Abstract

We describe the implementation of precision laser transmission spectroscopy for sizing and counting nanoparticles in suspension. Our apparatus incorporates a tunable laser and balanced optical system that measures light transmission over a wide (2102300nm) wavelength range with high precision and sensitivity. Spectral inversion is employed to determine both the particle size distribution and absolute particle density. In this paper we discuss results for particles with sizes (diameters) in the range from 5 to 3000nm. For polystyrene particles 404 to 1025nm in size, uncertainties of ±0.5% in size and ±4% in density were obtained. For polystyrene particles from 46 to 3000nm in size, the dynamic range of the system spans densities from 103/ml to 1010/ml (5×108 to 0.5 vol. %), implying a sensitivity 5 orders of magnitude higher than dynamic light scattering.

© 2010 Optical Society of America

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References

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2010 (1)

N. G. Khlebtsov and L. A. Dykman, “Optical properties and biomedical applications of plasmonic nanoparticles,” J. Quant. Spectrosc. Radiat. Transfer 111, 1–35 (2010).
[Crossref]

2009 (1)

S. W. Indratno and A. G. Ramm, “An interative method for solving Fredholm integral equations of the first kind,” Int. J. Comput. Sci. Math. 2, 354–379 (2009).
[Crossref]

2008 (1)

S. Srivastava, M. Haridas, and J. K. Basu, “Optical properties of polymer nanocomposites,” Bull. Mater. Sci. 31, 213–217(2008).
[Crossref]

2007 (2)

B. F. Vajargah and M. Moradi, “Monte Carlo algorithms for solving Fredholm integral equations and Fredholm differential integral equations,” Appl. Math. Sci. 1, 463–470 (2007).

C. Ye, S. S. Pan, X. M. Teng, and G. H. Li, “Optical properties of MgO-TiO2 amorphous composite films,” J. Appl. Phys. 102, 013520 (2007).
[Crossref]

2005 (2)

C. E. Rayford II, G. Schatz, and K. Shuford, “Optical properties of gold nanospheres,” Nanoscape 2, 27–33 (2005).

L. B. Scaffardi, N. Pellegri, O. de Sanctis, and J. O. Tocho, “Sizing gold nanoparticles by optical extinction spectroscopy,” Nanotechnology 16, 158–163 (2005).
[Crossref]

2003 (1)

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

2002 (1)

L. Wind and W. W. Szymanski, “Quantification of scattering corrections to the Beer–Lambert law for transmittance measurements in turbid media,” Meas. Sci. Technol. 13, 270–275(2002).
[Crossref]

1999 (1)

F. Alba, G. M. Crawley, J. Fatkin, D. M. J. Higgs, and P. G. Kippax, “Acoustic spectroscopy as a technique for the particle sizing of high concentration colloids, emulsions and suspensions,” Colloids Surf. A 153, 495–502 (1999).
[Crossref]

1998 (1)

F. Léonardi, A. Allal, and G. Marin, “Determination of the molecular weight distribution of linear polymers by inversion of a blending law on complex viscosities,” Rheol. Acta 37, 199–213(1998).
[Crossref]

1997 (1)

1994 (3)

1993 (1)

K. S. Shifrin and G. Tonna, “Inverse problems related to light scattering in the atmosphere and ocean,” Adv. Geophys. 34, 175–252 (1993).
[Crossref]

1992 (1)

J. Weese, “A reliable and fast method for the solution of Fredholm integral equations of the first kind based on Tikhonov regularization,” Computer Phys. Commun. 69, 99–111 (1992); see program ACGH_v1_0 at http://www.cpc.cs.qub.ac.uk/.
[Crossref]

1991 (1)

C. Elster, J. Honerkamp, and J. Weese, “Using regularization methods for the determination of relaxation and retardation spectra of polymeric liquids,” Rheol. Acta 30, 161–174 (1991).

