Abstract

An analysis of the function of a spatial domain filter employed in recent optical syntheses of molecular images from electron holograms is presented. The device is effective in ridding the primary image region of the naturally arising background intensity which, unless filtered, can severely obscure the image. The filter also introduces artifacts, however, which may confuse the interpretation of images, and excessive filtering reduces resolving power. It is shown how to calculate the effect of the filter variables in order to secure a reasonable compromise between resolution, backgroubackground noise, and spurious rings.

© 1979 Optical Society of America

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  1. L. S. Bartell and R. D. Johnson, "Molecular images by electron-wave holography," Nature 268, 707–708 (1977). In prior work, G. Saxon ["Division of wavefront side-band Fresnel holography with electrons," Optik 35, 195–210 (1972)] achieved a resolving power of 103 Å by a different variant of electron holography.
  2. L. S. Bartell and W. J. Gignac, "Images of gas molecules by electron holography. II. Experiment and comparison with theory," J. Chem. Phys. 70, 3958–3964 (1979).
  3. G. S. Stroke, An Introduction to Coherent Optics and Holography (Academic, New York, 1966), p. 119.
  4. L. S. Bartell, "Images of gas molecules by electron holography. I. Theory." J. Chem. Phys. 70, 3952–3957 (1979).
  5. L. S. Bartell, "Images of gas atoms by electron holography. I. Theory; II. Experiment and comparison with theory," Optik 43, 373–393, 403–418 (1975).
  6. E. N. Leith, "Photographic film as an element of a coherent optical system," Photogr. Sci. Eng. 6, 75–80 (1962).
  7. M. Born and E. Wolf, Principles of Optics, 2nd Ed. (Pergamon, New York, 1964), Chap. 8.
  8. F. Bowman, Introduction to Bessel Functions (Dover, New York, 1958), pp. 93, 102.
  9. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals Series and Products, 4th Ed. (Academic, New York, 1965), p. 667.
  10. And, indeed, did in the case of images of CF3OOCF3 molecules in Ref. 2.
  11. Data from F. B. Clippard and L. S. Bartell, "Molecular structures of arsenic trifluoride and arsenic pentafluoride as determined by electron diffraction," Inorg. Chem. 9, 805–811 (1970).
  12. Note that the FF image is not a primary holographic image arising from the electron interference fringes produced when the subject wave mixes with the reference wave. It arises from interference fringes produced by the mixing of waves from one part of the subject with waves from another part. See Refs. 2 and 4 for details.

1979

L. S. Bartell and W. J. Gignac, "Images of gas molecules by electron holography. II. Experiment and comparison with theory," J. Chem. Phys. 70, 3958–3964 (1979).

L. S. Bartell, "Images of gas molecules by electron holography. I. Theory." J. Chem. Phys. 70, 3952–3957 (1979).

1975

L. S. Bartell, "Images of gas atoms by electron holography. I. Theory; II. Experiment and comparison with theory," Optik 43, 373–393, 403–418 (1975).

1970

Data from F. B. Clippard and L. S. Bartell, "Molecular structures of arsenic trifluoride and arsenic pentafluoride as determined by electron diffraction," Inorg. Chem. 9, 805–811 (1970).

1962

E. N. Leith, "Photographic film as an element of a coherent optical system," Photogr. Sci. Eng. 6, 75–80 (1962).

Bartell, L. S.

L. S. Bartell and W. J. Gignac, "Images of gas molecules by electron holography. II. Experiment and comparison with theory," J. Chem. Phys. 70, 3958–3964 (1979).

L. S. Bartell, "Images of gas molecules by electron holography. I. Theory." J. Chem. Phys. 70, 3952–3957 (1979).

L. S. Bartell, "Images of gas atoms by electron holography. I. Theory; II. Experiment and comparison with theory," Optik 43, 373–393, 403–418 (1975).

Data from F. B. Clippard and L. S. Bartell, "Molecular structures of arsenic trifluoride and arsenic pentafluoride as determined by electron diffraction," Inorg. Chem. 9, 805–811 (1970).

