Page 127 - Modern Optical Engineering The Design of Optical Systems
P. 127
110 Chapter Six
The third-order aberration contributions of the individual surfaces
are given by Eqs. 6.2g through 6.2m, where
TSC is the transverse third-order spherical aberration contribution.
CC is the sagittal third-order coma contribution.
3CC is the tangential third-order coma contribution.
TAC is the transverse third-order astigmatism contribution.
TPC is the transverse third-order Petzval contribution.
DC is the third-order distortion.
TAchC is the paraxial transverse axial chromatic aberration contribution.
TchC is the paraxial lateral chromatic aberration contribution.
Note that TAchC and TchC are first-order aberrations; since they
are conveniently computed at the same time as the third-order aberra-
tions, the equations are presented here.
The longitudinal values of the contributions may be obtained by
dividing the transverse values by u′ k , the final slope of the axial ray, thus
TSC
SC
u′ k
TAC
AC
u′ k
(6.2n)
TPC
PC
u′ k
TAchC
LAchC
u′ k
The Seidel coefficients can be obtained by multiplying the transverse
third-order contributions or sums by ( 2n′ k u′ k ). Thus
S1 TSC (2n′ k u′ k )
S2 CC (2n′ k u′ k )
S3 TAC (2n′ k u′ k )
S4 TPC (2n′ k u′ k )
S5 DC (2n′ k u′ k )
The third-order aberrations at the final image are obtained by
adding together the contributions of all the surfaces to get TSC, CC,
TAC, etc. These contribution sums are as follows:
