Abstract

For subfringe measurement in electron-wave interferometry, the Fourier transform method of fringe-pattern analysis is applied to electron holographic interferometry. Experimental results of magnetic-field measurement are presented to demonstrate subfringe detection with a much higher sensitivity than h/e = 4.1 × 10−15 (Wb/fringe), the limit set by the Aharonov-Bohm effect.

© 1985 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 Inteference Microscopy,” Optik 53, 143 (1979).
  2. J. Endo, T. Matsuda, A. Tonomura, “Interference Electron Microscopy by Means of Holography,” Jpn. J. Appl. Phys. 18, 2291 (1979).
    [CrossRef]
  3. A. Tonomura, T. Matsuda, J. Endo, T. Arii, K. Mihama, “Direct Observation of Magnetic Domain Walls by Electron Holography,” Phys. Rev. Lett. 44, 1430 (1980).
    [CrossRef]
  4. A. Tonomura et al., “Electron Holography Technique for Investigating Thin Ferromagnetic Films,” Phys. Rev. B 25, 6799 (1981).
    [CrossRef]
  5. A. Tonomura et al., “Observation of Aharonov-Bohm Effects by Electron Holography,” Phys. Rev. Lett. 48, 1443 (1982).
    [CrossRef]
  6. A. Tonomura, H. Umezaki, T. Matsuda, N. Osakabe, J. Endo, Y. Sugita, “Is Magnetic Flux Quantized in a Toroidal Ferro-magnet?” Phys. Rev. Lett. 51, 331 (1983).
    [CrossRef]
  7. N. Osakabe et al., “Observation of Recorded Magnetization Pattern by Electron Holography,” Appl. Phys. Lett. 42, 746 (1983).
    [CrossRef]
  8. Y. Aharonov, D. Bohm, “Significance of Electromagnetic Potentials in the Quantum Theory,” Phys. Rev. 115, 485 (1959).
    [CrossRef]
  9. A. Tonomura, “Electron Holographic Interferometry,” in Digest of ICO-13, Sapporo (1984), pp. 472–475.
  10. O. Bryngdahl, A. W. Lohmann, “Interferograms and Image Holograms,” J. Opt. Soc. Am. 58, 141 (1968).
    [CrossRef]
  11. O. Bryngdahl, “Longitudinally Reversed Shearing Interferometry,” J. Opt. Soc. Am. 59, 142 (1969).
    [CrossRef]
  12. K. Matsumoto, M. Takashima, “Phase-Difference Amplification by Nonlinear Holograms,” J. Opt. Soc. Am. 60, 30 (1970).
    [CrossRef]
  13. 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]
  14. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital Wave-Front Measuring Interferometry: Some Systematic Error Sources,” Appl. Opt. 22, 3421 (1983).
    [CrossRef] [PubMed]
  15. J. Endo, T. Kawasaki, T. Matsuda, N. Osakabe, A. Tonomura, “Sensitivity Improvement in Electron Holographic Interferometry,” in Digest of ICO-13, Sapporo (1984), pp. 480 and 481.
  16. M. Takeda, H. Ina, S. Kobayashi, “Fourier-Transform Method of Fringe-Pattern Analysis for Computer-Based Topography and Interferometry,” J. Opt. Soc. Am. 72, 156 (1982).
    [CrossRef]
  17. M. Takeda, S. Kobayashi, “Lateral Aberration Measurements with a Digital Talbot Interferometer,” Appl. Opt. 23, 1760 (1984).
    [CrossRef] [PubMed]
  18. M. Takeda, K. Mutoh, “Fourier Transform Profilometry for the Automatic Measurement of 3-D Object Shapes,” Appl. Opt. 22, 3977 (1983).
    [CrossRef] [PubMed]
  19. A. V. Oppenheim, R. W. Schafer, T. G. Stockham, “Nonlinear Filtering of Multiplied and Convolved Signals,” Proc. IEEE 56, 1264 (1968).
    [CrossRef]

1984

1983

J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital Wave-Front Measuring Interferometry: Some Systematic Error Sources,” Appl. Opt. 22, 3421 (1983).
[CrossRef] [PubMed]

M. Takeda, K. Mutoh, “Fourier Transform Profilometry for the Automatic Measurement of 3-D Object Shapes,” Appl. Opt. 22, 3977 (1983).
[CrossRef] [PubMed]

A. Tonomura, H. Umezaki, T. Matsuda, N. Osakabe, J. Endo, Y. Sugita, “Is Magnetic Flux Quantized in a Toroidal Ferro-magnet?” Phys. Rev. Lett. 51, 331 (1983).
[CrossRef]

N. Osakabe et al., “Observation of Recorded Magnetization Pattern by Electron Holography,” Appl. Phys. Lett. 42, 746 (1983).
[CrossRef]

