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Distortion
+ Y
Wavelength:
486nm
588nm
656nm
Figure 3.10
-0.05 0 0.05
Percent
Figure 3.10: A distortion plot showing the variance of distortion with
respect to wavelength.
22 +44(0) 1904 788600 | Edmund Optics® targets AD PD
Figure 3.11
Distortion is calculated simply by relating the Actual Distance (AD) to
the Predicted Distance (PD) of the image using Equation 3.1. This is
done by using a pattern such as dot target shown in Figure 3.12.
Distortion vs. Image Height
Wavelength:
TS 656nm
TS 588nm
TS 486nm
5.0mm
”
½”
”
¼”
Figure 3.12
-2.0 0.0 2.0
Distortion (%)
Image Height (mm)
Figure 3.12: Negative, or barrel, distortion in a lens.
Note that while distortion runs negative or positive in a lens, it is not
necessarily linear across the image. Additionally, distortion changes
as wavelength changes. Finally, distortion can also change with
changes in working distance. Ultimately, it is important to consider
each lens used for an application to guarantee the highest level of accuracy
when looking to remove distortion from a system.
Examples of Distorted Curves
Figure 3.12 shows negative, or barrel, distortion in a 35mm lens system.
In this example, all the wavelengths analyzed have almost identical
distortion, thus wavelength-related issues are not present. In Figure
3.13, an interesting set of distortion characteristics is seen: there is
separation in the amount of distortion for the different wavelengths,
and both negative and positive distortion is present. Distortion of this
nature is referred to as wave, or moustache, distortion. This is often
seen in lenses designed for low levels of distortion, such as those designed
for measurement and gauging applications. In this scenario,
calibrating the system so that distortion is removed requires special
consideration for applications where different wavelengths are used.
Section 3.3: Distortion
The term distortion is often applied interchangeably with reduced image
quality. However, distortion is an individual aberration that does
not reduce the information in the image; most aberrations mix information
together to create image blur, distortion simply misplaces
information geometrically. This means that known distortion can be
mapped or calculated and removed from an image, whereas information
from other aberrations is lost and cannot easily be recreated.
More details on other aberrations can be found in Section 3.5. Note
that in high distortion environments, some information and detail can
be lost due to the change in resolution associated with magnification
or because of too much information is crowded onto a single pixel.
Distortion is a monochromatic optical aberration describing how
the magnification in an image changes across the FOV at a fixed
WD; this is critically important in precision machine vision and
gauging applications. Distortion is different from parallax, which is
the change in magnification (FOV) with WD (more on parallax is
provided in the section on telecentricity in Section 4). Note that
distortion varies with wavelength, as shown in Figure 3.10 and that
when calibrating distortion out of a machine vision system, the
wavelength of illumination must be known. Curves like the one in
Figure 3.10 are helpful to calibrate out distortion.
As with other aberrations, distortion is determined by the optical design
of the lens. Lenses with larger FOVs will exhibit greater amounts
of distortion because of the cubic field dependence. Distortion is a
third-order aberration that, for simple lenses, increases with the third
power of the field height; larger FOVs (a result of low magnification or
short focal length) are more susceptible to distortion than smaller FOVs
(high magnification or long focal length). The wide FOVs achieved by
short focal length lenses must be weighed against the aberrations introduced
to the system (such as distortion). In contrast, telecentric lenses
typically have little distortion, which is a consequence of the way in
which they function. It is important to note that when designing a lens
to have minimal distortion, the maximum achievable resolution can decrease.
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 Specified?
Distortion is specified as a percentage of the field height. Typically,
±2 to 3% distortion is unnoticed in a vision system if measurement
algorithms are not used. In simple lenses, there are two main types of
distortion: negative, barrel distortion, where points in the FOV appear
too close to the center; and positive, pincushion distortion, where
points are too far away. Barrel and pincushion refer to the shape of
the field when distorted, shown in Figure 3.11.
PD
AD
Predicted Distance
Actual Distance
Barrel
(negative)
Pincushion
(positive)
Non-Distorted Image
Figure 3.11: An illustration of negative and positive distortion.
AD – PD
D (%) = PD × 100% 3.1