Page 248 - Modern Optical Engineering The Design of Optical Systems

228 Chapter Ten

regardless of the angle at which it is illuminated or the angle from
which it is viewed. A perfect, or lambertian, diffuser is one which has
the same apparent brightness from any angle; thus the radiation emit-
ted per unit area in the surface is given by I 0 cos , where is the angle
to the surface normal and I 0 is the intensity of an element of area in a
direction perpendicular to the surface.
There are a number of quite good reflecting diffusers with relatively
high efficiencies. Matte white paper is a very convenient one and
reflects 70 to 80 percent of the incident visible light. Magnesium oxide
and magnesium carbonate are frequently used in photometric work
since their efficiencies are high, to the order of 97 or 98 percent.
The brightness (luminance) of a perfectly diffuse reflector is propor-
tional to the illumination falling on it and to its reflectivity. If the illu-
mination is measured in footcandles, multiplication by the reflectivity
yields the brightness in foot-lamberts. The brightness in lamberts is
2
given by the illumination in lumens per cm times the reflectivity, and
if this product is divided by , the result is the brightness in candles
2
per cm , or in lumens per steradian per cm . (See Chap. 12 for more
2
material on photometric considerations.)
As indicated above, a perfectly diffuse surface appears to have the
same brightness regardless of the angle at which it is viewed. A projec-
tion screen which is not perfectly diffuse can have a brightness ranging
from zero to that of the projector light source. For example, consider a
perfect mirror screen in the shape of an ellipsoid, with the viewer’s eye
placed at one focus and the projector at the other. All of the light will
be reflected to the eye; none will be scattered. From this eye position
the screen will have the same brightness as if one looked directly into
the projection lens; when viewed from any other location, the screen
will appear completely dark. The gain of a projection screen is the ratio
of its brightness to that of a perfectly diffuse (or lambertian) screen,
which by definition has a gain of 1.0. A diffuse screen can be viewed
from any direction, and its brightness, while low, is independent of the
viewing angle. The higher the gain of a screen, the smaller the
angle over which it has its rated gain. Beaded screens and facetted,
lenticular screens are used to concentrate and distribute the light in a
controlled manner. Aluminum paints are used to coat screens which
must maintain polarization, and with a smooth curved surface can
achieve gains as high as 4.0 in commercial products. Beaded screens
can achieve a gain as high as 10, but only over an extremely restricted
angle. Many projection screens are rated at a gain of about 2.0.
Transmitting diffusers are used for such applications as rear projec-
tion screens and to produce even illumination. The most commonly
used are opal glass and ground glass (Fig. 10.13). Opal glass contains
a suspension of minute colloidal particles and diffuses by multiple