Page 73 - Modern Optical Engineering The Design of Optical Systems

56 Chapter Four

and thus
f f
a b
f (4.5)
ab
f f d
a b
The back focus distance (measured from the second principal point
of b) is given by
y y (1 d )
a
a
B b
u′ y ( d )
b a a b a b
(4.6)
(1 d/f a) f (f d)

b
a
1/f 1/f d/f f f f d
a b a b a b
By substituting f ab /f a from Eq. 4.5, we get
f (f d)
ab
a
B (4.6a)
f
a
The front focus distance (ffd) for the system is found by reversing the
raytrace (i.e., trace from right to left) or more simply by substituting f b
for f a to get
(f d)
f ab
b
( )ffd (4.6b)
f
b
The inverse solution
Frequently it is useful to be able to solve for the focal lengths of the
components when the focal length, back focus distance, and spacing
are given for the system. Manipulation of Eqs. 4.5 and 4.6a will yield
df
ab
f (4.7)
a
f B
ab
dB
f (4.8)
b
f B d
ab
Equations 4.7 and 4.8 are probably the most widely used equations
in optical system layout work.
General equations for two-component finite
conjugate systems
Using the same technique, we can derive expressions which give us the
solution to all two-component optical problems. There are two types of
problems which occur. With reference to Fig. 4.3, the first type occurs