H
ΔH
Figure 3.15: TV distortion with both barrel and pincushion distortion.
Figure 3.16a: Lens layout showing keystone distortion.
Figure 3.16b: Manifestation of keystone distortion.
www.edmundoptics.co.uk/imaging 23
introduction fundamentals real world telecentricity lens mechanics lens selection guide
Non-Monotonic Distortion vs. Image Height
486nm
588nm
656nm
-0.5 0.0
0.5
Distortion (%)
Image Height (mm)
1/2”
1/3”
1/4”
performance lens specifications Geometric Distortion vs. TV Distortion: An Important
Difference
In lens datasheets, distortion is usually specifi ed in one of two ways:
radial, geometric distortion or RIAA TV distortion. Geometric distortion
is the distance between where points appear in the distorted image
and where they would be in a perfect system. In practice, this can
be measured using a distortion dot target. The diff erence between
the distance from the center of the target to any dot in the FOV and
the distance from the center of the image to the same, now misplaced
dot (shown in Figure 3.14), provides the radial distortion percentage
calculated with Equation 3.1.
Figure 3.14 Distortion Dot Target
The measurement of TV distortion is specifi ed by an RIAA imaging
standard and is determined by imaging a square target that only fi lls
the vertical FOV. The diff erence in height between the corners and
the center edge of the square is used to calculate the TV distortion
with Equation 3.2; this is the apparent straightness of a line appearing
at the edge of the image, which is the geometric distortion at a single
fi eld point. By only specifying distortion at one point in the fi eld, it
is possible to misrepresent a non-zero distortion lens as having 0%
distortion. In Figure 3.13, a 0% intercept can be found for any of the
wavelengths shown. However, when the full image circle is considered,
the lens has non-zero distortion. An example of how TV distortion
can be found is shown in Figure 3.15.
Shown in Figure 3.13, manufactured, compound imaging lens assemblies
have distortion that is not necessarily monotonic and can change
signs across the FOV, which is why radial distortion plots are preferable
to the single RIAA value. Because of how it is specifi ed, TV distortion
seems much lower than the maximum geometric distortion of the same
lens, thus it is important to be aware of the type of distortion being
specifi ed when choosing the most appropriate lens for an application.
Keystone Distortion
In addition to the previous distortion types mentioned, which are
inherent to the optical design of a lens, improper system alignment
can result in keystone distortion, which is a manifestation of parallax
(shown in Figure 3.16a and 3.16b).
When calibrating an imaging system against distortion, keystone distortion
must be considered in addition to radial geometric distortion.
Although distortion is often thought of as a cosmetic aberration that
can be removed, it should be carefully considered against other system
specifi cations when choosing the right lens. In addition to the
potential for a loss in image information, algorithmic distortion correction
takes additional processing time and power, which may not be
acceptable in high speed or embedded applications.
H
ΔH
Figure 3.15
Figure 3.13: A wave, or moustache, distortion in a lens.
Sensor Format
4.0mm
Wavelength:
Figure 3.13
ΔH
D H TV (%) = × 100% 3.2
Figure 3.16: Examples of keystone distortion.
PD
AD
Figure 3.14: Calibrated target (red circles) vs. imaged (black dots)
dot distortion pattern.
/imaging