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Section 2.4: f/#
(Lens Iris/Aperture Setting)
The f/# setting on a lens controls many of the lens’s parameters: overall
light throughput, depth of field, and the ability to produce contrast at
a given resolution. Fundamentally, f/# is the ratio of the effective focal
length (EFL) of the lens to the effective aperture diameter (DEP):
f/# = EFL
In most lenses, the f/# is set by the turning the iris adjusting ring,
thereby opening and closing the iris diaphragm inside. The numbers
labeling the ring denote light throughput with its associated aperture
diameter. The numbers usually increase by multiples of √ 2. Increasing
the f/# by a factor of √ 2 will halve the area of the aperture, effectively
decreasing the light throughput of the lens by a factor of 2.
Lenses with lower f/#s are considered fast and allow more light to
pass through the system, while lenses of higher f/#s are considered
slow and feature reduced light throughput.
Table 2.2 shows an example of f/#, aperture diameters, and effective
opening size for a 25 mm focal length lens. Notice that from the setting
of f/1 to f/2, and again for f/4 to f/8, the lens aperture is reduced by
half and the effective area is reduced by a factor of 4 at each interval.
This illustrates the reduction in throughput associated with increasing a
Contrast and Frequency
Figure 2.3: Two spots being imaged by the same lens. The top lens is
imaging objects at a low frequency, the bottom lens is imaging objects
at a higher frequency.
u f/# and Effects on a Lens’s Theoretical
Resolution, Contrast, and DOF:
The f/# impacts more than just light throughput. Specifically, f/# is
directly related to the theoretical resolution and contrast limits and the
Depth of Field (DOF) and depth of focus of the lens. Additionally, it
will influence the aberrations of a specific lens design.
As pixels continue to decrease in size, f/# becomes one of the most
important limiting factors of a system’s performance because its effects
on DOF and resolution move in opposite directions. As shown in Table
2.3, the requirements are often in direct conflict and compromises must
f/# Changes with Working Distance Change: – ADVANCED
The definition of f/# in Equation 2.9 is limited in the sense that it is
defined at an infinite working distance where the magnification is effectively
zero. Most often in machine vision applications, the object
is located much closer to the lens than an infinite distance away, and
f/# is more accurately represented by the working f/#, Equation 2.10.
(f/#)W ≈ (1 + |m|) x f/#
In the equation for working f/#, m represents the paraxial magnification
(ratio of image to object height) of the objective. Note that as m
approaches zero (as the object approaches infinity), the working f/#
is equal to the infinite f/#. It is especially important to keep working
f/# in mind at smaller working distances. For example, an f/2,8, 25
mm focal length lens operating with a magnification of -0,5X will have
an effective working f/# of f/4,2. This impacts image quality as well
as the lens’s ability to collect light.
f/# Lens Aperture Diameter (mm) Aperture Opening Area (mm2)
1 25,0 490,8
1,4 17,9 251,6
2 12,5 122,7
2,8 8,9 62,2
4 6,3 31,2
5,6 4,5 15,9
8 3,1 7,5
(Continued from page 13)
Lenses and Contrast Limitations
Lens contrast is typically defined in terms of the percentage of the
object contrast that is reproduced when assuming ideal illumination.
Resolution is actually somewhat meaningless unless defined at a specific
contrast. In Section 2.1, the example assumed perfect reproduction
on the object, including sharp transitions at the edge of the object
on the pixel. However, in reality this is never the case. Because of
the nature of light, even a perfectly designed and manufactured lens
cannot fully reproduce an object’s resolution and contrast. Even when
the lens is operating at the diffraction limit (described in Section 3.1),
the edges of the dots in Figure 2.3 will be blurred in the image. This
is where calculating a system’s resolution by simply counting pixels
loses accuracy, and can even become completely ineffective.
Consider two dots close to each other being imaged through a lens,
as in Figure 2.3. When the spots are far apart (in other words, at a low frequency),
the dots are distinct, though both somewhat blurry at the edges.
As they approach each other, the blurs overlap until the dots can no
longer be distinguished as separate entities. The system’s actual resolving
power depends on the imaging system’s ability to detect the space
between the dots. Even if there are ample pixels between the spots, if
the spots blend together due to lack of contrast, they will not easily be
resolved as two separate details. Therefore, the resolution of the system
depends on many things, including blur caused by diffraction and other
optical errors, the dot spacing, and the sensors ability to detect contrast.
Table 2.2: The relationship between f/# and effective area for a 25 mm
singlet lens. As the f/# increases, the area decreases, leading to a
slower system with less light throughput.
Table 2.3: Lens performance changes as the f/# varies.
p q p q q
q p q p p
(See Figure 2.4a)