Abstract

Confocal scanning optical microscopy can be used to investigate the structure of electro-optic materials. Application of an ac electric field allows one to measure sensitively small changes in the reflection of light from a sample surface, and those changes can be related to the electro-optic properties. We observe the axial dependence of the ac light intensity to be a linear combination of the dc component and its axial derivative. Our analysis shows that astigmatic aberrations and the azimuthal dependence of the optical index in anisotropic materials can explain this behavior.

© 2000 Optical Society of America

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References

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  1. R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59, 427–471 (1996).
    [CrossRef]
  2. T. Wilson, A. R. Carlini, “The effect of aberrations on the axial response of confocal imaging systems,” J. Microsc. 154, 243–256 (1989).
    [CrossRef]
  3. H. T. M. van der Voort, G. J. Brakenhoff, “3-D image formation in high-aperture fluorescence confocal microscopy: a numerical analysis,” J. Microsc. 158, 43–54 (1990).
    [CrossRef]
  4. C. J. R. Sheppard, M. Gu, “Aberration compensation in confocal microscopy,” Appl. Opt. 30, 3563–3568 (1991).
    [CrossRef] [PubMed]
  5. C. J. R. Sheppard, M. Gu, “Axial imaging through an aberrating layer of water in confocal microscopy,” Opt. Commun. 88, 180–190 (1992).
    [CrossRef]
  6. S. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
    [CrossRef]
  7. D. Jiang, J. J. Stamnes, “Numerical and asymptotic results for focusing of two-dimensional waves in uniaxial crystals,” Opt. Commun. 163, 55–71 (1999).
    [CrossRef]
  8. C. Hubert, J. Levy, A. C. Carter, W. Chang, S. W. Kiechoefer, J. S. Horwitz, D. B. Chrisley, “Confocal scanning optical microscopy of BaxSr1-xTiO3 thin films,” Appl. Phys. Lett. 71, 3353–3355 (1997).
    [CrossRef]
  9. O. Tikhomirov, B. Red’kin, A. Trivelli, J. Levy, “Visualization of 180 degree domain structures in uniaxial ferroelectrics using confocal scanning optical microscopy,” J. Appl. Phys. 87, 1932–1936 (2000).
    [CrossRef]
  10. W. J. Merz, “Domain formation and domain walls in ferroelectric BaTiO3 single crystals,” Phys. Rev. 95, 690–698 (1954).
    [CrossRef]
  11. C. J. R. Sheppard, T. Wilson, “Effects of high angles of convergence on V(z) in the scanning acoustic microscope,” Appl. Phys. Lett. 38, 858–859 (1981).
    [CrossRef]
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1965), p. 212.
  13. L. Levi, Applied Optics (Wiley, New York, 1980), Vol. 2, p. 282.

2000 (1)

O. Tikhomirov, B. Red’kin, A. Trivelli, J. Levy, “Visualization of 180 degree domain structures in uniaxial ferroelectrics using confocal scanning optical microscopy,” J. Appl. Phys. 87, 1932–1936 (2000).
[CrossRef]

1999 (1)

D. Jiang, J. J. Stamnes, “Numerical and asymptotic results for focusing of two-dimensional waves in uniaxial crystals,” Opt. Commun. 163, 55–71 (1999).
[CrossRef]

1997 (1)

C. Hubert, J. Levy, A. C. Carter, W. Chang, S. W. Kiechoefer, J. S. Horwitz, D. B. Chrisley, “Confocal scanning optical microscopy of BaxSr1-xTiO3 thin films,” Appl. Phys. Lett. 71, 3353–3355 (1997).
[CrossRef]

1996 (1)

R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59, 427–471 (1996).
[CrossRef]

1993 (1)

S. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

1992 (1)

C. J. R. Sheppard, M. Gu, “Axial imaging through an aberrating layer of water in confocal microscopy,” Opt. Commun. 88, 180–190 (1992).
[CrossRef]

1991 (1)

1990 (1)

H. T. M. van der Voort, G. J. Brakenhoff, “3-D image formation in high-aperture fluorescence confocal microscopy: a numerical analysis,” J. Microsc. 158, 43–54 (1990).
[CrossRef]

1989 (1)

T. Wilson, A. R. Carlini, “The effect of aberrations on the axial response of confocal imaging systems,” J. Microsc. 154, 243–256 (1989).
[CrossRef]

1981 (1)

C. J. R. Sheppard, T. Wilson, “Effects of high angles of convergence on V(z) in the scanning acoustic microscope,” Appl. Phys. Lett. 38, 858–859 (1981).
[CrossRef]

1954 (1)

W. J. Merz, “Domain formation and domain walls in ferroelectric BaTiO3 single crystals,” Phys. Rev. 95, 690–698 (1954).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1965), p. 212.