1989 (1)

U. Riebel and F. Löffler, “The fundamentals of particle size analysis by means of ultrasonic spectrometry,” Part. Part. Syst. Charact. 6, 135–143 (1989).
[Crossref]

1987 (1)

E. Gulari, G. Bazzi, Er. Gulari, and A. Annapragada, “Latex particle size distributions from multiwavelength turbidity spectra,” Part. Part. Syst. Charact. 4, 96–100 (1987).
[Crossref]

1984 (1)

N. G. Khlebtsov, “Role of multiple scattering in turbidimetric investigations of dispersed systems,” J. Appl. Spectrosc. 40, 243–247 (1984).
[Crossref]

1983 (2)

D. H. Melik and H. S. Fogler, “Turbidimetric determination of particle size distributions of colloidal systems,” J. Colloid Interface Sci. 92, 161–180 (1983).
[Crossref]

J. D. Felske, Z. Z. Chu, and J. C. Ku, “Mie scattering subroutines (DBMIE and MIEV0): a comparison of computational times,” Appl. Opt. 22, 2240–2241 (1983).
[Crossref] [PubMed]

1982 (2)

1980 (1)

R. L. Zollars, “Turbidimetric method for on-line determination of latex particle number and particle size distribution,” J. Colloid Interface Sci. 74, 163–172 (1980).
[Crossref]

1979 (1)

1978 (2)

1977 (1)

T. Inagaki, E. T. Arakawa, R. N. Hamm, and M. W. Williams, “Optical properties of polystyrene from the near-infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
[Crossref]

1971 (1)

R. J. Hanson, “A numerical method for solving Fredholm integral equations of the first kind using singular values,” SIAM J. Numer. Anal. 8, 616–622 (1971).
[Crossref]

1964 (1)

K. S. Shifrin and A. Y. Perelman, “Calculation of particle distribution by the data on spectral transparency,” Pure Appl. Geophys. 58, 208–220 (1964).
[Crossref]

1954 (1)

1943 (1)

A. N. Tychonoff, “On the stability of inverse problems,” Dokl. Akad. Nauk SSSR 39, 195–198 (1943).

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 330, 377–445 (1908).
[Crossref]

Alba, F.

F. Alba, G. M. Crawley, J. Fatkin, D. M. J. Higgs, and P. G. Kippax, “Acoustic spectroscopy as a technique for the particle sizing of high concentration colloids, emulsions and suspensions,” Colloids Surf. A 153, 495–502 (1999).
[Crossref]

Allal, A.

F. Léonardi, A. Allal, and G. Marin, “Determination of the molecular weight distribution of linear polymers by inversion of a blending law on complex viscosities,” Rheol. Acta 37, 199–213(1998).
[Crossref]

Annapragada, A.

E. Gulari, G. Bazzi, Er. Gulari, and A. Annapragada, “Latex particle size distributions from multiwavelength turbidity spectra,” Part. Part. Syst. Charact. 4, 96–100 (1987).
[Crossref]

Arakawa, E. T.

T. Inagaki, E. T. Arakawa, R. N. Hamm, and M. W. Williams, “Optical properties of polystyrene from the near-infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
[Crossref]

Bassini, A.

Basu, J. K.

S. Srivastava, M. Haridas, and J. K. Basu, “Optical properties of polymer nanocomposites,” Bull. Mater. Sci. 31, 213–217(2008).
[Crossref]

Bazzi, G.

E. Gulari, G. Bazzi, Er. Gulari, and A. Annapragada, “Latex particle size distributions from multiwavelength turbidity spectra,” Part. Part. Syst. Charact. 4, 96–100 (1987).
[Crossref]

Benz, K. W.

C. Eiche, D. Maier, J. Weese, and K. W. Benz, “Analysis of photoinduced current transient spectroscopy (PICTS) data by a regularization method: application of compensation defects in CdTe,” Adv. Mater. Opt. Electron. 3, 269–274(1994).
[Crossref]

Berne, B. J.

B. J. Berne and R. Pecora, Dynamic Light Scattering: with Applications to Chemistry, Biology, and Physics (Dover, 2000).

Bohren, C. F.

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

Brewster, M. Q.

Brock, R. S.

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

Chu, Z. Z.

Crawley, G. M.

