Dalsa Falcon 4-CLHS Series, User Manual

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Falcon™ 4 -CLHS Series Additional Reference Information • 81
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
Figure 1: 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:
𝑚 =
ℎ
′
ℎ
Where m is the magnification, h’ is the image
height (pixel size) and h is the object height
(desired object resolution size).
By similar triangles, the magnification is alternatively given by:
𝑚 =
𝑓
′
𝑂𝐷
Where f ’ is the focal length and OD is the
target object distance.
These equations can be combined to give their most useful form:
ℎ
′
ℎ
=
𝑓
′
𝑂𝐷
This is the governing equation for many object
and image plane parameters.
Example: An acquisition system has a 512 x 512-element 10  m pixel pitch, a lens with an
effective focal length of 45 mm. For each pixel in the image sensor to correspond to 100

m in the
object space, using the preceding equation, the object distance must be 450 mm (0.450 m).
10 𝜇𝑚
100 𝜇𝑚
=
45 𝑚𝑚
𝑂𝐷
𝑂𝐷 = 450 𝑚𝑚 (0.450 𝑚)