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 ( $210–2300\mathrm{nm}$ ) 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 $3000\mathrm{nm}$ . For polystyrene particles 404 to $1025\mathrm{nm}$ in size, uncertainties of $\pm 0.5\%$ in size and $\pm 4\%$ in density were obtained. For polystyrene particles from 46 to $3000\mathrm{nm}$ in size, the dynamic range of the system spans densities from $\sim {10}^3/\mathrm{ml}$ to $\sim {10}^{10}/\mathrm{ml}$ ( $5\times {10}^{-8}$ to $0.5\text{vol.}\%$ ), implying a sensitivity 5 orders of magnitude higher than dynamic light scattering.

© 2010 Optical Society of America

1. H. C. van de Hulst, Light Scattering by Small Particles(Dover, 1981).
2. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).
3. B. J. Berne and R. Pecora, Dynamic Light Scattering: with Applications to Chemistry, Biology, and Physics (Dover, 2000).
4. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).
5. 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]
6. 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]
7. 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]
8. M. R. Jones, B. P. Curry, M. Q. Brewster, and K. H. Leong, “Inversion of light-scattering measurements for particle size and optical constants: theoretical study,” Appl. Opt. 33, 4025–4034(1994). [CrossRef] [PubMed]
9. M. R. Jones, K. H. Leong, M. Q. Brewster, and B. P. Curry, “Inversion of light-scattering measurements for particle size and optical constants: experimental study,” Appl. Opt. 33, 4035–4041 (1994). [CrossRef] [PubMed]
10. 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]
11. F. Ferri, A. Bassini, and E. Paganini, “Commercial spectrophotometer for particle sizing,” Appl. Opt. 36, 885–891 (1997). [CrossRef] [PubMed]
12. G.Gouesbet and G.Gréhan (eds.), Optical Particle Sizing: Theory and Practice (Plenum, 1988).
13. K. S. Shifrin and G. Tonna, “Inverse problems related to light scattering in the atmosphere and ocean,” Adv. Geophys. 34, 175–252 (1993). [CrossRef]
14. 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]
15. 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]
16. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 330, 377–445 (1908). [CrossRef]
17. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
18. W. G. Tam and A. Zardecki, “Multiple scattering corrections to the Beer–Lambert law. 1: Open detector,” Appl. Opt. 21, 2405–2412 (1982). [CrossRef] [PubMed]
19. A. Zardecki and W. G. Tam, “Multiple scattering corrections to the Beer–Lambert law. 2: Detector with a variable field of view,” Appl. Opt. 21, 2413–2420 (1982). [CrossRef] [PubMed]
20. N. G. Khlebtsov, “Role of multiple scattering in turbidimetric investigations of dispersed systems,” J. Appl. Spectrosc. 40, 243–247 (1984). [CrossRef]
21. 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]
22. A. N. Tychonoff, “On the stability of inverse problems,” Dokl. Akad. Nauk SSSR 39, 195–198 (1943).
23. 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]
24. P. L. Laven, MiePlot (http://www.philiplaven.com/mieplot.htm).
25. 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]
26. 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).
27. 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]
28. 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]
29. 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]
30. 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]
31. E. D. Palik, Handbook of Optical Constants of Solids Volumes I & II (Elsevier, 1998).
32. C. E. Rayford II, G. Schatz, and K. Shuford, “Optical properties of gold nanospheres,” Nanoscape 2, 27–33 (2005).
33. G. Hass and C. D. Salzberg, “Optical properties of silicon monoxide in the wavelength region from 0.24 to 14.0 microns,” J. Opt. Soc. Am. 44, 181–183 (1954). [CrossRef]
34. 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]
35. S. Srivastava, M. Haridas, and J. K. Basu, “Optical properties of polymer nanocomposites,” Bull. Mater. Sci. 31, 213–217(2008). [CrossRef]
36. See http://www.dow.com/cyclotene/solution/refwave.htm.
37. See https://www.reaxys.com.
38. 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]
39. A. L. Fymat, “Analytical inversions in remote sensing of particle size distributions. I. Multispectral extinction in the anomalous diffraction approximation,” Appl. Opt. 17, 1675–1676 (1978). [CrossRef]
40. A. L. Fymat, “Analytical inversions in remote sensing of particle size distributions. II. Angular and spectral scattering in diffraction approximation,” Appl. Opt. 17, 1677–1678(1978). [CrossRef] [PubMed]
41. A. L. Fymat, “Analytical inversions in remote sensing of particle size distributions. III. Angular and spectral scattering in the Rayleigh–Gans–Born approximation for particles of various geometrical shapes,” Appl. Opt. 18, 126–130(1979). [CrossRef] [PubMed]
42. 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]
43. 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).
44. 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]
45. 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]
46. Malvern Instruments Zetasizer Nano ZS (http://www.malvern.com).
47. Beckman Coulter PCS Submicron Particle Analyzer, http://www.beckmancoulter.com.

