Page 71 - Modern Optical Engineering The Design of Optical Systems

54 Chapter Four

Figure 4.1 The principal planes
are planes of unit magnification,
so a ray appears to leave the
second principal plane at the
same height (y) that it appears
to strike the first principal plane.

a ray from the object point, which would (if extended) strike the first
principal plane at a distance y from the axis, emerges from the last
surface of the system as if it were coming from the same height y on
the second principal plane. For this reason we can write the following
delightfully simple relationships:
y y
u and u′
s s′
and substitute s y/u and s′ y/u′ into Eq. 2.4:
1 1 1

s′ s f
u′ u 1

y y f
y
u′ u
f

If we now replace the reciprocal focal length (1/f) with the component
power , we get the first equation of our ray:

u′ u y (4.1)
The transfer equations to the next component in the system are the
same as those used in the paraxial surface-by-surface raytrace of
Sec. 3.3:
y y du′ (4.2)
2 1 1

u′ u (4.3)
1 2
where y 1 and y 2 are the ray heights at the principal planes of components
#1 and #2, u′ 1 is the slope angle after passing through component #1,
and d is the axial distance from the second principal plane of compo-
nent #1 to the first principal plane of component #2.