Abstract

Differential interference contrast (DIC) microscopy is shown to be equivalent to an incomplete Stokes polarimeter capable of probing optical properties of materials on microscopic-length scales. The Mueller matrix for a DIC microscope is calculated for various types of samples, and the polarimetric properties for DIC component parts of a spaceflight microscope are spectrally measured. As a practical application, a measurement of the index mismatch between colloidal particles and a nearly index-matched fluid bath was performed.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Inoue, K. R. Spring, Video Microscopy: The Fundamentals (Plenum, New York, 1997).
    [CrossRef]
  2. M. Pluta, Specialized Methods, Vol. 2 of Advanced Light Microscopy (Elsevier, New York, 1989), Chap. 7, pp. 146–196.
  3. S. Inoué, “Ultrathin optical sectioning and dynamic volume investigation with conventional light microscopy,” in Three-Dimensional Confocal Microscopy: Volume Investigation of Biological SpecimensJ. K. Stevens, L. R. Mills, J. E. Trogades, eds. (Academic, London, 1994), Chap. 17, pp. 397–419.
    [CrossRef]
  4. The experiments are Physics of Colloids in Space 2 (PCS-II), Physics of Hard Spheres Experiment 2 (PHASE-II), and Low Volume Fraction Entropically Driven Colloidal Assembly (LϕCA).
  5. Z. G. Yu, X. Song, D. Chandler, “Polarizability fluctuations in dielectric materials with quenched disorder,” Phys. Rev. E 62, 4698–4701 (2000).
    [CrossRef]
  6. B. van Tiggelen, H. Stark, “Nematic liquid crystals as a new challenge for radiative transfer,” Rev. Mod. Phys. 72, 1017–1039 (2000).
    [CrossRef]
  7. See, for example, B. Berne, R. Pecora, Dynamic Light Scattering (Krieger, Malabar, Fla., 1990).
  8. See, for example, B. Dahneke, Measurement of Suspended Particles by Quasi-Elastic Light Scattering (Wiley, New York, 1983).
  9. See, for example, J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).
  10. P. Török, P. D. Higdon, T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148, 300–315 (1998).
    [CrossRef]
  11. R. Chipman, Polarimetry Handbook of Optics, M. Bass, ed. (McGraw-Hill, N.Y., 1995), Vol. 2, Chap. 22.
  12. See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier Science, Amsterdam, 1996).
  13. D. B. Chenault, “Infrared spectropolarimetry,” Ph.D. dissertation (University of Alabama, Huntsville, Ala., 1992).

2000

Z. G. Yu, X. Song, D. Chandler, “Polarizability fluctuations in dielectric materials with quenched disorder,” Phys. Rev. E 62, 4698–4701 (2000).
[CrossRef]

B. van Tiggelen, H. Stark, “Nematic liquid crystals as a new challenge for radiative transfer,” Rev. Mod. Phys. 72, 1017–1039 (2000).
[CrossRef]

1998

P. Török, P. D. Higdon, T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148, 300–315 (1998).
[CrossRef]

Azzam, R. M. A.

See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier Science, Amsterdam, 1996).

Bashara, N. M.

See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier Science, Amsterdam, 1996).

Berne, B.

See, for example, B. Berne, R. Pecora, Dynamic Light Scattering (Krieger, Malabar, Fla., 1990).

Chandler, D.

Z. G. Yu, X. Song, D. Chandler, “Polarizability fluctuations in dielectric materials with quenched disorder,” Phys. Rev. E 62, 4698–4701 (2000).
[CrossRef]

Chenault, D. B.

D. B. Chenault, “Infrared spectropolarimetry,” Ph.D. dissertation (University of Alabama, Huntsville, Ala., 1992).

Dahneke, B.

See, for example, B. Dahneke, Measurement of Suspended Particles by Quasi-Elastic Light Scattering (Wiley, New York, 1983).

Higdon, P. D.

P. Török, P. D. Higdon, T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148, 300–315 (1998).
[CrossRef]

Inoue, S.

