Editing F-number (section)

== Stops, f-stop conventions, and exposure ==
[[Image:Canon 7 with 50mm f0.95 IMG 0374.JPG|thumb|A [[Canon 7]] mounted with a {{val|50|u=mm}} lens capable of {{f/|0.95}}]]
[[Image:lens aperture side.jpg|thumb|A {{val|35|u=mm}} lens set to {{f/|11}}, as indicated by the white dot above the f-stop scale on the aperture ring. This lens has an aperture range of {{f/|2}} to {{f/|22}}.]]

The word ''stop'' is sometimes confusing due to its multiple meanings. A stop can be a physical object: an opaque part of an optical system that blocks certain rays. The ''[[aperture stop]]'' is the aperture setting that limits the brightness of the image by restricting the input pupil size, while a ''field stop'' is a stop intended to cut out light that would be outside the desired field of view and might cause flare or other problems if not stopped.

In photography, stops are also a ''unit'' used to quantify ratios of light or exposure, with each added stop meaning a factor of two, and each subtracted stop meaning a factor of one-half. The one-stop unit is also known as the EV ([[exposure value]]) unit. On a camera, the aperture setting is traditionally adjusted in discrete steps, known as '''''f-stops'''''. Each "'''stop'''" is marked with its corresponding f-number, and represents a halving of the light intensity from the previous stop. This corresponds to a decrease of the pupil and aperture diameters by a factor of 1/{{sqrt|2}} or about 0.7071, and hence a halving of the area of the pupil.

Most modern lenses use a standard f-stop scale, which is an approximately [[geometric sequence]] of numbers that corresponds to the sequence of the [[exponentiation|powers]] of the [[square root of 2]]:  {{f/|1}}, {{f/|1.4}}, {{f/|2}}, {{f/|2.8}}, {{f/|4}}, {{f/|5.6}}, {{f/|8}}, {{f/|11}}, {{f/|16}}, {{f/|22}}, {{f/|32}}, {{f/|45}}, {{f/|64}}, {{f/|90}}, {{f/|128}}, etc. Each element in the sequence is one stop lower than the element to its left, and one stop higher than the element to its right. The values of the ratios are rounded off to these particular conventional numbers, to make them easier to remember and write down.
The sequence above is obtained by approximating the following exact geometric sequence:

<math display=block>f/1 = \frac{f}{(\sqrt{2})^0},\ f/1.4 = \frac{f}{(\sqrt{2})^1},\ f/2 = \frac{f}{(\sqrt{2})^2},\ f/2.8 = \frac{f}{(\sqrt{2})^3},\ \ldots</math>
In the same way as one f-stop corresponds to a factor of two in light intensity, [[shutter speed]]s are arranged so that each setting differs in duration by a factor of approximately two from its neighbour. Opening up a lens by one stop allows twice as much light to fall on the film in a given period of time. Therefore, to have the same exposure at this larger aperture as at the previous aperture, the shutter would be opened for half as long (i.e., twice the speed). The film will respond equally to these equal amounts of light, since it has the property of ''[[Reciprocity (photography)|reciprocity]]''. This is less true for extremely long or short exposures, where there is [[reciprocity failure]]. Aperture, shutter speed, and film sensitivity are linked: for constant scene brightness, doubling the aperture area (one stop), halving the shutter speed (doubling the time open), or using a film twice as sensitive, has the same effect on the exposed image. For all practical purposes extreme accuracy is not required (mechanical shutter speeds were notoriously inaccurate as wear and lubrication varied, with no effect on exposure). It is not significant that aperture areas and shutter speeds do not vary by a factor of precisely two.

Photographers sometimes express other [[Exposure (photography)|exposure]] ratios in terms of 'stops'. Ignoring the f-number markings, the f-stops make a [[logarithmic scale]] of exposure intensity. Given this interpretation, one can then think of taking a half-step along this scale, to make an exposure difference of a "half stop".

=== Fractional stops ===
{{multiple image
 | width = 120
 | image1 = Povray focal blur animation.gif
 | alt1 = Changing a camera's aperture in half-stops
 | image2 = Povray focal blur animation mode tan.gif
 | alt2 = Changing a camera's aperture from zero to infinity
 | footer = Computer simulation showing the effects of changing a camera's aperture in half-stops (at left) and from zero to infinity (at right)
}}

Most twentieth-century cameras had a continuously variable aperture, using an [[iris diaphragm]], with each full stop marked. Click-stopped aperture came into common use in the 1960s; the aperture scale usually had a click stop at every whole and half stop.

