Abstract

A method for correcting the aberration of an electron-objective lens during the holographic reconstruction stage is proposed. In this method, a liquid-crystal spatial-light modulator is used as a computer-controlled phase plate on the Fourier plane of an optical reconstruction system. The effective refractive index of the liquid crystals changes with the applied electric field because of the crystals’s birefringence. Thus the phase of light passing through the liquid-crystal spatial-light modulator can be flexibly modulated to compensate for wave aberration. Experimental results on adjusting the focus of the image wave reconstructed from an electron-image hologram of magnesium oxide particles are presented.

© 1994 Optical Society of America

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References

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  1. D. Gabor, “Microscopy by reconstructed wavefronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
    [CrossRef]
  2. G. Möllenstedt, H. Düker, “Beobachtung und Messungen an Biprisma-interferezen mit Electronen Wellen,” Z. Phys. 145, 377–397 (1956).
    [CrossRef]
  3. A. V. Crewe, D. N. Eggenberger, D. N. Wall, L. N. Welter, “Electron gun using a field emission source,” Rev. Sci. Instrum. 39, 576–583 (1968).
    [CrossRef]
  4. A. Tonomura, T. Matsuda, J. Endo, H. Todokoro, T. Komoda, “Development of a field emission electron microscope,” J. Electron Microsc. 28, 1–11 (1979).
  5. A. Tonomura, “Electron holography: a new view of the microscopic,” Phys. Today 43(4), 22–29 (1990).
    [CrossRef]
  6. A. Tonomura, T. Matsuda, J. Endo, “Spherical-aberration correction of an electron lens by holography,” Jpn. J. Appl. Phys. 18, 1373–1377 (1979).
    [CrossRef]
  7. H. Lichte, “Electron holography approaching atomic resolution,” Ultramicroscopy 20, 293–304 (1986).
    [CrossRef]
  8. Q. Fu, H. Lichte, E. Völkl, “Correction of aberrations of an electron microscope by means of electron holography,” Phys. Rev. Lett. 67, 2319–2322 (1991).
    [CrossRef] [PubMed]
  9. H. Lichte, “Optimum focus for taking electron holograms,” Ultramicroscopy 38, 13–22 (1991).
    [CrossRef]
  10. N. Konforti, E. Marom, S. T. Wu, “Phase-only modulation with twisted nematic liquid-crystal spatial light modulators,” Opt. Lett. 13, 251–253 (1988).
    [CrossRef] [PubMed]
  11. K. H. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
    [CrossRef]
  12. J. Amako, T. Sonehara, “Kinoform using an electrically controlled birefringent liquid-crystal spatial light modulator,” Appl. Opt. 30, 4622–4628 (1991).
    [CrossRef] [PubMed]
  13. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
    [CrossRef] [PubMed]
  14. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 26, pp. 349–393.
    [CrossRef]
  15. O. L. Krivanek, “A method for determining the coefficient of spherical aberration from a single electron micrograph,” Optik (Stuttgart) 45, 97–101 (1976).

1991 (3)

Q. Fu, H. Lichte, E. Völkl, “Correction of aberrations of an electron microscope by means of electron holography,” Phys. Rev. Lett. 67, 2319–2322 (1991).
[CrossRef] [PubMed]

H. Lichte, “Optimum focus for taking electron holograms,” Ultramicroscopy 38, 13–22 (1991).
[CrossRef]

J. Amako, T. Sonehara, “Kinoform using an electrically controlled birefringent liquid-crystal spatial light modulator,” Appl. Opt. 30, 4622–4628 (1991).
[CrossRef] [PubMed]

1990 (2)

K. H. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

A. Tonomura, “Electron holography: a new view of the microscopic,” Phys. Today 43(4), 22–29 (1990).
[CrossRef]

1988 (1)

1986 (1)

H. Lichte, “Electron holography approaching atomic resolution,” Ultramicroscopy 20, 293–304 (1986).
[CrossRef]

1979 (2)

A. Tonomura, T. Matsuda, J. Endo, “Spherical-aberration correction of an electron lens by holography,” Jpn. J. Appl. Phys. 18, 1373–1377 (1979).
[CrossRef]

A. Tonomura, T. Matsuda, J. Endo, H. Todokoro, T. Komoda, “Development of a field emission electron microscope,” J. Electron Microsc. 28, 1–11 (1979).

1976 (1)

O. L. Krivanek, “A method for determining the coefficient of spherical aberration from a single electron micrograph,” Optik (Stuttgart) 45, 97–101 (1976).

