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Advanced Computing in Electron Microscopy pp 61–76Cite as

Sampling and the Fast Fourier Transform

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Abstract

This chapter takes a small detour and discusses some numerical approximations that will be necessary to theoretically compute electron microscopy images. Specifically, digital sampling (pixels and levels) and the all important fast Fourier transform are introduced. The FFT will be the principle tool to speed up later calculation. If you are familiar with these topics, this chapter may be skipped.

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Further Reading

Some Books on Computer Image Processing

  • K. R. Castleman, Digital Image Processing, Prentice Hall, 1979 [46]

    Google Scholar 

  • R.C. Gonzalez and R.E. Woods, Digital Image Processing, 3nd edition, Prentice-Hall, 2008 [125]

    Google Scholar 

  • E.L. Hall, Computer Image Processing and Recognition, Academic Press, 1979 [143]

    Google Scholar 

  • B. Jahne, Digital Image Processing, 3rd edition, Springer, 1995 [183]

    Google Scholar 

  • A. Jain, Fundamentals of Digital Image Processing, Prentice Hall, 1989 [184]

    Google Scholar 

  • D.L. Missel, Image Analysis, Enhancement annd Interpretation, North Holland, 1978 [243]

    Google Scholar 

  • W.K. Pratt, Digital Image Processing, Wiley, 1978 [287]

    Google Scholar 

  • A. Rosenfeld and A.C. Kak,Digital Picture Processing, Academic Press, 1976 [305]

    Google Scholar 

  • W.O. Saxton, Computer Techniques for Image Processing in Electron Microscopy, Adv. in Electronics and Electron Physics, Supplement 10, Academic Press, 1978 [309]

    Google Scholar 

Some Books on Fourier Transforms and Fourier Optics

  • E.O. Brigham, The Fast Fourier Transform, Prentice-Hall, 1974 [39]

    Google Scholar 

  • J.W. Goodman, Intro. to Fourier Optics, 3rd. edit., Roberts and Co., 2005 [126]

    Google Scholar 

  • James S. Walker, Fast Fourier Transforms, 2nd edit., CRC Press, 1996 [362]

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Applied and Engineering Physics, Cornell University, 212 Clark Hall, Ithaca, NY, 14853, USA

    Earl J. Kirkland

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  1. Earl J. Kirkland
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Correspondence to Earl J. Kirkland .

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© 2010 Springer Science+Business Media, LLC

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Kirkland, E.J. (2010). Sampling and the Fast Fourier Transform. In: Advanced Computing in Electron Microscopy. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6533-2_4

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