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Fig. 6C —Fourier spaces and k-space
[7,
8]. Fourier transform (FT) of
an image is represented by a 2D gray-scale magnitude image in which each pixel
represents a particular spatial frequency. By convention, high frequencies are
mapped to the periphery and low frequencies to the origin. Pixel intensity
corresponds to the relative contribution of that frequency to the entire
image. Any image (which can be thought of as a complicated wave of varying
pixel intensity) can be constructed by the combination of different spatial
frequencies (simple waves). Fourier transform of a simple white square on a
black background, for instance, shows a cruciate pattern of increased
intensity along the traditional x- and y-axes. This reflects
the contribution of spatial frequencies (given by the inverse FT = iFT) most
necessary to recreate the image, which happen to be orthogonal to the edges of
the square. Because essentially no diagonals or curves are present in the
image, these spatial frequencies are not as highly represented in the Fourier
space. (Fourier transform and inverse Fourier transform images (iFT) generated
with ImageJ, National Institutes of Health, Bethesda, MD)