1982

1981

1980

A. Tonomura, T. Matsuda, J. Endo, T. Arii, K. Mihama, “Direct Observation of Magnetic Domain Walls by Electron Holography,” Phys. Rev. Lett. 44, 1430 (1980).
[CrossRef]

1979

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

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

1970

1969

1968

O. Bryngdahl, A. W. Lohmann, “Interferograms and Image Holograms,” J. Opt. Soc. Am. 58, 141 (1968).
[CrossRef]

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, “Nonlinear Filtering of Multiplied and Convolved Signals,” Proc. IEEE 56, 1264 (1968).
[CrossRef]

1959

Y. Aharonov, D. Bohm, “Significance of Electromagnetic Potentials in the Quantum Theory,” Phys. Rev. 115, 485 (1959).
[CrossRef]

Aharonov, Y.

Y. Aharonov, D. Bohm, “Significance of Electromagnetic Potentials in the Quantum Theory,” Phys. Rev. 115, 485 (1959).
[CrossRef]

Arii, T.

A. Tonomura, T. Matsuda, J. Endo, T. Arii, K. Mihama, “Direct Observation of Magnetic Domain Walls by Electron Holography,” Phys. Rev. Lett. 44, 1430 (1980).
[CrossRef]

Bohm, D.

Y. Aharonov, D. Bohm, “Significance of Electromagnetic Potentials in the Quantum Theory,” Phys. Rev. 115, 485 (1959).
[CrossRef]

Bryngdahl, O.

Burow, R.

Elssner, K.-E.

Endo, J.

A. Tonomura, H. Umezaki, T. Matsuda, N. Osakabe, J. Endo, Y. Sugita, “Is Magnetic Flux Quantized in a Toroidal Ferro-magnet?” Phys. Rev. Lett. 51, 331 (1983).
[CrossRef]

A. Tonomura, T. Matsuda, J. Endo, T. Arii, K. Mihama, “Direct Observation of Magnetic Domain Walls by Electron Holography,” Phys. Rev. Lett. 44, 1430 (1980).
[CrossRef]

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

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 Digest of ICO-13, Sapporo (1984), pp. 480 and 481.

Freund, C. H.

Grzanna, J.

Hariharan, P.

Ina, H.

Kawasaki, T.

J. Endo, T. Kawasaki, T. Matsuda, N. Osakabe, A. Tonomura, “Sensitivity Improvement in Electron Holographic Interferometry,” in Digest of ICO-13, Sapporo (1984), pp. 480 and 481.

Kobayashi, S.

Lohmann, A. W.

Matsuda, K.

Matsuda, T.

A. Tonomura, H. Umezaki, T. Matsuda, N. Osakabe, J. Endo, Y. Sugita, “Is Magnetic Flux Quantized in a Toroidal Ferro-magnet?” Phys. Rev. Lett. 51, 331 (1983).
[CrossRef]

A. Tonomura, T. Matsuda, J. Endo, T. Arii, K. Mihama, “Direct Observation of Magnetic Domain Walls by Electron Holography,” Phys. Rev. Lett. 44, 1430 (1980).
[CrossRef]

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

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 Digest of ICO-13, Sapporo (1984), pp. 480 and 481.

Matsumoto, K.

Merkel, K.

Mihama, K.

A. Tonomura, T. Matsuda, J. Endo, T. Arii, K. Mihama, “Direct Observation of Magnetic Domain Walls by Electron Holography,” Phys. Rev. Lett. 44, 1430 (1980).
[CrossRef]

Mutoh, K.

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, “Nonlinear Filtering of Multiplied and Convolved Signals,” Proc. IEEE 56, 1264 (1968).
[CrossRef]

Osakabe, N.

A. Tonomura, H. Umezaki, T. Matsuda, N. Osakabe, J. Endo, Y. Sugita, “Is Magnetic Flux Quantized in a Toroidal Ferro-magnet?” Phys. Rev. Lett. 51, 331 (1983).
[CrossRef]

N. Osakabe et al., “Observation of Recorded Magnetization Pattern by Electron Holography,” Appl. Phys. Lett. 42, 746 (1983).
[CrossRef]

J. Endo, T. Kawasaki, T. Matsuda, N. Osakabe, A. Tonomura, “Sensitivity Improvement in Electron Holographic Interferometry,” in Digest of ICO-13, Sapporo (1984), pp. 480 and 481.

Schafer, R. W.

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, “Nonlinear Filtering of Multiplied and Convolved Signals,” Proc. IEEE 56, 1264 (1968).
[CrossRef]

Schwider, J.

Spolaczyk, R.

Stockham, T. G.

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, “Nonlinear Filtering of Multiplied and Convolved Signals,” Proc. IEEE 56, 1264 (1968).
[CrossRef]

Sugita, Y.

