Lens Selection, Small Sensors Lens Selection,400
Working Distance (mm)
742.5
594
445.5
297
148.5
0
Horizontal FOV (mm, ." Sensor)
875
Lens Selection, Small Sensors Lens Selection, Medium Format Sensors
1595
0 100 200 300 400 500 600 700 800 900 1000
www.edmundoptics.eu/imaging 39
resource guide telecentric liquid lens/specialty objectives cameras illumination targets
fixed focal length filters/accessories microscopy /
ing points describes the best starting point of investigation for which
lens to use and considerably narrows the large fi eld of lenses from
which to choose.
Additionally, these plots also illustrate several important points
about fi xed focal length lenses in machine vision. First, longer focal
length lenses have longer minimum WDs, which is a consequence of
the optical designs. Minimum WD can be reduced by placing spacers
between the lens and camera, but image quality will eventually suffer
(see Section 5.2, Lens Spacers, Shims and Focal Length Extenders on
pages 34-35 for more information). Second, larger sensors provide a
larger FOV with the same focal length lens. For example, at a WD of
350 mm, a 12 mm lens on a 2/3 ” sensor will have a FOV of about 370
mm, but on a 1” sensor at the same WD, the FOV is approximately
530 mm - an increase of 43%. Lastly, the gaps in the plot where lines
do not exist indicate the absence of standard, off -the-shelf fi xed focal
length lenses which perform at the corresponding specifi cations. For
example, it is impossible to achieve a 525 mm FOV at a 600 mm WD
with a 2/3 ” sensor with available focal lengths. The closest lens that exists
is an 8,5 mm focal length, which would need to be used at a WD
of about 510 mm to achieve that FOV.
These plots should only be used as the fi rst step in narrowing down
which lens is the best for an application. They do not answer questions
about image quality, distortion, relative illumination, or any other
important qualities of an imaging lens; they merely address FOV
relative to sensor size.
How to Choose a Fixed Magnifi cation Lens
At fi rst glance, lenses such as telecentrics or microscope objectives can
seem intimidating to specify an imaging system as they do not behave
the same way as traditional fi xed focal length lenses. However, the
selection process is actually much more straightforward than a
traditional lens.
With a few exceptions,500
fi xed magnifi cation lenses generally only
function properly at a single WD. They are also specifi ed by their
magnifi cation, such as a 2,0X telecentric lens. Because the magnifi -
cations are physically listed on the lenses, that is where they always
work, and their FOV can be described simply by rearranging Equation
1.1 from Section 1.2: Imaging Fundamentals to:
742.5
H
m
where m is the magnifi cation specifi ed for the lens and H is the sensor
size. This equation shows that regardless of the sensor size, the magnifi
cation will remain the same; only the FOV changes.
500
300
200
100
0
Horizontal FOV (mm, " Sensor)
Figure 6.3: Lenses of diff erent focal lengths and their FOVs on ⅓ ”
and 1⁄1.8” sensors
700
525
350
175
0
Horizontal FOV (mm, " Sensor) 0 100 200 300 400 500 600 700 800 900 1000
0 100 200 300 f=3.5mm
f=4.5mm
f=6mm
f=8.5mm
f=12mm
f=6mm
f=f=16mm
f=25mm
f=35mm
f=50mm
f=100mm
f=35mm
f=875
Figure 6.4: Lenses of diff erent focal lengths and their FOVs on 2/3 ”
and 1” sensors.
Working Distance (mm)
400
300
200
100
0
1276
957
638
319
0
Horizontal FOV (mm, " Sensor)
Horizontal FOV (mm, 1" Sensor)
594
445.5
297
148.5
0
Horizontal FOV (mm, ." Sensor)
700
525
350
175
0
Horizontal FOV (mm, " Sensor)
0 100 200 300 400 500 600 700 800 900 1000
Working Distance (mm)
f=3.5mm
f=16mm
f=4.5mm
f=25mm
f=6mm
f=35mm
f=8.5mm
f=50mm
f=12mm
f=100mm
f=6mm
f=35mm
f=8.5mm
f=50mm
f=12mm
f=100mm
f=16mm f=25mm
FOV = 6.4
Section 6.3: Advanced Lens Selection
For example, an application requires the visual measurement of a
bore into a machined part. The bore is 20 mm in diameter and the
part can vary slightly in placement underneath the imaging system, so
a FOV of 24 mm is required. A camera has been chosen that has a
1⁄1,8” sensor (7,2 mm horizontal sensor size), so using Equation 6.4, the
magnifi cation should be 0,3X. Since this is a measurement application,
a telecentric lens should be chosen with that magnifi cation.
Note that in the above example, a camera had already been chosen;
were a camera not chosen, the lens selection would be more complicated.
Section 6.3 spends time discussing how to select a lens when no
camera has been chosen.
The prior section explained lens selection primarily from the perspective
of the lens as the fi nal component to be chosen in the machine
vision system. This section approaches lens and camera selection holistically,
choosing both at the same time, depending on what is important
for the specifi c application. This section will walk through an example
starting from scratch where a 2D barcode needs to be imaged from
200 mm away, as shown in Figure 6.5.
100μm
Figure 6.5: Image of the 2D barcode that must be imaged from 200
mm away.
Starting with the object to be inspected and breaking it down into its
constituent parts is the fi rst step in lens selection. What are the important
features? How large are these features? How many pixels do I need
to cover the feature that I am trying to observe in order for my machine
vision software to function properly?
Often, the best place to start is feature size and pixel coverage. For
the barcode in Figure 6.5, these are fairly straightforward numbers. The
feature size is 100 μm, with empty space of at least 100 μm in between
features. This means that the frequency that this feature corresponds to
is 5lp/mm (see Section 2.2: Resolution for a review of this math) in object
space. This number is the fi rst piece of the puzzle in determining the
required magnifi cation of the lens.
Next, the entire FOV needs to be considered. This means not only
the size of the barcode itself, but space must be allowed for positional
uncertainty within the FOV. If the barcode is 25 mm × 25 mm, it is
likely safe to say that a FOV of 35 mm is required. In this particular example,
it is necessary to have at least three pixels covering each feature
on the barcode. Since the feature size on the barcode is 100 μm, it is
then required to have at least 33 μm per pixel on the object plane.
/imaging