S. Inoue, K. R. Spring, Video Microscopy: The Fundamentals (Plenum, New York, 1997).
[CrossRef]

Inoué, S.

S. Inoué, “Ultrathin optical sectioning and dynamic volume investigation with conventional light microscopy,” in Three-Dimensional Confocal Microscopy: Volume Investigation of Biological SpecimensJ. K. Stevens, L. R. Mills, J. E. Trogades, eds. (Academic, London, 1994), Chap. 17, pp. 397–419.
[CrossRef]

Joannopoulos, J. D.

See, for example, J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Meade, R. D.

See, for example, J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Pecora, R.

See, for example, B. Berne, R. Pecora, Dynamic Light Scattering (Krieger, Malabar, Fla., 1990).

Pluta, M.

M. Pluta, Specialized Methods, Vol. 2 of Advanced Light Microscopy (Elsevier, New York, 1989), Chap. 7, pp. 146–196.

Song, X.

Z. G. Yu, X. Song, D. Chandler, “Polarizability fluctuations in dielectric materials with quenched disorder,” Phys. Rev. E 62, 4698–4701 (2000).
[CrossRef]

Spring, K. R.

S. Inoue, K. R. Spring, Video Microscopy: The Fundamentals (Plenum, New York, 1997).
[CrossRef]

Stark, H.

B. van Tiggelen, H. Stark, “Nematic liquid crystals as a new challenge for radiative transfer,” Rev. Mod. Phys. 72, 1017–1039 (2000).
[CrossRef]

Török, P.

P. Török, P. D. Higdon, T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148, 300–315 (1998).
[CrossRef]

van Tiggelen, B.

B. van Tiggelen, H. Stark, “Nematic liquid crystals as a new challenge for radiative transfer,” Rev. Mod. Phys. 72, 1017–1039 (2000).
[CrossRef]

Wilson, T.

P. Török, P. D. Higdon, T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148, 300–315 (1998).
[CrossRef]

Winn, J. N.

See, for example, J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Yu, Z. G.

Z. G. Yu, X. Song, D. Chandler, “Polarizability fluctuations in dielectric materials with quenched disorder,” Phys. Rev. E 62, 4698–4701 (2000).
[CrossRef]

Opt. Commun.

P. Török, P. D. Higdon, T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148, 300–315 (1998).
[CrossRef]

Phys. Rev. E

Z. G. Yu, X. Song, D. Chandler, “Polarizability fluctuations in dielectric materials with quenched disorder,” Phys. Rev. E 62, 4698–4701 (2000).
[CrossRef]

Rev. Mod. Phys.

B. van Tiggelen, H. Stark, “Nematic liquid crystals as a new challenge for radiative transfer,” Rev. Mod. Phys. 72, 1017–1039 (2000).
[CrossRef]

Other

See, for example, B. Berne, R. Pecora, Dynamic Light Scattering (Krieger, Malabar, Fla., 1990).

See, for example, B. Dahneke, Measurement of Suspended Particles by Quasi-Elastic Light Scattering (Wiley, New York, 1983).

See, for example, J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

S. Inoue, K. R. Spring, Video Microscopy: The Fundamentals (Plenum, New York, 1997).
[CrossRef]

M. Pluta, Specialized Methods, Vol. 2 of Advanced Light Microscopy (Elsevier, New York, 1989), Chap. 7, pp. 146–196.

S. Inoué, “Ultrathin optical sectioning and dynamic volume investigation with conventional light microscopy,” in Three-Dimensional Confocal Microscopy: Volume Investigation of Biological SpecimensJ. K. Stevens, L. R. Mills, J. E. Trogades, eds. (Academic, London, 1994), Chap. 17, pp. 397–419.
[CrossRef]

The experiments are Physics of Colloids in Space 2 (PCS-II), Physics of Hard Spheres Experiment 2 (PHASE-II), and Low Volume Fraction Entropically Driven Colloidal Assembly (LϕCA).

R. Chipman, Polarimetry Handbook of Optics, M. Bass, ed. (McGraw-Hill, N.Y., 1995), Vol. 2, Chap. 22.

See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier Science, Amsterdam, 1996).

