Biomimetic Vision Sensors - Engineered Biomimicry - page 7

diffraction limit, but that is beyond the scope
of this discussion [20] .
Any discussion of aperture should mention
that the various subfields of optics (astronomy,
microscopy, fiber optics, photography, etc.) use
different terms to describe the aspects related to
the effective aperture of the system [21] . In
astronomy, the actual aperture size as discussed
before is typically used. In microscopy, it is
common to use numerical aperture ( NA ) , defined
as NA = n sin φ , where n is the index of refraction
of the medium through which the light travels,
and φ is the half-angle of the maximum cone of
light that can enter the lens. The angular
resolution of a standard microscope is often
specified as λ/2NA . For multimode fiber optics,
numerical apert ure is typically defined as
NA = n sin φ ≈

photosensitive area of an individual photode-
tector (e.g., the size of a single pixel in a CCD
array), then one could say that the optics have
been overdesigned. A blur spot nearly the same
size as the photosensitive area of an individual
photodetector results when the optics have been
tuned to match the sensors (ignoring for the
moment the unavoidable spatial sampling that
a photodetector array will impose on the image).
There are many instances, sometimes due to
considerations such as cost, or weight, or size of
the optical system and sometimes due to other
reasons as described in the case study of the fly-
eye sensor, in which the optical system is pur-
posely designed to result in a blur spot larger
than the photosensitive area of an individual
photodetector.
Example Problem : For the webcam problem
described earlier, what aperture size would be
needed to approximately match a diffraction-
limited blur spot to the pixel size?
Solution : The angular blur spot size is
approximately ( λ / D ), so the linear blur spot size
at the image plane is ( λ / D )s i . The pixel size was
previously found to be 15 µ m. If we assume a
wavelength near the midband of visible light,
550 nm, then the requirement is for D = 825 µ m.
Since the focal length of the lens was given as
22.5 mm, this would require a lens with an
f-number of f / D = 27.27, which is an achievable
aperture for the lens system. However, the likeli-
hood of a low quality lens in the webcam would
mean that aberrations (discussed later) would
probably dominate the size of the blur spot, not
diffraction. Aberrations always make the blur
spot larger, so if aberrations are significant then
a larger aperture would be needed to get the
blur spot back down to the desired size.

− n 2 , where n 1 is the index
of refraction of the core and n 2 is the index of
refraction of the cladding. This can provide an
approximation for the largest acceptance angle
φ for the cone of light that can enter the fiber
such that it will propagate along the core of the
fiber. Light arriving at the fiber from an angle
greater than φ would not continue very far down
the fiber. In photography, the more common
measure is called f-number (written by various
authors as f# or F ), defined as F = f / D , where f
is the focal length and D is the effective aperture.
A larger F a d mits less light; an increase in F by
a factor of

n 1

√

2 ≈ 1. 414 is called an increase of one
f-stop and will reduce the admitted light by one-
half. Note that to obtain the same image
exposure, an increase of one f-stop must be
matched by twice the integration time (called the
shutter speed in photography) of the photosensor.
Typical lenses for still and video cameras have
values of F that range from 1.4 to 22. Whether
the designer uses D , NA , F , or some other
measure is dependent on the application.
How is this pertinent to someone developing
biomimetic vision sensors? We sometimes desire
to somewhat match the optics to the photosen-
sors. For example, if the optics design results in
a blur spot that is significantly smaller than the

1.2.1.3 Depth of Field
The size of the effective aperture of the optics
not only helps determine the size of the blur
spot, but also helps determine the depth of field
(DOF) of the image. While Figure 1.1 implies
there is only a single distance s o for which an