handbook of modern sensors

144 4 Optical Components of Sensors
x approaches the lower part of the fiber at an angle which is less than 0 —the angle of
total internal reflection [Eq. (4.33)]. Thus, instead of being reflected, light is refracted
and moves in the direction y through the fiber wall. The closer the deformers come to
each other, the more light goes astray and the less light is transmitted along the fiber.
For operation in the spectral range where loss in fibers is too great, hollow tubes are
generally used for light channeling (Fig. 4.19B). The tubes are highly polished inside
and coated with reflective metals. For instance, to channel thermal radiation, a tube
may be fabricated of brass and coated inside by two layers: nickel as an underlayer
to level the surface, and the optical-quality gold having thickness in the range 500–
1000Å. Hollow waveguides may be bent to radii of 20 or more of their diameters.
Although fiber optics use the effect of the total internal reflection, tubular waveguides
use a first surface mirror reflection, which is always less than 100%. As a result, loss
in a hollow waveguide is a function of a number of reflections; that is, loss is higher
for the smaller diameter and the longer length of a tube. At length/diameter ratios
more than 20, hollow waveguides become quite inefficient.
4.8 Concentrators
Regarding optical sensors and their applications, there is an important issue of the
increasing density of the photon flux impinging on the sensor’s surface. In many
cases, when only the energy factors are of importance and a focusing or imaging
is not required, special optical devices can be used quite effectively. These are the
so-called nonimaging collectors, or concentrators [5]. They have some properties of
the waveguides and some properties of the imaging optics (like lenses and curved
mirrors). The most important characteristic of a concentrator is the ratio of the area of
the input aperture divided by the area of the output aperture. The concentration ratio
C is always more than unity; that is, the concentrator collects light from a larger area
and directs it to a smaller area (Fig. 4.20A) where the sensing element is positioned.
There is a theoretical maximum for C:
C max = 1
sin 2 , (4.37)
i
where i is the maximum input semiangle. Under these conditions, the light rays
emerge at all angles up to π/2 from the normal to the exit face. This means that
the exit aperture diameter is smaller by sin i times the input aperture. This gives
an advantage in the sensor design, as its linear dimensions can be reduced by that
number while maintaining a near equal efficiency. The input rays entering at angle
will emerge within the output cone with angles dependent of point of entry.
The concentrators can be fabricated with reflective surfaces (mirrors) or refractive
bodies, or as a combination of both. A practical shape of the reflective parabolic
concentrator is shown in Fig. 4.20B. It is interesting to note that cone light receptors
in the retina of a human eye have a shape similar to that shown in Fig. 4.20B [6].
The tilted parabolic concentrators have very high efficiency 2 : They can collect
and concentrate well over 90% of the incoming radiation. If a lesser efficiency is ac-
2 This assumes that the reflectivity of the inner surface of the concentrator is ideal.