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Lens Modeling
Any lens surrounded by air can be modeled for camera purposes using three primary points: the
first and second principal points and the second focal point. The primary points for a lens should be
available from the lens data sheet or from the lens manufacturer. Primed quantities denote
characteristics of the image side of the lens. That is, h is the object height and h' is the image
height.
The focal point is the point at which the image of an infinitely distant object is brought to focus.
The effective focal length (f') is the distance from the second principal point to the second focal
point. The back focal length (BFL) is the distance from the image side of the lens surface to the
second focal point. The object distance (OD) is the distance from the first principal point to the
object.
Primary Points in a Lens System
Magnification and Resolution
The magnification of a lens is the ratio of the image size to the object size:
h
'
m
=
h
By similar triangles, the magnification is alternatively given by:
f
'
m
=
OD
These equations can be combined to give their most useful form:
h
f
'
'
=
h
OD
Example: An acquisition system has a 512 x 512 element, 10µm pixel pitch area scan camera, a lens
with an effective focal length of 45mm, and requires that 100µm in the object space correspond to
each pixel in the image sensor. Using the preceding equation, the object distance must be 450mm
(0.450m).
µ
10
m
45
mm
=
µ
100
m
OD
Linea CLHS Series Camera
Where m is the magnification, h' is the image height (pixel
size) and h is the object height (desired object resolution
size).
This is the governing equation for many object and image
plane parameters.
OD =
450
mm
(
. 0
450
m
)
Additional Reference Information
47
•
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