Editing F-number (section)

== History ==
The system of f-numbers for specifying relative apertures evolved in the late nineteenth century, in competition with several other systems of aperture notation.

=== Origins of relative aperture ===
In 1867, Sutton and Dawson defined "apertal ratio" as essentially the reciprocal of the modern f-number. In the following quote, an "apertal ratio" of "{{frac|24}}" is calculated as the ratio of {{convert|6|in|mm}} to {{convert|1/4|in|mm}}, corresponding to an {{f/|24}} f-stop:

<blockquote>In every lens there is, corresponding to a given apertal ratio (that is, the ratio of the diameter of the stop to the focal length), a certain distance of a near object from it, between which and infinity all objects are in equally good focus. For instance, in a single view lens of 6-inch focus, with a {{1/4}} in. stop (apertal ratio one-twenty-fourth), all objects situated at distances lying between 20 feet from the lens and an infinite distance from it (a fixed star, for instance) are in equally good focus. Twenty feet is therefore called the 'focal range' of the lens when this stop is used. The focal range is consequently the distance of the nearest object, which will be in good focus when the ground glass is adjusted for an extremely distant object. In the same lens, the focal range will depend upon the size of the diaphragm used, while in different lenses having the same apertal ratio the focal ranges will be greater as the focal length of the lens is increased. The terms 'apertal ratio' and 'focal range' have not come into general use, but it is very desirable that they should, in order to prevent ambiguity and circumlocution when treating of the properties of photographic lenses.<ref name="Sutton">Thomas Sutton and George Dawson, ''A Dictionary of Photography'', London: Sampson Low, Son & Marston, 1867, (p. 122).</ref></blockquote>

In 1874, [[John Henry Dallmeyer]] called the ratio <math>1/N</math> the "intensity ratio" of a lens:

<blockquote>The ''rapidity'' of a lens depends upon the relation or ratio of the aperture to the equivalent focus. To ascertain this, divide the ''equivalent focus'' by the diameter of the actual ''working aperture'' of the lens in question; and note down the quotient as the denominator with 1, or unity, for the numerator. Thus to find the ratio of a lens of 2 inches diameter and 6 inches focus, divide the focus by the aperture, or 6 divided by 2 equals 3; i.e., {{1/3}} is the intensity ratio.<ref name="Dallmeyer">John Henry Dallmeyer, ''Photographic Lenses: On Their Choice and Use – Special Edition Edited for American Photographers'', pamphlet, 1874.</ref></blockquote>

Although he did not yet have access to [[Ernst Abbe]]'s theory of stops and pupils,<ref>{{Cite book| url =  https://archive.org/details/principlesandme01soutgoog/page/n493 | page = 537 | title = The Principles and Methods of Geometrical Optics: Especially as applied to the theory of optical instruments | publisher = Macmillan | last1 = Southall | first1 = James P. C. | year = 1910}}</ref> which was made widely available by [[Siegfried Czapski]] in 1893,<ref name="Czapski">Siegfried Czapski, ''Theorie der optischen Instrumente, nach Abbe,'' Breslau: Trewendt, 1893.</ref> Dallmeyer knew that his ''working aperture'' was not the same as the physical diameter of the aperture stop:

<blockquote>It must be observed, however, that in order to find the real ''intensity ratio'', the diameter of the actual working aperture must be ascertained. This is easily accomplished in the case of single lenses, or for double combination lenses used with the full opening, these merely requiring the application of a pair of compasses or rule; but when double or triple-combination lenses are used, with stops inserted ''between'' the combinations, it is somewhat more troublesome; for it is obvious that in this case the diameter of the stop employed is not the measure of the actual pencil of light transmitted by the front combination. To ascertain this, focus for a distant object, remove the focusing screen and replace it by the collodion slide, having previously inserted a piece of cardboard in place of the prepared plate. Make a small round hole in the centre of the cardboard with a piercer, and now remove to a darkened room; apply a candle close to the hole, and observe the illuminated patch visible upon the front combination; the diameter of this circle, carefully measured, is the actual working aperture of the lens in question for the particular stop employed.<ref name="Dallmeyer"/></blockquote>

This point is further emphasized by Czapski in 1893.<ref name="Czapski"/> According to an English review of his book, in 1894, "The necessity of clearly distinguishing between effective aperture and diameter of physical stop is strongly insisted upon."<ref>Henry Crew, "Theory of Optical Instruments by Dr. Czapski," in ''Astronomy and Astro-physics'' XIII pp. 241–243, 1894.</ref>

J. H. Dallmeyer's son, [[Thomas Rudolphus Dallmeyer]], inventor of the telephoto lens, followed the ''intensity ratio'' terminology in 1899.<ref>Thomas R. Dallmeyer, ''Telephotography: An elementary treatise on the construction and application of the telephotographic lens'', London: Heinemann, 1899.</ref>

=== Aperture numbering systems ===
[[File:No1-A Autographic Kodak Jr.jpg|thumb|right | A 1922 Kodak with aperture marked in U.S. stops. An f-number conversion chart has been added by the user.]]

