1.2
Chapter 1.2
Theory of imaging
Menn
1.2.1 Optical aberrations
1.2.1.1 General consideration. Ray fan
and aberration plot. Concept of wave
aberrations
We will procee d by considering the concept of imaging as
described in Section 1.1.2 of Chapter 1.1 and pay most
attention to the real imaging situation experienced in
practice. Fig. 1.2.1 demonstrates the basic difference
between ideal imaging and real imaging. Let the rays
originating in a point source A come to the system, each
one at a different angle u. If the medium is homogeneous
(has the same refractive index everywhere) the wave-
front W in the object space is a sphere. If in the image
space all rays intersect at a single point A
0
then the beam
remains homo-centric, with a spherical wavefront W
0
,
and A
0
is a stigmatic (ideal) image of A. However, in most
situations this does not happen and the rays of different
angles u
0
come to different points on the axis OO
0
(or, for
tilted beams, to different off-axis locations). As a result,
the real wavefront in the image space is not spherical, the
homocentricity of the output beam is violated, and in-
stead of a sharp point image there is a blurred spot. Such
violation of stigmatic imaging is defined as optical
aberrations.
Numerically aberrations are characterized by the de-
viation of a real image A
0
from the ideal image A
0
0
obtained in the paraxial range. This deviation can be
determined either by the horizontal segment, ds
0
, along
the optical axis, as in Fig. 1.2.2 (and then it is called the
lateral aberration) or it can be related to the vertical
segment r (then it is called the transverse aberration).
The geometrical relation between lateral and transverse
aberrations is quite obvious:
r
¼
d
s
0
tan u z
d
s
0
h
S
0
; (1.2.1)
in which the fact is taken into account that ds
0
S
0
. Since
for each ray aberrations depend on the height of the ray
Fig. 1.2.1 (a) Ideal imaging and (b) real imaging.
Practical Optics; ISBN: 9780750684507
Copyright Ó 2004 Elsevier Inc. All rights of reproduction, in any form, reserved.
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