Abstract

This work describes the design and use of an optical apparatus to measure the far-field elastic light-scattering pattern for a single particle over two angular-dimensions. A spatial filter composed of a mirror with a small through-hole is used to enable collection of the pattern uncommonly close to the forward direction; to within tenths of a degree. Minor modifications of the design allow for the simultaneous measurement of a particle’s image along with its two-dimensional scattering pattern. Example measurements are presented involving single micrometer-sized glass spherical particles confined in an electrodynamic trap and a dilute suspension of polystyrene latex particles in water. A small forward-angle technique, called Guinier analysis, is used to determine a particle-size estimate directly from the measured pattern without a priori knowledge of the particle refractive index. Comparison of these size estimates to those obtained by fitting the measurements to Mie theory reveals relative errors as low as 2%.

© 2010 Optical Society of America

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References

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  1. C. M. Sorensen, “Light scattering by fractal aggregates: A review,” Aerosol Sci. Technol. 35, 648–687 (2001).
  2. R. Dhaubhadel, An Experimental Study of Dense Aerosol Aggregations, Doctoral Thesis, (Kansas State University, 2008), freely available at http://hdl.handle.net/2097/663.
  3. K. B. Aptowicz, R. G. Pinnick, S. C. Hill, Y. L. Pan, and R. K. Chang, “Optical scattering patterns from single urban aerosol particles at Adelphi, Maryland, USA: A classification relating to particle morphologies,” J. Geophys. Res. 111, D12212 (2006).
    [CrossRef]
  4. M. I. Mishchenko, “Electromagnetic scattering by nonspherical particles: A tutorial review,” J. Quant. Spectrosc. Radiat. Transf. 110, 808–832 (2009).
    [CrossRef]
  5. C. M. Sorensen, and D. Shi, “Guinier analysis for homogeneous dielectric spheres of arbitrary size,” Opt. Commun. 178, 31–36 (2000).
    [CrossRef]
  6. M. J. Berg, C. M. Sorensen, and A. Chakrabarti, “Reflection symmetry of a sphere’s internal field and its consequences on scattering: a microphysical approach,” J. Opt. Soc. Am. A 25, 98–107 (2008).
    [CrossRef]
  7. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds., Light Scattering by Nonspherical Particles (Academic Press, San Diego 2000), pts. IV–V.
  8. A. Guinier, and G. Fournet, Small-Angle Scattering of X-Rays (Wiely, 1955).
  9. F. Ferri, “Use of a charged coupled device camera for low-angle elastic light scattering,” Rev. Sci. Instrum. 68, 2265–2273 (1997).
    [CrossRef]
  10. S. Arnold, and L. M. Folan, “Spherical void electrodynamic levitator,” Rev. Sci. Instrum. 58, 1732–1735 (1987).
    [CrossRef]
  11. S. Arnold, and L. M. Folan, “Fluorescence spectrometer for a single electrodynamically levitated microparticle,” Rev. Sci. Instrum. 57, 2250–2253 (1986).
    [CrossRef]
  12. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005), pp. 103–108.
  13. J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, 1999) pp. 490–492.
  14. C. F. Bohren, and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983) Ch. 4.
  15. M. J. Berg, C. M. Sorensen, and A. Chakrabarti, “Explanation of the patterns in Mie theory,” J. Quant. Spectrosc. Radiat. Transf. 111, 782–794 (2010).
    [CrossRef]

2010 (1)

M. J. Berg, C. M. Sorensen, and A. Chakrabarti, “Explanation of the patterns in Mie theory,” J. Quant. Spectrosc. Radiat. Transf. 111, 782–794 (2010).
[CrossRef]

2009 (1)

M. I. Mishchenko, “Electromagnetic scattering by nonspherical particles: A tutorial review,” J. Quant. Spectrosc. Radiat. Transf. 110, 808–832 (2009).
[CrossRef]

2008 (1)

2006 (1)

K. B. Aptowicz, R. G. Pinnick, S. C. Hill, Y. L. Pan, and R. K. Chang, “Optical scattering patterns from single urban aerosol particles at Adelphi, Maryland, USA: A classification relating to particle morphologies,” J. Geophys. Res. 111, D12212 (2006).
[CrossRef]

2001 (1)

C. M. Sorensen, “Light scattering by fractal aggregates: A review,” Aerosol Sci. Technol. 35, 648–687 (2001).

2000 (1)

C. M. Sorensen, and D. Shi, “Guinier analysis for homogeneous dielectric spheres of arbitrary size,” Opt. Commun. 178, 31–36 (2000).
[CrossRef]

1997 (1)

F. Ferri, “Use of a charged coupled device camera for low-angle elastic light scattering,” Rev. Sci. Instrum. 68, 2265–2273 (1997).
[CrossRef]

1987 (1)

S. Arnold, and L. M. Folan, “Spherical void electrodynamic levitator,” Rev. Sci. Instrum. 58, 1732–1735 (1987).
[CrossRef]

1986 (1)

S. Arnold, and L. M. Folan, “Fluorescence spectrometer for a single electrodynamically levitated microparticle,” Rev. Sci. Instrum. 57, 2250–2253 (1986).
[CrossRef]

Aptowicz, K. B.