Brakenhoff, G. J.

H. T. M. van der Voort, G. J. Brakenhoff, “3-D image formation in high-aperture fluorescence confocal microscopy: a numerical analysis,” J. Microsc. 158, 43–54 (1990).
[CrossRef]

Carlini, A. R.

T. Wilson, A. R. Carlini, “The effect of aberrations on the axial response of confocal imaging systems,” J. Microsc. 154, 243–256 (1989).
[CrossRef]

Carter, A. C.

C. Hubert, J. Levy, A. C. Carter, W. Chang, S. W. Kiechoefer, J. S. Horwitz, D. B. Chrisley, “Confocal scanning optical microscopy of BaxSr1-xTiO3 thin films,” Appl. Phys. Lett. 71, 3353–3355 (1997).
[CrossRef]

Chang, W.

C. Hubert, J. Levy, A. C. Carter, W. Chang, S. W. Kiechoefer, J. S. Horwitz, D. B. Chrisley, “Confocal scanning optical microscopy of BaxSr1-xTiO3 thin films,” Appl. Phys. Lett. 71, 3353–3355 (1997).
[CrossRef]

Chrisley, D. B.

C. Hubert, J. Levy, A. C. Carter, W. Chang, S. W. Kiechoefer, J. S. Horwitz, D. B. Chrisley, “Confocal scanning optical microscopy of BaxSr1-xTiO3 thin films,” Appl. Phys. Lett. 71, 3353–3355 (1997).
[CrossRef]

Cremer, C.

S. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

Gu, M.

C. J. R. Sheppard, M. Gu, “Axial imaging through an aberrating layer of water in confocal microscopy,” Opt. Commun. 88, 180–190 (1992).
[CrossRef]

C. J. R. Sheppard, M. Gu, “Aberration compensation in confocal microscopy,” Appl. Opt. 30, 3563–3568 (1991).
[CrossRef] [PubMed]

Hell, S.

S. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

Horwitz, J. S.

C. Hubert, J. Levy, A. C. Carter, W. Chang, S. W. Kiechoefer, J. S. Horwitz, D. B. Chrisley, “Confocal scanning optical microscopy of BaxSr1-xTiO3 thin films,” Appl. Phys. Lett. 71, 3353–3355 (1997).
[CrossRef]

Hubert, C.

C. Hubert, J. Levy, A. C. Carter, W. Chang, S. W. Kiechoefer, J. S. Horwitz, D. B. Chrisley, “Confocal scanning optical microscopy of BaxSr1-xTiO3 thin films,” Appl. Phys. Lett. 71, 3353–3355 (1997).
[CrossRef]

Jiang, D.

D. Jiang, J. J. Stamnes, “Numerical and asymptotic results for focusing of two-dimensional waves in uniaxial crystals,” Opt. Commun. 163, 55–71 (1999).
[CrossRef]

Kiechoefer, S. W.

C. Hubert, J. Levy, A. C. Carter, W. Chang, S. W. Kiechoefer, J. S. Horwitz, D. B. Chrisley, “Confocal scanning optical microscopy of BaxSr1-xTiO3 thin films,” Appl. Phys. Lett. 71, 3353–3355 (1997).
[CrossRef]

Levi, L.

L. Levi, Applied Optics (Wiley, New York, 1980), Vol. 2, p. 282.

Levy, J.

O. Tikhomirov, B. Red’kin, A. Trivelli, J. Levy, “Visualization of 180 degree domain structures in uniaxial ferroelectrics using confocal scanning optical microscopy,” J. Appl. Phys. 87, 1932–1936 (2000).
[CrossRef]

C. Hubert, J. Levy, A. C. Carter, W. Chang, S. W. Kiechoefer, J. S. Horwitz, D. B. Chrisley, “Confocal scanning optical microscopy of BaxSr1-xTiO3 thin films,” Appl. Phys. Lett. 71, 3353–3355 (1997).
[CrossRef]

Merz, W. J.

