Abstract

Holographic interferometry in an electron microscope and its phase analysis technique are described. The fringe scanning method is used to gain high sensitivity in phase detection. An example of measuring a magnetic field of a fine particle is presented. The measurement accuracy for median filtering is about 1/70 fringe corresponding to the magnetic flux sensitivity of 6 × 10−17 Wb. Noise reduction techniques are also discussed.

© 1987 Optical Society of America

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References

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  1. A. Tonomura, J. Endo, T. Matsuda, “An Application of Electron Holography to Interference Microscopy,” Optik 53, 143 (1979).
  2. A. Tonomura et al., “Electron Holography Technique for Investigating Thin Ferromagnetic Films,” Phys. Rev. B 25, 6799 (1981).
    [CrossRef]
  3. A. Tonomura, “Application of Electron Holography Using a Field-Emission Electron Microscope,” J. Electron Microsc. 33, 101 (1984).
  4. D. Gabor, “Microscopy by Reconstructed Wave Fronts,” Proc. Soc. London Ser. A 197, 454 (1949).
    [CrossRef]
  5. D. Gabor, “Microscopy by Reconstructed Wavefronts: II,” Proc. Phys. Soc. B 64, 449 (1951).
    [CrossRef]
  6. A. Tonomura, T. Matsuda, J. Endo, Jpn. J. Appl. Phys. 18, 1373 (1979).
    [CrossRef]
  7. J. Endo, T. Matsuda, A. Tonomura, “Interference Electron Microscopy by Means of Holography,” Jpn. J. Appl. Phys. 18, 2291 (1979).
    [CrossRef]
  8. K. Matsumoto, M. Takashima, “Phase-Difference Amplification by Nonlinear Holograms,” J. Opt. Soc. Am. 60, 30 (1970).
    [CrossRef]
  9. K. Matsuda, C. H. Freund, P. Hariharan, “Phase-Difference Amplification Using Longitudinally Reversed Shearing Interferometry: An Experimental Study,” Appl. Opt. 20, 2763 (1981).
    [CrossRef] [PubMed]
  10. J. Endo, T. Kawasaki, T. Matsuda, N. Osakabe, A. Tonomura, “Sensitivity Improvement in Electron Holographic Interferometry,” in Conference Digest, Thirteenth Congress of the International Commission for Optics, Sapporo (1984), p. 480.
  11. M. Takeda, Q-S. Ru, “Computer-Based Highly Sensitive Electron-Wave Interferometry,” Appl. Opt. 24, 3068 (1985).
    [CrossRef] [PubMed]
  12. J. H. Bruning, D. R. Herriot, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses,” Appl. Opt. 13, 2693 (1974).
    [CrossRef] [PubMed]
  13. T. Yatagai, T. Kanou, “Aspherical Surface Testing with Shearing Interferometer Using Fringe Scanning Detection Method,” Opt. Eng. 23, 357 (1984).
    [CrossRef]

1985 (1)

1984 (2)

T. Yatagai, T. Kanou, “Aspherical Surface Testing with Shearing Interferometer Using Fringe Scanning Detection Method,” Opt. Eng. 23, 357 (1984).
[CrossRef]

A. Tonomura, “Application of Electron Holography Using a Field-Emission Electron Microscope,” J. Electron Microsc. 33, 101 (1984).

1981 (2)

1979 (3)

A. Tonomura, T. Matsuda, J. Endo, Jpn. J. Appl. Phys. 18, 1373 (1979).
[CrossRef]

J. Endo, T. Matsuda, A. Tonomura, “Interference Electron Microscopy by Means of Holography,” Jpn. J. Appl. Phys. 18, 2291 (1979).
[CrossRef]

A. Tonomura, J. Endo, T. Matsuda, “An Application of Electron Holography to Interference Microscopy,” Optik 53, 143 (1979).

1974 (1)

1970 (1)

1951 (1)

D. Gabor, “Microscopy by Reconstructed Wavefronts: II,” Proc. Phys. Soc. B 64, 449 (1951).
[CrossRef]

1949 (1)

D. Gabor, “Microscopy by Reconstructed Wave Fronts,” Proc. Soc. London Ser. A 197, 454 (1949).
[CrossRef]

Brangaccio, D. J.

