Biomimetic Vision Sensors - Engineered Biomimicry - page 8

decreases, and there is a certain point at which
DOF rear extends to optical infinity; this value of
s o is called the hyperfocal distance. At this setting,
all objects from ( s o − DOF front ) to ∞ would be
imaged with acceptable sharpness. When the
sensor system is set to the hyperfocal distance,
the DOF extends from half the hyperfocal dis-
tance to infinity, and the DOF is the largest
possible for a given focal length and aperture
size. Therefore, the hyperfocal distance is often
of interest to the sensor system designer.

FIGURE 1.5 Front and rear DOF.

1.2.1.4 Field of View
The field of view (FOV) for a sensor system is
the span over which a given scene is imaged.
Although it may seem at first that the aperture
size might determine FOV, in typical imaging
situations it does not. 3 The approximate FOV
is determined only by the geometry of Figure
1.1 , where x i would be one-half the size (in that
dimension) of the imaging sensor array or of the
film, and x o would be one-half the spatial FOV
at distance s o . Since angular FOV is independent
of object distance, it is the more frequently used
form of FOV. For an imaging sensor (or film) of
size a in a given direction, the angular FOV in
that direction is 2 arctan( a /2 s i ) . When the sys-
tem is set to focus at optical infinity, this takes
on the familiar form of 2 arctan( a /2 f ) . The shape
of the FOV matches the shape of the sensor
array or film that is used to capture the image,
not the shape of the aperture. Although optics
are typically transversely circular, sensor arrays
and film are more often rectangular, so the FOV
would then also be rectangular.
Example Problem: For the webcam problem
described earlier, assume that the diameter of the
lens aperture is approximately 8 mm. (a) What is
the F for this camera? (b) What is the angular
FOV of the camera? (c) How much of the snow
fence will be imaged at the maximum distance
of the camera from the fence?

object can be brought to focus at distance s i ,
DOF describes the practical reality that there
is an axial distance over which objects are
imaged with acceptable sharpness. Thus, an
object within the range of s o − DOF front to

would be imaged with accept-
able sharpness (see Figure 1.5 ). With reference
to Figure 1.3 , note that, for a given focal length,
a larger aperture results in a larger angle of
convergence of light from the aperture plane
to the image plane. This larger angle means
that any change in d will have a greater blur-
ring effect than it would for a smaller aperture.
Thus, the DOF is smaller for larger apertures.
Combining what is shown in both Figures 1.1
and 1.3 , along with Eq. (1.1) , we can show that
focal length f also affects DOF; longer focal-
length lenses have a smaller DOF for a given
aperture size. There is no specific equation for
DOF, since it is based on what is considered
acceptable sharpness, and that is very much
application dependent.
Photographers often manipulate DOF for
artistic purposes, but sensor system designers
are usually more interested in maximizing the
DOF. In general, the DOF front is always less
than DOF rear . At relatively small values of s o ,
the ratio of DOF front / DOF rear is close to unity.
As s o is increased, the ratio of DOF front / DOF rear

s o + DOF rear

3 If too small of an aperture is used at the wrong point in an optical system, it can restrict the FOV to less than the full sensor
dimensions. This is almost always unintentional.