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Sampling and the Fast Fourier Transform

Chapter

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.

Keywords

Fast Fourier Transform Spatial Frequency Discrete Fourier Transform Digital Image Processing Reciprocal Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Further Reading

Some Books on Computer Image Processing

  1. K. R. Castleman, Digital Image Processing, Prentice Hall, 1979 [46]Google Scholar
  2. R.C. Gonzalez and R.E. Woods, Digital Image Processing, 3nd edition, Prentice-Hall, 2008 [125]Google Scholar
  3. E.L. Hall, Computer Image Processing and Recognition, Academic Press, 1979 [143]Google Scholar
  4. B. Jahne, Digital Image Processing, 3rd edition, Springer, 1995 [183]Google Scholar
  5. A. Jain, Fundamentals of Digital Image Processing, Prentice Hall, 1989 [184]Google Scholar
  6. D.L. Missel, Image Analysis, Enhancement annd Interpretation, North Holland, 1978 [243]Google Scholar
  7. W.K. Pratt, Digital Image Processing, Wiley, 1978 [287]Google Scholar
  8. A. Rosenfeld and A.C. Kak,Digital Picture Processing, Academic Press, 1976 [305]Google Scholar
  9. 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

  1. E.O. Brigham, The Fast Fourier Transform, Prentice-Hall, 1974 [39]Google Scholar
  2. J.W. Goodman, Intro. to Fourier Optics, 3rd. edit., Roberts and Co., 2005 [126]Google Scholar
  3. James S. Walker, Fast Fourier Transforms, 2nd edit., CRC Press, 1996 [362]Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of Applied and Engineering PhysicsCornell UniversityIthacaUSA

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