Bruning, J. H.

Endo, J.

A. Tonomura, J. Endo, T. Matsuda, “An Application of Electron Holography to Interference Microscopy,” Optik 53, 143 (1979).

A. Tonomura, T. Matsuda, J. Endo, Jpn. J. Appl. Phys. 18, 1373 (1979).
[CrossRef]

J. Endo, T. Matsuda, A. Tonomura, “Interference Electron Microscopy by Means of Holography,” Jpn. J. Appl. Phys. 18, 2291 (1979).
[CrossRef]

J. Endo, T. Kawasaki, T. Matsuda, N. Osakabe, A. Tonomura, “Sensitivity Improvement in Electron Holographic Interferometry,” in Conference Digest, Thirteenth Congress of the International Commission for Optics, Sapporo (1984), p. 480.

Freund, C. H.

Gabor, D.

D. Gabor, “Microscopy by Reconstructed Wavefronts: II,” Proc. Phys. Soc. B 64, 449 (1951).
[CrossRef]

D. Gabor, “Microscopy by Reconstructed Wave Fronts,” Proc. Soc. London Ser. A 197, 454 (1949).
[CrossRef]

Hariharan, P.

Herriot, D. R.

Kanou, T.

T. Yatagai, T. Kanou, “Aspherical Surface Testing with Shearing Interferometer Using Fringe Scanning Detection Method,” Opt. Eng. 23, 357 (1984).
[CrossRef]

Kawasaki, T.

J. Endo, T. Kawasaki, T. Matsuda, N. Osakabe, A. Tonomura, “Sensitivity Improvement in Electron Holographic Interferometry,” in Conference Digest, Thirteenth Congress of the International Commission for Optics, Sapporo (1984), p. 480.

Matsuda, K.

Matsuda, T.

J. Endo, T. Matsuda, A. Tonomura, “Interference Electron Microscopy by Means of Holography,” Jpn. J. Appl. Phys. 18, 2291 (1979).
[CrossRef]

A. Tonomura, T. Matsuda, J. Endo, Jpn. J. Appl. Phys. 18, 1373 (1979).
[CrossRef]

A. Tonomura, J. Endo, T. Matsuda, “An Application of Electron Holography to Interference Microscopy,” Optik 53, 143 (1979).

J. Endo, T. Kawasaki, T. Matsuda, N. Osakabe, A. Tonomura, “Sensitivity Improvement in Electron Holographic Interferometry,” in Conference Digest, Thirteenth Congress of the International Commission for Optics, Sapporo (1984), p. 480.

Matsumoto, K.

Osakabe, N.

J. Endo, T. Kawasaki, T. Matsuda, N. Osakabe, A. Tonomura, “Sensitivity Improvement in Electron Holographic Interferometry,” in Conference Digest, Thirteenth Congress of the International Commission for Optics, Sapporo (1984), p. 480.

Rosenfeld, D. P.

Ru, Q-S.

Takashima, M.

Takeda, M.

Tonomura, A.

A. Tonomura, “Application of Electron Holography Using a Field-Emission Electron Microscope,” J. Electron Microsc. 33, 101 (1984).

A. Tonomura et al., “Electron Holography Technique for Investigating Thin Ferromagnetic Films,” Phys. Rev. B 25, 6799 (1981).
[CrossRef]

A. Tonomura, J. Endo, T. Matsuda, “An Application of Electron Holography to Interference Microscopy,” Optik 53, 143 (1979).

A. Tonomura, T. Matsuda, J. Endo, Jpn. J. Appl. Phys. 18, 1373 (1979).
[CrossRef]

J. Endo, T. Matsuda, A. Tonomura, “Interference Electron Microscopy by Means of Holography,” Jpn. J. Appl. Phys. 18, 2291 (1979).
[CrossRef]

J. Endo, T. Kawasaki, T. Matsuda, N. Osakabe, A. Tonomura, “Sensitivity Improvement in Electron Holographic Interferometry,” in Conference Digest, Thirteenth Congress of the International Commission for Optics, Sapporo (1984), p. 480.

White, A. D.

Yatagai, T.

