AFOV/2
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introduction fundamentals lens specifications real world performance telecentricity lens mechanics lens selection guide
The 14.25° derived in Example 1 (see white box below) can be used
to determine the lens that is needed, but the sensor size must also be
chosen. As the sensor size is increased or decreased it will change how
much of the lens’s image is utilized; this will alter the AFOV of the system
and thus the overall FOV. The larger the sensor, the larger the obtainable
AFOV for the same focal length. For example, a 25mm lens could be
used with a ½” (6.4mm horizontal) sensor or a 35mm lens could be used
with a 2/3” (8.8mm horizontal) sensor as they would both approximately
produce a 14.5° AFOV on their respective sensors.
Alternatively if the sensor has already been chosen, the focal
length can be determined directly from the FOV and WD by substituting
Equation 1.2 in Equation 1.3, as shown in Equation 1.4,
f = (H × WD)
FOV
1.4
As previously stated, some amount of flexibility to the system’s WD
should be factored in, as the above examples are only first-order
approximations and they also do not take distortion into account.
Calculating FOV Using a Lens with a Fixed Magnification
Generally, lenses that have fixed magnifications have fixed or limited
WD ranges. While using a Telecentric or other Fixed Magnification
Lens can be more constraining, as they do not allow for different
FOVs by varying the WD, the calculations for them are very direct, as
shown in Equation 1.5.
FOV = H
m
Since the desired FOV and sensor are often known, the lens selection
process can be simplified by using Equation 1.1.
m = H
FOV
1.1
If the required magnification is already known and the WD is constrained,
Equation 1.4 can be rearranged (replacing H÷FOV with magnification)
and used to determine an appropriate fixed focal length
lens, as shown in Equation 1.6.
m = f
WD
Be aware that Equation 1.6 is an approximation and will rapidly deteriorate
for magnifications greater than 0.1 or for short working distances.
For magnifications beyond 0.1, either a Fixed Magnification
Lens or computer simulations (e.g. Zemax) with the appropriate lens
model should be used. For the same reasons, lens calculators commonly
found on the internet should only be used for reference. When
in doubt, consult a lens specification table.
Note: Horizontal FOV is typically used in discussions of FOV as
a matter of convenience, but the sensor aspect ratio (ratio of a sensor’s
width to its height) must be taken into account to ensure that the
entire object fits into the image where the aspect ratio is used as a
fraction (e.g. 4:3 = 4/3), Equation 1.7.
Horizontal FOV = Vertical FOV × Aspect Ratio
While most sensors are 4:3, 5:4 and 1:1 are also quite common. This
distinction in aspect ratio also leads to varying dimensions of sensors
of the same sensor format. All of the equations used in this section
can also be used for vertical FOV as long as the sensor’s vertical
dimension is substituted in for the horizontal dimension specified in
the equations.
LENS FOCAL LENGTH EXAMPLES
Using WD and FOV to Determine Focal Length
Example 1: For a system with a desired WD of 200mm and
a FOV of 50mm, what is the AFOV?
2 × tan-1 50mm
= AFOV
2 × 200mm
AFOV = 14.25°
Calculating FOV Using a Lens with a Fixed Magnification
Example 2: For an application using a ½” sensor, which has
a horizontal sensor size of 6.4mm, a horizontal FOV of 25mm
is desired.
By reviewing a list of Fixed Magnification or Telecentric
Lenses, a proper magnification can be selected. Note: As the
magnification increases, the size of the field of view will decrease;
a magnification that is lower than what is calculated
is usually desirable so that the full field of view can be visualized.
In the case of Example 2, a 0.25X lens is the closest common
option, which yields a 25.6mm FOV on the same sensor.
1.5
1.6
1.7
BFL
Lens
Entrance
Pupil
Exit
Pupil
WD
FOV H
Object Plane
Image Plane
Figure 1.4
Figure 1.4: Relationship between FOV, sensor size, and WD for a given
AFOV.
m = 6.4mm m = 0.256X
25mm
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