1974 (1)

1968 (1)

A. V. Crewe, D. N. Eggenberger, D. N. Wall, L. N. Welter, “Electron gun using a field emission source,” Rev. Sci. Instrum. 39, 576–583 (1968).
[CrossRef]

1956 (1)

G. Möllenstedt, H. Düker, “Beobachtung und Messungen an Biprisma-interferezen mit Electronen Wellen,” Z. Phys. 145, 377–397 (1956).
[CrossRef]

1949 (1)

D. Gabor, “Microscopy by reconstructed wavefronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
[CrossRef]

Amako, J.

Brangaccio, D. J.

Bruning, J. H.

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 26, pp. 349–393.
[CrossRef]

Crewe, A. V.

A. V. Crewe, D. N. Eggenberger, D. N. Wall, L. N. Welter, “Electron gun using a field emission source,” Rev. Sci. Instrum. 39, 576–583 (1968).
[CrossRef]

Düker, H.

G. Möllenstedt, H. Düker, “Beobachtung und Messungen an Biprisma-interferezen mit Electronen Wellen,” Z. Phys. 145, 377–397 (1956).
[CrossRef]

Eggenberger, D. N.

A. V. Crewe, D. N. Eggenberger, D. N. Wall, L. N. Welter, “Electron gun using a field emission source,” Rev. Sci. Instrum. 39, 576–583 (1968).
[CrossRef]

Endo, J.

A. Tonomura, T. Matsuda, J. Endo, H. Todokoro, T. Komoda, “Development of a field emission electron microscope,” J. Electron Microsc. 28, 1–11 (1979).

A. Tonomura, T. Matsuda, J. Endo, “Spherical-aberration correction of an electron lens by holography,” Jpn. J. Appl. Phys. 18, 1373–1377 (1979).
[CrossRef]

Fu, Q.

Q. Fu, H. Lichte, E. Völkl, “Correction of aberrations of an electron microscope by means of electron holography,” Phys. Rev. Lett. 67, 2319–2322 (1991).
[CrossRef] [PubMed]

Gabor, D.

D. Gabor, “Microscopy by reconstructed wavefronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
[CrossRef]

Gallagher, J. E.

Herriott, D. R.

Komoda, T.

A. Tonomura, T. Matsuda, J. Endo, H. Todokoro, T. Komoda, “Development of a field emission electron microscope,” J. Electron Microsc. 28, 1–11 (1979).

Konforti, N.

Krivanek, O. L.

O. L. Krivanek, “A method for determining the coefficient of spherical aberration from a single electron micrograph,” Optik (Stuttgart) 45, 97–101 (1976).

Lichte, H.

Q. Fu, H. Lichte, E. Völkl, “Correction of aberrations of an electron microscope by means of electron holography,” Phys. Rev. Lett. 67, 2319–2322 (1991).
[CrossRef] [PubMed]

H. Lichte, “Optimum focus for taking electron holograms,” Ultramicroscopy 38, 13–22 (1991).
[CrossRef]

H. Lichte, “Electron holography approaching atomic resolution,” Ultramicroscopy 20, 293–304 (1986).
[CrossRef]

Lu, K. H.

K. H. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Marom, E.

Matsuda, T.

A. Tonomura, T. Matsuda, J. Endo, H. Todokoro, T. Komoda, “Development of a field emission electron microscope,” J. Electron Microsc. 28, 1–11 (1979).

A. Tonomura, T. Matsuda, J. Endo, “Spherical-aberration correction of an electron lens by holography,” Jpn. J. Appl. Phys. 18, 1373–1377 (1979).
[CrossRef]

Möllenstedt, G.

G. Möllenstedt, H. Düker, “Beobachtung und Messungen an Biprisma-interferezen mit Electronen Wellen,” Z. Phys. 145, 377–397 (1956).
[CrossRef]

Rosenfeld, D. P.

Saleh, B. E. A.

K. H. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Sonehara, T.

Todokoro, H.

A. Tonomura, T. Matsuda, J. Endo, H. Todokoro, T. Komoda, “Development of a field emission electron microscope,” J. Electron Microsc. 28, 1–11 (1979).

Tonomura, A.

A. Tonomura, “Electron holography: a new view of the microscopic,” Phys. Today 43(4), 22–29 (1990).
[CrossRef]

A. Tonomura, T. Matsuda, J. Endo, “Spherical-aberration correction of an electron lens by holography,” Jpn. J. Appl. Phys. 18, 1373–1377 (1979).
[CrossRef]

A. Tonomura, T. Matsuda, J. Endo, H. Todokoro, T. Komoda, “Development of a field emission electron microscope,” J. Electron Microsc. 28, 1–11 (1979).

Völkl, E.

Q. Fu, H. Lichte, E. Völkl, “Correction of aberrations of an electron microscope by means of electron holography,” Phys. Rev. Lett. 67, 2319–2322 (1991).
[CrossRef] [PubMed]

Wall, D. N.

