Astronomy Principles and Practice Fourth Edition.pdf

248 The optics of telescope collectors
Figure 16.9. The combined diffraction pattern obtained from two point sources which are separated by an angle
given by Rayleigh’s criterion.
Figure 16.10. Intensity scan through a diffraction pattern obtained from two point sources which are separated by
an angle given by Rayleigh’s criterion.
wavelength of light and D the diameter of the telescope. Since the diffraction pattern is small,
sin α ≈ α and, therefore, minima are obtained at angles given by
The numerical factors are:
α n = m nλ
D . (16.13)
m = 1·22 for n = 1
m = 2·23 for n = 2
m = 3·24 for n = 3.
If two point sources are very close together, their images will result in a combination, being the
superimposition of two diffraction patterns. It will only be possible to resolve the resultant image as
being made of two components if the individual Airy disks are sufficiently separated. According to
Rayleigh’s criterion for resolution, the two images are said to be resolved when the centre of one
Airy disc falls on the first minimum of the other diffraction pattern. This condition is illustrated in
figure 16.9 and an intensity scan through such an image is illustrated in figure 16.10.