Abstract

It has previously been shown that - in theory - magnification variations can occur in an imaging system as a function of defocus, depending on the field curvature of the illuminating system. We here present the results of practical experiments to verify this effect in the transmission electron microscope. We find that with illumination settings typically used in the electron microscopy of biological macromolecules, systematic variations in magnification of ∼ 0.5% per μm defocus can easily occur. This work highlights the need for a magnification-invariant imaging mode to eliminate or to compensate for this effect.

© 2005 Optical Society of America

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References

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  1. M. Adrian, J. Dubochet, J. Lepault, and A. W. McDowall, "Cryo-electron microscopy of viruses," Nature 308, 32-36 (1984).
    [CrossRef] [PubMed]
  2. R. Henderson, "The potential and limitations of neutrons, electrons and x-rays for atomic-resolution microscopy of unstained biological molecules," Q. Rev. Biophys. 28, 171-193 (1995).
    [CrossRef] [PubMed]
  3. M. van Heel, B. Gowen, R. Matadeen, E. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, and A. Patwardhan, "Single-particle electron cryo-microscopy: towards atomic resolution," Q. Rev. Biophys. 33, 307-369 (2000).
    [CrossRef]
  4. B. P. Klaholz, A. G. Myasnikov, and M. van Heel, "Visualization of release factor 3 on the ribosome during termination of protein synthesis," Nature 427, 862-865 (2004).
    [CrossRef] [PubMed]
  5. M. van Heel and J. Frank, "Use of multivariate statistics in analysing the images of biological macromolecules,"Ultramicroscopy 6, 187-194 (1981).
    [PubMed]
  6. M. van Heel, "Multivariate statistical classification of noisy images (randomly oriented biological macromolecules)," Ultramicroscopy 13, 165-183 (1984).
    [CrossRef] [PubMed]
  7. M. van Heel, "Angular reconstitution: a posteriori assignment of projection directions for 3D reconstruction," Ultramicroscopy 21, 111-124 (1987).
    [CrossRef] [PubMed]
  8. F. Zernike, "Phase contrast, a new method for the microscopic observation of transparent objects," Physica IX, 686-698 (1942).
    [CrossRef]
  9. O. Scherzer, "The theoretical resolution limit of the electron microscope," J. Appl. Phys. 20, 20-29 (1949).
    [CrossRef]
  10. J. W. Goodman, Introduction to fourier optics (The McGraw-Hill Companies, Inc., Singapore, 1996).
  11. K.-J. Hanzen, "The optical transfer theory of the electron microscope: fundamental principles and applications,"Advances in optical and electron microscopy 4, 1-84 (1971).
  12. L. Reimer, Transmission Electron Microscopy: Physics of Image Formation and Microanalysis (Springer-Verlag, New York, 1997).
  13. J. Frank, "The envelope of electron microscopic transfer functions for partially coherent illumination," Optik 38, 519-536 (1973).
  14. C. J. Humphreys and J. C. H. Spence, "Resolution and illumination coherence in electron microscopy," Optik 58, 125-144 (1981).
  15. R. H. Wade and J. Frank, "Electron microscope transfer functions for partially coherent axial illumination and chromatic defocus spread," Optik 49, 81-92 (1977).
  16. D. L. Misell, "On the validity of the weak-phase and other approximations in the analysis of electron microscope images," J. Phys. D 9, 1849-1866 (1976).
    [CrossRef]
  17. M. van Heel, "On the imaging of relatively strong objects in partially coherent illumination in optics and electron optics," Optik 47, 389-408 (1978).
  18. W. O. Saxton, Computer Techniques for Image Processing in Electron Microscopy (Academic Press, New York, 1978).
  19. A. Aldroubi, B. L. Trus, M. Unser, F. P. Booy, and A. C. Steven, "Magnification mismatches between micrographs: corrective procedures and implications for structural analysis," Ultramicroscopy 46, 175-188 (1992).
    [CrossRef] [PubMed]
  20. M. M. Bijlholt, M. G. van Heel, and E. F. van Bruggen, "Comparison of 4 X 6-meric hemocyanins from three different arthropods using computer alignment and correspondence analysis," J. Mol. Biol. 161, 139-153 (1982).
    [CrossRef] [PubMed]
  21. A. Patwardhan, "Coherent non-planar illumination of a defocused specimen: consequences for transmission electron microscopy," Optik 113, 4-12 (2002).
    [CrossRef]
  22. A. Patwardhan, "Transmission electron microscopy of weakly scattering objects described by operator algebra," J. Opt. Soc. Am. A 20, 1210-1222 (2003).
    [CrossRef]
  23. N. G. Wrigley, "The lattice spacing of crystalline catalase as an internal standard of length in electron microscopy," J. Ultrastruct. Res. 24, 454-464 (1968).
    [CrossRef] [PubMed]

Advances in optical and electron microsc

K.-J. Hanzen, "The optical transfer theory of the electron microscope: fundamental principles and applications,"Advances in optical and electron microscopy 4, 1-84 (1971).