On modern cameras, especially when aperture is set on the camera body, f-number is often divided more finely than steps of one stop. Steps of one-third stop ({{1/3}} EV) are the most common, since this matches the ISO system of [[film speed]]s. Half-stop steps are used on some cameras. Usually the full stops are marked, and the intermediate positions click but are not marked. As an example, the aperture that is one-third stop smaller than {{f/|2.8}} is {{f/|3.2}}, two-thirds smaller is {{f/|3.5}}, and one whole stop smaller is {{f/|4}}. The next few f-stops in this sequence are:

<math display=block>f/4.5,\ f/5,\ f/5.6,\ f/6.3,\ f/7.1,\ f/8,\ \ldots</math>

To calculate the steps in a full stop (1 EV) one could use

<math display=block>(\sqrt{2})^{0},\ (\sqrt{2})^{1},\ (\sqrt{2})^{2},\ (\sqrt{2})^{3},\ (\sqrt{2})^{4},\ \ldots</math>

The steps in a half stop ({{1/2}} EV) series would be

<math display=block>(\sqrt{2})^{\frac{0}{2}},\ (\sqrt{2})^{\frac{1}{2}},\ (\sqrt{2})^{\frac{2}{2}},\ (\sqrt{2})^{\frac{3}{2}},\ (\sqrt{2})^{\frac{4}{2}},\ \ldots</math>

The steps in a third stop ({{1/3}} EV) series would be

<math display=block>(\sqrt{2})^{\frac{0}{3}},\ (\sqrt{2})^{\frac{1}{3}},\ (\sqrt{2})^{\frac{2}{3}},\ (\sqrt{2})^{\frac{3}{3}},\ (\sqrt{2})^{\frac{4}{3}},\ \ldots</math>

As in the earlier DIN and ASA film-speed standards, the ISO speed is defined only in one-third stop increments, and shutter speeds of digital cameras are commonly on the same scale in reciprocal seconds. A portion of the ISO range is the sequence

<math display=block>\ldots 16/13^\circ,\ 20/14^\circ,\ 25/15^\circ,\ 32/16^\circ,\ 40/17^\circ,\ 50/18^\circ,\ 64/19^\circ,\ 80/20^\circ,\ 100/21^\circ,\ 125/22^\circ,\ \ldots</math>

while shutter speeds in reciprocal seconds have a few conventional differences in their numbers ({{frac|15}}, {{frac|30}}, and {{frac|60}} second instead of {{frac|16}}, {{frac|32}}, and {{frac|64}}).

In practice the maximum aperture of a lens is often not an [[integer|integral]] power of {{sqrt|2}} (i.e., {{sqrt|2}} to the power of a whole number), in which case it is usually a half or third stop above or below an integral power of {{sqrt|2}}.

Modern electronically controlled interchangeable lenses, such as those used for SLR cameras, have f-stops specified internally in {{frac|8}}-stop increments, so the cameras' {{1/3}}-stop settings are approximated by the nearest {{frac|8}}-stop setting in the lens.{{citation needed|date=December 2021}}

==== Standard full-stop f-number scale ====
Including [[APEX system|aperture value]] AV:
<math display=block>N = \sqrt{2^{\text{AV}}}</math>

Conventional and calculated f-numbers, full-stop series:
{|class="wikitable" style="text-align:center"
! scope="row" | AV
| −2 || −1 || 0 || 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 || 12 || 13 || 14 || 15 || 16
|-bgcolor="#CCFFCD"
! scope="row" | ''N''
| 0.5 || 0.7 || 1.0 || 1.4 || 2 || 2.8 || 4 || 5.6 || 8 || 11 || 16 || 22 || 32 || 45 || 64 || 90 || 128 || 180 || 256
|-
! scope="row" | calculated
| 0.5 || 0.707... || 1.0 || 1.414... || 2.0 || 2.828... || 4.0 || 5.657... || 8.0 || 11.31... || 16.0 || 22.62... || 32.0 || 45.25... || 64.0 || 90.51... || 128.0 || 181.02... || 256.0
|}