W. J. Merz, “Domain formation and domain walls in ferroelectric BaTiO3 single crystals,” Phys. Rev. 95, 690–698 (1954).
[CrossRef]

Red’kin, B.

O. Tikhomirov, B. Red’kin, A. Trivelli, J. Levy, “Visualization of 180 degree domain structures in uniaxial ferroelectrics using confocal scanning optical microscopy,” J. Appl. Phys. 87, 1932–1936 (2000).
[CrossRef]

Reiner, G.

S. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard, M. Gu, “Axial imaging through an aberrating layer of water in confocal microscopy,” Opt. Commun. 88, 180–190 (1992).
[CrossRef]

C. J. R. Sheppard, M. Gu, “Aberration compensation in confocal microscopy,” Appl. Opt. 30, 3563–3568 (1991).
[CrossRef] [PubMed]

C. J. R. Sheppard, T. Wilson, “Effects of high angles of convergence on V(z) in the scanning acoustic microscope,” Appl. Phys. Lett. 38, 858–859 (1981).
[CrossRef]

Stamnes, J. J.

D. Jiang, J. J. Stamnes, “Numerical and asymptotic results for focusing of two-dimensional waves in uniaxial crystals,” Opt. Commun. 163, 55–71 (1999).
[CrossRef]

Stelzer, E. H. K.

S. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

Tikhomirov, O.

O. Tikhomirov, B. Red’kin, A. Trivelli, J. Levy, “Visualization of 180 degree domain structures in uniaxial ferroelectrics using confocal scanning optical microscopy,” J. Appl. Phys. 87, 1932–1936 (2000).
[CrossRef]

Trivelli, A.

O. Tikhomirov, B. Red’kin, A. Trivelli, J. Levy, “Visualization of 180 degree domain structures in uniaxial ferroelectrics using confocal scanning optical microscopy,” J. Appl. Phys. 87, 1932–1936 (2000).
[CrossRef]

van der Voort, H. T. M.

H. T. M. van der Voort, G. J. Brakenhoff, “3-D image formation in high-aperture fluorescence confocal microscopy: a numerical analysis,” J. Microsc. 158, 43–54 (1990).
[CrossRef]

Webb, R. H.

R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59, 427–471 (1996).
[CrossRef]

Wilson, T.

T. Wilson, A. R. Carlini, “The effect of aberrations on the axial response of confocal imaging systems,” J. Microsc. 154, 243–256 (1989).
[CrossRef]

C. J. R. Sheppard, T. Wilson, “Effects of high angles of convergence on V(z) in the scanning acoustic microscope,” Appl. Phys. Lett. 38, 858–859 (1981).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1965), p. 212.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

C. Hubert, J. Levy, A. C. Carter, W. Chang, S. W. Kiechoefer, J. S. Horwitz, D. B. Chrisley, “Confocal scanning optical microscopy of BaxSr1-xTiO3 thin films,” Appl. Phys. Lett. 71, 3353–3355 (1997).
[CrossRef]

C. J. R. Sheppard, T. Wilson, “Effects of high angles of convergence on V(z) in the scanning acoustic microscope,” Appl. Phys. Lett. 38, 858–859 (1981).
[CrossRef]

J. Appl. Phys. (1)

O. Tikhomirov, B. Red’kin, A. Trivelli, J. Levy, “Visualization of 180 degree domain structures in uniaxial ferroelectrics using confocal scanning optical microscopy,” J. Appl. Phys. 87, 1932–1936 (2000).
[CrossRef]

J. Microsc. (3)

S. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

T. Wilson, A. R. Carlini, “The effect of aberrations on the axial response of confocal imaging systems,” J. Microsc. 154, 243–256 (1989).
[CrossRef]

H. T. M. van der Voort, G. J. Brakenhoff, “3-D image formation in high-aperture fluorescence confocal microscopy: a numerical analysis,” J. Microsc. 158, 43–54 (1990).
[CrossRef]

Opt. Commun. (2)

D. Jiang, J. J. Stamnes, “Numerical and asymptotic results for focusing of two-dimensional waves in uniaxial crystals,” Opt. Commun. 163, 55–71 (1999).
[CrossRef]

C. J. R. Sheppard, M. Gu, “Axial imaging through an aberrating layer of water in confocal microscopy,” Opt. Commun. 88, 180–190 (1992).
[CrossRef]

Phys. Rev. (1)

W. J. Merz, “Domain formation and domain walls in ferroelectric BaTiO3 single crystals,” Phys. Rev. 95, 690–698 (1954).
[CrossRef]

Rep. Prog. Phys. (1)

R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59, 427–471 (1996).
[CrossRef]

Other (2)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1965), p. 212.

