Page 101 - Modern Optical Engineering The Design of Optical Systems

84 Chapter Five

Figure 5.11 Lateral color, or chromatic difference of magnification,
results in different-sized images for different wavelengths.

When a lens system forms images of different sizes for different
wavelengths, or spreads the image of an off-axis point into a rainbow,
the difference between the image heights for different colors is called
lateral color, or chromatic difference of magnification. In Fig. 5.11 a
simple lens with a displaced diaphragm is shown forming an image of
an off-axis point. Since the diaphragm limits the rays which reach the
lens, the ray bundle from the off-axis point strikes the lens above
the axis and is bent downward as well as being brought to a focus. The
blue rays are bent downward more than the red and thus form their
image nearer the axis. If the stop is to the right of the lens the blue
rays will be imaged further from the axis than the red ray.
The chromatic variation of index also produces a variation of the
monochromatic aberrations discussed in Sec. 5.2. Since each aberration
results from the manner in which the rays are bent at the surfaces of
the optical system, it is to be expected that, since rays of different color
are bent differently, the aberrations will be somewhat different for each
color. In general this proves to be the case, and these effects are of prac-
tical importance when the basic aberrations are well corrected.

5.4 The Effect of Lens Shape and Stop
Position on the Aberrations

A consideration of either the thick-lens focal length equation

1 1 1 n 1 t
(n 1)
f R R n R R
1 2 1 2
or the thin-lens focal length equation

1 1 1
(n 1) (n 1) (C C )
1
2
f R R
1 2