f-number

For other uses, seeF-number (disambiguation).

Diagram of decreasingapertures,that is, increasing f-numbers, in one-stop increments; each aperture has half the light-gathering area of the previous one.

Anf-numberis a measure of the light-gathering ability of an optical system such as acamera lens.It is calculated by dividing the system'sfocal lengthby the diameter of theentrance pupil( "clearaperture").The f-number is also known as thefocal ratio,f-ratio,orf-stop,and it is key in determining thedepth of field,diffraction,andexposureof a photograph.The f-number isdimensionlessand is usually expressed using a lower-casehooked fwith the formatf/N,whereNis the f-number.

The f-number is also known as theinverse relative aperture,because it is theinverseof therelative aperture,defined as the aperture diameter divided by focal length.The relative aperture indicates how much light can pass through the lens at a given focal length. A lower f-number means a larger relative aperture and more light entering the system, while a higher f-number means a smaller relative aperture and less light entering the system. The f-number is related to thenumerical aperture(NA) of the system, which measures the range of angles over which light can enter or exit the system. The numerical aperture takes into account therefractive indexof the medium in which the system is working, while the f-number does not.

Notation

The f-numberNis given by:

$$N={\frac {f}{D}}\$$

wherefis thefocal length,andDis the diameter of the entrance pupil (effective aperture). It is customary to write f-numbers preceded by "f/",which forms a mathematical expression of the entrance pupil's diameter in terms offandN.For example, if alens'sfocal length were100 mmand its entrance pupil's diameter were50 mm,the f-number would be 2. This would be expressed as"f/2"in a lens system. The aperture diameter would be equal tof/2.

Most lenses have an adjustablediaphragm,which changes the size of theaperture stopand thus the entrance pupil size. This allows the user to vary the f-number as needed. The entrance pupil diameter is not necessarily equal to the aperture stop diameter, because of the magnifying effect of lens elements in front of the aperture.

Ignoring differences in light transmission efficiency, a lens with a greater f-number projects darker images. The brightness of the projected image (illuminance) relative to the brightness of the scene in the lens's field of view (luminance) decreases with the square of the f-number. A100 mmfocal lengthf/4lens has an entrance pupil diameter of25 mm.A100 mmfocal lengthf/2lens has an entrance pupil diameter of50 mm.Since the area is proportional to the square of the pupil diameter,the amount of light admitted by thef/2lens is four times that of thef/4lens. To obtain the samephotographic exposure,the exposure time must be reduced by a factor of four.

A200 mmfocal lengthf/4lens has an entrance pupil diameter of50 mm.The200 mmlens's entrance pupil has four times the area of the100 mmf/4lens's entrance pupil, and thus collects four times as much light from each object in the lens's field of view. But compared to the100 mmlens, the200 mmlens projects an image of each object twice as high and twice as wide, covering four times the area, and so both lenses produce the same illuminance at the focal plane when imaging a scene of a given luminance.

Stops, f-stop conventions, and exposure

ACanon 7mounted with a50 mmlens capable off/0.95

A35 mmlens set tof/11,as indicated by the white dot above the f-stop scale on the aperture ring. This lens has an aperture range off/2tof/22.

The wordstopis 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. Theaperture stopis the aperture setting that limits the brightness of the image by restricting the input pupil size, while afield stopis 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 aunitused 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 asf-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/√2or 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 approximatelygeometric sequenceof numbers that corresponds to the sequence of thepowersof thesquare 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:

$$f/1={\frac {f}{({\sqrt {2}})^{0}}},\ f/1.4={\frac {f}{({\sqrt {2}})^{1}}},\ f/2={\frac {f}{({\sqrt {2}})^{2}}},\ f/2.8={\frac {f}{({\sqrt {2}})^{3}}},\ \ldots$$ In the same way as one f-stop corresponds to a factor of two in light intensity,shutter speedsare 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 ofreciprocity.This is less true for extremely long or short exposures, where there isreciprocity 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 otherexposureratios in terms of 'stops'. Ignoring the f-number markings, the f-stops make alogarithmic scaleof 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

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 aniris 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 (1⁄3EV) are the most common, since this matches the ISO system offilm speeds.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 thanf/2.8isf/3.2,two-thirds smaller isf/3.5,and one whole stop smaller isf/4.The next few f-stops in this sequence are:

$$f/4.5,\ f/5,\ f/5.6,\ f/6.3,\ f/7.1,\ f/8,\ \ldots$$

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

$$({\sqrt {2}})^{0},\ ({\sqrt {2}})^{1},\ ({\sqrt {2}})^{2},\ ({\sqrt {2}})^{3},\ ({\sqrt {2}})^{4},\ \ldots$$

The steps in a half stop (1⁄2EV) series would be

$$({\sqrt {2}})^{\frac {0}{2}},\ ({\sqrt {2}})^{\frac {1}{2}},\ ({\sqrt {2}})^{\frac {2}{2}},\ ({\sqrt {2}})^{\frac {3}{2}},\ ({\sqrt {2}})^{\frac {4}{2}},\ \ldots$$

The steps in a third stop (1⁄3EV) series would be

$$({\sqrt {2}})^{\frac {0}{3}},\ ({\sqrt {2}})^{\frac {1}{3}},\ ({\sqrt {2}})^{\frac {2}{3}},\ ({\sqrt {2}})^{\frac {3}{3}},\ ({\sqrt {2}})^{\frac {4}{3}},\ \ldots$$

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

$$\ldots 16/13^{\circ },\ 20/14^{\circ },\ 25/15^{\circ },\ 32/16^{\circ },\ 40/17^{\circ },\ 50/18^{\circ },\ 64/19^{\circ },\ 80/20^{\circ },\ 100/21^{\circ },\ 125/22^{\circ },\ \ldots$$

while shutter speeds in reciprocal seconds have a few conventional differences in their numbers (1⁄15,1⁄30,and1⁄60second instead of1⁄16,1⁄32,and1⁄64).

