The f Stops here....

In search of the origin of the f-stop

For some time I have wondered how it is that we have come to call the aperture of a lens the f-stop. I have run into a myriad of various explanations but none have been completely satisfying or seemed entirely plausible.

I had assumed that it came from a scientific or mathematical expression, and indeed I believe I have found that formula.

Where f is the focal length, and D is the diameter of the entrance pupil. By convention, "f/#" is treated as a single symbol, and specific values of f/# are written by replacing the number sign with the value. For example, if the focal length is 16 times the pupil diameter, the f-number is f/16, or N = 16. The greater the f-number, the less light per unit area reaches the image plane.

The literal interpretation of the f/N notation for f-number N is as an arithmetic expression for the effective aperture diameter (input pupil diameter), the focal length divided by the f-number: D = f / N.

Apparently Optical Engineers Sutton and Dawson defined the f-stop in 1867, and was adopted by lens manufactures soon afterward. Although apparently the f expression was unanimously adopted by lens makers the numbering scale was not. By 1901 there were at least 5 separate numerical scales used to denote the f-stop.

By 1920, the term f-number appeared in books both as F number and f/number. In modern publications, the forms f-number and f number are more common, though the earlier forms, as well as F-number are still found in a few books; not uncommonly, the initial lower-case f in f-number or f/number is set as the hooked italic f as in f/#. Notations for f-numbers were also quite variable in the early part of the twentieth century. They were sometimes written with a capital F, sometimes with a dot (period) instead of a slash, and sometimes set as a vertical fraction.

Although by the 1940’s most of the world had settled with the current f-stop scale we use today it wasn’t until 1961 that the ASA created the f-stop as an official standard. PH2.12-1961 American Standard General-Purpose Photographic Exposure Meters (Photoelectric Type) specifies that "The symbol for relative apertures shall be f/ or f : followed by the effective f-number." Note that they show the hooked italic f not only in the symbol, but also in the term f-number, which today is more commonly set in an ordinary non-italic face.