handbook of modern sensors

and the facet pitch is
6.5 Optoelectronic Motion Detectors 243
p = 2nd, (6.11)
where L is the distance to the object, d is the width of the sensing element, n is the
number of sensing elements (evenly spaced), and is the object’s minimum displacement
which must result in detection. For example, if the sensor has two sensing
elements of d = 1 mm, each of which are positioned at 1 mm apart, and the object’s
minimum displacement = 25 cm at a distance L = 10 m, the facet focal length is
calculated from Eq. (6.10) as f = (1000 cm)(0.1cm)/25 cm = 4 cm, and the facets
should be positioned with a pitch of p = 8 mm from one another as per Eq. (6.11).
By combining facets, one may design a lens which covers a large field of view
(Fig. 6.11B) where each facet creates a relatively narrow-angle sensitive zone. Each
zone projects an image of an object into the same sensing element. When the object
moves, it crosses the zone boundaries, thus modulating the sensor’s output.
6.5.2 Visible and Near-Infrared Light Motion Detectors
Most of the objects (apart from those very hot) radiate electromagnetic waves only in
a far-infrared spectral range. Hence, visible and near-infrared light motion detectors
have to rely on the additional source of light which illuminates the object. The light is
reflected by the object’s body toward the focusing device for the subsequent detection.
Such illumination may be sunlight or the invisible infrared light from an additional
near-infrared light source (a projector). The use of a visible light for detecting moving
objects goes back to 1932 when, in the preradar era, inventors were looking for ways
to detect flying airplanes. In one invention, an airplane detector was built in the form
of a photographic camera where the focusing lens made of glass was aimed at the sky.
A moving plane’s image was focused on a selenium photodetector, which reacted to
the changing contrast in the sky image. Naturally, such a detector could operate only
in daytime to detect planes flying below clouds. Obviously, those detectors were not
very practical. Another version of a visible light motion detector was patented for
less demanding applications: controlling lights in a room [5] and making interactive
toys [6].
To turn the lights off in an unoccupied room, the visible-range motion detector
(Motion Switch manufactured by Intermatic, Inc., IL) was combined with a timer and a
power solid-state relay. The detector is activated when the room is illuminated. Visible
light carries a relatively high energy and may be detected by quantum photovoltaic or
photoconductive cells whose detectivity is quite high. Thus, the optical system may
be substantially simplified. In the Motion Switch, the focusing device was built in a
form of a pinhole lens (Fig. 6.12C). Such a lens is just a tiny hole in an opaque foil.
To avoid a light-wave diffraction, the hole diameter must be substantially larger than
the longest detectable wavelength. Practically, the Motion Switch has a three-facet
pinhole lens, where each hole has an aperture of 0.2 mm (Fig. 6.12C). Such a lens
has a theoretically infinitely deep focusing range; hence, the photodetector can be
positioned at any distance from it. For practical reasons, that distance was calculated
for a maximum of the object’s displacement and the photoresistor’s dimensions used
in the design. The photoresistor was selected with a serpentine pattern of the sensing