Image-Space Telecentricity
Entrance Pupil
Embedded in System
Object Space Image Space
Focal Length of Back Half of System
Telecentric Comparison
Doubly Telecentric
Object Space Telecentric
Non-Telecentric
-4 -2 0 2 4
WD (mm)
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Figure 4.13 Object-Space Telecentric Lens
Object Planes
Figure 4.13: An object-space telecentric lens where the chief rays are all parallel to the optical axis in object space. Note that the FOV does not
change regardless of where the object plane is positioned, as the chief rays defining the FOV are all parallel to the optical axis.
Image-Space Telecentricity
As object-space telecentricity is defined by the position in object space of
the entrance pupil, image-space telecentricity can be defined by the exit
pupil being located at infinity in image space. This is shown in Figure 4.15.
Much in the same way that the magnification of an object will not
change if a lens is object-space telecentric, when a lens is image-
space telecentric the magnification will not change with respect to the
placement of the sensor plane, as shown in Figure 4.16. This means
that sensor placement tolerance for cameras is not as important with
image-space telecentric lenses, as small shifts toward or away from
optimal position will not cause differences in magnification between
two systems with identical lenses.
Additionally, image-space telecentric lenses do not suffer from radiometric
cos4θ roll-off (described in detail in Section 3.2, pages 20-21)
since the rays land perpendicular to the sensor across its entire area.
This is advantageous because it allows the image to have a more even
RI profile assuming selective vignetting has not been built into the
lens design.
Figure 4.15
Exit Pupil Located at
Infinity in Object Space
Figure 4.15: A lens which is image-space telecentric, with the exit
pupil projected to image-space infinity.
Figure 4.16 Image-Space Telecentric Lens
Figure 4.16: An image-space telecentric lens, where the chief rays are
all parallel to the optical axis in image-space. Note that the image height
does not change regardless of where the sensor plane is positioned, as
the chief rays defining image height are all parallel to the optical axis.
Figure 4.17
Doubly Telecentric Lens Figure 4.18
Object Space Image Space
Exit Pupil Located at
Infinity in Object Space
Entrance Pupil Located at
Infinity in Image Space
Focal Length of
Front Half System
Focal Length of
Back Half System
Figure 4.17: A doubly telecentric lens, with the entrance and exit
pupils projected to image and object-space infinity, respectively.
Dimensional Error (%)
5
4
3
2
1
Figure 4.18: Plot comparing three different types of lenses (non-telecentric,
object-space telecentric, and doubly telecentric) and the dimensional
error that is associated with each as the WD is changed.
Double Telecentricity
While object-space telecentricity provides a substantial boost to
gauging accuracy over conventional lenses, even greater accuracy
can be achieved if a lens is both object and image-space telecentric
(doubly telecentric). The same principles of image and object-space
telecentricity hold true; in a doubly telecentric lens, both the entrance
and exit pupils are projected to their respective infinities, as shown in
Figure 4.17.
Doubly telecentric lenses are the most accurate type of telecentric
lens, as the FOV is completely unaffected to change caused by shifts
of the object position or the sensor position, nor do they suffer from
any cos4θ roll-off.
Figure 4.18 shows a plot comparing three different lenses - a fixed
focal length lens, an object-space-only telecentric lens, and a doubly
telecentric lens - with the x-axis representing the change in WD (in
mm) from nominal and the y-axis representing the dimensional error
as a percentage from the actual value.
As is shown in the plot, the doubly telecentric lens is the most accurate
of the group, with less than 0.2% error throughout a 4mm shift in
WD. Doubly telecentric lenses should be used in applications requiring
the highest accuracy and precision.
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