F. Alba, G. M. Crawley, J. Fatkin, D. M. J. Higgs, and P. G. Kippax, “Acoustic spectroscopy as a technique for the particle sizing of high concentration colloids, emulsions and suspensions,” Colloids Surf. A 153, 495–502 (1999).
[Crossref]

Curry, B. P.

de Sanctis, O.

L. B. Scaffardi, N. Pellegri, O. de Sanctis, and J. O. Tocho, “Sizing gold nanoparticles by optical extinction spectroscopy,” Nanotechnology 16, 158–163 (2005).
[Crossref]

Dykman, L. A.

N. G. Khlebtsov and L. A. Dykman, “Optical properties and biomedical applications of plasmonic nanoparticles,” J. Quant. Spectrosc. Radiat. Transfer 111, 1–35 (2010).
[Crossref]

Eiche, C.

C. Eiche, D. Maier, J. Weese, and K. W. Benz, “Analysis of photoinduced current transient spectroscopy (PICTS) data by a regularization method: application of compensation defects in CdTe,” Adv. Mater. Opt. Electron. 3, 269–274(1994).
[Crossref]

Elster, C.

C. Elster, J. Honerkamp, and J. Weese, “Using regularization methods for the determination of relaxation and retardation spectra of polymeric liquids,” Rheol. Acta 30, 161–174 (1991).

Fatkin, J.

F. Alba, G. M. Crawley, J. Fatkin, D. M. J. Higgs, and P. G. Kippax, “Acoustic spectroscopy as a technique for the particle sizing of high concentration colloids, emulsions and suspensions,” Colloids Surf. A 153, 495–502 (1999).
[Crossref]

Felske, J. D.

Ferri, F.

Fogler, H. S.

D. H. Melik and H. S. Fogler, “Turbidimetric determination of particle size distributions of colloidal systems,” J. Colloid Interface Sci. 92, 161–180 (1983).
[Crossref]

Fymat, A. L.

Gulari, E.

E. Gulari, G. Bazzi, Er. Gulari, and A. Annapragada, “Latex particle size distributions from multiwavelength turbidity spectra,” Part. Part. Syst. Charact. 4, 96–100 (1987).
[Crossref]

Gulari, Er.

E. Gulari, G. Bazzi, Er. Gulari, and A. Annapragada, “Latex particle size distributions from multiwavelength turbidity spectra,” Part. Part. Syst. Charact. 4, 96–100 (1987).
[Crossref]

Hamm, R. N.

T. Inagaki, E. T. Arakawa, R. N. Hamm, and M. W. Williams, “Optical properties of polystyrene from the near-infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
[Crossref]

Hanson, R. J.

R. J. Hanson, “A numerical method for solving Fredholm integral equations of the first kind using singular values,” SIAM J. Numer. Anal. 8, 616–622 (1971).
[Crossref]

Haridas, M.

S. Srivastava, M. Haridas, and J. K. Basu, “Optical properties of polymer nanocomposites,” Bull. Mater. Sci. 31, 213–217(2008).
[Crossref]

Hass, G.

Higgs, D. M. J.

F. Alba, G. M. Crawley, J. Fatkin, D. M. J. Higgs, and P. G. Kippax, “Acoustic spectroscopy as a technique for the particle sizing of high concentration colloids, emulsions and suspensions,” Colloids Surf. A 153, 495–502 (1999).
[Crossref]

Honerkamp, J.

C. Elster, J. Honerkamp, and J. Weese, “Using regularization methods for the determination of relaxation and retardation spectra of polymeric liquids,” Rheol. Acta 30, 161–174 (1991).

Hu, X.-H.

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

Huffman, D. R.

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

Inagaki, T.

T. Inagaki, E. T. Arakawa, R. N. Hamm, and M. W. Williams, “Optical properties of polystyrene from the near-infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
[Crossref]

Indratno, S. W.

S. W. Indratno and A. G. Ramm, “An interative method for solving Fredholm integral equations of the first kind,” Int. J. Comput. Sci. Math. 2, 354–379 (2009).
[Crossref]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

Jacobs, K. M.

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

Jones, M. R.

Khlebtsov, N. G.

