Master Thesis - Fachbereich Informatik

3.2. CAMERA SETUP 41
further distance can be imaged over the whole image size with such lenses. However, the
minimum object distance is larger for long focal length lenses.
For two-dimensional measuring tasks most accurate and precise results can be achieved
with telecentric lenses (see Figure 3.5). These special lenses are designed to map objects of
the same size in the world to the same image size, even if the object to lens distance differs.
It is important to note that the maximum object size can not be larger than the diameter
of the lens. This makes telecentric lenses useful only in connection with relatively small
objects. In addition, such lenses reach a size of over 0.5m for objects of about 100mm and
a mass of approximated 4kg [18]. Finally, telecentric lenses are very expensive.
Although a telecentric lens would be advantageous in the imaging properties, a less
expensive solution had to be found for the prototype development in this application. The
optical system must be able to map objects between 20 and 100mm to an 1/2” CDD
sensor at a relative short camera-object distance, and which is expected not to be affected
too much by aberrations and radial distortion.
However, this is an optimization problem that has no universal solution for all tube
lengths. Different tube lengths need different magnification factors and field of views if the
maximum possible resolution should be exploited to reach the highest accuracy. Changing
the magnification factor means changing either the focal length of the optical system or
the distance between object and camera, or both. If moving the camera toward the object,
the minimum object distance of the lens has to be considered to be able to yield sharp
images. Zoom lenses could be used to change the focal length without changing the whole
optical system. However, zoom lenses should be avoided in machine vision applications
[40], since they have to make larger compromises than fix-focal lenses and usually have
a minimum working distance of one meter and more. Hence, if using a fix-focal lens,
this implies changing the camera-object distance to adapt to different tube lengths, or to
physically exchange the lens when a new length is cut by the machine which can not be
covert by the current lens.
Several commercial lenses designed for machine vision applications have been compared
to find the lens that is best suited to inspect different tube sizes (see Table 3.1). Figure 3.6
gives an overview on the parameters that influence a camera’s field of view. The angle
of view θ is specified by the lens manufacturer, and is depending on the focal length and
the camera sensor size. All values in the following are oriented at an 1/2” CCD sensor,
since this is the sensor size of the Marlin F-033C and F-046B. The working distance d
is here defined as the distance between lens and conveyor. O represents the object size,
and L indicates the size of the measuring area with respect to a certain tube size. L
canbeapproximatedastwicetheobjectsizeO. The goal is to find a combination of a
lens with a working distance that yields a visual field so that the size V of the imaged
region of the conveyor equals the measuring area L. Note, in this context size can be
replaced by length in horizontal, i.e. in the moving direction of the conveyor, since this
is the measuring direction in this constraint application. Thus, in the following only this
direction is considered.
The geometry in Figure 3.6 leads to the following relationship between θ, d and V :
� �
θrad
V =2dtan
(3.5)
2