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imaging resource guide imaging lenses filters microscopy cameras illumination targets
Section 4.5: Distortion
The term distortion is often applied interchangeably with reduced image
quality. Distortion is an individual aberration that does not technically
reduce the information in the image; while most aberrations actually mix
information together to create image blur, distortion simply misplaces
information geometrically. This means that distortion can actually be
calculated or mapped out of an image, whereas information from other
aberrations is essentially lost in the image and cannot easily be recreated.
More details on other aberrations can be found in Section 6. Please note
that in extreme high distortion environments, some information and detail
can be lost due to resolution change with magni cation or because of
too much information being crowded onto a single pixel.
Distortion is a monochromatic optical aberration that describes
how the magni cation in an image changes across the eld of view at
a xed working distance; this is critically important in precision machine
vision and gauging applications. Distortion is distinct from parallax,
which is a change in magni cation ( eld of view) with working
distance (more on parallax is provided in the section on telecentricity
in Section 5.1. It is important to keep in mind that distortion varies
with wavelength, as shown in Figure 4.28, and that when calibrating
distortion out of a machine vision system the wavelength of the illumination
needs to be taken into account. Curves like the one in Figure
4.28 are very helpful in determining how to calibrate out distortion.
As with other aberrations, distortion is determined by the optical design
of the lens. Lenses with larger elds of view will generally exhibit
greater amounts of distortion because of its cubic eld dependence.
Distortion is a third-order aberration that, for simple lenses, increases
with the third power of the eld height; this means that larger elds
of view (a result of low magni cation or short focal length) are more
susceptible to distortion than smaller elds of view (high magni cation
or long focal length). The wide elds of view achieved by short
focal length lenses should be weighed against aberrations introduced
in the system (such as distortion). On the other hand, telecentric lenses
typically have very little distortion: a consequence of the way that
they function. It is also important to note that when designing a lens
to have minimal distortion, the maximum achievable resolution can
be decreased. In order to minimize distortion while maintaining high
resolution, the complexity of the system must be increased by adding
elements to the design or by utilizing more complex optical glasses.
How is Distortion Specifi ed?
Distortion is typically speci ed as a percentage of the eld height.
Typically, ±2 to 3% distortion is unnoticed in a vision system if measurement
algorithms are not in use. In simple lenses, there are two
main types of distortion: positive, barrel distortion, where points in
the eld of view appear too close to the center; and negative, pincushion
distortion, where the points are too far away. Barrel and pincushion
refer to the shape a rectangular eld will take when subjected to
the two distortion types, as shown in Figure 4.29.
Distortion can be calculated simply by relating the Actual Distance
(AD) to the Predicted Distance (PD) of the image using Equation 4.2.
This is done by using a pattern such as dot target shown in Figure 4.30.
Distortion (%) = AD - PD
It is important to note that while distortion generally runs negative or
positive in a lens, it is not necessarily linear in its manifestation across
the image for a multi-element assembly. Additionally, as wavelength
changes, so does the level of distortion. Finally, distortion can change
with changes in working distance. Ultimately, it is important to individually
consider each lens that will be used for a speci c application
in order guarantee the highest level of accuracy when looking to remove
distortion from a system.
(Continued on page 34)
Figure 4.28: Distortion plot showing the variance of distortion with
respect to wavelength.
Figure 4.29: An illustration of positive and negative distortion.
Figure 4.30: Calibrated target (red circles) vs. imaged (black dots)
dot distortion pattern.
x 100 4.2
Distortion Dot Target