handbook of modern sensors

140 4 Optical Components of Sensors
Fig. 4.15. Comparison of spherical and aspheric lens profiles.
It is known that a spherical surface of a lens will produce a spherical aberration.
Therefore, for applications where high-quality focusing is required, the continuous
surface from which the contours of the groves are determined should not be spherical,
but aspherical. The profile of a continuous aspherical surface can often be described
by a standard equation of a conic, axially symmetrical about the z axis (Fig. 4.15):
Z =
CY 2
1 + √ 1 − (K + 1)C 2 Y 2 , (4.32)
where Z and Y are the coordinates of the surface, C is the vertex curvature, and
K is the conic constant. The vertex curvature and the conic constant can be chosen
depending on the desired characteristics of the lens, and the contours of each grove
can be figured using this equation. C and K will depend on several factors, such as
the desired focal length, the index of refraction, and the particular application.
4.7 Fiber Optics and Waveguides
Although light does not go around the corner, it can be channeled along complex paths
by the use of waveguides. To operate in the visible and near-infrared spectral ranges,
the guides may be fabricated of glass or polymer fibers. For the mid- and far-infrared
spectral ranges, the waveguides are made as hollow tubes with highly reflective inner
surfaces. The waveguide operates on the principle of the internal reflections where
light beams travel in a zigzag pattern. A fiber can be used to transmit light energy in
the otherwise inaccessible areas without any transport of heat from the light source.
The surface and ends of a round or other cross-section fiber are polished. An outside
cladding may be added. When glass is hot, the fibers can be bent to curvature radii of
20–50 times their section diameter and after cooling, to 200–300 diameters. Plastic
fibers fabricated of polymethyl methacrylate may be bent at much smaller radii than
glass fibers. A typical attenuation for a 0.25-mm polymer fiber is in the range of 0.5
dB/meter of length. Light propagates through a fiber by means of a total internal
reflection, as shown in Fig. 4.16B. It follows from Eq. (4.23) that light passing to air