N. G. Khlebtsov and L. A. Dykman, “Optical properties and biomedical applications of plasmonic nanoparticles,” J. Quant. Spectrosc. Radiat. Transfer 111, 1–35 (2010).
[Crossref]

N. G. Khlebtsov, “Role of multiple scattering in turbidimetric investigations of dispersed systems,” J. Appl. Spectrosc. 40, 243–247 (1984).
[Crossref]

Kippax, P. G.

F. Alba, G. M. Crawley, J. Fatkin, D. M. J. Higgs, and P. G. Kippax, “Acoustic spectroscopy as a technique for the particle sizing of high concentration colloids, emulsions and suspensions,” Colloids Surf. A 153, 495–502 (1999).
[Crossref]

Ku, J. C.

Lacis, A. A.

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

Laven, P. L.

P. L. Laven, MiePlot (http://www.philiplaven.com/mieplot.htm).

Léonardi, F.

F. Léonardi, A. Allal, and G. Marin, “Determination of the molecular weight distribution of linear polymers by inversion of a blending law on complex viscosities,” Rheol. Acta 37, 199–213(1998).
[Crossref]

Leong, K. H.

Li, G. H.

C. Ye, S. S. Pan, X. M. Teng, and G. H. Li, “Optical properties of MgO-TiO2 amorphous composite films,” J. Appl. Phys. 102, 013520 (2007).
[Crossref]

Löffler, F.

U. Riebel and F. Löffler, “The fundamentals of particle size analysis by means of ultrasonic spectrometry,” Part. Part. Syst. Charact. 6, 135–143 (1989).
[Crossref]

Lu, J. Q.

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

Ma, X.

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

Maier, D.

C. Eiche, D. Maier, J. Weese, and K. W. Benz, “Analysis of photoinduced current transient spectroscopy (PICTS) data by a regularization method: application of compensation defects in CdTe,” Adv. Mater. Opt. Electron. 3, 269–274(1994).
[Crossref]

Marin, G.

F. Léonardi, A. Allal, and G. Marin, “Determination of the molecular weight distribution of linear polymers by inversion of a blending law on complex viscosities,” Rheol. Acta 37, 199–213(1998).
[Crossref]

Melik, D. H.

D. H. Melik and H. S. Fogler, “Turbidimetric determination of particle size distributions of colloidal systems,” J. Colloid Interface Sci. 92, 161–180 (1983).
[Crossref]

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 330, 377–445 (1908).
[Crossref]

Mishchenko, M. I.

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

Moradi, M.

B. F. Vajargah and M. Moradi, “Monte Carlo algorithms for solving Fredholm integral equations and Fredholm differential integral equations,” Appl. Math. Sci. 1, 463–470 (2007).

Paganini, E.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids Volumes I & II (Elsevier, 1998).

Pan, S. S.

C. Ye, S. S. Pan, X. M. Teng, and G. H. Li, “Optical properties of MgO-TiO2 amorphous composite films,” J. Appl. Phys. 102, 013520 (2007).
[Crossref]

Pecora, R.

B. J. Berne and R. Pecora, Dynamic Light Scattering: with Applications to Chemistry, Biology, and Physics (Dover, 2000).

Pellegri, N.

L. B. Scaffardi, N. Pellegri, O. de Sanctis, and J. O. Tocho, “Sizing gold nanoparticles by optical extinction spectroscopy,” Nanotechnology 16, 158–163 (2005).
[Crossref]

Perelman, A. Y.

K. S. Shifrin and A. Y. Perelman, “Calculation of particle distribution by the data on spectral transparency,” Pure Appl. Geophys. 58, 208–220 (1964).
[Crossref]

Ramm, A. G.

S. W. Indratno and A. G. Ramm, “An interative method for solving Fredholm integral equations of the first kind,” Int. J. Comput. Sci. Math. 2, 354–379 (2009).
[Crossref]

Rayford, C. E.

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C. Ye, S. S. Pan, X. M. Teng, and G. H. Li, “Optical properties of MgO-TiO2 amorphous composite films,” J. Appl. Phys. 102, 013520 (2007).
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L. B. Scaffardi, N. Pellegri, O. de Sanctis, and J. O. Tocho, “Sizing gold nanoparticles by optical extinction spectroscopy,” Nanotechnology 16, 158–163 (2005).
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C. Elster, J. Honerkamp, and J. Weese, “Using regularization methods for the determination of relaxation and retardation spectra of polymeric liquids,” Rheol. Acta 30, 161–174 (1991).