Adv. Geophys.

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

Adv. Mater. Opt. Electron.

• 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]

Ann. Phys.

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

Appl. Math. Sci.

• 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).

Appl. Opt.

• A. L. Fymat, “Analytical inversions in remote sensing of particle size distributions. I. Multispectral extinction in the anomalous diffraction approximation,” Appl. Opt. 17, 1675–1676 (1978). [CrossRef]
• A. L. Fymat, “Analytical inversions in remote sensing of particle size distributions. II. Angular and spectral scattering in diffraction approximation,” Appl. Opt. 17, 1677–1678(1978). [CrossRef] [PubMed]
• A. L. Fymat, “Analytical inversions in remote sensing of particle size distributions. III. Angular and spectral scattering in the Rayleigh–Gans–Born approximation for particles of various geometrical shapes,” Appl. Opt. 18, 126–130(1979). [CrossRef] [PubMed]
• 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]
• F. Ferri, A. Bassini, and E. Paganini, “Commercial spectrophotometer for particle sizing,” Appl. Opt. 36, 885–891 (1997). [CrossRef] [PubMed]
• W. G. Tam and A. Zardecki, “Multiple scattering corrections to the Beer–Lambert law. 1: Open detector,” Appl. Opt. 21, 2405–2412 (1982). [CrossRef] [PubMed]
• A. Zardecki and W. G. Tam, “Multiple scattering corrections to the Beer–Lambert law. 2: Detector with a variable field of view,” Appl. Opt. 21, 2413–2420 (1982). [CrossRef] [PubMed]
• M. R. Jones, B. P. Curry, M. Q. Brewster, and K. H. Leong, “Inversion of light-scattering measurements for particle size and optical constants: theoretical study,” Appl. Opt. 33, 4025–4034(1994). [CrossRef] [PubMed]
• M. R. Jones, K. H. Leong, M. Q. Brewster, and B. P. Curry, “Inversion of light-scattering measurements for particle size and optical constants: experimental study,” Appl. Opt. 33, 4035–4041 (1994). [CrossRef] [PubMed]

Bull. Mater. Sci.

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

Colloids Surf. A

• 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]

Computer Phys. Commun.

• 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]

Dokl. Akad. Nauk SSSR

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

Int. J. Comput. Sci. Math.

• 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]

J. Appl. Phys.

• 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]

J. Appl. Spectrosc.

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

J. Colloid Interface Sci.

• 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]
• 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. Opt. Soc. Am.

• G. Hass and C. D. Salzberg, “Optical properties of silicon monoxide in the wavelength region from 0.24 to 14.0 microns,” J. Opt. Soc. Am. 44, 181–183 (1954). [CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

• 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]

Meas. Sci. Technol.

• 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

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

Nanotechnology

• 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.

• 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.

• 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

• 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.

• 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

• 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).
• 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]

SIAM J. Numer. Anal.

• 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]

Other

• 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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