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Telecentricity and Distortion
Another advantage of using Telecentric Lenses in metrology applications
is that Telecentric Lenses typically have lower distortion values
than Fixed Focal Length Lenses. Distortion causes the actual position
of an object to appear as though it is in a diff erent location, which can
further decrease measurement accuracy (see Section 4.5 for more information
on distortion, pages 30-32). For example, Figure 5.5a shows
jumper pins on a circuit board that has been imaged by a Fixed Focal
Length Lens with high distortion. The distortion, coupled with the
parallax error inherent to non-telecentric lenses, makes the pins toward
the edge of the image appear as though they are bent toward the
center. When looking at the same pins with a Telecentric Lens, as in
Figure 5.5b, it is apparent that the pins are indeed straight.
While it is true that distortion can be calibrated out of images to
partially improve the accuracy, the parallax is still present and will
cause error. The other advantage to not needing to calibrate out the
distortion from the Telecentric Lens is that the measurement process
can run faster as there is less computing that the software needs to do,
reducing CPU load and directly leading to higher system throughput
and more parts measured per minute.
Because Telecentric Lenses tend to have such low distortion, they
are more prone to having non-monotonic wave distortion than fi xed
focal length lenses, as shown in Figure 5.6. While the magnitude of
the distortion is generally low enough to not have a signifi cant impact
on the measurement of the part under inspection, it is still important
to check the distortion specifi cations of the Telecentric Lens and to
properly calibrate the imaging system utilizing the Telecentric Lens.
This property is also why distortion plots should be used rather than a
single numerical value, as the lens can have zero distortion at the fi eld
point where it is specifi ed, but be non-zero elsewhere.
Focus and Defocused Pixel Values
395 400 405 410 415 420 425 430
Figure 5.4: Plot showing the diff erence in slope between a focused and
defocused edge. The defocused edge takes up many more pixels; fi nding
the edge becomes easier without relying on sub-pixel interpolation.
Telecentric Lenses and Depth of Field
It is a common misconception that Telecentric Lenses inherently have
a larger depth of fi eld than conventional lenses. While depth of fi eld
is still ultimately governed by the wavelength and f/# of the lens, it
is true that Telecentric Lenses can have a larger usable depth of fi eld
than conventional lenses due to the symmetrical blurring on either
side of best focus. As the part under inspection shifts toward or away
from the lens, it will follow the angular fi eld of view (or the chief ray)
that is associated with it. In a non-telecentric lens, when an object is
moved in and out of focus, the part blurs asymmetrically due to parallax
and the magnifi cation change that is associated with its angular
fi eld of view. Telecentric Lenses, however, blur symmetrically since
there is no angular component to the fi eld of view. In practice, this
means that features such as edges retain their center of mass location;
an accurate measurement can still be made when the object is beyond
best focus as long as the contrast remains high enough for the algorithm
being used by the machine vision system to function properly.
While it may seem counterintuitive, blur can be used advantageously
in certain applications with Telecentric Lenses. For example,
if a machine vision system needs to fi nd the center location of a pin,
as shown in Figure 5.3a, the transition from white to black is quite
sharp when the lens is in focus. In Figure 5.3b, the same pin is shown
Looking at a plot of the image grey levels from a line profi le taken
across the edge of the part, as in Figure 5.4, the slope of the line is
much shallower for the slightly defocused image, as the pin edge is
spread over more pixels. Due to the symmetric blurring of the Telecentric
Lens, this blur is still usable as the centroid has not moved
and the amount of sub-pixel interpolation needed is decreased. This
reduces sensitivity to grey level fl uctuations caused by sensor noise
and allows the pin center location to be found more reliably and with
Figure 5.3a and b: The same pin imaged both in and out of focus.
Note that the transition from white to black covers many more pixels
when the lens is slightly out of focus (b), which can be advantageous.
Fixed Focal Length Lens
Figure 5.5: Comparison of jumpers on a circuit board. Figure 5.5a
shows an image that has been taken with a Fixed Focal Length Lens.
Figure 5.5b shows an image that has been taken with a Telecentric
Lens. Note that the pins do not appear bent in the telecentric image.