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


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*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.