T. Yatagai, T. Kanou, “Aspherical Surface Testing with Shearing Interferometer Using Fringe Scanning Detection Method,” Opt. Eng. 23, 357 (1984).
[CrossRef]

Appl. Opt. (3)

J. Electron Microsc. (1)

A. Tonomura, “Application of Electron Holography Using a Field-Emission Electron Microscope,” J. Electron Microsc. 33, 101 (1984).

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (2)

A. Tonomura, T. Matsuda, J. Endo, Jpn. J. Appl. Phys. 18, 1373 (1979).
[CrossRef]

J. Endo, T. Matsuda, A. Tonomura, “Interference Electron Microscopy by Means of Holography,” Jpn. J. Appl. Phys. 18, 2291 (1979).
[CrossRef]

Opt. Eng. (1)

T. Yatagai, T. Kanou, “Aspherical Surface Testing with Shearing Interferometer Using Fringe Scanning Detection Method,” Opt. Eng. 23, 357 (1984).
[CrossRef]

Optik (1)

A. Tonomura, J. Endo, T. Matsuda, “An Application of Electron Holography to Interference Microscopy,” Optik 53, 143 (1979).

Phys. Rev. B (1)

A. Tonomura et al., “Electron Holography Technique for Investigating Thin Ferromagnetic Films,” Phys. Rev. B 25, 6799 (1981).
[CrossRef]

Proc. Phys. Soc. B (1)

D. Gabor, “Microscopy by Reconstructed Wavefronts: II,” Proc. Phys. Soc. B 64, 449 (1951).
[CrossRef]

Proc. Soc. London Ser. A (1)

D. Gabor, “Microscopy by Reconstructed Wave Fronts,” Proc. Soc. London Ser. A 197, 454 (1949).
[CrossRef]

Other (1)

J. Endo, T. Kawasaki, T. Matsuda, N. Osakabe, A. Tonomura, “Sensitivity Improvement in Electron Holographic Interferometry,” in Conference Digest, Thirteenth Congress of the International Commission for Optics, Sapporo (1984), p. 480.

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Figures (13)

Fig. 1
Fig. 1

Schematic diagram of an electron hologram recording.

Fig. 2
Fig. 2

Optical reconstruction system of an electron hologram. Phase difference amplification is done by using higher-order diffracted waves.

Fig. 3
Fig. 3

Schematic diagram of hologram reconstruction and fringe analysis.

Fig. 4
Fig. 4

Flow diagram of the software system for automatic data acquisition and phase analysis.

Fig. 5
Fig. 5

Magnified version of an electron hologram. Holographic carrier fringes are observed between the arrows.

Fig. 6
Fig. 6

Reconstructed image of a cobalt particle.

Fig. 7
Fig. 7

Interference micrograph of (a) magnetic particle and (b) its fringe intensity profile along a central cross section.

Fig. 8
Fig. 8

Interferometric micrograms with different reference phases.

Fig. 9
Fig. 9

Calculated phase distribution: (a) wrapped phase and (b) its profile along a central cross section.

Fig. 10
Fig. 10

Result of median window filtering of phase distribution shown in Fig. 9.

Fig. 11
Fig. 11

(a) Unwrapped phase distribution and (b) its profile along a central cross section.

Fig. 12
Fig. 12

Three-dimensional plot of the phase distribution shown in Fig. 11.

Fig. 13
Fig. 13

Phase profiles in linear parts of Figs. 9(b) and 10(b). Evaluated phase variances are 1/50 and 1/70 fringes, respectively.

Equations (8)

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n = 1 + V 0 / 2 ϕ 0 ,
Δ ϕ = n · d .
Δ ϕ = - 2 π · e / h · B n d S ,
f ( x , y , δ n ) = a ( x , y ) + b ( x , y ) cos [ ϕ ( x , y ) + δ n ] ,
δ n = 2 π / N             ( N = 1 , 2 , , N - 1 ) ,
c ( x , y ) = n = 0 N - 1 f ( x , y , δ n ) cos 2 π n / N ,
s ( x , y ) = n = 0 N - 1 f ( x , y , δ n ) sin 2 π n / N
ϕ ( x , y ) = tan - 1 s ( x , y ) c ( x , y ) .

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