieving radius, concentration, optical depth, and mass of different types of aerosols from high-resolution infrared nadir spectra,” Appl. Optics 49, 3713–3722 (2010).
[Crossref]

Atmos. Chem. Phys. (1)

S. K. Ebmeier, A. M. Sayer, R. G. Grainger, T. A. Mather, and E. Carboni, “Systematic satellite observations of the impact of aerosols from passive volcanic degassing on local cloud properties,” Atmos. Chem. Phys. 14, 10601–10618 (2014).
[Crossref]

Bull. Volcanol. (1)

C. J. Horwell and P. J. Baxter, “The respiratory health hazards of volcanic ash: a review for volcanic risk mitigation,” Bull. Volcanol. 69, 1–24 (2006).
[Crossref]

Geol. Soc. Am. Bull. (2)

L. Kittleman, “Glass-bead silica determination for a suite of volcanic rocks from the Owyee Plateau, Oregon,” Geol. Soc. Am. Bull. 73, 1405 (1963).

J. Keller, W. B. F. Ryan, D. Ninkovich, and R. Altherr, “Explosive volcanic activity in the Mediterranean over the past 200,000 yr as recorded in deep-sea sediments,” Geol. Soc. Am. Bull. 89, 591–604 (1978).
[Crossref]

Geophys. Res. Lett. (1)

E. M. Patterson, C. O. Pollard, and I. Galindo, “Optical-properties of the ashes from El-Chichon volcano,” Geophys. Res. Lett. 10, 317–320 (1983).
[Crossref]

Icarus (3)

J. B. Pollack, O. B. Toon, and B. N. Khare, “Optical properties of some terrestrial rocks and glasses,” Icarus 19, 372–389 (1973).
[Crossref]

W. Egan, T. Hilgeman, and K. Pang, “Ultraviolet complex refractive-index of Martian dust — Laboratory measurements of terrestrial analogs,” Icarus 25, 344–355 (1975).
[Crossref]

O. B. Toon, J. B. Pollack, and C. Sagan, “Physical properties of the particles composing the Martian dust storm of 1971–1972,” Icarus 30, 663–696 (1977).
[Crossref]

J. Geophys. Res. (1)

K. Turnbull, B. Johnson, F. Marenco, J. Haywood, A. Minikin, B. Weinzierl, H. Schlager, U. Schumann, S. Leadbetter, and A. Woolley, “A case study of observations of volcanic ash from the Eyjafjallajökull eruption: 1. In situ airborne observations,” J. Geophys. Res. 117, D20 (2012).

J. Geophys. Res. Atmos. (1)

J. G. C. Ball, B. E. Reed, R. G. Grainger, D. M. Peters, T. A. Mather, and D. M. Pyle, “Measurements of the complex refractive index of volcanic ash at 450, 546.7 and 650 nm,” J. Geophys. Res. Atmos. 120, 7747–7757 (2015).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Quant. Spectrosc. Radiat. Transfer (2)

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. Transfer 60, 309–324 (1998).
[Crossref]

N. A. Krotkov, D. E. Flittner, A. J. Krueger, A. Kostinski, C. Riley, W. Rose, and O. Torres, “Effect of particle non-sphericity on satellite monitoring of drifting volcanic ash clouds,” J. Quant. Spectrosc. Radiat. Transfer 63, 613–630 (1999).
[Crossref]

Opt. Express (2)

R. G. Barrera, A. García-Valenzuela, C. Sánchez-Pérez, A. Reyes-Coronado, and E. R. Mendez, “Coherent reflection of light from a turbid suspension of particles in an internal reflection configuration: Theory versus experiment,” Opt. Express 18, 6724 (2005).

A. García-Valenzuela, R. G. Barrera, and E. Gutiérrez-Reyes, “Rigorous theoretical framework for particle sizing in turbid colloids using light refraction,” Opt. Express 16, 19741–19756 (2008).
[Crossref] [PubMed]

Opt. Mater. (1)

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater. 29, 1481–1490 (2007).
[Crossref]

Phys. Med. Biol. (1)

M. Xiaoyan, Q. L. Jun, R. S. Brock, K. M. Jacobs, P. Yang, and X. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[Crossref]

Phys. Rev. A (1)

P. Grossel, J. M. Vigoureux, and F. Baïda, “Nonlocal approach to scattering in a one-dimensional problem,” Phys. Rev. A 50, 3627–3637 (1994).
[Crossref] [PubMed]

Phys. Rev. B (1)

R. G. Barrera, A. Reyes-Coronado, and A. García-Valenzuela, “Nonlocal nature of the electrodynamic response of colloidal systems,” Phys. Rev. B 75, 184202 (2007).
[Crossref]

Phys. Status Solidi B (1)

E. Gutiérrez-Reyes, A. García-Valenzuela, and R. G. Barrera, “Overview of an effective-medium approach to the reflection and refraction of light at a turbid colloidal half-space,” Phys. Status Solidi B 249, 1140–1147 (2012).
[Crossref]

Physica B (1)

