Page 133 - Modern Optical Engineering The Design of Optical Systems

116 Chapter Six

The relations between the thin-lens contributions and the various
measures of the aberrations are the same as indicated in Sec. 6.3.
2
n (n 1) 2 (n 1) (n 1)
G G
1
5
2 n
(2n 1) (n 1) (3n 2) (n 1)
G G
2
6
2 2n
(6.3u)
(3n 1) (n 1) (2n 1) (n 1)
G G
3
7
2 2n
(n 2) (n 1) n (n 1)
G G
4
8
2n 2
∗
∗
The contributions, TSC , CC , etc., are determined for each element
in the system. The individual contributions are then added to get
∗
∗
TSC , CC , etc., and, to the extent that (1) the thin-lens fiction is
valid, and (2) the third-order aberrations adequately represent the
total aberration of the system,
SC ≈ L′ l′
∗ 1
CC ≈ coma S ≈
coma T
3
∗ ∗
PC AC ≈ x s (sagittal field curvature)
∗ ∗
PC 3 AC ≈ x t (tangential field curvature)
1
Petzval radius

n
100 DC ∗
≈ percentage distortion
h
LchC l′ F l′ C
∗
TchC h F h C

SchC l′ d l′ C
The thin-lens third-order aberration expressions (which are frequently
called G-sums) can be used with the specific data of an optical system
to determine the (approximate) aberration values. Another usage is in
design work where the curvatures and/or spacings and powers of the
elements are to be determined in such a way that the aberration