K. B. Aptowicz, R. G. Pinnick, S. C. Hill, Y. L. Pan, and R. K. Chang, “Optical scattering patterns from single urban aerosol particles at Adelphi, Maryland, USA: A classification relating to particle morphologies,” J. Geophys. Res. 111, D12212 (2006).
[CrossRef]

Arnold, S.

S. Arnold, and L. M. Folan, “Spherical void electrodynamic levitator,” Rev. Sci. Instrum. 58, 1732–1735 (1987).
[CrossRef]

S. Arnold, and L. M. Folan, “Fluorescence spectrometer for a single electrodynamically levitated microparticle,” Rev. Sci. Instrum. 57, 2250–2253 (1986).
[CrossRef]

Berg, M. J.

M. J. Berg, C. M. Sorensen, and A. Chakrabarti, “Explanation of the patterns in Mie theory,” J. Quant. Spectrosc. Radiat. Transf. 111, 782–794 (2010).
[CrossRef]

M. J. Berg, C. M. Sorensen, and A. Chakrabarti, “Reflection symmetry of a sphere’s internal field and its consequences on scattering: a microphysical approach,” J. Opt. Soc. Am. A 25, 98–107 (2008).
[CrossRef]

Chakrabarti, A.

M. J. Berg, C. M. Sorensen, and A. Chakrabarti, “Explanation of the patterns in Mie theory,” J. Quant. Spectrosc. Radiat. Transf. 111, 782–794 (2010).
[CrossRef]

M. J. Berg, C. M. Sorensen, and A. Chakrabarti, “Reflection symmetry of a sphere’s internal field and its consequences on scattering: a microphysical approach,” J. Opt. Soc. Am. A 25, 98–107 (2008).
[CrossRef]

Chang, R. K.

K. B. Aptowicz, R. G. Pinnick, S. C. Hill, Y. L. Pan, and R. K. Chang, “Optical scattering patterns from single urban aerosol particles at Adelphi, Maryland, USA: A classification relating to particle morphologies,” J. Geophys. Res. 111, D12212 (2006).
[CrossRef]

Ferri, F.

F. Ferri, “Use of a charged coupled device camera for low-angle elastic light scattering,” Rev. Sci. Instrum. 68, 2265–2273 (1997).
[CrossRef]

Folan, L. M.

S. Arnold, and L. M. Folan, “Spherical void electrodynamic levitator,” Rev. Sci. Instrum. 58, 1732–1735 (1987).
[CrossRef]

S. Arnold, and L. M. Folan, “Fluorescence spectrometer for a single electrodynamically levitated microparticle,” Rev. Sci. Instrum. 57, 2250–2253 (1986).
[CrossRef]

Hill, S. C.

K. B. Aptowicz, R. G. Pinnick, S. C. Hill, Y. L. Pan, and R. K. Chang, “Optical scattering patterns from single urban aerosol particles at Adelphi, Maryland, USA: A classification relating to particle morphologies,” J. Geophys. Res. 111, D12212 (2006).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, “Electromagnetic scattering by nonspherical particles: A tutorial review,” J. Quant. Spectrosc. Radiat. Transf. 110, 808–832 (2009).
[CrossRef]

Pan, Y. L.

K. B. Aptowicz, R. G. Pinnick, S. C. Hill, Y. L. Pan, and R. K. Chang, “Optical scattering patterns from single urban aerosol particles at Adelphi, Maryland, USA: A classification relating to particle morphologies,” J. Geophys. Res. 111, D12212 (2006).
[CrossRef]

Pinnick, R. G.

K. B. Aptowicz, R. G. Pinnick, S. C. Hill, Y. L. Pan, and R. K. Chang, “Optical scattering patterns from single urban aerosol particles at Adelphi, Maryland, USA: A classification relating to particle morphologies,” J. Geophys. Res. 111, D12212 (2006).
[CrossRef]

Shi, D.

C. M. Sorensen, and D. Shi, “Guinier analysis for homogeneous dielectric spheres of arbitrary size,” Opt. Commun. 178, 31–36 (2000).
[CrossRef]

Sorensen, C. M.