A. Tonomura, H. Umezaki, T. Matsuda, N. Osakabe, J. Endo, Y. Sugita, “Is Magnetic Flux Quantized in a Toroidal Ferro-magnet?” Phys. Rev. Lett. 51, 331 (1983).
[CrossRef]

Takashima, M.

Takeda, M.

Tonomura, A.

A. Tonomura, H. Umezaki, T. Matsuda, N. Osakabe, J. Endo, Y. Sugita, “Is Magnetic Flux Quantized in a Toroidal Ferro-magnet?” Phys. Rev. Lett. 51, 331 (1983).
[CrossRef]

A. Tonomura et al., “Observation of Aharonov-Bohm Effects by Electron Holography,” Phys. Rev. Lett. 48, 1443 (1982).
[CrossRef]

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

A. Tonomura, T. Matsuda, J. Endo, T. Arii, K. Mihama, “Direct Observation of Magnetic Domain Walls by Electron Holography,” Phys. Rev. Lett. 44, 1430 (1980).
[CrossRef]

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

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

A. Tonomura, “Electron Holographic Interferometry,” in Digest of ICO-13, Sapporo (1984), pp. 472–475.

J. Endo, T. Kawasaki, T. Matsuda, N. Osakabe, A. Tonomura, “Sensitivity Improvement in Electron Holographic Interferometry,” in Digest of ICO-13, Sapporo (1984), pp. 480 and 481.

Umezaki, H.

A. Tonomura, H. Umezaki, T. Matsuda, N. Osakabe, J. Endo, Y. Sugita, “Is Magnetic Flux Quantized in a Toroidal Ferro-magnet?” Phys. Rev. Lett. 51, 331 (1983).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

N. Osakabe et al., “Observation of Recorded Magnetization Pattern by Electron Holography,” Appl. Phys. Lett. 42, 746 (1983).
[CrossRef]

J. Opt. Soc. Am.

Jpn. J. Appl. Phys.

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

Optik

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

Phys. Rev.

Y. Aharonov, D. Bohm, “Significance of Electromagnetic Potentials in the Quantum Theory,” Phys. Rev. 115, 485 (1959).
[CrossRef]

Phys. Rev. B

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

Phys. Rev. Lett.

A. Tonomura et al., “Observation of Aharonov-Bohm Effects by Electron Holography,” Phys. Rev. Lett. 48, 1443 (1982).
[CrossRef]

A. Tonomura, H. Umezaki, T. Matsuda, N. Osakabe, J. Endo, Y. Sugita, “Is Magnetic Flux Quantized in a Toroidal Ferro-magnet?” Phys. Rev. Lett. 51, 331 (1983).
[CrossRef]

A. Tonomura, T. Matsuda, J. Endo, T. Arii, K. Mihama, “Direct Observation of Magnetic Domain Walls by Electron Holography,” Phys. Rev. Lett. 44, 1430 (1980).
[CrossRef]

Proc. IEEE

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, “Nonlinear Filtering of Multiplied and Convolved Signals,” Proc. IEEE 56, 1264 (1968).
[CrossRef]

Other

A. Tonomura, “Electron Holographic Interferometry,” in Digest of ICO-13, Sapporo (1984), pp. 472–475.

J. Endo, T. Kawasaki, T. Matsuda, N. Osakabe, A. Tonomura, “Sensitivity Improvement in Electron Holographic Interferometry,” in Digest of ICO-13, Sapporo (1984), pp. 480 and 481.

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of the experimental system.

Fig. 2
Fig. 2

(A) Fourier spectra of the electron hologram; (B) filtered spectrum.

Fig. 3
Fig. 3

Experimentl results: (A) phase distribution and (B) its contour map obtained by this work (contours are drawn at intervals of 1/18.5 fringes. (C) Fringe contour map obtained by Osakabe et al. using the optical technique with ten-time phase amplification (contours appear at intervals of 1/10 fringes).

Fig. 4
Fig. 4

(A) Directions of magnetization and lines of force determined uniquely from the (B) wave front shape which has no ambiguity in its hills and valleys.

Equations (6)

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Δ ϕ = ( e / ћ ) B n d S ,
g ( x , y ) = a ( x , y ) + b ( x , y ) cos [ 2 π f 0 x + ϕ ( x , y ) ] ,
g ( x , y ) = a ( x , y ) + c ( x , y ) exp ( 2 π j f 0 x ) + c * ( x , y ) exp ( 2 π j f 0 x ) ,
c ( x , y ) = ( 1 / 2 ) b ( x , y ) exp [ j ϕ ( x , y ) ] .
G ( f , y ) = A ( f , y ) + C ( f f 0 , y ) + C * ( f f 0 , y ) ,
log [ c ( x , y ) ] = log [ ( 1 / 2 ) b ( x , y ) ] + j ϕ ( x , y ) ,

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