A. García-Valenzuela, C. Sánchez-Pérez, and E. Gutiérrez-Reyes, “On the retrieval of particle size from the effective optical properties of colloids,” Physica B 405, 3016–3021 (2010).
[Crossref]

Remote Sens. Environ. (1)

G. Gangale, A. J. Prata, and L. Clarisse, “The infrared spectral signature of volcanic ash determined from high-spectral resolution satellite measurements,” Remote Sens. Environ. 114, 414–425 (2010).
[Crossref]

Science (1)

E. M. Patterson, “Measurements of the imaginary part of the refractive index between 300 and 700 nanometers for Mount St. Helens ash,” Science 211, 836–838 (1981).
[Crossref] [PubMed]

Talanta (1)

I. Niskanen and J. R. K. Erik Peiponen, “Determination of the refractive index of microparticles by utilizing light dispersion properties of the particle and an immersion liquid,” Talanta 115, 68–73 (2013).
[Crossref] [PubMed]

Other (12)

C. Sánchez-Pérez, A. García-Valenzuela, R. Y. Sato-Berrú, J. O. Flores-Flores, and R. G. Barrera, “Sizing colloidal particles from their contribution to the effective refractive index: Experimental results,” J. Phys. Conf. Ser.274 (2011).
[Crossref]

A. García-Valenzuela, C. Sánchez-Pérez, R. G. Barrera, and A. Reyes-Coronado, “Surface Effects on the Coherent Reflection of Light from a Polydisperse Colloid,” in Progress in Electromagnetics Research Symposium 2005 (PIERS Online, 2005), pp. 650–653.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983).

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds., Light Scattering by Nonspherical Particles: Theory, Measurements and Applications (Academic Press, 2000).

C. D. Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Practice (World Scientific, 2000).

E. M. Patterson, “Optical absorption coefficients of soil-aerosol particles and volcanic ash between 1 and 16 μm,” Proceedings of the Second Conference on Atmospheric Radiation pp. 177–180 (1994).

R. Blong, Volcanic Hazards: A Sourcebook on the Effects of Eruptions (Academic Press, 1984).

P. Forster, V. Ramaswamy, P. Artaxo, T. Bernsten, R. Betts, D. Fahey, J. Haywood, J. Lean, D. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. V. Dorland, “Changes in atmospheric consituents and in radiative forcing,” in Climate Change 2007: The Physical Science Basis. Contribution of Working Group 1 to the Fourth assesment report of Intergovernmental Panel on Climate Change, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miler, eds. (Cambridge University Press, 2007).

K. H. Lee, Z. Li, Y. J. Kim, and A. Kokhanovsky, “Atmospheric aerosol monitoring from satellite observations: A history of three decades,” in Atmospheric and Biological Environmental Monitoring (Springer, 2009).
[Crossref]

European Commission, The Impact of the Volcanic Ash Cloud Crisis on the Air Transport Industry SEC (2010) 533, 27April, Brussels 2010).

R. G. Grainger, D. M. Peters, G. E. Thomas, A. J. A. Smith, R. Siddans, E. Carboni, and A. Dudhia, Remote Sensing of Volcanoes and Volcanic Processes: Integrating Observation and Modelling (Geol. Soc. London Spec. Publ., 2013), vol. 380, chap. Measuring volcanic plume and ash properties from space, pp. 293–320.

F. J. K. Becke, “Beziehungen zwischen Dynamometamorphose und Moldkularcolumen,” Neues Jahrbuch für Mineralogie pp. 182–183 (1896).

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Figures (7)

Fig. 1
Fig. 1

Schematic of the experimental setup. The 635 nm incident beam from the AlGaInP laser diode enters the optic at normal incidence. It is then reflected at the back surface of the optic at the interface with the sample medium, before exiting the optic and travelling to the detector.

Fig. 2
Fig. 2

Reflectivity from an N-layered system of slabs. Only the penetrating beam is shown after the initial interface. The compound reflectivity at the initial interface, Γ0,1, has a component from reflectivity at each subsequent interface according to Eq. (5).

Fig. 3
Fig. 3

Reflectivity from two systems containing random spheres.

Fig. 4
Fig. 4

Illustration of modelling the reflectivity from a polydisperse colloid, using an N-slab transition region extending from z = 0 to z = NΔz. The diagram illustrates how in slab m the distribution of particles is restricted to those with radius a < mΔz.

Fig. 5
Fig. 5

The contributions to uncertainty in the retrieval of real refractive index for a monodisperse system plotted against (a) real refractive index and (b) size parameter. The contributions to the uncertainty and the combined uncertainty are shown: (blue line) volume filling fraction, (red line) incidence angle, (turquoise line) laser power, (orange line) particle radius, (purple line) laser wavelength and (black line) combined uncertainty. Uncertainty resulting from assuming non-absorbing particles was less than 0.001. The reference state was taken to be the retrieved state for a polystyrene latex sample with a measured volume filling fraction f = 6.70 %.

Fig. 6
Fig. 6

The contributions to uncertainty in the retrieval of real refractive index for a polydisperse distribution taking into account the interface region using a 50 slab system: (red line) incidence angle, (turquoise line) laser power, (purple line) non-spherical effects, (blue line) non-absorbing assumption and (black line) combined uncertainty. The reference state was taken to be the retrieved state for the sand retrieval with a retrieved volume filling fraction of f = 5.01 %.

