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Section 1.3: Understanding Focal Length and Field of View
H
8 +44 (0) 1904 788600 | Edmund Optics® targets FOV = 2 × WD × tan AFOV
2
Fixed Focal Length Lenses
A fixed focal length lens, also known as a conventional or entocentric
lens, is a lens with a fixed angular field of view (AFOV). By
focusing the lens for different working distances (WDs), differently
sized field of view (FOV) can be obtained, though the viewing angle
is constant. AFOV is typically specified as the full angle (in degrees)
associated with the horizontal dimension (width) of the sensor that
the lens is to be used with.
Note: fixed focal length lenses should not be confused with fixed
focus lenses. Fixed focal length lenses can be focused for different
distances; fixed focus lenses are intended for use at a single, specific
WD. Examples of fixed focus lenses are many telecentric lenses and
microscope objectives.
The focal length of a lens defines the AFOV. For a given sensor
size, the shorter the focal length, the wider the AFOV. Additionally, the
shorter the focal length of the lens, the shorter the distance needed
to obtain the same FOV compared to a longer focal length lens. For
a simple, thin, convex lens, the focal length is the distance from the
back surface of the lens to the plane of the image formed of an object
placed infinitely far in front of the lens. From this definition, it can be
shown that the AFOV of a lens is related to the focal length (Equation
1.2), where f is the focal length and H is the sensor size (Figure 1.3).
AFOV = 2 × tan-1
2f
1.2
In general, however, the focal length is measured from the rear
principal plane, rarely located at the mechanical back of an imaging
lens; this is one of the reasons why working distances (WDs)
calculated using paraxial equations are only approximations and the
mechanical design of a system should only be laid out using data
produced by computer simulation or data taken from lens specification
tables. Paraxial calculations, as from lens calculators, are a good
starting point to speed up the lens selection process, but the numerical
values produced should be used with caution.
When using fixed focal length lenses, there are three ways to
change the FOV of the system (camera and lens). The first and often
easiest option is to change the WD from the lens to the object; moving
the lens farther away from the object plane increases the FOV.
The second option is to swap out the lens with one of a different focal
length. The third option is to change the size of the sensor; a larger
sensor will yield a larger FOV for the same WD, as defined in Equation
1.2.
While it may be convenient to have a very wide AFOV, there are
some negatives to consider. First, the level of distortion that is associated
with some short focal length lenses can greatly influence the
actual AFOV and can cause variations in the angle with respect to WD
due to distortion. Next, short focal length lenses generally struggle
to obtain the highest level of performance when compared against
longer focal length options (see Best Practice #3 on page 4). Additionally,
short focal length lenses can have difficulties covering medium
to large sensor sizes, which can limit their usability, as discussed in
Section 3.2, on pages 20-21.
Another way to change the FOV of a system is to use either a
varifocal lens or a zoom lens; these types of lenses allow for adjustment
of their focal lengths and thus have variable AFOV. Varifocal
and zoom lenses often have size and cost drawbacks compared
to fixed focal length lenses, and often cannot offer the same level of
performance as fixed focal length lenses.
Using WD and FOV to Determine Focal Length
In many applications, the required distance from an object and the
desired FOV (typically the size of the object with additional buffer
space) are known quantities. This information can be used to directly
determine the required AFOV via Equation 1.3. Equation 1.3
is the equivalent of finding the vertex angle of a triangle with its
height equal to the WD and its base equal to the horizontal FOV, as
shown in Figure 1.4. Note: In practice, the vertex of this triangle is
1.3
Figure 1.3: For a given sensor size, H, shorter focal lengths produce wider AFOVs.
Longer f
Shorter f
H/2
AFOV/2
AFOV/2
H/2
Figure 1.3 Object at Infinity
rarely located at the mechanical front of the lens, from which WD is
measured, and is only to be used as an approximation unless the
entrance pupil location is known.
Once the required AFOV has been determined, the focal length can
be approximated using Equation 1.2 and the proper lens can be chosen
from a lens specification table or datasheet by finding the closest available
focal length with the necessary AFOV for the sensor being used.
AFOV = 2 × tan-1 or FOV
2 × WD