Astronomy Principles and Practice Fourth Edition.pdf

254 The optics of telescope collectors
Figure 16.17. A range of lenses with different shape factors.
Figure 16.18. Longitudinal spherical aberration for (a) a single lens and (b) a corrected doublet.
telescope objectives. However, this process can be costly and it is not the only way to remove spherical
aberration.
For a negative lens, the spherical aberration is also negative, i.e. the numerical value of the
focal length increases as incident rays which are more distant from the optic axis are considered.
A combination of a positive and a negative lens can be designed to provide a system which is free
from spherical aberration. This is particularly convenient as we have already seen that chromatic
aberration can be reduced by a two-lens system. Thus, achromatic lenses are designed to have minimal
spherical aberration. The residual effect of spherical aberration for a corrected objective is illustrated in
figure 16.18. In the same figure, the effect of spherical aberration of a single lens is drawn for contrast.
If effects of chromatic and spherical aberration have not been removed completely, they may be
noticeable when the primary image is viewed with an eyepiece. However, an eyepiece normally limits
the field of view to a small angle and these may be the only defects of the image that will be detected.
By increasing the field of view, either by using a special wide-angle eyepiece or by placing a twodimensional
imaging detector in the focal plane of the telescope, other types of aberration may become
apparent. Such aberrations that might be detected in this way are: coma, astigmatism, field-curvature
and field-distortion. Any of these aberrations may be present in images which result from incident rays
which arrive at an angle to the optic axis. The effects and causes of each of these aberrations will now
be discussed briefly.
16.5.4 Coma
The effect of coma derives its name from the comet-like appearance that an image can have when a
point object is off the axis of a lens. Its cause can be considered by treating a lens as being made of a
series of annuli. Each annular zone gives rise to an annular image in the focal plane. The total aberrated
image results from the combination of each component image. The effect of coma is illustrated in a
simplified way in figure 16.19.