3.2. Lens-based Illumination Systems 97
If mid- or far-IR wavelengths are required then special IR emitters should be
exploited. The Nernst rod made of zirconium ceramics and heated to a color tem-
perature of about 2,000 K was one of the ﬁrst wideband sources. Another kind of
IR emitter in use is the silicon carbide ceramic element of 1,300 K color temper-
ature. In both sources the radiating element is a cylinder of several millimeters in
diameter heated by a DC electric current of about 4–5 A. In the wavelength range
from 1 to about 28 μm IR emitters have a smooth continuous spectrum.
3.1. A QTH lamp operated at 12 V DC has a ﬁlament of 4. 2 × 2. 3 mm heated to
a temperature of 3,234 K. Assuming a tungsten emissivity of 0.8, ﬁnd the spectral
irradiance for a wavelength of 0.5 μm: (a) at nominal voltage; (b) after the voltage
is reduced by 5%.
[Note: For the given source the temperature and the voltage supplied are related
to each other as follows: d(T/T
) = 0. 4.]
3.2. Thelamp described in Problem 3.1 is used as the source of a linear illumination
system. At a distance of 60 mm from the lamp ﬁlament a plane convex cylindrical
lens is positioned. The lens is made of BK-7 glass, its refraction surface is of
20.65 mm radius and its size is 20 mm (height) by 100 mm (width). Find the
location of the illuminated line and the intensity distribution along it.
3.2. Lens-based Illumination Systems
In a variety of optical architectures illumination is generated inside the system by
a module or sub-assembly, which is an integral part of the whole conﬁguration.
We will consider such a module as a separate illumination system.
All illumination systems are intended either for the creation of stratiﬁed light (a
pattern of a special shape, like a straight line, or a ring, or a more complex form) or
for illuminating an object in an imaging arrangement. Examples of systems from
the ﬁrst group are considered in Problems 3.2 and 3.12. In this section we discuss
illumination for imaging optics.
In general, uniform illumination of the ﬁeld of view is of our main concern.
To achieve this goal the principal rule is to avoid the creation of the light source
image in the object plane or in the image plane (and also not in the vicinity of these
planes). There exist several ways to do this. An illumination system with a single
lens is shown in Fig. 3.2. The lens L transfers the image of the light source S into
the entrance pupil of the imaging optics (objective L
in this case) which builds
98 3 ♦ Sources of Light and Illumination Systems
Figure 3.2 Single-lens illumination system.
Figure 3.3 Two-lens illumination system.
the image of the object y in the plane y
. Illumination on lens L is of the highest
uniformity since each part of the source S contributes light to each point in the
plane L (in the ﬁgure the rays originating in the center of the source are drawn as
solid lines whereas the dotted lines are related to points A and B at both sides of
the ﬁlament). The object is positioned very close to lens L and therefore it is not
affected by non-uniformity of the source S.
The conﬁguration depicted in Fig. 3.3 comprises two lenses, L
illuminating the object y. The source image is transferred by the ﬁrst lens into
the plane of the second lens where a diaphragm of variable size is positioned.
Changing the diaphragm enables one to select illumination from a different part
of the source. Lens L
builds the image of lens L
in the object plane y. Again, the
highest uniformity is achieved here because all points of the source S contribute
radiation to each point of the object. The drawback of the conﬁguration becomes
evident if we consider the side rays coming to the imaging objective L
rays originating in the source S are cut by the ﬁnal size of the objective lens which
might result in considerable vignetting. This problem is eliminated in the three-lens
architecture shown in Fig. 3.4. The ﬁrst two lenses and the source S are located
and function as in the previous case of the two-lens system. An additional lens
transfers the image of S further into the plane of the entrance pupil P of the
imaging optics objective, L
, providing in such a way that all relevant rays from
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