Page 104 - Modern Optical Engineering The Design of Optical Systems

The Primary Aberrations 87

Figure 5.14 Effect of shifting the stop position on the aberrations of a
simple lens. The arrow indicates the “natural” stop position where coma
is zero. (efl 100, C 1 0.02, speed f/10, field 17°.)

tangential field curvature as a function of the stop position. The most
pronounced effects of moving the stop are found in the variations of
coma and astigmatism. As the stop is moved toward the object, the
coma decreases linearly with the stop position, and has a zero value
when the stop is about 18.5 mm in front of the lens. The astigmatism
becomes less negative so that the position of the tangential image
approaches the paraxial focal plane. Since astigmatism is a quadratic
function of the stop position, the tangential field curvature (x t ) plots as
a parabola. Notice that the parabola has a maximum at the same stop
position for which the coma is zero. This is called the natural position
of the stop, and for all lenses with undercorrected primary spherical
aberration, the natural, or coma-free, stop position produces a more
backward curving (or less inward curving) field than any other stop
position.
Figure 5.12 showed the effect of lens shape with the stop fixed in
contact with the lens, and Fig. 5.14 showed the effect of the stop position
with the lens shape held constant. There is a “natural” stop position for
each shape of the simple lens we are considering. In Fig. 5.15, the