Page 126 - Modern Optical Engineering The Design of Optical Systems

Third-Order Aberration Theory and Calculation 109

The final image height h′ (i.e., the intersection point of the paraxial
principal ray with the image plane), is determined from the principal
ray, or by

(6.2b)
h′ Inv/n′ k u′ k
where n′ k and u′ k are the index and slope of the axial ray after passing
through the last surface of the system.
Then the following are evaluated for each surface of the system:

i cy u (6.2c)
(6.2d)
i p cy p u p
n(n′ n)
B y(u′ i) (6.2e)
2n′Inv

n(n′ n)
B p y p (u′ p i p ) (6.2f)
2n′Inv
2
TSC Bi h (6.2g)
CC Bii p h (6.2h)
2
TAC Bi p h (6.2i)
(n n′) chInv
TPC (6.2j)
2nn′
2
2
1
DC h [B p ii p
(u′ p u p )] (6.2k)
2
yi n
TAchC
n
n′ (6.2l)
n′ k u′ k n′
n
n′
yi p
TchC
n (6.2m)
n′
n′ k u′ k
As previously, primed symbols refer to quantities after refraction at
a surface. Most of the symbols (y, n, u, c) are defined in Sec. 6.2, or
immediately above. Those which have not been previously defined are:

B and B p Intermediate steps in the calculation.
i The paraxial angle of incidence.

n The dispersion of the medium, equal to the difference between the
index of refraction for the short wavelength and long wavelength.
For visual work,
n n F n C , or
n (n 1)/V.
Inv The optical invariant hnu h′n′u′.