OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 21 — Jul. 20, 2013
  • pp: 5289–5296

Mueller matrix holographic method for small particle characterization: theory and numerical studies

Meng Gao, Ping Yang, David McKee, and George W. Kattawar  »View Author Affiliations

Applied Optics, Vol. 52, Issue 21, pp. 5289-5296 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (1291 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Holographic imaging has proved to be useful for spherical particle characterization, including the retrieval of particle size, refractive index, and 3D location. In this method, the interference pattern of the incident and scattered light fields is recorded by a camera and compared with the relevant Lorenz–Mie solutions. However, the method is limited to spherical particles, and the complete polarized scattering components have not been studied. This work extends the Mueller matrix formalism for the scattered light to describe the interference light field, and proposes a Mueller matrix holography method, through which complete polarization information can be obtained. The mathematical formalism of the holographic Mueller matrix is derived, and numerical examples of birefringent spheres are provided. The Mueller matrix holography method may provide a better opportunity than conventional methods to study anisotropic particles.

© 2013 Optical Society of America

OCIS Codes
(090.0090) Holography : Holography
(160.1190) Materials : Anisotropic optical materials
(290.5855) Scattering : Scattering, polarization

ToC Category:

Original Manuscript: April 3, 2013
Revised Manuscript: June 17, 2013
Manuscript Accepted: June 18, 2013
Published: July 19, 2013

Meng Gao, Ping Yang, David McKee, and George W. Kattawar, "Mueller matrix holographic method for small particle characterization: theory and numerical studies," Appl. Opt. 52, 5289-5296 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. B. J. Thompson, “Holographic particle sizing techniques,” J. Phys. E 7, 781–788 (1974). [CrossRef]
  2. G. Pan and H. Meng, “Digital holography of particle fields: reconstruction by use of complex amplitude,” Appl. Opt. 42, 827–833 (2003). [CrossRef]
  3. J. P. Fugal, R. A. Shaw, E. W. Saw, and A. V. Sergeyev, “Airborne digital holographic system for cloud particle measurements,” Appl. Opt. 43, 5987–5995 (2004). [CrossRef]
  4. S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005). [CrossRef]
  5. J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. 45, 3893–3901 (2006). [CrossRef]
  6. X. Wu, G. GrÈhan, S. Meunier-Guttin-Cluzel, L. Chen, and K. Cen, “Sizing of particles smaller than 5 μm in digital holographic microscopy,” Opt. Lett. 34, 857–859 (2009). [CrossRef]
  7. E. Darakis, T. Khanam, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044 (2010). [CrossRef]
  8. G. W. Graham and W. A. M. N. Smith, “The application of holography to the analysis of size and settling velocity of suspended cohesive sediments,” Limnol. Oceanogr. 8, 1–15 (2010).
  9. M. J. Berg and G. Videen, “Digital holographic imaging of aerosol particles in flight,” J. Quant. Spectrosc. Radiat. Transfer 112, 1776–1783 (2011). [CrossRef]
  10. X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coetmellec, K. Cen, and G. Grehan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020 (2012). [CrossRef]
  11. F. Slimani, G. Grehan, G. Gouesbet, and D. Allano, “Near-field Lorenz–Mie theory and its application to microholography,” Appl. Opt. 23, 4140–4148 (1984). [CrossRef]
  12. S.-H. Lee, Y. Roichman, G.-R. Yi, S.-H. Kim, S.-M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 15, 18275–18282 (2007). [CrossRef]
  13. F. C. Cheong, K. Xiao, D. J. Pine, and D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matt. 7, 6816–6819 (2011). [CrossRef]
  14. L. M. Mäthger, S. L. Senft, M. Gao, S. Karaveli, G. R. R. Bell, R. Zia, A. M. Kuzirian, P. B. Dennis, W. J. Crookes-Goodson, R. R. Naik, G. W. Kattawar, and R. T. Hanlon, “Bright white scattering from protein spheres in color changing, flexible cuttlefish skin,” Adv. Funct. Mater. (to be published).
  15. K. Kuroda, Y. Matsuhashi, R. Fujimura, and T. Shimura, “Theory of polarization holography,” Opt. Rev. 18, 374–382 (2011). [CrossRef]
  16. W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53, 468–478 (1985). [CrossRef]
  17. R. J. Perry, A. J. Hunt, and D. R. Huffman, “Experimental determinations of Mueller scattering matrices for nonspherical particles,” Appl. Opt. 17, 2700–2710 (1978). [CrossRef]
  18. H.-Z. Liu, J. L.-W. Li, M. S. Leong, and S. Zouhdi, “Transparent uniaxial anisotropic spherical particles designed using radial anisotropy,” Phys. Rev. E 84, 016605 (2011). [CrossRef]
  19. K. L. Wong and H. T. Chen, “Electromagnetic scattering by a uniaxially anisotropic sphere,” IEE Proc. Microw. Anten. Propag. 139, 314–318 (1992). [CrossRef]
  20. L. M. Mäthger, E. J. Denton, N. J. Marshall, and R. T. Hanlon, “Mechanisms and behavioural functions of structural coloration in cephalopods,” J. R. Soc. Interface 6, S149–S163 (2009). [CrossRef]
  21. M. Gao, Y. You, P. Yang, and G. W. Kattawar, “Backscattering properties of small layered plates: a model for iridosomes,” Opt. Express 20, 25111–25120 (2012). [CrossRef]
  22. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2004).
  23. C. Li, G. W. Kattawar, and P. Yang, “Identification of aerosols by their backscattered Mueller images,” Opt. Express 14, 3616–3621 (2006). [CrossRef]
  24. S. Jiao, G. Yao, and L. V. Wang, “Depth-resolved two-dimensional stokes vectors of backscattered light and Mueller matrices of biological tissue measured with optical coherence tomography,” Appl. Opt. 39, 6318–6324 (2000). [CrossRef]
  25. H. C. van de Hulst, Light Scattering by Small Particles (Dover Publications, 1981).
  26. A. J. Hunt and D. R. Huffman, “A new polarization-modulated light scattering instrument,” Rev. Sci. Instrum. 44, 1753–1762 (1973). [CrossRef]
  27. R. C. Thompson, J. R. Bottiger, and E. S. Fry, “Measurement of polarized light interactions via the Mueller matrix,” Appl. Opt. 19, 1323–1332 (1980). [CrossRef]
  28. M. Gao, P. Yang, and G. W. Kattawar, “Polarized extinction properties of plates with large aspect ratios “ J. Quant. Spectrosc. Radiat. Transfer (2013, to be published).
  29. E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973). [CrossRef]
  30. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988). [CrossRef]
  31. M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transfer 112, 2234–2247 (2011). [CrossRef]
  32. P. Yang and K. N. Liou, “Finite difference time domain method for light scattering by nonspherical and inhomogeneous particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 2000).
  33. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
  34. E. S. Thiele and R. H. French, “Computation of light scattering by anisotropic spheres of rutile titania,” Adv. Mater. 10, 1271–1276 (1998). [CrossRef]
  35. J. R. Devore, “Refractive indices of rutile and sphalerite,” J. Opt. Soc. Am. 41, 416–417 (1951). [CrossRef]
  36. M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed., Vol. IV of Optical properties of materials, nonlinear optics, quantum optics (McGraw-Hill, 2010).
  37. P. Yang and K. N. Liou, “Geometric-optics integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996). [CrossRef]
  38. P. Yang and K. N. Liou, “Light scattering by hexagonal ice crystals: solutions by a ray-by-ray integration algorithm,” J. Opt. Soc. Am. A 14, 2278–2289 (1997). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited