Abstract

In an effort to establish the imaging properties of a new type of polarized-light microscope, we recorded images of small, uniaxial, birefringent crystals. We show that the sequence of in-focus and out-of-focus images, the so-called point-spread function, of a submicroscopic crystal can be used to measure the orientation of its optic axis in three-dimensional space. By analogy to conoscopic images out-of-focus images reveal the changes in relative phase shift between the extraordinary and the ordinary rays that propagate at different directions through the crystal. We also present simulated images of a pointlike anisotropic scattering particle and compare these with our experimental findings. The theoretical model is based on a complete vectorial theory for partial coherent imaging by use of polarized light and high-numerical-aperture lenses.

© 2000 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  3. M. Shribak, Y. Otani, T. Yoshizawa, “Return-path polarimeter for two dimensional birefringence distribution measurement,” in Polarization: Measurement, Analysis, and Remote Sensing II, Proc. SPIE3754, 144–149 (1999).
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    [CrossRef]
  5. G. Yao, L. V. Wang, “Two-dimensional depth-resolved Mueller matrix characterization of biological tissue by optical coherence tomography,” Opt. Lett. 24, 537–539 (1999).
    [CrossRef]
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    [CrossRef]
  7. S. F. Gibson, F. Lanni, “Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy,” J. Opt. Soc. Am. A 9, 154–166 (1992).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. P. Török, S. J. Hewlett, P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
    [CrossRef]
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    [CrossRef] [PubMed]
  11. P. Török, “Imaging of small birefringent objects by polarised light conventional and confocal microscopes,” Opt. Commun. 181, 7–18 (2000).
    [CrossRef]
  12. E. Hecht, Optics, 3rd ed. (Addison-Wesley, Reading, Mass., 1998).
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    [CrossRef] [PubMed]
  14. R. Oldenbourg, E. D. Salmon, P. T. Tran, “Birefringence of single and bundled microtubules,” Biophys. J. 74, 645–654 (1998).
    [CrossRef] [PubMed]
  15. S. Inoué, R. Oldenbourg, “Microscopes,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, pp. 17.1–17.52.

2000 (1)

P. Török, “Imaging of small birefringent objects by polarised light conventional and confocal microscopes,” Opt. Commun. 181, 7–18 (2000).
[CrossRef]

1999 (2)

B. Wang, T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level linear birefringence,” Rev. Sci. Instrum. 70, 3847–3854 (1999).
[CrossRef]

G. Yao, L. V. Wang, “Two-dimensional depth-resolved Mueller matrix characterization of biological tissue by optical coherence tomography,” Opt. Lett. 24, 537–539 (1999).
[CrossRef]

1998 (1)

R. Oldenbourg, E. D. Salmon, P. T. Tran, “Birefringence of single and bundled microtubules,” Biophys. J. 74, 645–654 (1998).
[CrossRef] [PubMed]

1997 (1)

P. Török, S. J. Hewlett, P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
[CrossRef]

1996 (1)

R. Oldenbourg, “A new view on polarization microscopy,” Nature 381, 811–812 (1996).
[CrossRef] [PubMed]

1995 (2)

R. Oldenbourg, G. Mei, “New polarized light microscope with precision universal compensator,” J. Microsc. 180, 140–147 (1995).
[CrossRef] [PubMed]

L. Tao, C. Nicholson, “The three-dimensional point spread functions of a microscope objective in image and object space,” J. Microsc. 178, 267–271 (1995).
[CrossRef] [PubMed]

1994 (1)

Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

1992 (1)

Agard, D. A.

D. A. Agard, Y. Hiraoka, P. Shaw, J. W. Sedat, “Fluorescence microscopy in three dimensions,” in Methods of Cell Biology, D. L. Taylor, Y.-L. Wang, eds. (Academic, San Diego, 1989), Vol. 30, pp. 353–377.
[CrossRef]

Gibson, S. F.

Hecht, E.

E. Hecht, Optics, 3rd ed. (Addison-Wesley, Reading, Mass., 1998).

Hewlett, S. J.

P. Török, S. J. Hewlett, P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
[CrossRef]

Hiraoka, Y.

D. A. Agard, Y. Hiraoka, P. Shaw, J. W. Sedat, “Fluorescence microscopy in three dimensions,” in Methods of Cell Biology, D. L. Taylor, Y.-L. Wang, eds. (Academic, San Diego, 1989), Vol. 30, pp. 353–377.
[CrossRef]

Inoué, S.

S. Inoué, R. Oldenbourg, “Microscopes,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, pp. 17.1–17.52.

Lanni, F.

Mei, G.

R. Oldenbourg, G. Mei, “New polarized light microscope with precision universal compensator,” J. Microsc. 180, 140–147 (1995).
[CrossRef] [PubMed]

G. Mei, R. Oldenbourg, “Fast imaging polarimetry with precision universal compensator,” in Polarization Analysis and Measurement II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE2265, 29–39 (1994).
[CrossRef]

Nicholson, C.

L. Tao, C. Nicholson, “The three-dimensional point spread functions of a microscope objective in image and object space,” J. Microsc. 178, 267–271 (1995).
[CrossRef] [PubMed]

Oakberg, T. C.

B. Wang, T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level linear birefringence,” Rev. Sci. Instrum. 70, 3847–3854 (1999).
[CrossRef]

Oldenbourg, R.

R. Oldenbourg, E. D. Salmon, P. T. Tran, “Birefringence of single and bundled microtubules,” Biophys. J. 74, 645–654 (1998).
[CrossRef] [PubMed]

R. Oldenbourg, “A new view on polarization microscopy,” Nature 381, 811–812 (1996).
[CrossRef] [PubMed]

R. Oldenbourg, G. Mei, “New polarized light microscope with precision universal compensator,” J. Microsc. 180, 140–147 (1995).
[CrossRef] [PubMed]

S. Inoué, R. Oldenbourg, “Microscopes,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, pp. 17.1–17.52.

G. Mei, R. Oldenbourg, “Fast imaging polarimetry with precision universal compensator,” in Polarization Analysis and Measurement II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE2265, 29–39 (1994).
[CrossRef]

Otani, Y.

Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

M. Shribak, Y. Otani, T. Yoshizawa, “Return-path polarimeter for two dimensional birefringence distribution measurement,” in Polarization: Measurement, Analysis, and Remote Sensing II, Proc. SPIE3754, 144–149 (1999).

Salmon, E. D.

R. Oldenbourg, E. D. Salmon, P. T. Tran, “Birefringence of single and bundled microtubules,” Biophys. J. 74, 645–654 (1998).
[CrossRef] [PubMed]

Sedat, J. W.

D. A. Agard, Y. Hiraoka, P. Shaw, J. W. Sedat, “Fluorescence microscopy in three dimensions,” in Methods of Cell Biology, D. L. Taylor, Y.-L. Wang, eds. (Academic, San Diego, 1989), Vol. 30, pp. 353–377.
[CrossRef]

Shaw, P.

D. A. Agard, Y. Hiraoka, P. Shaw, J. W. Sedat, “Fluorescence microscopy in three dimensions,” in Methods of Cell Biology, D. L. Taylor, Y.-L. Wang, eds. (Academic, San Diego, 1989), Vol. 30, pp. 353–377.
[CrossRef]

Shimada, T.

Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

Shribak, M.

M. Shribak, Y. Otani, T. Yoshizawa, “Return-path polarimeter for two dimensional birefringence distribution measurement,” in Polarization: Measurement, Analysis, and Remote Sensing II, Proc. SPIE3754, 144–149 (1999).

Tao, L.

L. Tao, C. Nicholson, “The three-dimensional point spread functions of a microscope objective in image and object space,” J. Microsc. 178, 267–271 (1995).
[CrossRef] [PubMed]

Török, P.

P. Török, “Imaging of small birefringent objects by polarised light conventional and confocal microscopes,” Opt. Commun. 181, 7–18 (2000).
[CrossRef]

P. Török, S. J. Hewlett, P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
[CrossRef]

Tran, P. T.

R. Oldenbourg, E. D. Salmon, P. T. Tran, “Birefringence of single and bundled microtubules,” Biophys. J. 74, 645–654 (1998).
[CrossRef] [PubMed]

Umeda, N.

Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

Varga, P.

P. Török, S. J. Hewlett, P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
[CrossRef]

Wang, B.

B. Wang, T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level linear birefringence,” Rev. Sci. Instrum. 70, 3847–3854 (1999).
[CrossRef]

Wang, L. V.

Yao, G.

Yoshizawa, T.

Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

M. Shribak, Y. Otani, T. Yoshizawa, “Return-path polarimeter for two dimensional birefringence distribution measurement,” in Polarization: Measurement, Analysis, and Remote Sensing II, Proc. SPIE3754, 144–149 (1999).

Biophys. J. (1)

R. Oldenbourg, E. D. Salmon, P. T. Tran, “Birefringence of single and bundled microtubules,” Biophys. J. 74, 645–654 (1998).
[CrossRef] [PubMed]

J. Microsc. (3)

L. Tao, C. Nicholson, “The three-dimensional point spread functions of a microscope objective in image and object space,” J. Microsc. 178, 267–271 (1995).
[CrossRef] [PubMed]

P. Török, S. J. Hewlett, P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
[CrossRef]

R. Oldenbourg, G. Mei, “New polarized light microscope with precision universal compensator,” J. Microsc. 180, 140–147 (1995).
[CrossRef] [PubMed]

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

Nature (1)

R. Oldenbourg, “A new view on polarization microscopy,” Nature 381, 811–812 (1996).
[CrossRef] [PubMed]

Opt. Commun. (1)

P. Török, “Imaging of small birefringent objects by polarised light conventional and confocal microscopes,” Opt. Commun. 181, 7–18 (2000).
[CrossRef]

Opt. Eng. (1)

Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

B. Wang, T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level linear birefringence,” Rev. Sci. Instrum. 70, 3847–3854 (1999).
[CrossRef]

Other (5)

G. Mei, R. Oldenbourg, “Fast imaging polarimetry with precision universal compensator,” in Polarization Analysis and Measurement II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE2265, 29–39 (1994).
[CrossRef]

M. Shribak, Y. Otani, T. Yoshizawa, “Return-path polarimeter for two dimensional birefringence distribution measurement,” in Polarization: Measurement, Analysis, and Remote Sensing II, Proc. SPIE3754, 144–149 (1999).

