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Telecentricity
A lens is telecentric if the chief rays are parallel to one another . Most commonly , they are
also parallel to the lens axis and perpendicular to the object and / or image planes that are
perpendicular to the axis , Fig . 30 . Telecentricity is often described by speaking of pupils at
infinity , but the consideration of ray angles is more concrete and more directly relevant . A
lens is telecentric in object space if the chief rays in object space are parallel to the axis ,
a 0 5 0 and b 0 5 0 . In this case the image of the aperture formed by the portion of the lens
preceding it is at infinity and the aperture is at the rear focal plane of the portion preceding
it . Similarly , a lens is telecentric in image space if the aperture is at the front focal point of
the subsequent optics , so a 0 9 5 0 and b 0 9 5 0 . More generally , but less commonly , the chief
rays can be parallel to each other , but not necessarily to the axis , and not necessarily
perpendicular to a (possibly tilted) object or image plane .
With tilted object and image surfaces and nonaxial pupils , the chief rays are not
perpendicular to the object and / or image surfaces , but their angles are everywhere the
same , so defocus can result in a rigid shift of the entire image .
A focal lens can be nontelecentric or telecentric on either side , but it cannot be doubly
telecentric . An afocal lens can be nontelecentric , or doubly telecentric , but it cannot be
telecentric on one side . A doubly telecentric lens must be afocal , and a singly telecentric
lens cannot be afocal .
For a lens that is telecentric in image space , if the receiving surface is defocused , the
image of a point is blurred , but its centroid is fixed . However , if it is not telecentric in
object space , then the scale changes if the object is defocused . The converse holds for
object-space telecentricity without image-space telecentricity . For a doubly telecentric lens ,
an axial shift of either the object or the receiving plane produces blurring without a
centroid shift . Although the magnification of an afocal lens does not change with
conjugates , there can be an ef fective change with defocus if it is not telecentric .
If the pupil is not on the axis or if the object and image planes are tilted ,
there can be telecentricity without the chief rays being perpendicular to the object and / or image planes . In these
cases , defocus results in a rigid shift of the entire image .
Nominal telecentricity can be negated in several ways . Pupil aberrations may change
the chief ray angles across the field . For an extended object that is externally illuminated
the pupil may not be filled uniformly by light from a given region , so defocus can product a
lateral image shift .