Abstract

This work presents a new concept to measure the extinction cross section for a single particle in situ. The concept involves recording the hologram produced by the interference of a particle’s forward-scattered light with the incident light. This interference pattern is fundamentally connected to the energy flow that gives rise to extinction, and, by integrating this measured pattern, one obtains an approximation for the cross section. Mie theory is used to show that this approximation can be as little as 1% in error of the true value for many cases of practical interest. Moreover, since an image of the particle can be computationally reconstructed from a measured hologram using the Fresnel–Kirchhoff diffraction theory, one can obtain the cross section simultaneously with the particle shape and size.

© 2014 Optical Society of America

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References

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1957).
  2. C. F. Borhen and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  3. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).
  4. M. J. Berg, C. M. Sorensen, and A. Chakrabarti, J. Opt. Soc. Am. A 25, 1504 (2008).
    [CrossRef]
  5. M. I. Mishchenko, M. J. Berg, C. M. Sorensen, and C. V. M. van der Mee, J. Quant. Spectrosc. Radiat. Transfer 110, 323 (2009).
    [CrossRef]
  6. T. Kreis, Handbook of Holographic Interferometry; Optical and Digital Methods (Wiley, 2005).
  7. M. J. Berg and G. Videen, J. Quant. Spectrosc. Radiat. Transfer 112, 1776 (2011).
    [CrossRef]
  8. M. J. Berg, C. M. Sorensen, and A. Chakrabarti, J. Opt. Soc. Am. A 25, 1514 (2008).
    [CrossRef]

2011 (1)

M. J. Berg and G. Videen, J. Quant. Spectrosc. Radiat. Transfer 112, 1776 (2011).
[CrossRef]

2009 (1)

M. I. Mishchenko, M. J. Berg, C. M. Sorensen, and C. V. M. van der Mee, J. Quant. Spectrosc. Radiat. Transfer 110, 323 (2009).
[CrossRef]

2008 (2)

Berg, M. J.

M. J. Berg and G. Videen, J. Quant. Spectrosc. Radiat. Transfer 112, 1776 (2011).
[CrossRef]

M. I. Mishchenko, M. J. Berg, C. M. Sorensen, and C. V. M. van der Mee, J. Quant. Spectrosc. Radiat. Transfer 110, 323 (2009).
[CrossRef]

M. J. Berg, C. M. Sorensen, and A. Chakrabarti, J. Opt. Soc. Am. A 25, 1514 (2008).
[CrossRef]

M. J. Berg, C. M. Sorensen, and A. Chakrabarti, J. Opt. Soc. Am. A 25, 1504 (2008).
[CrossRef]

Borhen, C. F.

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

Chakrabarti, A.

Huffman, D. R.

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

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry; Optical and Digital Methods (Wiley, 2005).

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).

Mishchenko, M. I.

M. I. Mishchenko, M. J. Berg, C. M. Sorensen, and C. V. M. van der Mee, J. Quant. Spectrosc. Radiat. Transfer 110, 323 (2009).
[CrossRef]

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

Sorensen, C. M.

Travis, L. D.

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

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1957).

van der Mee, C. V. M.

M. I. Mishchenko, M. J. Berg, C. M. Sorensen, and C. V. M. van der Mee, J. Quant. Spectrosc. Radiat. Transfer 110, 323 (2009).
[CrossRef]

Videen, G.

M. J. Berg and G. Videen, J. Quant. Spectrosc. Radiat. Transfer 112, 1776 (2011).
[CrossRef]

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

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

M. J. Berg and G. Videen, J. Quant. Spectrosc. Radiat. Transfer 112, 1776 (2011).
[CrossRef]

M. I. Mishchenko, M. J. Berg, C. M. Sorensen, and C. V. M. van der Mee, J. Quant. Spectrosc. Radiat. Transfer 110, 323 (2009).
[CrossRef]

Other (4)

T. Kreis, Handbook of Holographic Interferometry; Optical and Digital Methods (Wiley, 2005).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1957).

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

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 (3)

Fig. 1.
Fig. 1.

Sketch of the spherical surface Ssph and composite surface S1S2 in relation to the particle and incident wave. Also shown is particle–detector separation d and detector angle θdet.

Fig. 2.
Fig. 2.

Behavior of the f and δ curves of Eqs. (9) and (10) as a function of θdet. Plots (a)–(c) show the curves for nonabsorbing spheres with m=1.33+0i and R=λ, 2λ, and 5λ, respectively, whereas the sphere in plot (d) is absorbing with m=1.55+0.1i and R=5λ. Also shown are the points along the f curve, after which its error in approximating Cext drops below 10% (all plots) and 1% in plots (c) and (d).

Fig. 3.
Fig. 3.

Same as Fig. 2 except here the plots show the behavior of f and δ for increasing particle-detector separation d, ranging from the near field to the far field as shown. The particle is the same in each plot, with m=1.33+0i and R=2λ.

Equations (11)

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Wabs=V·StdV,
St=Sinct+Sscat+Sextt,
Sextt=12μoRe{Einc×Bsca*+Esca×Binc*},
Wext=Wabs+Wsca,
Cext=WextIinc,Cabs=WabsIinc,Csca=WscaIinc,
Wabs={S1St·r^da+S2St·z^da},
Iodet=S2Sinct·z^daandIdet=S2St·z^da,
IodetIdet=Wext+S1Sextt·r^da.
f(θdet)=1Iinc[Iodet(θdet)Idet(θdet)],
δ(θdet)=1IincS1Sextt·r^da,
Cext=f(θdet)+δ(θdet).

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