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C. Eiche, D. Maier, J. Weese, and K. W. Benz, “Analysis of photoinduced current transient spectroscopy (PICTS) data by a regularization method: application of compensation defects in CdTe,” Adv. Mater. Opt. Electron. 3, 269–274(1994).
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J. Weese, “A reliable and fast method for the solution of Fredholm integral equations of the first kind based on Tikhonov regularization,” Computer Phys. Commun. 69, 99–111 (1992); see program ACGH_v1_0 at http://www.cpc.cs.qub.ac.uk/.
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A. N. Tychonoff, “On the stability of inverse problems,” Dokl. Akad. Nauk SSSR 39, 195–198 (1943).

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C. Ye, S. S. Pan, X. M. Teng, and G. H. Li, “Optical properties of MgO-TiO2 amorphous composite films,” J. Appl. Phys. 102, 013520 (2007).
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L. Wind and W. W. Szymanski, “Quantification of scattering corrections to the Beer–Lambert law for transmittance measurements in turbid media,” Meas. Sci. Technol. 13, 270–275(2002).
[Crossref]

Nanoscape (1)

C. E. Rayford II, G. Schatz, and K. Shuford, “Optical properties of gold nanospheres,” Nanoscape 2, 27–33 (2005).

Nanotechnology (1)

L. B. Scaffardi, N. Pellegri, O. de Sanctis, and J. O. Tocho, “Sizing gold nanoparticles by optical extinction spectroscopy,” Nanotechnology 16, 158–163 (2005).
[Crossref]

Part. Part. Syst. Charact. (2)

E. Gulari, G. Bazzi, Er. Gulari, and A. Annapragada, “Latex particle size distributions from multiwavelength turbidity spectra,” Part. Part. Syst. Charact. 4, 96–100 (1987).
[Crossref]

U. Riebel and F. Löffler, “The fundamentals of particle size analysis by means of ultrasonic spectrometry,” Part. Part. Syst. Charact. 6, 135–143 (1989).
[Crossref]

Phys. Med. Biol. (1)

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

Phys. Rev. B (1)

T. Inagaki, E. T. Arakawa, R. N. Hamm, and M. W. Williams, “Optical properties of polystyrene from the near-infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
[Crossref]

Pure Appl. Geophys. (1)

K. S. Shifrin and A. Y. Perelman, “Calculation of particle distribution by the data on spectral transparency,” Pure Appl. Geophys. 58, 208–220 (1964).
[Crossref]

Rheol. Acta (2)

C. Elster, J. Honerkamp, and J. Weese, “Using regularization methods for the determination of relaxation and retardation spectra of polymeric liquids,” Rheol. Acta 30, 161–174 (1991).

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Other (12)

Malvern Instruments Zetasizer Nano ZS (http://www.malvern.com).

Beckman Coulter PCS Submicron Particle Analyzer, http://www.beckmancoulter.com.

P. L. Laven, MiePlot (http://www.philiplaven.com/mieplot.htm).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

E. D. Palik, Handbook of Optical Constants of Solids Volumes I & II (Elsevier, 1998).

See http://www.dow.com/cyclotene/solution/refwave.htm.

See https://www.reaxys.com.

G.Gouesbet and G.Gréhan (eds.), Optical Particle Sizing: Theory and Practice (Plenum, 1988).