L. S. Bartell and R. D. Johnson, "Molecular images by electron-wave holography," Nature 268, 707–708 (1977). In prior work, G. Saxon ["Division of wavefront side-band Fresnel holography with electrons," Optik 35, 195–210 (1972)] achieved a resolving power of 103 Å by a different variant of electron holography.

Born, M.

M. Born and E. Wolf, Principles of Optics, 2nd Ed. (Pergamon, New York, 1964), Chap. 8.

Bowman, F.

F. Bowman, Introduction to Bessel Functions (Dover, New York, 1958), pp. 93, 102.

Clippard, F. B.

Data from F. B. Clippard and L. S. Bartell, "Molecular structures of arsenic trifluoride and arsenic pentafluoride as determined by electron diffraction," Inorg. Chem. 9, 805–811 (1970).

Gignac, W. J.

L. S. Bartell and W. J. Gignac, "Images of gas molecules by electron holography. II. Experiment and comparison with theory," J. Chem. Phys. 70, 3958–3964 (1979).

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals Series and Products, 4th Ed. (Academic, New York, 1965), p. 667.

Johnson, R. D.

L. S. Bartell and R. D. Johnson, "Molecular images by electron-wave holography," Nature 268, 707–708 (1977). In prior work, G. Saxon ["Division of wavefront side-band Fresnel holography with electrons," Optik 35, 195–210 (1972)] achieved a resolving power of 103 Å by a different variant of electron holography.

Leith, E. N.

E. N. Leith, "Photographic film as an element of a coherent optical system," Photogr. Sci. Eng. 6, 75–80 (1962).

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals Series and Products, 4th Ed. (Academic, New York, 1965), p. 667.

Stroke, G. S.

G. S. Stroke, An Introduction to Coherent Optics and Holography (Academic, New York, 1966), p. 119.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 2nd Ed. (Pergamon, New York, 1964), Chap. 8.

Inorg. Chem.

Data from F. B. Clippard and L. S. Bartell, "Molecular structures of arsenic trifluoride and arsenic pentafluoride as determined by electron diffraction," Inorg. Chem. 9, 805–811 (1970).

J. Chem. Phys.

L. S. Bartell and W. J. Gignac, "Images of gas molecules by electron holography. II. Experiment and comparison with theory," J. Chem. Phys. 70, 3958–3964 (1979).

L. S. Bartell, "Images of gas molecules by electron holography. I. Theory." J. Chem. Phys. 70, 3952–3957 (1979).

Optik

L. S. Bartell, "Images of gas atoms by electron holography. I. Theory; II. Experiment and comparison with theory," Optik 43, 373–393, 403–418 (1975).

Photogr. Sci. Eng.

E. N. Leith, "Photographic film as an element of a coherent optical system," Photogr. Sci. Eng. 6, 75–80 (1962).

Other

M. Born and E. Wolf, Principles of Optics, 2nd Ed. (Pergamon, New York, 1964), Chap. 8.

F. Bowman, Introduction to Bessel Functions (Dover, New York, 1958), pp. 93, 102.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals Series and Products, 4th Ed. (Academic, New York, 1965), p. 667.

And, indeed, did in the case of images of CF3OOCF3 molecules in Ref. 2.

G. S. Stroke, An Introduction to Coherent Optics and Holography (Academic, New York, 1966), p. 119.

Note that the FF image is not a primary holographic image arising from the electron interference fringes produced when the subject wave mixes with the reference wave. It arises from interference fringes produced by the mixing of waves from one part of the subject with waves from another part. See Refs. 2 and 4 for details.

L. S. Bartell and R. D. Johnson, "Molecular images by electron-wave holography," Nature 268, 707–708 (1977). In prior work, G. Saxon ["Division of wavefront side-band Fresnel holography with electrons," Optik 35, 195–210 (1972)] achieved a resolving power of 103 Å by a different variant of electron holography.

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