==== Typical one-half-stop f-number scale ====
{|class="wikitable" style="text-align:center"
! scope="row" | AV
| −1 || −{{frac|2}} || 0 || {{frac|2}} || 1 || {{frac|1|1|2}} || 2 || {{frac|2|1|2}} || 3 || {{frac|3|1|2}} || 4 || {{frac|4|1|2}} || 5 || {{frac|5|1|2}} || 6 || {{frac|6|1|2}} || 7 || {{frac|7|1|2}} || 8 || {{frac|8|1|2}} || 9 || {{frac|9|1|2}} || 10 || {{frac|10|1|2}} || 11 || {{frac|11|1|2}} || 12 || {{frac|12|1|2}} || 13 || {{frac|13|1|2}} || 14
|-bgcolor="#FFFFCC"
! scope="row" | ''N''
|style="background:#CCFFCC;"| 0.7 || 0.8 ||style="background:#CCFFCC;"| 1.0 || 1.2 ||style="background:#CCFFCC;"| 1.4 || 1.7 ||style="background:#CCFFCC;"| 2 || 2.4 ||style="background:#CCFFCC;"| 2.8 || 3.3 ||style="background:#CCFFCC;"| 4 || 4.8 ||style="background:#CCFFCC;"| 5.6 || 6.7 ||style="background:#CCFFCC;"| 8 || 9.5 ||style="background:#CCFFCC;"| 11 || 13 ||style="background:#CCFFCC;"| 16 || 19 ||style="background:#CCFFCC;"| 22 || 27 ||style="background:#CCFFCC;"| 32 || 38 ||style="background:#CCFFCC;"| 45 || 54 ||style="background:#CCFFCC;"| 64 || 76 ||style="background:#CCFFCC;"| 90 || 107 ||style="background:#CCFFCC;"| 128
|}

==== Typical one-third-stop f-number scale ====
{|class="wikitable" style="text-align:center"
! scope="row" | AV
| −1 || −{{frac|2|3}} || −{{frac|3}} || 0 || {{frac|3}} || {{frac|2|3}} || 1 || {{frac|1|1|3}} || {{frac|1|2|3}} || 2 || {{frac|2|1|3}} || {{frac|2|2|3}} || 3 || {{frac|3|1|3}} || {{frac|3|2|3}} || 4 || {{frac|4|1|3}} || {{frac|4|2|3}} || 5 || {{frac|5|1|3}} || {{frac|5|2|3}} || 6 || {{frac|6|1|3}} || {{frac|6|2|3}} || 7 || {{frac|7|1|3}} || {{frac|7|2|3}} || 8 || {{frac|8|1|3}} || {{frac|8|2|3}} || 9 || {{frac|9|1|3}} || {{frac|9|2|3}} || 10 || {{frac|10|1|3}} || {{frac|10|2|3}} || 11 || {{frac|11|1|3}} || {{frac|11|2|3}} || 12 || {{frac|12|1|3}} || {{frac|12|2|3}} || 13
|-bgcolor="#e5d1cb"
! scope="row" | ''N''
|style="background:#CCFFCC;"| 0.7 || 0.8 || 0.9 ||style="background:#CCFFCC;"| 1.0 || 1.1 || 1.2 ||style="background:#CCFFCC;"| 1.4 || 1.6 || 1.8 ||style="background:#CCFFCC;"| 2 || 2.2 || 2.5 ||style="background:#CCFFCC;"| 2.8 || 3.2 || 3.5 ||style="background:#CCFFCC;"| 4 || 4.5 || 5.0 ||style="background:#CCFFCC;"| 5.6 || 6.3 || 7.1 ||style="background:#CCFFCC;"| 8 || 9 || 10 || style="background:#CCFFCC;"|11 || 13 || 14 ||style="background:#CCFFCC;"| 16 || 18 || 20 ||style="background:#CCFFCC;"| 22 || 25 || 29 ||style="background:#CCFFCC;"| 32 || 36 || 40 ||style="background:#CCFFCC;"| 45 || 51 || 57 ||style="background:#CCFFCC;"| 64 || 72 || 80 ||style="background:#CCFFCC;"| 90
|}

Sometimes the same number is included on several scales; for example, an aperture of {{f/|1.2}} may be used in either a half-stop<ref>
{{cite book
 | url = https://books.google.com/books?id=YjAzP4i1oFcC&pg=PA136
 | title = Set lighting technician's handbook: film lighting equipment, practice, and electrical distribution
 | author = Harry C. Box
 | edition = 3rd
 | publisher = Focal Press
 | year = 2003
 | isbn = 978-0-240-80495-8
 }}</ref>
or a one-third-stop system;<ref>
{{cite book
 | url = https://books.google.com/books?id=DvYMl-s1_9YC&pg=PA19
 | title = Underwater photography
 | author = Paul Kay
 | publisher = Guild of Master Craftsman
 | year = 2003
 | isbn = 978-1-86108-322-7
 }}</ref>
sometimes {{f/|1.3}} and {{f/|3.2}} and other differences are used for the one-third stop scale.<ref>
{{cite book
 | url = https://books.google.com/books?id=IWkpoJKM_ucC&pg=PA145
 | title = Manual for cinematographers
 | author = David W. Samuelson
 | edition = 2nd
 | publisher = Focal Press
 | year = 1998
 | isbn = 978-0-240-51480-2
 }}</ref>

