Dimensional Measurement using Vision Systems - NPL Publications ...

Measurement Good Practice Guide No. 39
The angle of view is important as it defines the physical position of the lens and camera.
The angle of view can be expressed as:
β = 2 tan -1 ( b/2f )
…..(11)
4.1.3 Depth of field
Equation 7 indicates the relationship between the focal length and the object and image
distances for a single thin lens where it is assumed that the lens dimensions do not affect
the formation of the image. In this case there is only one image distance at which an object
will appear in focus for a given object distance and focal length. In reality, the lens
dimensions do affect the image and a typical camera lens will consist of several lenses.
With such lens assemblies there will be a range of object distances at which there will be
no discernable defocusing of the image.
As we are imaging on to a CCD camera, we may consider the object’s depth to be a series
of points, with any given point, half the size of one pixel. Selecting the point size as half a
pixel means that it cannot illuminate two pixels at the same time. The point is out of focus
if it does not appear as a point (i.e. it is imaged as greater in size than 1 pixel). On the
image plane, it is imaged as a circle of confusion. In Figure 23, P1 indicates the image
distance of point 1 on the object and P2, the image distance of a point 2 on the object. The
distance P2-P1 indicates the depth of field and ‘C’ is the diameter of the circle of confusion
created by point 2 on the image plane of point 1. Despite divergence of the border rays of
point 2, if the circle of confusion is less than one pixel, the point will remain sharp in the
image.
Figure 23: Circle of confusion.
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