A first example examines the linear Fourier model for intensity contrast when the object is a single black spot of width, 2a. Assume that the spot contrast is unity (Cobj = 1). For simplicity, work in one dimension, x. Let the DSF be modeled by the hyperbolic Hill function:

Figure 5.2-4 illustrates this system. The Fourier transform of this DSF is well known:

The one-dimensional, "black spot" object is centered over the ommatidium. It is described by p(x) = Io {1 - [U(x + a) - U(x - a)]} 5.2-23

The one-dimensional Fourier transform of the object can be shown to be

P(u) = lo n ยง(u) - 2a sin(au) J = lo {2 n 8(u) - (2a) sinc(au/ n)} 5.2-24

Of interest is the intensity contrast when the spot is at x = x, and when it is directly over the ommatidium (x = 0),

Black spot |
Io |
P(x) | ||

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