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

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

B. J. Berne and R. Pecora, Dynamic Light Scattering: with Applications to Chemistry, Biology, and Physics (Dover, 2000).

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

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Figures (6)

Fig. 1
Fig. 1 Schematic of the laser transmission spectrometer.
Fig. 2
Fig. 2 (a) Theoretical (Mie model) and experimental extinction versus wavelength for samples containing homogeneous polystyrene spheres at three densities. (b) Corresponding plots of the density distribution versus diameter after inversion The Mie model result has been linearly scaled for ease of presentation as noted in the text. The distribution given by the manufacturer is also shown.
Fig. 3
Fig. 3 Accuracy tests. (a) Inversion results for theoretically generated (input) extinction data for particles of a given diameter. (b) Inversion results for theoretically generated (input) extinction data for particles of a given density (n). (c) Multiple results for measurements of particle diameter compared with manufacturer’s reference values. (d) Multiple results for measurements of particle density compared with manufacturer’s reference values.
Fig. 4
Fig. 4 Evaluation of the resolution capabilities of LTS for mixtures of two diameters ( D 1 and D 2 ) of polystyrene spheres of near equal densities. (a) Outcome of the inversion for simulated mixtures of two particle diameters. Green areas indicate resolved peaks, yellow areas indicate conditional resolution (see text), white areas indicate lack of resolution. (b) Separate experimental results for two samples, each with a different particle diameter (red and blue curves and data points), and a sample comprising a mixture of particles with these same two diameters at near equal densities (solid black curve and data points). The peak positions and the integral under each peak are indicated on the plot.
Fig. 5
Fig. 5 Numerical inversion results for theoretically generated comb and Gaussian distribution functions. (a) Input comb distribution in black (simulating a sample with the same distribution) and resultant inversion in red. (b) Results for a theoretically generated Gaussian distribution (black) and inversion (red).
Fig. 6
Fig. 6 (a) Sensitivity comparison between DLS (green circles) and LTS (orange squares for gold and blue squares for polystyrene) as a function of particle diameter. (b) Resolution comparison of DLS and LTS. The blue and red data points and curves are LTS results for homogeneous equal-volume-percent samples of 46 and 206 nm particles, respectively. The lower black curve (square data points) with the two peaks is the LTS measurement of an equal-volume-percent mixture of these particles. The LTS peaks for the larger-diameter particles have been magnified for clarity. The green points and curve is the DLS result for the same mixed sample as measured by LTS (black curve and data points).

Equations (12)

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T ( λ ) = P out ( λ ) P in ( λ ) = exp [ α ( λ ) z ] .
σ ext ( λ i , r j ) = σ abs ( λ i , r j ) + d σ scat ( λ i , r j ) d Ω d Ω = σ abs ( λ i , r j ) + σ scat ( λ i , r j ) .
T ( λ i ) = j = 1 N T ( λ i , r j ) = exp [ z j = 1 N σ ext ( λ i , r j ) n j ] .
α theory ( λ i ) j = 1 N σ ext ( λ i , r j ) n j = ln T ( λ i ) z | theory .
D A P ( λ i ) = signal through particles and fluid in beam A , D B F ( λ i ) = signal through fluid alone in beam B , D A F ( λ i ) = signal through fluid alone in beam A , D B P ( λ i ) = signal through particles and fluid in beam B .
D A P ( λ i ) = ε A ( λ i ) T P ( λ i ) T F ( λ i ) P A ( λ i ) , D B F ( λ i ) = ε B ( λ i ) T F ( λ i ) P B ( λ i ) , D A F ( λ i ) = ε A ( λ i ) T F ( λ i ) P A ( λ i ) , D B P ( λ i ) = ε B ( λ i ) T P ( λ i ) T F ( λ i ) P B ( λ i ) .
R ( λ i ) = D A P ( λ i ) D B F ( λ i ) D A F ( λ i ) D B P ( λ i ) = ε A ( λ i ) T P ( λ i ) T F ( λ i ) P A ( λ i ) ε B ( λ i ) T F ( λ i ) P B ( λ i ) ε A ( λ i ) T F ( λ i ) P A ( λ i ) ε B ( λ i ) T P ( λ i ) T F ( λ i ) P B ( λ i ) = [ T P ( λ i ) ] 2 .
T P ( λ i ) | meas = R ( λ i ) = D A P ( λ i ) D B F ( λ i ) D A F ( λ i ) D B P ( λ i ) .
α meas ( λ i ) = ln T P ( λ i ) z | meas .
α meas ( λ i ) j = 1 N σ ext ( λ i , r j ) n j .
[ α i ] = [ σ i j ] · [ n j ] or more compactly α = σ · n .
σ · n α 2 + a Γ · n 2 .

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