==== Typical one-quarter-stop f-number scale ====
{|class="wikitable" style="text-align:center"
! scope="row" | AV
| 0 || {{frac|4}} || {{frac|2}} || {{frac|3|4}} || 1 || {{frac|1|1|4}} || {{frac|1|1|2}} || {{frac|1|3|4}} || 2 || {{frac|2|1|4}} || {{frac|2|1|2}} || {{frac|2|3|4}} || 3 || {{frac|3|1|4}} || {{frac|3|1|2}} || {{frac|3|3|4}} || 4 || {{frac|4|1|4}} || {{frac|4|1|2}} || {{frac|4|3|4}} || 5 
|-bgcolor="#5D8AA8"
! scope="row" | ''N''
|style="background:#CCFFCC;"| 1.0 || 1.1 ||style="background:#FFFFCC;"| 1.2 || 1.3 ||style="background:#CCFFCC;"| 1.4 || 1.5 ||style="background:#FFFFCC;"| 1.7 || 1.8 ||style="background:#CCFFCC;"| 2 || 2.2 ||style="background:#FFFFCC;"| 2.4 || 2.6 ||style="background:#CCFFCC;"| 2.8 || 3.1 ||style="background:#FFFFCC;"| 3.3 || 3.7 ||style="background:#CCFFCC;"| 4 || 4.4 ||style="background:#FFFFCC;"| 4.8 || 5.2 ||style="background:#CCFFCC;"| 5.6
|}
{|class="wikitable" style="text-align:center"
! scope="row" | AV
| 5 || {{frac|5|1|4}} || {{frac|5|1|2}} || {{frac|5|3|4}} || 6 || {{frac|6|1|4}} || {{frac|6|1|2}} || {{frac|6|3|4}} || 7 || {{frac|7|1|4}} || {{frac|7|1|2}} || {{frac|7|3|4}} || 8 || {{frac|8|1|4}} || {{frac|8|1|2}} || {{frac|8|3|4}} || 9 || {{frac|9|1|4}} || {{frac|9|1|2}} || {{frac|9|3|4}} || 10
|-bgcolor="#5D8AA8"
! scope="row" | ''N''
|style="background:#CCFFCC;"| 5.6 || 6.2 ||style="background:#FFFFCC;"| 6.7 || 7.3 ||style="background:#CCFFCC;"| 8 || 8.7 ||style="background:#FFFFCC;"| 9.5 || 10 ||style="background:#CCFFCC;"| 11 || 12 ||style="background:#FFFFCC;"| 14 || 15 ||style="background:#CCFFCC;"| 16 || 17 ||style="background:#FFFFCC;"| 19 || 21 ||style="background:#CCFFCC;"| 22 || 25 ||style="background:#FFFFCC;"| 27 || 29 ||style="background:#CCFFCC;"| 32
|}

=== H-stop ===
<!-- This section header is used in redirects -->
An '''H-stop''' (for hole, by convention written with capital letter H) is an f-number equivalent for effective exposure based on the area covered by the holes in the [[diffusion disc]]s or [[sieve aperture]] found in [[Rodenstock Imagon]] lenses.

=== T-stop ===
<!-- This section header is used in redirects -->
A '''T-stop''' (for transmission stops, by convention written with capital letter T) is an f-number adjusted to account for light transmission efficiency (''[[transmittance]]''). A lens with a T-stop of {{mvar|N}} projects an image of the same brightness as an ideal lens with 100% transmittance and an f-number of {{mvar|N}}. A particular lens's T-stop, {{mvar|T}}, is given by dividing the f-number by the square root of the transmittance of that lens:
<math display=block>T = \frac{N}{\sqrt{\text{transmittance}}}.</math>
For example, an {{f/|2.0}} lens with transmittance of 75% has a T-stop of 2.3:
<math display=block>T = \frac{2.0}{\sqrt{0.75}} = 2.309...</math>
Since real lenses have transmittances of less than 100%, a lens's T-stop number is always greater than its f-number.<ref>[https://www.dxomark.com/glossary/transmission-light-transmission/ Transmission, light transmission] {{Webarchive|url=https://web.archive.org/web/20210508111318/https://www.dxomark.com/glossary/transmission-light-transmission/ |date=2021-05-08  }}, DxOMark</ref>

