Image Space Telecentricity
Entrance Pupil
Embedded in System
Object Space Image Space
Figure 4.15
Exit Pupil Located at
Infinity in Object Space
Focal Length of Back Half of System
Telecentric Comparison
Doubly Telecentric
Object Space Telecentric
Non-Telecentric
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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 field of view
does not change regardless of where the object plane is positioned, as the chief rays defining the field of view 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 relative illumination profile assuming selective vignetting has
not been built into the lens design.
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 working distance 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 field of view 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 working
distance (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 working distance. Doubly Telecentric Lenses should be used
in applications requiring the highest accuracy and precision.
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