D. B. Chenault, “Infrared spectropolarimetry,” Ph.D. dissertation (University of Alabama, Huntsville, Ala., 1992).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Schematic of spectropolarimetric measurement.

Fig. 2
Fig. 2

Measured extinction values for the compensator plate.

Fig. 3
Fig. 3

Absolute value of the retardation angle of the compensator plate.

Fig. 4
Fig. 4

Spectral transmission relative to 540 nm at 90° compensator orientation.

Fig. 5
Fig. 5

Image of a Wollaston prism between crossed polarizers.

Fig. 6
Fig. 6

Geometry of a sphere in fluid.

Fig. 7
Fig. 7

DIC image of glass microspheres in Cargille type FF immersion oil.

Fig. 8
Fig. 8

Calibration data.

Fig. 9
Fig. 9

Index mismatch measurement.

Tables (3)

Tables Icon

Table 1 Indices of Cargille Fluids at Various Wavelengths

Tables Icon

Table 2 Slopes of the Fit Line for Glass Microspheres in Cargille Fluids

Tables Icon

Table 3 Calculated Index of Refraction of Glass Microspheres

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

Msys=R-90McR90R-45Mw-Ψ×R45MsR-45MwΨR45Mp,
Mp=121100110000000000.
Msys=141-cos Ψ0-sin Ψ-cos δcos Ψ cos δ0sin Ψ cos δ0000-sin δcos Ψ sin δ0sin Ψ sin δ×Ms1100cos Ψcos Ψ000000sin Ψsin Ψ00,
Mw=1000010000cos Ψsin Ψ00-sin Ψcos Ψ,
Ms=0abca0-d-ebd0-fcef0+I
Ms=0ΔaΔbΔc00ΔdΔe000Δf0000,
Msys=14zz00-z cos δ-z cos δ000000-z sin δ-z sin δ00,z=Δc sinΨ+cosΨΔa-Δe sinΨ.
Ms=1ΔaΔbΔc0pΔdΔe00qΔf000r.
Msys=14zz00-z cos δ-z cos δ000000-z sin δ-z sin δ00,z=1+cosΨΔa-p cosΨ+sinΨ×Δc-Δe cosΨ-r sinψ.
Ms=000000ΔdΔe000Δf0000.
Msys=14-z-z00z cos δz cos δ000000z sin δz sin δ00,z=Δe sinΨcosΨ.
Id=MθI0,
Idδδδ=mθ00mθ01δδδδδδδδδδδδδδ1100,
mθ00=m00,mθ01=m01 cos2θ-m02 sin2θ.
E=m00-m01m00+m01.
Mc=MpR-γMrRγ
Mc=RγMrR-γMp,
Id=Mc00+Mc01 cos2θ-Mc02 sin2θ=½ τmax+τmin+τmax-τmincos2θ,
Mc=12abcos2 2γ+cos δ sin2 2γb sin 2γ cos 2γ1-cos δ-b sin δ sin 2γbacos2 2γ+cos δ sin2 2γa sin 2γ cos 2γ1-cos δ-a sin δ sin 2γ0c sin 2γ cos 2γ1-cos δccos2 2γ cos δ+sin2 2γc sin δ cos 2γ0c sin δ sin 2γ-c sin δ cos 2γc cos δ.
Id=Mc00+Mc01 cos2θ-Mc02 sin2θ=½ τmax+τmin+cos2 2γ+cos δ sin2 2γ×τmax-τmincos 2θ-cos 2γ sin 2γ1-cos δτmax-τminsin 2θ.
Id=½ τmax+τmin+cos δτmax-τmincos 2θ.
M=141-cos Ψ1-cos Ψ00-1+cos Ψ-1+cos Ψ0000000000,
ϕy=2nr+δnhy,
hy=r2-y21/2,
ϕyy=2δn yr2-y21/2,
slope1slope2-1 nglass=slope1slope2 nfluid2-nfluid1.

Metrics