Page 152 - Modern Optical Engineering The Design of Optical Systems

Prism and Mirror Systems 135

Figure 7.14 Aberration intro-
duced by a plane parallel plate.

t(n 1)
Chromatic aberration l′ l′
F C 2
n V
t n cos U
Spherical aberration L′ l′ 1 (exact)

n n sin U
2
2
2
2
tu (n 1)
(third order)
2n 3
t
Astigmatism (l′ l′ )
n sin U

s t
2
2
p
2
2
n cos U p
1 (exact)
2
2
(n sin U p)
2
2
tu p (n 1)
(third order)
n 3
2
2
tu u p (n 1)
Sagittal coma (third order)
2n 3
tu p(n 1)
Lateral chromatic (third order)
2
n V
These expressions are extremely useful in estimating the effect that
the introduction (or removal) of a plate or a prism system will have on
the state of correction of an optical system.
A common use for a glass plate is as a beam splitter, tilted at an angle
of 45°. In this orientation the astigmatism is approximately a quarter
of the thickness of the plate. Since this can severely degrade the
image, such plate beam splitters are not recommended in convergent
or divergent beams (i.e., where u in Fig. 7.14 is nonzero). Note that the
astigmatism can be nullified by inserting another identical plate which