Page 128 - Modern Optical Engineering The Design of Optical Systems

Third-Order Aberration Theory and Calculation 111

TSC is the third-order transverse spherical aberration.
SC is the third-order longitudinal spherical aberration.
CC is the third-order sagittal coma.
3 CC is the third-order tangential coma.
TAC is the third-order transverse astigmatism.
AC is the third-order longitudinal astigmatism.
TPC is the third-order transverse Petzval sum.
PC is the third-order longitudinal Petzval sum.
DC is the third-order distortion.
TAchC is the first-order transverse axial color.
LchC is the first-order longitudinal axial color.
TchC is the first-order lateral color.

To the extent that the first- and third-order aberrations approximate
the complete aberration expansions, the following relationships are valid:
SC ≈ L′ l′ (spherical)
1
3 CC ≈
(H′ A H′ B ) H′ p (tangential coma)
2
z s ≈ PC AC (sag. curvature of field, x s )
z t ≈ PC 3 AC (tan. curvature of field, x t )
h 2
(Petzval radius of curvature)
2 PC
2
h u′ p

2 TPC
100 DC
≈ percentage distortion
h
(axial color)
LAchC ≈ l′ F l′ C
(lateral color)
TchC ≈ h′ F h′ C

Contributions from aspheric surfaces
For raytracing purposes, an aspheric surface of rotation is conveniently
represented by an equation of the form

cs 2
2
4
z f(x, y) A 2 s A 4 s . . . A j s j (6.2o)
2 2
[1 1 c s ]