Equation 5.2-15 for G*(ju) is the result of the complex convolution of G(ju) and Px(ju); it is in the so-called Poisson sum form, which helps visualize the effects of n=-œ
n=—oo the ideal sampling process in the spatial frequency domain. Figure 5.2-2A illustrates the spectrum of an ideally sampled, one-dimensional intensity, g(x), which is bandwidth limited so that it has no spectral energy above uN = us/2 r/mm, the Nyquist frequency (Northrop 1997). When |G(ju)| contains significant spectral energy above the Nyquist frequency, a phenomenon known as aliasing occurs, shown schematically in Figure 5.2-2B. The overlap of the high-frequency spectral components of the baseband of |G*(ju)| with the high-frequency portions of the first harmonic terms of |G*(ju)| generate an aliased, high-frequency portion of the baseband of |G*(ju)| that represents unrecoverable or lost information. Note that the more the spectrum of |G(ju)| extends past the spatial Nyquist frequency, the more spectral energy in the baseband of |G*(ju)| is unrecoverable. One way to avoid aliasing, whether sampling in the time or space domains, is to precede the sampler with a low-pass filter that attenuates high frequency energy in |G(ju)| beyond the spatial Nyquist frequency, uN = n/X r/mm. Such a low-pass filter is appropriately called an antialiasing filter.
In the CE, each point in the sampling array (i.e., each ommatidium) has a built-in low-pass filter that attenuates high spatial frequencies of the object and decreases aliasing. This filter is, of course, the DSF. To be effective, S(uN)/S(0) < 0.01. For the Hill DSF, given above,
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