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What is the best reference for an introduction to the use of Fourier analysis in crystallography?

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Depending on how far back you want to go, the standard books on solid state physics are good choices: The books by Ashcroft & Mermin, and by Charles Kittel, are good choices. Not sure if the solid state physics book by Ibach and Lüth has been translated into English, but that would be a good starting point as well. –  Lagerbaer Aug 12 '11 at 22:10
    
That. Not much else to add; Ibach & Lueth does have an English translation. Chaikin & Lubensky is a personal favorite introductory cond-mat book, with an appendix on FT somewhere I think. –  wsc Aug 13 '11 at 15:06
    
Do you have a specific question? –  Jen Aug 15 '11 at 10:56

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The comments list the cond-mat canonical texts, and I think the Kittel intro is a bit more accessible. Nevertheless, the International Tables of Crystallography (should be available at a university library) are the go to for anything related to crystallography. For a brute force introduction, Volume B on reciprocal space has a comprehensive introduction to the topic of Fourier analysis as applied to crystallography.

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Also, this is cute, and has some relevant interpretation information: ysbl.york.ac.uk/~cowtan/fourier/fourier.html –  Jen Aug 15 '11 at 10:56

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