E. Hecht, Optics, 3rd ed. (Addison-Wesley, Reading, Mass., 1998).

D. A. Agard, Y. Hiraoka, P. Shaw, J. W. Sedat, “Fluorescence microscopy in three dimensions,” in Methods of Cell Biology, D. L. Taylor, Y.-L. Wang, eds. (Academic, San Diego, 1989), Vol. 30, pp. 353–377.
[CrossRef]

S. Inoué, R. Oldenbourg, “Microscopes,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, pp. 17.1–17.52.

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Figures (6)

Fig. 1
Fig. 1

Images of a calcite crystal imaged between crossed, circular polarizers by use of a Model Plan Apochromat oil-immersion objective with a NA of 1.4 and a condenser lens with the same NA. The crystal is embedded in a medium with a refractive index of 1.52. The diagonal series of images were taken in the orthoscopic mode with the crystal located in different z positions. The z positions are indicated by the labels to the right of each image (for positive z positions the crystal was moved away from the objective lens, whereas for negative z positions the crystal was moved toward the objective lens). At the bottom left-hand side the conoscopic crystal image is shown. The conoscopic image is superimposed by use of a black line that bisects the obtuse crystal face in the in-focus image and by a circle that corresponds to all the propagation directions that are tilted by 45° to the microscope axis in specimen space. The dark region near 1.5 o’clock of the conoscopic pattern is located at the intersection of the two curves and corresponds to the optic-axis direction of the crystal.

Fig. 2
Fig. 2

Schematic diagram of the cleavage form of the calcite crystal that shows the face angles and the optic-axis direction.

Fig. 3
Fig. 3

Pol-Scope retardance maps of a 4-µm-diameter calcite crystal whose optic axis lies parallel to the microscope axis. The focus series of Pol-Scope images shows (a) the measured orientation of the birefringence axis and (b) the retardance magnitude. In the gray-scale images of (b) the white areas correspond to a 13-nm retardance and the black areas to zero retardance. From the orientation images of (a), one can see short lines that indicate the slow-axis orientations at regular grid locations. The birefringence pattern in the out-of-focus images is circularly symmetrical about the optic axis of the crystal. Rays that have traveled parallel to the optic axis form the dark center of the donut-shaped pattern. With increasing distance to the center the rays are more inclined toward the optic axis, the corresponding crystal retardance increases, and its slow-axis direction is perpendicular to the optic axis. Remarkable is the very reduced retardance measured in the in-focus image of the crystal. For comparison, in (c) we show the crystal image when viewed directly between crossed, circular polarizers. The in-focus image shows a very bright crystal, whereas in the out-of-focus image the light is spread over a larger area and is therefore much dimmer.

Fig. 4
Fig. 4

Focal series of images obtained by use of the Pol-Scope retardance maps of a submicrometer-sized calcite crystal whose optic axis is nearly parallel to the microscope axis: (a) The measured orientation of the birefringence axis, (b) the magnitude of the retardance, (c) the crystal image when viewed directly between crossed, circular polarizers. Qualitatively, the same image features are observed in this small calcite crystal as are seen in the images of the larger crystal shown in Fig. 3. In (b) the white areas indicate a 3-nm retardance.

Fig. 5
Fig. 5

Focal series of images of the retardance maps of a submicroscopic calcite crystal with an approximately 100-nm diameter (as estimated from the measured crystal retardance) that was imaged with the Pol-Scope: The asymmetrical distributions of (a) the birefringence-axis orientation and (b) the magnitude in the out-of-focus images indicate that the optic axis is tilted toward the microscope axis by approximately 45°. The magnitude images were contrast enhanced such that the maximum retardance decreases from 10 nm (white areas) in the in-focus image to 2 and 1 nm in the 0.8-µm and the 1.6-µm z positions, respectively.

Fig. 6
Fig. 6

Simulated Pol-Scope retardance maps of an anisotropic scatterer: (a) The orientation of the birefringence axis and (b) the magnitude of the retardance. The images are based on a vectorial theory of polarized-light imaging by use of high-NA lenses. The top images were calculated for a uniaxial scatterer with its optic axis parallel to the microscope axis, whereas the bottom images were calculated for an optic axis that was tilted by 45° in the vertical direction. The width of each image corresponds to 4 µm in specimen space.

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