112 3 Sources of Light and Illumination Systems
In order to improve the image contrast with regard to the surroundings, espe-
cially in bright sunlight, an interference ﬁlter F (coating reﬂectivity R =95%,
FWHM δλ =10 nm) is introduced in the imaging branch.
(a) Find the intensity distribution in the generated line of light.
(b) Assuming the sun illumination at sea level is E
S
= 1, 350 W/m
2
and the
sun temperature is 6,000 K, calculate the image contrast at the center and
at the side of the light line.
3.13. A laser beam generated by a laser diode followed by a collimator has an
elliptical cross-section with principal diameters of 4 mm and 8 mm. Find the
anamorphic prism pair capable of correcting the ellipticity of the beam.
3.4. Light Emitting Diodes (LEDs)
In general, LEDs, like laser diodes, transform electrical energy directly into optical
energy. They also comprise a semiconductor p–n junction fed by a DC current,
but there is no resonator and photons are emitted spontaneously generating non-
coherent radiation. The wavelengths available are not only in the IR and red
regions, but also in the green and blue regions. A step in their development was a
combination of several semiconductor sources generating different wavelengths in
a single housing to create white light radiation. Indeed, white LEDs have become
widely available in the last few years.
The spectral properties of monochromatic LEDs are inferior to those of laser
diodes. Usually the bandwidth of LEDs is about 30–50 nm.
LEDs are usually operated at low voltage (2–5 V) and low current (20–100 mA)
and their efﬁciency in energy transformation is as high as in laser diodes (up
to 30%).
LEDs are manufactured in two basic conﬁgurations (see Fig. 3.18) with a ﬂat
window and with the lens incorporated as a part of the casing.
a) b)
Figure 3.18 LED with (a) a ﬂat window and (b) a lens.
3.4. Light Emitting Diodes (LEDs) 113
a) b)
Figure 3.19 Angular diagrams of a LED intensity distribution: (a) LED with a front
window; (b) LED with a lens.
In applications of LEDs as light sources the angular distribution of the emit-
ted radiation is a main concern. Examples of angular diagrams are presented in
Fig. 3.19 for both types of LED design. It also should be mentioned that radiation
emitted by a LED suffers from low uniformity in a cross-section perpendicular to
the chip. This feature is especially noticeable at small distances from the source.
Setting a diffusing glass in front of the source or even grinding the LED itself
allow one to obtain much more homogeneous radiation in a wide spatial angle (an
example of such an approach is given in Problem 3.14).
Problems
3.14. Dark ﬁeld illumination with a single LED. Imaging of an opaque object in
dark ﬁeld illumination means that the whole ﬁeld of view remains black except
for some details which, due to their specular reﬂectivity, appear as white.
In the system depicted in Fig. 3.20 lens L
1
of 12 mm diameter and 25 mm focal
length performs imaging of an object P onto an area sensor (1/2

CCD, size 4.8 mm
× 6.4 mm) at magniﬁcation V
1
=−0. 25. The working distance (WD) deﬁned
as the free space between the object and the system has to be 16 mm at least.
The illumination branch of the system which provides on-axis illumination for
dark ﬁeld consists of a LED followed by a condenser lens L
2
(diameter 45 mm,
f # = 1. 0). The LED front surface was grinded until a ﬂat diffuse area of 3 mm in
diameter was created.
Aiming at the most compact architecture, ﬁnd the location of all elements of the
system and a minimum size of the beam splitter, BS, required for operation in the
full ﬁeld of view if acceptable vignetting everywhere should not exceed 50%.
3.15. Oblique illumination with a LED array. Providing a minimum working
distance of 16 mm, how does one incorporate in the system in Problem 3.14 a LED
ring array for oblique illumination of the object P in two colors (red and green)?

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