Page 131 - Modern Optical Engineering The Design of Optical Systems

114 Chapter Six

After tracing the axial and “principal” rays through the system, the
following are computed for each element
u u′
v or v′ (6.3d)
y y
y p
Q (6.3e)
y

where u and y are taken from the data of the axial ray and y p is from
the principal ray data.
Then the aberration contributions may be determined using the stop
shift equations:
TSC* TSC (6.3f)

CC* CC Q TSC (6.3g)
2
TAC* TAC 2Q CC Q TSC (6.3h)
TPC* TPC (6.3i)
3
2
DC* DC Q(TPC 3TAC) 3Q CC Q TSC (6.3j)
TAchC* TAchC (6.3k)
TchC* TchC Q TAchC (6.3l)

The starred terms are the contributions from an element which is
not at the stop—that is, one for which y p ≠ 0. The unstarred terms are
the contributions from the element when it is in contact with the stop
(and y p 0) and are given by the following equations:

y 4
2
2
2
2
3
TSC (G 1 c G 2 c c 1 G 3 c v G 4 cc 1 G 5 cc 1 v G 6 cv )
u′ k
y 4
2
3
2
2
2
(G 1 c G 2 c c 2 G 3 c v′ G 4 cc 2 G 5 cc 2 v′ G 6 cv′ ) (6.3m)
u′ k
2
2
CC hy (0.25G 5 cc 1 G 7 cv G 8 c )
2
2
hy (0.25G 5 cc 2 G 7 cv′ G 8 c ) (6.3n)
2
h u′ k
TAC (6.3o)
2