Page 80 - Modern Optical Engineering The Design of Optical Systems

Optical System Considerations 63

where s is the distance from the object to the first surface. (Note that
this surface may be the entrance pupil if desired.)
Now, substituting into Eq. 4.24 for the focal length, we get:

efl y /u′ y h/(y u ′ hu ′)
3 3 3 3 2 1
Where the primed data are in image space.
Most optical computer programs make use of Eqs. 4.24 to 4.26 (or
the equation immediately above) to calculate the focal lengths,
because such programs usually put a nominally infinitely distant
object at a large, but finite, distance, and thus cannot use the axial ray
to exactly calculate the focal length directly by f y 1 /u′ k .

Aperture stop and entrance pupil

Another optical software application of this principle involves the
determination of the entrance pupil location when the location of the
aperture stop is specified. Again, assuming that an axial ray (y and u)
and a principal ray ( y p and u p ) have been traced, we determine the
constant B for use in Eqs. 4.20 and 4.21 which will shift the princi-
pal ray so that its height at the desired stop surface is zero. This
yields
B y /y
p
where y p and y are taken at the stop surface. Then the new principal
ray data at the first surface are

New y old y By
p p
New u old u Bu
p p
The entrance pupil location corresponding to this stop position is then
L p y p /u p , and a principal ray aimed at the center of the pupil will
pass through the center of the stop.

4.3 Matrix Optics
The general form of the paraxial raytracing equations (Eqs. 3.16 and
3.17 or Eqs. 4.1 and 4.2) is A B CD. Using Eqs. 4.1 and 4.2, for
example, and adding two obvious identities, we have

u′ u y (plus y y)
y y du′ (plus u u′ )
2 1 1 2 1