A. V. Crewe, D. N. Eggenberger, D. N. Wall, L. N. Welter, “Electron gun using a field emission source,” Rev. Sci. Instrum. 39, 576–583 (1968).
[CrossRef]

Welter, L. N.

A. V. Crewe, D. N. Eggenberger, D. N. Wall, L. N. Welter, “Electron gun using a field emission source,” Rev. Sci. Instrum. 39, 576–583 (1968).
[CrossRef]

White, A. D.

Wu, S. T.

Appl. Opt. (2)

J. Electron Microsc. (1)

A. Tonomura, T. Matsuda, J. Endo, H. Todokoro, T. Komoda, “Development of a field emission electron microscope,” J. Electron Microsc. 28, 1–11 (1979).

Jpn. J. Appl. Phys. (1)

A. Tonomura, T. Matsuda, J. Endo, “Spherical-aberration correction of an electron lens by holography,” Jpn. J. Appl. Phys. 18, 1373–1377 (1979).
[CrossRef]

Opt. Eng. (1)

K. H. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Opt. Lett. (1)

Optik (Stuttgart) (1)

O. L. Krivanek, “A method for determining the coefficient of spherical aberration from a single electron micrograph,” Optik (Stuttgart) 45, 97–101 (1976).

Phys. Rev. Lett. (1)

Q. Fu, H. Lichte, E. Völkl, “Correction of aberrations of an electron microscope by means of electron holography,” Phys. Rev. Lett. 67, 2319–2322 (1991).
[CrossRef] [PubMed]

Phys. Today (1)

A. Tonomura, “Electron holography: a new view of the microscopic,” Phys. Today 43(4), 22–29 (1990).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

D. Gabor, “Microscopy by reconstructed wavefronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
[CrossRef]

Rev. Sci. Instrum. (1)

A. V. Crewe, D. N. Eggenberger, D. N. Wall, L. N. Welter, “Electron gun using a field emission source,” Rev. Sci. Instrum. 39, 576–583 (1968).
[CrossRef]

Ultramicroscopy (2)

H. Lichte, “Optimum focus for taking electron holograms,” Ultramicroscopy 38, 13–22 (1991).
[CrossRef]

H. Lichte, “Electron holography approaching atomic resolution,” Ultramicroscopy 20, 293–304 (1986).
[CrossRef]

Z. Phys. (1)

G. Möllenstedt, H. Düker, “Beobachtung und Messungen an Biprisma-interferezen mit Electronen Wellen,” Z. Phys. 145, 377–397 (1956).
[CrossRef]

Other (1)

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 26, pp. 349–393.
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic illustration showing structure and principal operation of a TNLC panel (spaced lozenge-shaped line, without an electric field applied; continuous circle line, with an electric field applied).

Fig. 2
Fig. 2

Mach–Zehnder interferometer used for measuring the dependence of phase response to applied voltage in the LCSLM.

Fig. 3
Fig. 3

Phase-modulation characteristics of the LCSLM: (a) three-dimensional plot of the measured phase distribution; (b) dependence of the phase modulation on the applied voltage.

Fig. 4
Fig. 4

Phase plates for correction of spherical aberration and defocusing of the electron-objective lens: (a) computer-generated video pattern, (b) phase plate generated by the LCSLM.

Fig. 5
Fig. 5

Schematic diagram of the optical system used for hologram reconstruction and aberration correction with the LCSLM: L c , Collimator; L1, L2, lenses.

Fig. 6
Fig. 6

Schematic diagram of the electron holographic system.

Fig. 7
Fig. 7

(a) Electron-image hologram of magnesium oxide fine particles (negative film), (b) reconstructed image from the optical system shown in Fig. 5 without an electric field applied to the LCSLM.

Fig. 8
Fig. 8

Results of changing the focus of the reconstructed image wave by using the LCSLM: (a) underfocused image, (b) over-focused image.

Equations (7)

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o ( x , y ) = a ( x , y ) exp [ i ϕ ( x , y ) ] .
b ( x , y ) = o ( x , y ) * PSF ( x , y ) ,
O ( R x , R y ) exp [ i χ ( R x , R y ) ] ,
χ ( R ) = 2 π ( c s 4 λ 3 R 4 - Δ f 2 λ R 2 ) ,
r ( x , y ) = exp ( i 2 π R 0 x ) ,
I ( x , y ) = b ( x , y ) + r ( x , y ) 2 = 1 + b ( x , y ) 2 + b ( x , y ) exp ( i 2 π R 0 x ) + b * ( x , y ) exp ( - i 2 π R 0 x ) ,
FT [ I ( x , y ) ] = δ ( R x , R y ) + FT [ b ( x , y ) 2 ] + O ( R x - R 0 , R y ) exp [ i χ ( R x - R 0 , R y ) ] + O * ( R x + R 0 , R y ) exp [ - i χ ( R x + R 0 , R y ) ] ,

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