Astronomy Principles and Practice Fourth Edition.pdf

Refractors 253
Figure 16.16. Spherical aberration produced by a single positive lens; F represents the focal length measured to
the circle of least confusion and F (exaggerated for clarity) represents the spread of the image.
objective is designed accordingly. Hence, some objectives are termed to be visual or photographic.
Not all objectives are constructed in the form of a cemented doublet; there are some variations
which have an air-gap between the two elements. One special objective, known as a photovisual,
is constructed of three elements. The achromatism produced by this system is so effective that it can
be used either visually or with photographic plates, as its name implies.
16.5.3 Spherical aberration
The simple theory for lens design is based on the effects of refraction produced by spherical surfaces
and this is particularly convenient as a spherical surface is one of the easiest to obtain on an optical
grinding and polishing machine. However, simple lens theory only takes into account paraxial rays,
i.e. rays that are very close to the optic axis, allowing sin θ to be written as θ. For a point source at
infinity, lying on the axis of a single lens, the image produced by the lens does not retain a point-like
appearance and is spread out into a disc. This effect results from the rays which cannot be considered
as paraxial. The position of the focus for any incident ray depends on its distance from the optic axis.
The defect of the image is known as spherical aberration and its effect is illustrated in figure 16.16.
If the spread in focus is denoted by F, the severity of any spherical aberration may be expressed
by assessing the value of the ratio F/F. As in the case of chromatic aberration, there is one plane
through the spread of focus which contains the smallest image, again known as the circle of least
confusion. Also the spread of an image along the optic axis is known as longitudinal spherical
aberration and the spread of an image in the plane containing the circle of least confusion is known
as lateral spherical aberration. The size of any image can be predicted by the physical properties of
the lens or by performing a ray-tracing analysis.
The amount of spherical aberration depends on the shape of a lens. It is, therefore, convenient to
define what is known as the shape factor of a lens. By denoting the radii of the two lens surfaces as r 1
and r 2 , the shape factor, q, is expressed as
q = r 2 + r 1
r 2 − r 1
. (16.21)
Typical shapes of lenses have been drawn in figure 16.17 with a range of shape factors running between
q < −1andq > +1.
By examination of lenses over the complete range of shape factors, it is found that spherical
aberration has minimal effect when q is close to +0·7—it never goes to zero.
Spherical aberration can be overcome completely by figuring a lens so that the curvature of the
faces is not constant. This process is known as aspherizing and is sometimes used in producing