Figure 6.11: Field Point with
Figure 6.12: O axis asymmetry.
Chromatic Focal Shift
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Section 6.2: How Aberrations Affect
Machine Vision Lenses – ADVANCED
While aberration theory is a vast subject, basic knowledge of a few
fundamental concepts can ease understanding: spherical aberration,
astigmatic aberrations, eld curvature, and chromatic aberration.
Spherical aberration refers to rays focusing at di erent distances depending
on where across the aperture they meet the lens, and is a function
of aperture size. The steeper the angle of incidence light has on
the surface of a spherical lens, the greater the error in how the lens will
refract the light (Figure 6.9). Lenses with large apertures (small f/#s) are
more likely to have spherical aberration negatively impact the image
quality. If a lens has a lot spherical aberration, image quality can be
improved by increasing the f/# by closing the iris, but there is a limit
to how much this will improve image quality. Closing the iris too much
will cause di raction to limit the performance (see di raction limit in
Section 3.1). Optical designs that include high index glass or additional
elements can be used to correct for spherical aberration in a fast (small
f/#) lens; these designs will reduce the amount of refraction at each
surface and, with it, the amount of spherical aberration. However, this
can cause increases in the size, weight, and cost of the lens assembly.
Astigmatism is a function of eld angles. To summarize, astigmatic
aberration occurs when a lens has to perform over a wide eld, but
the performance in the direction of the eld is reduced compared to
the performance orthogonal to the eld. If one looks at a series of
bars that are half horizontal and half vertical, the bars in one direction
will be in focus, but the bars in the other direction will be out of focus
(as shown in Figures 6.10 and 6.11). This is caused by the fact that rays
away from the center of the object do not pass through rotationally
symmetric surfaces like the on axis rays do (Figure 6.12). To correct
this, two things need to be done: have symmetric designs about the
aperture and have designs with low angles of incidence for the eld
rays. Keeping a design symmetric leads to forms that are similar to a
double gauss lens. Keep in mind that symmetric designs prevent the
use of telephoto or reverse telephoto designs, which can cause long
focal length designs to be large and short focal length designs to have
small back focal lengths. Reducing the angles of incidence, much like
one does for spherical aberration, requires higher index glasses and
additional elements, leading to an increase in size, weight, and cost
of the lens. The simpli ed de nition used here intentionally combines
the e ects for astigmatism and coma for ease of understanding.
Field curvature (Figure 6.13) is the aberration that describes the magnitude
to which the image plane wants to be naturally curved. This aberration
is caused by the sum of the focal lengths of the lens elements in
the system multiplied by their index of refraction not equaling zero. If
the sum is positive, which is typical for an imaging lens, the image plane
will have a concave curvature to it; this is why movie theaters tend to
have slightly curved screens. Since curving the image plane is seldom
an option for a machine vision lens, the designers must insert negative
powered corrective elements to reduce the sum of the focal lengths.
This makes lenses longer and typically forces a negative lens to be close
to the image plane, reducing the back focal length of the lens.
Chromatic aberration implies di erent wavelengths of light focus at
di erent points. Because the dispersion of a glass determines the refractive
power of the glass at di erent wavelengths, chromatic aberration
can be removed by designing an imaging lens that contains both
positive and negative lenses that are made using glasses with di erent
dispersions. This is illustrated in Figure 6.14, which compares a singlet
to an achromatic doublet lens. A downside to such a design is that it
increases the number of elements needed for a lens.
(Continued on page 42)
Figure 6.9: Example of spherical aberration. The light incident near
the edges of the lens come to focus too early.
Figure 6.10: Field Point without
Figure 6.13: Field curvature example showing non-planer surface
of best focus.
Red & Blue
Figure 6.14: Comparison of singlet and doublet lens spots.