Page 200 - Modern Optical Engineering The Design of Optical Systems

Stops, Apertures, Pupils and Diffraction 183

Figure 9.8 The telecentric stop is located at the focal point
of the projection system shown, so that the principal ray is
parallel to the axis at the object. When the object is slightly
out of focus (dotted) there is no error in the size of the pro-
jected image as there is in the system with the stop at the
lens, shown in the lower sketch.

9.7 Apertures and Image Illumination—
ƒ-Number and Cosine-Fourth
ƒ-Number
When a lens forms the image of an extended object, the amount of
energy collected from a small area of the object is directly proportional
to the area of the clear aperture, or entrance pupil, of the lens. At the
image, the illumination (power per unit area) is inversely proportional
to the image area over which this object is spread. Now the aperture
area is proportional to the square of the pupil diameter, and the image
area is proportional to the square of the image distances, or focal
length (f). Thus, the square of the ratio of these two dimensions is a
measure of the relative illumination produced in the image.
The ratio of the focal length to the clear aperture of a lens system is
called the relative aperture, f-number, or “speed” of the system, and
(other factors being equal), the illumination in an image is inversely
proportional to the square of this ratio. The relative aperture is
given by:

f/# f-number efl/clear aperture (9.1)
As an example, an 8-in focal length lens with a 1-in clear aperture
has an f-number of 8; this is customarily written f/8 or f:8.