M. J. Berg, C. M. Sorensen, and A. Chakrabarti, “Explanation of the patterns in Mie theory,” J. Quant. Spectrosc. Radiat. Transf. 111, 782–794 (2010).
[CrossRef]

M. J. Berg, C. M. Sorensen, and A. Chakrabarti, “Reflection symmetry of a sphere’s internal field and its consequences on scattering: a microphysical approach,” J. Opt. Soc. Am. A 25, 98–107 (2008).
[CrossRef]

C. M. Sorensen, “Light scattering by fractal aggregates: A review,” Aerosol Sci. Technol. 35, 648–687 (2001).

C. M. Sorensen, and D. Shi, “Guinier analysis for homogeneous dielectric spheres of arbitrary size,” Opt. Commun. 178, 31–36 (2000).
[CrossRef]

Aerosol Sci. Technol. (1)

C. M. Sorensen, “Light scattering by fractal aggregates: A review,” Aerosol Sci. Technol. 35, 648–687 (2001).

J. Geophys. Res. (1)

K. B. Aptowicz, R. G. Pinnick, S. C. Hill, Y. L. Pan, and R. K. Chang, “Optical scattering patterns from single urban aerosol particles at Adelphi, Maryland, USA: A classification relating to particle morphologies,” J. Geophys. Res. 111, D12212 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

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

M. J. Berg, C. M. Sorensen, and A. Chakrabarti, “Explanation of the patterns in Mie theory,” J. Quant. Spectrosc. Radiat. Transf. 111, 782–794 (2010).
[CrossRef]

M. I. Mishchenko, “Electromagnetic scattering by nonspherical particles: A tutorial review,” J. Quant. Spectrosc. Radiat. Transf. 110, 808–832 (2009).
[CrossRef]

Opt. Commun. (1)

C. M. Sorensen, and D. Shi, “Guinier analysis for homogeneous dielectric spheres of arbitrary size,” Opt. Commun. 178, 31–36 (2000).
[CrossRef]

Rev. Sci. Instrum. (3)

F. Ferri, “Use of a charged coupled device camera for low-angle elastic light scattering,” Rev. Sci. Instrum. 68, 2265–2273 (1997).
[CrossRef]

S. Arnold, and L. M. Folan, “Spherical void electrodynamic levitator,” Rev. Sci. Instrum. 58, 1732–1735 (1987).
[CrossRef]

S. Arnold, and L. M. Folan, “Fluorescence spectrometer for a single electrodynamically levitated microparticle,” Rev. Sci. Instrum. 57, 2250–2253 (1986).
[CrossRef]

Other (6)

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005), pp. 103–108.

J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, 1999) pp. 490–492.

C. F. Bohren, and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983) Ch. 4.

R. Dhaubhadel, An Experimental Study of Dense Aerosol Aggregations, Doctoral Thesis, (Kansas State University, 2008), freely available at http://hdl.handle.net/2097/663.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds., Light Scattering by Nonspherical Particles (Academic Press, San Diego 2000), pts. IV–V.

A. Guinier, and G. Fournet, Small-Angle Scattering of X-Rays (Wiely, 1955).

Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1.

Cross-sectional view of the spherical void electrodynamic levitator (SVEL), diagram (a), and its driving circuit, diagram (b). Single charged particle can be trapped in the SVEL as described in the text.

Fig. 2.
Fig. 2.

Optical arrangement used to obtain two-dimensional scattering patterns for single particles. The bottom-left inset diagram shows detail of the spatial-filter mirror (SFM). In short, the near-forward angular range of the measurements is achieved by the SFM and lens L 1; unscattered incident light is focused into the through-hole in the SFM while the scattering pattern is reflected. See text for further explanation.

Fig. 3.
Fig. 3.

Comparison between scattering-pattern measurement and calculation for a single trapped glass-microsphere. Plot (a) shows the azimuthally averaged scattering curve while plots (b) and (c) show the two-dimensional measured and calculated patterns, respectively. The horizontal streak seen in plot (b) is due to blooming on the CCD chip and is not a feature of the scattering pattern.

Fig. 4.
Fig. 4.

Application of Guinier analysis to estimate particle size D est without knowledge of the refractive index. The particles here are single trapped glass-microspheres with four nominal sizes ranging from 8–20μm in diameter and labeled (a)–(d). The Guinier-analysis determined size-estimates are shown along with those resulting from Mie-theory fits. The polynomial fit to the forward most portion of the measured data, used to determine I(0), is shown by the fine-dashed curves.

Fig. 5.
Fig. 5.

Optical arrangement used to obtain simultaneous particle images and two-dimensional scattering patterns. The design is similar to Fig. 2 with the modifications described it the text. Figure 6 presents a movie showing an example of the images and patterns observed on the copy paper screen.

Fig. 6.
Fig. 6.

Single-frame excerpt from a video recording of the images seen on the copy-paper screen in Fig. 5. The particles are 20μm diameter polystyrene latex microspheres in solution. Images of these particles along with their two-dimensional far-field scattering pattern can be seen on the left and right side of the screen, respectively. Notice that the motion of the particles does not disturb the pattern, thus illustrating the translational invariance of the optical design. A real-time video is linked to this figure (Media 1).

Equations (1)

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D est π q o where I ( q o ) 0.6 I ( 0 ) .

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