Contrast Transfer Function of a Transmission Electron Microscope

Tanaka, Nobuo

doi:10.1007/978-4-431-56502-4_17

Nobuo Tanaka²

2294 Accesses

Abstract

As explained in Chap. 16, a lens is a kind of phase shifter depending on incident angle of optical ray to the lens. In this section, we derive the formula of the phase shift. Let us start with the function of a convex lens.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 79.99; Price excludes VAT (USA)

Softcover Book: USD 99.99; Price excludes VAT (USA)

Hardcover Book: USD 99.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

1.
Previously, another definition of the amount of defocus such as Δf > 0 for underfocus was used. Recently, many researchers change to use the present definition Δf > 0 for overfocus.
2.
The original papers are written by J. Frank (1973) and by Fejes (1977).
3.
These lattice fringes are named “nonlinear lattice fringes .” The narrowest lattice fringes formed between the direct beam and diffracted one, that is, “linear lattice fringes ” are of 64 pm, which are formed by the interference between 000 wave and 620 waves of gold (Akashi et al. 2005).
It is considered that the value may come up to the limitation of the linear imaging.
4.
The damping functions of linear and nonlinear terms were discussed also in relation to the channeling theory for HRTEM imaging by Van Aert et al. (2010).
5.
By the development of a spherical aberration corrector since the twenty-first century, the damping function in Eq. (17.17) has been extended to higher spatial frequencies. The importance of the term due to the fluctuation in Eq. (17.16) still remains.

References

Akashi, T., et al. (2005). Applied Physics Letters, 87, 174101.
Article Google Scholar
Barthel, J., & Thust, A. (2010). Ultramicroscopy, 111, 27.
Google Scholar
Fejes, P. C. (1977). Acta Crystallographica, A33, 10.
Google Scholar
Frank, J. (1973). Optik, 38, 519.
Google Scholar
Ishizuka, K. (1980). Ultramicroscopy, 5, 55.
Article Google Scholar
Kawasaki, T., et al. (2000). Applied Physics Letters, 76, 1342.
Article Google Scholar
Kimoto, K., et al. (2012). Ultramicroscopy, 121, 31.
Article Google Scholar
Kimoto, K., et al. (2013). Ultramicroscopy, 134, 86.
Article Google Scholar
O’Keefe, M. (1979). Proc. 37th Annual Meeting of EMSA (San Antonio), pp. 556.
Google Scholar
Scherzer, O. (1949). Journal of Applied Physics, 20, 20.
Article Google Scholar
Uhlemann, S. et al. (2013). Physical Review Letters, 111, 046101.
Google Scholar
Van Aert, S., et al. (2010). Ultramicroscopy, 107, 551.
Article Google Scholar

Download references

Author information

Authors and Affiliations

Nagoya University, Nagoya, Japan
Nobuo Tanaka

Authors

Nobuo Tanaka
View author publications
You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nobuo Tanaka .

Rights and permissions

Reprints and permissions

Copyright information

About this chapter

Cite this chapter

Tanaka, N. (2017). Contrast Transfer Function of a Transmission Electron Microscope. In: Electron Nano-Imaging. Springer, Tokyo. https://doi.org/10.1007/978-4-431-56502-4_17

Download citation

DOI: https://doi.org/10.1007/978-4-431-56502-4_17
Published: 05 April 2017
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-56500-0
Online ISBN: 978-4-431-56502-4
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)

Publish with us

Policies and ethics