CHAPTER 10 FOURIER TRANSFORMS IN TWO AND THREE DIMENSIONS
This chapter introduces Fourier and related transforms in two and three dimensions. We shall see that much of the mathematics extends straightforwardly from the one-dimensional transforms developed in Chapters 3–6. Applications include the Fourier analysis of images, which are treated as two- and three-dimensional signals, and more realistic models of wave propagation at radio and optical frequencies, including the diffraction analysis of crystals. We shall encounter special cases of the Fourier transform when the functions under consideration have radial and spherical symmetry, and also the Radon transform, which is the mathematical basis for tomographic (cross-sectional) X-ray imaging.
10.1 TWO-DIMENSIONAL FOURIER TRANSFORM
10.1.1 Definition and Interpretation
The Fourier transform in two dimensions is defined:
The transform kernel 
is just the product of two one-dimensional kernels, 
. The extension to ...
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