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Fig. 3.102. Fraunhofer diffraction at a circular aperture showing the function 1 2

Fig. 3.102. Fraunhofer diffraction at a circular aperture showing the function 1 2

in which the normalized angle w is defined by w = kpm w (3.444)

The function is similar to that for a slit (Fig. 3.100), but the secondary maxima are relatively weaker. The positions of the zero intensity minima and the maxima are determined by the function J and are given in Table 3.25. The minima are no longer equally spaced, although the separation tends towards the value n of the slit case if w becomes large. The appearance is shown in Fig. 3.103, in which the central peak has been overexposed in order to reveal the subsidiary maxima better. In a small telescope, well-corrected for spherical aberration, it is not easy to see even the first subsidiary maximum as its intensity from Table 3.25 is only 1.75% of the central maximum. When it is readily seen, it is normally a sign that aberrations have displaced energy into the subsidiary maxima from the central peak, as we shall see below.

The Eq. (3.442) was first derived in a different form by Airy [3.129] in a classical paper defining the so-called Airy disk (the effective diameter of the central maximum) as the diameter of the first minimum of the intensity function.

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