Page 118 - Modern Optical Engineering The Design of Optical Systems

The Primary Aberrations 101

The aberrations are related as follows:
The longitudinal aberrations are defined as position differences
along the optical (or z) axis.

For spherical LA L′ l′
For chromatic LA l′ l′
ch F C
For field aberrations
x (sagittal focus distance ) l′
∗
s
x (tangential focus distance ) l′
∗
t
x (3x x )/2
p s t
astigmatism x x
t s
∗ measured parallel to the z-axis, from the vertex of the last surface to the image focus
(found along the principal ray)
The transverse versions of these aberrations are simply the product
of the longitudinal aberration and (the negative of) the slope of the
marginal ray. For aberrations such as field curvature and paraxial
chromatic in general, the slope of the axial marginal ray (either paraxial
or trignometric) is used. For aberrations associated with a specific ray
(e.g., spherical or the transverse field curvature of a specific ray in the
presence of vignetting), the slope of that ray is used. Thus for marginal
spherical,

TA M LA M tan U M

and for zonal spherical

TA Z LA Z tan U Z
For astigmatism, either

T astig (x t x s ) tan U M
or

T astig (x t x s ) U M
is commonly used.
Field curvature along any ray in the aperture is equal to the slope
of the H–tan U plot at that ray. In the meridional ray-intercept plot
this slope equals x t ; in the sagittal ray-intercept plot it is x s . These
field curvatures are effectively a measure of the imagery of the system
if a pinhole aperture were appropriately placed at the aperture stop.