The U.S. f-Stop System

Understanding the idea of aperture, or “f-stops”, is not always a straightforward concept for beginning photographers.  There are two ways of controlling the amount of light that falls on the film: the exposure time, or shutter speed, and the size of the lens opening, or aperture.  The concept of aperture is complicated by the fact that, when comparing different lenses,

Canon 35mm Camera with Unusual f/0.95 Lens

having the same size opening does not necessarily mean that the same amount of light falls on the film.  Rather, the amount of light admitted by a given opening depends on the focal length of the lens.  In other words, if the iris diaphragm opening is 25 mm, it will expose the film only one-quarter as much on a 200 mm telephoto lens as it will on a 50 mm lens.

In modern times (i.e., after the mid-1920s), the aperture has been expressed as an “f-stop” or “f-number”, with the f-number being expressed as the ratio between the focal length of the lens and the diameter of the pupil in the iris diaphragm:

f = (Lens focal length)/(diameter of iris diaphragm opening).

Consequently, our  50 mm lens with a 25 mm opening is a nice fast f/2 lens, while our 200 mm telephoto lens with a 25 mm opening is frustratingly slow at f/8.  This gives one some insight into why fast telephoto lenses are large, bulky, and expensive- a modest 200 mm telephoto lens with a maximum aperture of  f/2 has an opening of 100 mm, or about 4 inches!

The beauty of the f-stop system is that, at a given f-number, every lens will allow exactly the same amount of light per square centimeter to fall on the film.  Thus an exposure of 1/100 second at f/5.6 will be exactly the same no matter which lens or film size one uses.

Before the f-stop system was adopted, however, things were nowhere this simple, and a variety of systems were in use to express lens aperture.  In 1899, a summary of the most common systems looked something like this:

Aperture Systems Circa 1899

Clearly, the situation with respect to aperture expression at the turn of the century was extraordinarily confusing.  However, this table does contain the seeds of our modern, streamlined system.  The left column expresses the aperture according to our modern concept of the f-stop, even though the numbers are not neatly rounded off to f-numbers of 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, 45, and 64 as they are on the aperture scale of a modern camera.  What is also important to note is the second column, which tabulates the “U.S.” or Universal System (also called the “Uniform System”).

U.S. System f-Stop Scale

Many cameras produced before the early 1920s employed this system, which was a simple numerical progression doubling at each stop and having no direct relationship to the focal length of the lens.

The relationship between the U.S. and modern systems can be expressed more simply as follows:

f/stop	4	5.6	8	11	16	22	32	45
U.S.	1	2	4	8	16	32	64	256
Simple lens (Approximate)				1	2	3	4	–

This table also includes the approximate correspondence to a simple numerical system used by Kodak on some of their most basic cameras.  Note that the U.S. and modern systems intersect at f/16.  The U.S. system is found quite commonly on early Kodak cameras such as the No. 1 Kodak Junior shown in the image above.  Although the maximum aperture appears as “4”, this, like most of the Rapid Rectilinears, is actually an f/8 lens.

References:

“F-number.”  Wikipedia Article.  http://en.wikipedia.org/wiki/F-number.

Konig, Mischa.  Kodak Classics:  Kodak Folding Cameras (Includes discussion of f-stop systems).  http://kodak.3106.net/index.php?p=213.