Page 96 - Modern Optical Engineering The Design of Optical Systems

The Primary Aberrations 79

circle twice in accord with the B 2 terms in Eqs. 5.1 and 5.2. The primed
rays of the smaller circle in the aperture also form a correspondingly
smaller circle in the image, and the central ray P is at the point of the
figure. Thus the comatic image can be viewed as being made up of a
series of different-sized circles arranged tangent to a 60° angle. The
size of the image circle is proportional to the square of the diameter of
the aperture circle.
In Fig. 5.6b the distance from P to AB is the tangential coma of Eq. 5.6.
The distance from P to CD is called the sagittal coma and is one-third
as large as the tangential coma. About half of all the energy in the
coma patch is concentrated in the small triangular area between P
and CD; thus the sagittal coma is a somewhat better indication of the
effective size of the image blur than is the tangential coma.
Coma is a particularly disturbing aberration since its flare is non-
symmetrical. Its presence is very detrimental to accurate determina-
tion of the image position since it is much more difficult to locate the
“center of gravity” of a coma patch than for a circular blur such as that
produced by spherical aberration.
Coma varies with the shape of the lens element and also with the
position of any apertures or diaphragms which limit the bundle of rays
forming the image. In an axially symmetrical system there is no coma
on the optical axis. The size of the coma patch varies linearly with its
distance from the axis. The offense against the Abbe sine condition
(OSC) is discussed in Chap. 6. Coma is zero on the axis.

Astigmatism and field curvature
In the preceding section on coma, we introduced the terms “tangential”
and “sagittal”; a fuller discussion of these terms is appropriate at this
point. If a lens system is represented by a drawing of its axial section,
rays which lie in the plane of the drawing are called meridional or
tangential rays. Thus rays A, P, and B of Fig. 5.6 are tangential rays.
Similarly, the plane through the axis is referred to as the meridional
or tangential plane, as may any plane which includes the axis.
Rays which do not lie in a meridional plane are called skew rays. The
oblique meridional ray through the center of the aperture stop of a lens
system is called the principal, or chief, ray. If we imagine a plane pass-
ing through the chief ray and perpendicular to the meridional plane,
then the (skew) rays from the object which lie in this sagittal plane are
sagittal rays. Thus in Fig. 5.6 all the rays except A, A′, P, B′, and B
are skew rays, and the sagittal rays are C, C′, D′, and D.
As shown in Fig. 5.7, the image of a point source formed by oblique
fans of rays in the tangential plane will be a line image; this line, called
the tangential image, is perpendicular to the tangential plane; i.e., it lies