Section 1.3: Understanding Focal Length and Field of View
10 +44 (0)1904 788600 • EDMUND OPTICS® imaging lenses filters microscopy cameras illumination targets imaging resource guide
Fixed Focal Length Lenses
A Fixed Focal Length Lens, also known as a conventional or entocentric
lens, is a lens with a xed Angular Field of View (AFOV).
By focusing the lens for di erent working distances, di erently sized
Fields of View (FOV) can be obtained, though the viewing angle is
held constant. AFOV is typically speci ed 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 have the ability to
be focused for di erent distances; Fixed Focus Lenses are intended
for use at a single, speci c working distance. Examples of Fixed Focus
Lenses are many Telecentric Lenses and Microscope Objectives.
The focal length of a lens de nes the lens’s angular eld of view.
For a given sensor size, the shorter the focal length, the wider the angular
eld of the lens. 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 of the lens to the plane of
the image formed of an object placed in nitely far in front of the lens.
From this de nition, it can be shown that the angular eld of view of
a lens is related to the focal length (Equation 1.2), where f is the focal
length in millimeters and h is the horizontal dimension of the sensor
in millimeters (Figure 1.3).
AFOV(°) = 2 x tan-1
In general, however, the focal length is measured from the lens’s
rear principal plane, which is rarely located at the mechanical back
of an imaging lens; this is one of the reasons that working distances
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 speci cation
tables. Paraxial calculations, as from lens calculators, are a good
starting point to speed 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 eld of view of the system (camera and lens). The rst
and often easiest option is to change the working distance from the
lens to the object; moving the lens farther away from the object plane
increases the eld of view. The second option is to swap out the lens
that is being used with one of a di erent focal length. The third option
is to change the size of the sensor that is being used; a larger sensor
will yield a larger eld of view for the same working distance, as de-
ned in Equation 1.2.
While it may often be convenient to have a very wide angular
eld of view, there are some negatives to consider. First, the level
of distortion that is associated with some short focal length lenses
can greatly in uence the actual AFOV and can cause variations in
the angle with respect to Working Distance (WD) due to the varying
magnitude of the 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 in Section
1.1, page 8). Additionally, short focal length lenses can have di culties
covering medium to large sensor sizes, which can limit their usability,
as discussed in Section 4.2, pages 24-27.
Another way to change the eld of view of a system is to use
either a Varifocal Lens or a Zoom Lens; these types of lenses
allow for the adjustment of their focal lengths and thus have variable
angular elds of view. Varifocal and Zoom Lenses often have
drawbacks in terms of size and cost in comparison to Fixed Focal
Length Lenses, and often cannot o er 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 eld of view (typically the size of the object with additional
bu er space) are known quantities. This information can be used to
directly determine the required angular eld of view via the formulas
shown in Equation 1.3, where WD is the Working Distance from the
lens and AFOV is the Angular Field of View. Equation 1.3 is the equiv-
Figure 1.3: For a given sensor size, h, shorter focal lengths produce wider AFOV’s.
Longer Focal Length
Figure 1.3 Object at Infinity
alent of nding the vertex angle of a triangle with its height equal to
the working distance and its base equal to the horizontal eld of view,
as shown in Figure 1.4. Note: In practice, the vertex of this triangle is
rarely located at the mechanical front of the lens, from which working
distance is measured, and should only be used as an approximation
unless the entrance pupil location is known.
AFOV(°) = 2 x tan-1 Horizontal FOV (mm)
2 x WD (mm)
Horizontal FOV (mm) = 2 x WD (mm) x tan AFOV(°)