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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
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
102 • Technical Specifications
is the image height.
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
)
Genie Monochrome Series-GigE Vision Camera
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