With 8% loss per air-glass surface on lenses without coating, [[History of photographic lens design#Anti-reflection coating|multicoating]] of lenses is the key in lens design to decrease transmittance losses of lenses. Some reviews of lenses do measure the T-stop or transmission rate in their benchmarks.<ref>[https://www.dxomark.com/sigma-85mm-f1-4-art-lens-review-new-benchmark/ Sigma 85mm F1.4 Art lens review: New benchmark] {{Webarchive|url=https://web.archive.org/web/20180104073126/https://www.dxomark.com/sigma-85mm-f1-4-art-lens-review-new-benchmark/ |date=2018-01-04  }}, DxOMark</ref><ref>[https://www.lenstip.com/129.1-article-Colour_rendering_in_binoculars_and_lenses.html Colour rendering in binoculars and lenses - Colours and transmission] {{Webarchive|url=https://web.archive.org/web/20180104013937/https://www.lenstip.com/129.1-article-Colour_rendering_in_binoculars_and_lenses.html |date=2018-01-04  }}, LensTip.com</ref> T-stops are sometimes used instead of f-numbers to more accurately determine exposure, particularly when using external [[light meter]]s.<ref name=KMPCF>{{cite web |publisher=[[Eastman Kodak]] |url=http://www.kodak.com/US/en/motion/support/h2/intro01P.shtml |title=Kodak Motion Picture Camera Films |date= November 2000 |access-date=2 September 2007 |archive-url=https://web.archive.org/web/20021002095739/http://www.kodak.com/US/en/motion/support/h2/intro01P.shtml |archive-date=2002-10-02}}</ref> Lens transmittances of 60%–95% are typical.<ref>{{Cite web |url=http://forums.dpreview.com/forums/post/33785655 |title=Marianne Oelund, "Lens T-stops", dpreview.com, 2009 |access-date=2013-01-11  |archive-date=2012-11-10  |archive-url=https://web.archive.org/web/20121110221724/http://forums.dpreview.com/forums/post/33785655 |url-status=live }}</ref> T-stops are often used in cinematography, where many images are seen in rapid succession and even small changes in exposure will be noticeable. Cinema camera lenses are typically calibrated in T-stops instead of f-numbers.<ref name=KMPCF/> In still photography, without the need for rigorous consistency of all lenses and cameras used, slight differences in exposure are less important; however, T-stops are still used in some kinds of special-purpose lenses such as [[Smooth Trans Focus]] lenses by [[Minolta]] and [[Sony]].

=== ASA/ISO numbers ===
[[Photographic film]]'s and electronic camera sensor's [[photosensitivity|sensitivity to light]] is often specified using [[Film speed|ASA/ISO numbers]]. Both systems have a linear number where a doubling of sensitivity is represented by a doubling of the number, and a logarithmic number. In the ISO system, a 3° increase in the logarithmic number corresponds approximately to a doubling of sensitivity. Doubling or halving the sensitivity is equal to a difference of one T-stop in terms of light transmittance.

=== Gain ===
[[File:Panasonic_Iris-Gain_relationship.png|thumb|300px|right|Iris/gain relationship on Panasonic camcorders as described in the HC-V785 operating manual]]
Most electronic cameras allow the user to adjust the amplification of the signal coming from the image sensor. This amplification is usually called '''[[Gain (electronics)|gain]]''' and is measured in decibels. A {{val|6|u=dB}} of gain is roughly equivalent to one T-stop in terms of light transmittance. Many camcorders have a unified control over the lens f-number and gain. In this case, starting from (arbitrarily defined) zero gain and a fully open iris, one can either increase the f-number by reducing the iris size while gain remains zero, or increase the gain while the iris remains fully open.

=== Sunny 16 rule ===
An example of the use of f-numbers in photography is the ''[[sunny 16 rule]]'': an approximately correct exposure will be obtained on a sunny day by using an aperture of {{f/|16}} and the shutter speed closest to the [[Multiplicative inverse|reciprocal]] of the ISO speed of the film; for example, using ISO 200 film, an aperture of {{f/|16}} and a shutter speed of {{frac|200}} second. The f-number may then be adjusted downwards for situations with lower light. Selecting a lower f-number is "opening up" the lens. Selecting a higher f-number is "closing" or "stopping down" the lens.