Abstract
Sampling a signal too slowly results in temporal frequency aliasing; sampling a wave too infrequently in space causes spatial aliasing. Slowness aliasing is another problem that can occur in some cases, even when temporal and spatial frequency aliasing are absent. As its name suggests, slowness aliasing can cause a wave with one value of slowness to be interpreted as a wave with a different value of slowness. For a 2D signal, or an image, the penalty of undersampling is that we may misrepresent both the spatial frequency and the orientation of the pattern. If the pattern is moving, then the direction of motion may also be misrepresented. The linear Radon transform (Deans, 1983), or the related slope–intercept form (Durrani and Bisset, 1984), is a useful tool to analyze seismic data (Foster and Mosher, 1992; Dunne and Beresford, 1995), although sampling and aliasing are two recurring problems (Turner, 1990; Marfurt et al., 1996; Bardan, 1998). On the other hand, in the optical literature (Fowles, 1989), the effect of Fraunhofer diffraction indicates what is happening when a grating is illuminated by a monochromatic plane wave. This paper demonstrates how sampling and inverting of the linear Radon transform is related to Fraunhofer diffraction patterns.
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