Page 302 - Modern Optical Engineering The Design of Optical Systems

Principles of Radiometry and Photometry 281

Telescope brightness
The apparent brightness of an image as seen by the eye is a function
of the diameter of the pupil of the eye, since it determines the illumi-
nation of the retina, in accordance with Eq. 12.11a. When the eye is
used with an optical instrument, such as a telescope, the exit pupil of
the instrument enters the picture. If the exit pupil is larger than that
of the eye, then the apparent brightness of the object seen through the
instrument is equal to the brightness of the object (modified by trans-
mission losses and index effects), since the solid angle subtended by
the pupil from the retina is unchanged. When the instrument exit
pupil is smaller than that of the eye, then the apparent brightness of
the object is reduced in proportion to the relative areas of the pupils.
The exception to these brightness relationships of object and image
occurs when the object is smaller than the diffraction limit of the opti-
cal system (e.g., a star). Since this is not an extended source, all the
energy in the retinal image is concentrated on a few retinal receptors,
and when the magnification and aperture of a telescope are increased
so that its exit pupil diameter stays the same, its effective collection
area is increased (at the objective) so that more energy is concentrated
on the same retinal cells (because the size of the retinal image is the
same, being governed by the diffraction limit), resulting in an increase
in the apparent brightness of the source. For example, if a high enough
power telescope of large aperture is used, stars may be seen in daylight,
since their apparent brightness is increased while that of the sky (as
an extended object) is not.

Integrating sphere
An integrating sphere is often used in the measurement of light and
light sources, and also as a uniform lambertian (diffuse) source of
light. It is a hollow sphere, coated on the inside with a highly reflective
white diffuse paint. If spot A on the inside of the sphere is illuminated,
the light reflected from this spot produces an illumination at some
other point B on the inside of the sphere. This illumination varies with
the cosines of angles and made by the line connecting A and B with
the normals to the sphere surface at A and B. Thus the illumination at
B varies as
cos cos
(12.25)
D 2

where D is the distance from A to B. This expression, for the inside of
a sphere, is a constant. Thus the entire inner surface of the sphere is
uniformly illuminated by the light reflected from the illuminated spot.