What is the best reference for an introduction to the use of Fourier analysis in crystallography?
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2$\begingroup$ 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. $\endgroup$– LagerbaerAug 12, 2011 at 22:10
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$\begingroup$ 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. $\endgroup$– wscAug 13, 2011 at 15:06
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$\begingroup$ Do you have a specific question? $\endgroup$– JenAug 15, 2011 at 10:56
2 Answers
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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1$\begingroup$ Also, this is cute, and has some relevant interpretation information: ysbl.york.ac.uk/~cowtan/fourier/fourier.html $\endgroup$– JenAug 15, 2011 at 10:56
It depends a lot on your background. If you are familiar with the mathematical background of the (analytical) Fourier Transform and (numerical) Fast Fourier Transform, then the suggested books (International Tables Volume B, books on solid state physics) are alright in my point of view. International Tables Volume B is very detailed, books on solid state physics might be too brief.
A book that is suitable for all aspects and is neither too long nor too brief: Fundamentals of Crystallography, edited by Carmelo Giacovazzo. I am sure you will find your answers there, especially in Chapter 3: "The diffraction of X-rays by crystals".
If, however, you do not feel very confident juggling with the formulas, then I recommend as a first read the very basic introduction to crystallography by Christopher Hammond: The basics of crystallography and diffraction Chapter 13, "Fourier analysis in diffraction and image formation", is dedicated to your question.
- Link to Publisher (Oxford University Press): https://global.oup.com/academic/product/the-basics-of-crystallography-and-diffraction-9780198738688
- Link to Google Preview: https://books.google.cz/books?id=OIkSDAAAQBAJ&lpg=PP1&pg=PR13
If you are still not happy with the suggestion, I recommend searching for explanations of X-ray diffraction. In crystallography the main application of the Fourier transform is the mathematical description of X-ray diffraction.