Fig. 7
Fig. 7

Reflectivity scans for polystyrene latex spheres in distilled water at differing volume filling fractions. Shown are the fitted reflectivity curve (red line) using the monodisperse CSM and the Fresnel reflectivity curve (blue dotted line) for a suspension medium containing no scatterers with a refractive index equal to the retrieved value of nm.

Tables (5)

Tables Icon

Table 1 Summary of contributions to the propagated uncertainty in the retrieval of np for the retrieval using the monodisperse CSM performed on the polystyrene latex particle reflectivity data. The values shown were calculated at the retrieved state of the f = 6.70 % scan.

Tables Icon

Table 2 Summary of the contributions to the propagated uncertainty in the retrieval of np for the polydisperse model taking into account the interface region using a 50 slab system. The reference state was taken to be the retrieved state for the sand retrieval with a retrieved volume filling fraction of f = 5.01 %.

Tables Icon

Table 3 Summary of polystyrene latex sphere retrieval results using the monodisperse CSM.

Tables Icon

Table 4 Summary of the retrieval results on the sand sample.

Tables Icon

Table 5 Summary of the retrieval results on samples made from an Icelandic volcanic ash. Sample A underwent a 12 hour sedimentation process whilst for Sample B the period was 24 hours.

Equations (25)

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

( E S E S ) = exp ( i k r ) i k r [ S 2 ( θ ) S 4 ( θ ) S 3 ( θ ) S 1 ( θ ) ] ( E i E i )
r Fres = ( E r E i ) = μ t n i cos ( θ i ) μ i n t cos ( θ t ) μ t n i cos ( θ i ) + μ i n t cos ( θ t ) , r Fres = ( E r E i ) = ε t n i cos ( θ i ) ε i n t cos ( θ t ) ε i n t cos ( θ i ) + ε t n i cos ( θ t ) ,
n = ε μ / μ 0 ε 0 ,
Γ 0 , 1 ( θ 0 ) = r 0 , 1 hs ( θ 0 ) + Γ 1 , 2 ( θ 1 ) exp ( 2 i k 1 z Δ z 1 ) 1 + r 0 , 1 hs ( θ 0 ) Γ 1 , 2 ( θ 1 ) exp ( 2 i k 1 z Δ z 1 ) ,
Γ m , m + 1 ( θ m ) = r m , m + 1 hs ( θ m ) + Γ m + 1 , m + 2 ( θ m + 1 ) exp ( 2 i k m + 1 z Δ z m + 1 ) 1 + r m , m + 1 hs ( θ m ) Γ m + 1 , m + 2 ( θ m + 1 ) exp ( 2 i k m + 1 z Δ z m + 1 ) ,
θ m = sin 1 ( n m 1 n m sin θ m 1 ) .
μ eff μ 0 = 1 + i γ S ( 1 ) ( θ i ) cos 2 ( θ i ) ,
ε eff ε 0 = 1 + i γ [ 2 S + ( 1 ) ( θ i ) S ( 1 ) ( θ i ) tan 2 θ i ] ,
S + ( j ) ( θ i ) = 1 2 [ S ( 0 ) + S j ( π 2 θ i ) ] ,
S ( j ) ( θ i ) = S ( θ i ) S j ( π 2 θ i ) .
ε eff ε 0 = 1 + i γ S ( 2 ) ( θ i ) cos 2 θ i ,
μ eff μ 0 = 1 + i γ [ 2 S + ( 2 ) θ i S ( 2 ) ( θ i ) tan 2 θ i ] .
r hs eff ( θ i ) = γ S j ( π 2 θ i ) / cos θ i i ( cos θ i + { cos 2 θ i + 2 i γ S ( 0 ) γ 2 cos 2 θ i [ S ( 0 ) 2 S j ( π 2 θ i ) 2 ] } 1 / 2 ) γ S ( 0 ) cos θ i
k z eff = ( k m z ) 2 2 i χ S ( 0 ) k m z / cos θ i + ( χ 2 / cos 2 θ i ) [ S j ( π 2 θ i ) 2 S ( 0 ) 2 ]
r = r i , m Fres + r hs eff ( θ m ) exp ( 2 i k m z a ) 1 + r i , m Fres r hs eff ( θ m ) exp ( 2 i k m z a ) ,
n ( a , z ) = U ( z a ) n ( a ) ,
n ( a ) = 1 2 π ln ( S ) a exp [ ln ( a ) ln ( a 0 ) 2 ln 2 ( S ) ] .
y = F ( x , b ) + ε ,
y F ( x 0 , b ) = K ( x x 0 ) + ε ,
x ^ = R ( y , b ) ,
x ^ = Gy ,
( y Kx ) T S ε 1 ( y Kx ) ,
G = ( K T S ε 1 K ) K T S ε 1 .
S x = G S ε G T + G K b S b K b T G T .
G Δ f = G [ f ( x , b , b ) F ( x , b ) ] ,

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