At the same time, there were a number of aperture numbering systems designed with the goal of making exposure times vary in direct or inverse proportion with the aperture, rather than with the square of the f-number or inverse square of the apertal ratio or intensity ratio. But these systems all involved some arbitrary constant, as opposed to the simple ratio of focal length and diameter.

For example, the ''Uniform System'' (U.S.) of apertures was adopted as a standard by the [[Royal Photographic Society|Photographic Society of Great Britain]] in the 1880s. Bothamley in 1891 said "The stops of all the best makers are now arranged according to this system."<ref>C. H. Bothamley, ''Ilford Manual of Photography'', London: Britannia Works Co. Ltd., 1891.</ref> U.S. 16 is the same aperture as {{f/|16}}, but apertures that are larger or smaller by a full stop use doubling or halving of the U.S. number, for example {{f/|11}} is U.S. 8 and {{f/|8}} is U.S. 4. The exposure time required is directly proportional to the U.S. number. [[Eastman Kodak]] used U.S. stops on many of their cameras at least in the 1920s.

By 1895, Hodges contradicts Bothamley, saying that the f-number system has taken over: "This is called the {{f/|''x''}} system, and the diaphragms of all modern lenses of good construction are so marked."<ref>John A. Hodges, ''Photographic Lenses: How to Choose, and How to Use'', Bradford: Percy Lund & Co., 1895.</ref>

Here is the situation as seen in 1899:
[[File:Diaphragm Numbers.gif|center|823 px]]

Piper in 1901<ref>C. Welborne Piper, ''A First Book of the Lens: An Elementary Treatise on the Action and Use of the Photographic Lens'', London: Hazell, Watson, and Viney, Ltd., 1901.</ref> discusses five different systems of aperture marking: the old and new [[Carl Zeiss|Zeiss]] systems based on actual intensity (proportional to reciprocal square of the f-number); and the U.S., C.I., and Dallmeyer systems based on exposure (proportional to square of the f-number). He calls the f-number the "ratio number", "aperture ratio number", and "ratio aperture". He calls expressions like {{f/|8}} the "fractional diameter" of the aperture, even though it is literally equal to the "absolute diameter" which he distinguishes as a different term. He also sometimes uses expressions like "an aperture of f 8" without the division indicated by the slash.

Beck and Andrews in 1902 talk about the Royal Photographic Society standard of {{f/|4}}, {{f/|5.6}}, {{f/|8}}, {{f/|11.3}}, etc.<ref>Conrad Beck and Herbert Andrews, ''Photographic Lenses: A Simple Treatise'', second edition, London: R. & J. Beck Ltd., c. 1902.</ref> The R.P.S. had changed their name and moved off of the U.S. system some time between 1895 and 1902.

=== Typographical standardization ===
[[File:Yashica-D front.jpg|thumb|[[Yashica#TLRs|Yashica-D TLR]] camera front view. This is one of the few cameras that actually says "F-NUMBER" on it.]]
[[File:Yashica-D top.jpg|thumb|From the top, the Yashica-D's aperture setting window uses the "f:" notation. The aperture is continuously variable with no "stops".]]

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 in a hooked italic form: ƒ.<ref>[https://books.google.com/books?as_q=lens+aperture&num=50&as_epq=f-number Google search]</ref>

Notations for f-numbers were also quite variable in the early part of the twentieth century. They were sometimes written with a capital F,<ref>{{cite book| url=https://books.google.com/books?id=ypakouuKvwYC&pg=RA2-PA61| format=Google| access-date=12 March 2007| title=Airplane Photography| last=Ives| first=Herbert Eugene| publisher=J. B. Lippincott| location= Philadelphia| year=1920| pages=61| isbn=9780598722225}}</ref> sometimes with a dot (period) instead of a slash,<ref>{{cite book| url=https://books.google.com/books?id=V7MCVGREPfkC&q=aperture+lens+uniform-system+date:0-1930| access-date=12 March 2007| title=The Fundamentals of Photography| first=Charles Edward Kenneth| last=Mees| publisher=Eastman Kodak| year=1920| pages=28}}</ref> and sometimes set as a vertical fraction.<ref>{{cite book| url=https://books.google.com/books?id=AN6d4zTjquwC&pg=PA83| format=Google| access-date=12 March 2007| title=Photography for Students of Physics and Chemistry| first=Louis| last=Derr| location=London| publisher=Macmillan| year=1906| pages=83}}</ref>

The 1961 [[American National Standards Institute|ASA]] standard PH2.12-1961 ''American Standard General-Purpose Photographic Exposure Meters (Photoelectric Type)'' specifies that "The symbol for relative apertures shall be {{not a typo|ƒ/}} or {{not a typo|ƒ:}} followed by the effective ƒ-number." They show the hooked italic 'ƒ' not only in the symbol, but also in the term ''f-number'', which today is more commonly set in an ordinary non-italic face.