J. Appl. Phys.

O. Scherzer, "The theoretical resolution limit of the electron microscope," J. Appl. Phys. 20, 20-29 (1949).
[CrossRef]

J. Mol. Biol.

M. M. Bijlholt, M. G. van Heel, and E. F. van Bruggen, "Comparison of 4 X 6-meric hemocyanins from three different arthropods using computer alignment and correspondence analysis," J. Mol. Biol. 161, 139-153 (1982).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

J. Phys. D

D. L. Misell, "On the validity of the weak-phase and other approximations in the analysis of electron microscope images," J. Phys. D 9, 1849-1866 (1976).
[CrossRef]

J. Ultrastruct. Res.

N. G. Wrigley, "The lattice spacing of crystalline catalase as an internal standard of length in electron microscopy," J. Ultrastruct. Res. 24, 454-464 (1968).
[CrossRef] [PubMed]

Nature

M. Adrian, J. Dubochet, J. Lepault, and A. W. McDowall, "Cryo-electron microscopy of viruses," Nature 308, 32-36 (1984).
[CrossRef] [PubMed]

B. P. Klaholz, A. G. Myasnikov, and M. van Heel, "Visualization of release factor 3 on the ribosome during termination of protein synthesis," Nature 427, 862-865 (2004).
[CrossRef] [PubMed]

Optik

M. van Heel, "On the imaging of relatively strong objects in partially coherent illumination in optics and electron optics," Optik 47, 389-408 (1978).

J. Frank, "The envelope of electron microscopic transfer functions for partially coherent illumination," Optik 38, 519-536 (1973).

C. J. Humphreys and J. C. H. Spence, "Resolution and illumination coherence in electron microscopy," Optik 58, 125-144 (1981).

R. H. Wade and J. Frank, "Electron microscope transfer functions for partially coherent axial illumination and chromatic defocus spread," Optik 49, 81-92 (1977).

A. Patwardhan, "Coherent non-planar illumination of a defocused specimen: consequences for transmission electron microscopy," Optik 113, 4-12 (2002).
[CrossRef]

Physica

F. Zernike, "Phase contrast, a new method for the microscopic observation of transparent objects," Physica IX, 686-698 (1942).
[CrossRef]

Q. Rev. Biophys.

R. Henderson, "The potential and limitations of neutrons, electrons and x-rays for atomic-resolution microscopy of unstained biological molecules," Q. Rev. Biophys. 28, 171-193 (1995).
[CrossRef] [PubMed]

M. van Heel, B. Gowen, R. Matadeen, E. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, and A. Patwardhan, "Single-particle electron cryo-microscopy: towards atomic resolution," Q. Rev. Biophys. 33, 307-369 (2000).
[CrossRef]

Ultramicroscopy

M. van Heel and J. Frank, "Use of multivariate statistics in analysing the images of biological macromolecules,"Ultramicroscopy 6, 187-194 (1981).
[PubMed]

M. van Heel, "Multivariate statistical classification of noisy images (randomly oriented biological macromolecules)," Ultramicroscopy 13, 165-183 (1984).
[CrossRef] [PubMed]

M. van Heel, "Angular reconstitution: a posteriori assignment of projection directions for 3D reconstruction," Ultramicroscopy 21, 111-124 (1987).
[CrossRef] [PubMed]

A. Aldroubi, B. L. Trus, M. Unser, F. P. Booy, and A. C. Steven, "Magnification mismatches between micrographs: corrective procedures and implications for structural analysis," Ultramicroscopy 46, 175-188 (1992).
[CrossRef] [PubMed]

Other

W. O. Saxton, Computer Techniques for Image Processing in Electron Microscopy (Academic Press, New York, 1978).

L. Reimer, Transmission Electron Microscopy: Physics of Image Formation and Microanalysis (Springer-Verlag, New York, 1997).

J. W. Goodman, Introduction to fourier optics (The McGraw-Hill Companies, Inc., Singapore, 1996).

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Figures (3)

Fig. 1.
Fig. 1.

Schematic of the model system used to describe the imaging properties of the transmission electron microscope in this study. A defocused image of the point source is imaged onto the specimen via a condenser lens (rays in cyan). The specimen is imaged onto the image plane by the objective lens (rays in magenta). The conjugate object and image distances, for an objective lens with a focal length f, are do and di respectively. The specimen is defocused by changing the focal length of the objective lens by Δf. dc is the distance between the objective lens and the illumination cross-over and d23 is the distance between the specimen and the condenser lens. wc is the diameter of the condenser aperture and ws is the diameter of its projection onto the specimen. The naming convention used here has been adopted from [21,22].

Fig. 2.
Fig. 2.

Magnification variation as a function of defocus. Each graph consists of two data sets, one corresponding to full screen illumination (red triangles) and one corresponding to half screen illumination (blue circles). Linear fits to these data sets, along with the equations of best fit and regression coefficients are shown in corresponding colors. The title of each graph specifies whether overfocused or underfocused illumination was used and the magnification. Comparing the graphs on the left (overfocused illumination) with those on the right (underfocused illumination); the sign of the variation can be seen to change. Comparing graphs row-by-row from top to bottom, the magnitude of the variation can be seen to increase with magnification. The magnitude of the variation can also be seen to be consistently higher for the half screen case than the full screen one in each graph.

Fig. 3.
Fig. 3.

(a) Magnification variation with defocus for two, more extreme cases of illumination than those shown in Fig. 2. The red triangles correspond to a case where the illumination is much more convergent than the half screen case, i.e., the inner circle case, and the blue circles correspond to the case where the condenser projection onto the specimen is approximately twice as large as the full screen case. (b) Comparison of the magnification variation for two different condenser aperture diameters and half screen illumination. The variation is stronger for the larger aperture diameter.

Equations (7)

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CTF ( v ) = 2 sin [ π 2 ( C s λ 3 v 4 2 Δ v 2 ) ] ,
M eff = M o [ 1 Δ f f ( 1 + d o d c d o ) ( d o f + Δ f ) ] ,
Δ d = Δ f .
M eff M o ( 1 + Δ d d c d o )
w s w c = d c d o d 23 ( d c d o ) d c d o d 23 .
w s = α ( M ref M eff ) w ref α ( M ref M o ) w ref ,
M eff M o M o = Δ d d c d o = sgn ( d c d o ) α ( M o w s Δ d M ref w ref d 23 ) ,

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