handbook of modern sensors

138 4 Optical Components of Sensors
(A)
(B)
(C)
Fig. 4.13. Concept of a Fresnel lens.
detectors. Fresnel lenses may be fabricated of glass, acrylic (visible and near-infrared
range), or polyethylene (far-infrared range). The history of Fresnel lenses began in
1748, when Count Buffon proposed grinding out a solid piece of glass lens in steps
of the concentric zones in order to reduce the thickness of the lens to a minimum and
to lower energy loss. He realized that only the surface of a lens is needed to refract
light, because once the light is inside the lens, it travels in a straight line. His idea
was modified in 1822 by Augustin Fresnel (1788–1827), who constructed a lens in
which the centers of curvature of the different rings receded from the axis according
to their distances from the center, so as to practically eliminate spherical aberration.
The concept of that lens is illustrated in Fig. 4.13, where a regular plano-convex
lens is depicted. The lens is sliced into several concentric rings. After slicing, all rings
still remain lenses which refract incident rays into a common focus defined by Eq.
(4.24). A change in an angle occurs when a ray exits a curved surface. The section
of a ring marked by the letter x does not contribute to the focusing properties. If all
such sections are removed, the lens will look like it is shown in Fig. 4.13B and will
fully retain its ability to focus light rays. Now, all of the rings may be shifted with
respect to one another to align their flat surfaces (Fig. 4.13C). A resulting near-flat
lens is called Fresnel, which has nearly the same focusing properties as the original
plano-convex lens.AFresnel lens basically consists of a series of concentric prismatic
grooves, designed to cooperatively direct incident light rays into a common focus.
The Fresnel lens has several advantages over a conventional lens, such as low
weight, thin size, ability to be curved (for a plastic lens) to any desirable shape, and,
most importantly, lower absorption loss of light flux. The last feature is very important
for the fabrication of mid- and far-infrared lenses where absorption in the material
may be significant. This is the reason why polymer Fresnel lenses are used almost
exclusively in the far-infrared motion detectors.
Two common types of Fresnel lenses are presently manufactured. One is a
constant-step lens (Fig. 4.14A) and the other is a constant depth lens (Fig. 4.14B). In
practice, it is difficult to maintain a curved surface of each small groove; hence, the
profile of a groove is approximated by a flat surface. This demands that the steps be
positioned close to each other. In fact, the closer the steps, the more accurate the lens.
In a constant-step lens, a slope angle ϕ of each groove is a function of its distance
h from the optical axis.As a result, the depths of the grooves increase with the distance