L. Levi, Applied Optics (Wiley, New York, 1980), Vol. 2, p. 282.

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Figures (8)

Fig. 1
Fig. 1

Experimental setup of the CSOM technique.

Fig. 2
Fig. 2

Scanning confocal image of the ferroelectric surface in (a) dc and (b) ac modes. Mark size is 10 μm.

Fig. 3
Fig. 3

Experimental dependence of the dc [(a)–(c)] and ac [(d)–(f)] components of the confocal signal on the axial position of the sample. The angle γ between the z axis and the light polarization plane is (a), (d) 116°; (b), (e) 112°; and (c), (f) 104°.

Fig. 4
Fig. 4

Variation of the fitting coefficients (a) F and (b) D with the light polarization angle in reference to the z axis. The different symbols represent data obtained from two antiparallel domains.

Fig. 5
Fig. 5

Coordinate system and light field components for an optical ray coming from a point P of the objective. The z axis coincides with the ferroelectric c axis of the crystal. ϕ and θ are the azimuthal and polar angles used in the computations, γ is the orientation of the light electric vector, and β is the orientation of the external electric field causing the electro-optic effect.

Fig. 6
Fig. 6

Effect of the astigmatism aberration on the axial distribution of the light intensity: (a), (c) dc component; (b), (d) ac component. (a), (b) C=0; (c), (d) C=5.    

Fig. 7
Fig. 7

Variation of the fitting components F (a) and D (b) with angle γ for calculated axial characteristics in ac mode.

Fig. 8
Fig. 8

Typical distribution of the reflection coefficients (a) R0 and (b) R1 for rays coming from different points of the objective (xz plane). β=80° and γ=172°. θ=0 for the center of the circle and θ=α at the edge of the objective. ϕ=0 for the z axis (vertical up).

Equations (27)

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Iac(y)=FIdc(y)+D Idc(y)y.
I(y)=0α02πE{exp[i(Φ+ky cos θ)]×R sin θ cos θ}dϕdθ 2,
R=n2 cos θi-n1 cos θtn2 cos θi+n1 cos θt,
R=n1 cos θi-n2 cos θtn1 cos θi+n2 cos θt,
R=n2 cos θ-(n2-sin2 θ)1/2n2 cos θ+(n2-sin2 θ)1/2,
R=cos θ-(n2-sin2 θ)1/2cos θ+(n2-sin2 θ)1/2.
R0=n02 cos θ-pn02 cos θ+p,
R1=2n0n1 cos θ(n02-2 sin2 θ)p(n02 cos θ+p)2,
R0=cos θ-pcos θ+p,
R1=-2n0n1cos θ+p,
p=(n02-sin2 θ)1/2.
1n02=ex2+ey2nx2+ez2nz2,
Δ1n2=Eext[r31 cos β(ex2+ey2)+r33 cos βez2+2r51 sin βezex-2r22 sin βexey]
n1=-n032 Δ1n2,
Ex=E cos(ϕ-γ)cos θ sin ϕ,
Ey=E cos(ϕ-γ)sin θ,
Ez=E cos(ϕ-γ)cos θ cos ϕ,
Ex=-E sin(ϕ-γ)cos ϕ,
Ey=0,
Ez=E sin(ϕ-γ)sin ϕ.
eij=1E Eij.
Ex=-E(R sin(ϕ-γ)cos ϕ+R cos(ϕ-γ)sin ϕ),
Ez=E(R sin(ϕ-γ)sin ϕ-R cos(ϕ-γ)cos ϕ),
Ey=0
Φ=C sin2 θ sin2 ϕ.
I(y)=[E0(y)+E1(y)]2E02(y)+2E0(y)E1(y)=I0(y)+I1(y),
I1(y)=2E0(y)E1(y)const×E0(y)E0(y-a)const×E0(y)E0(y)-a dE0dy=FI0(y)+D dI0dy,

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