In practice the maximum aperture of a lens is often not anintegralpower of√2(i.e.,√2to the power of a whole number), in which case it is usually a half or third stop above or below an integral power of√2.

Modern electronically controlled interchangeable lenses, such as those used for SLR cameras, have f-stops specified internally in1⁄8-stop increments, so the cameras'1⁄3-stop settings are approximated by the nearest1⁄8-stop setting in the lens.

Standard full-stop f-number scale

Includingaperture valueAV: $$N={\sqrt {2^{\text{AV}}}}$$

Conventional and calculated f-numbers, full-stop series:

AV	−2	−1	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
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
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

AV	−1	−1⁄2	0	1⁄2	1	1+1⁄2	2	2+1⁄2	3	3+1⁄2	4	4+1⁄2	5	5+1⁄2	6	6+1⁄2	7	7+1⁄2	8	8+1⁄2	9	9+1⁄2	10	10+1⁄2	11	11+1⁄2	12	12+1⁄2	13	13+1⁄2	14
N	0.7	0.8	1.0	1.2	1.4	1.7	2	2.4	2.8	3.3	4	4.8	5.6	6.7	8	9.5	11	13	16	19	22	27	32	38	45	54	64	76	90	107	128

Typical one-third-stop f-number scale

AV	−1	−2⁄3	−1⁄3	0	1⁄3	2⁄3	1	1+1⁄3	1+2⁄3	2	2+1⁄3	2+2⁄3	3	3+1⁄3	3+2⁄3	4	4+1⁄3	4+2⁄3	5	5+1⁄3	5+2⁄3	6	6+1⁄3	6+2⁄3	7	7+1⁄3	7+2⁄3	8	8+1⁄3	8+2⁄3	9	9+1⁄3	9+2⁄3	10	10+1⁄3	10+2⁄3	11	11+1⁄3	11+2⁄3	12	12+1⁄3	12+2⁄3	13
N	0.7	0.8	0.9	1.0	1.1	1.2	1.4	1.6	1.8	2	2.2	2.5	2.8	3.2	3.5	4	4.5	5.0	5.6	6.3	7.1	8	9	10	11	13	14	16	18	20	22	25	29	32	36	40	45	51	57	64	72	80	90

Sometimes the same number is included on several scales; for example, an aperture off/1.2may be used in either a half-stop or a one-third-stop system; sometimesf/1.3andf/3.2and other differences are used for the one-third stop scale.

Typical one-quarter-stop f-number scale

AV	0	1⁄4	1⁄2	3⁄4	1	1+1⁄4	1+1⁄2	1+3⁄4	2	2+1⁄4	2+1⁄2	2+3⁄4	3	3+1⁄4	3+1⁄2	3+3⁄4	4	4+1⁄4	4+1⁄2	4+3⁄4	5
N	1.0	1.1	1.2	1.3	1.4	1.5	1.7	1.8	2	2.2	2.4	2.6	2.8	3.1	3.3	3.7	4	4.4	4.8	5.2	5.6

AV	5	5+1⁄4	5+1⁄2	5+3⁄4	6	6+1⁄4	6+1⁄2	6+3⁄4	7	7+1⁄4	7+1⁄2	7+3⁄4	8	8+1⁄4	8+1⁄2	8+3⁄4	9	9+1⁄4	9+1⁄2	9+3⁄4	10
N	5.6	6.2	6.7	7.3	8	8.7	9.5	10	11	12	14	15	16	17	19	21	22	25	27	29	32

H-stop

AnH-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 thediffusion discsorsieve aperturefound inRodenstock Imagonlenses.

T-stop

AT-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 ofNprojects an image of the same brightness as an ideal lens with 100% transmittance and an f-number ofN.A particular lens's T-stop,T,is given by dividing the f-number by the square root of the transmittance of that lens: $$T={\frac {N}{\sqrt {\text{transmittance}}}}.$$ For example, anf/2.0lens with transmittance of 75% has a T-stop of 2.3: $$T={\frac {2.0}{\sqrt {0.75}}}=2.309...$$ Since real lenses have transmittances of less than 100%, a lens's T-stop number is always greater than its f-number.

With 8% loss per air-glass surface on lenses without coating,multicoatingof 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.T-stops are sometimes used instead of f-numbers to more accurately determine exposure, particularly when using externallight meters.Lens transmittances of 60%–95% are typical.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.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 asSmooth Trans Focuslenses byMinoltaandSony.

ASA/ISO numbers

Photographic film's and electronic camera sensor'ssensitivity to lightis often specified usingASA/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 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

Iris/Gain relationship on Panasonic camcorders as described in the HC-V785 operating manual

Most electronic cameras allow to amplify the signal coming from the pickup element. This amplification is usually calledgainand is measured in decibels. Every6 dBof gain is 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 zero gain and fully open iris, one can either increase f-number by reducing the iris size while gain remains zero, or one can increase gain while iris remains fully open.

Sunny 16 rule

An example of the use of f-numbers in photography is thesunny 16 rule:an approximately correct exposure will be obtained on a sunny day by using an aperture off/16and the shutter speed closest to thereciprocalof the ISO speed of the film; for example, using ISO 200 film, an aperture off/16and a shutter speed of1⁄200second. 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.

Effects on image sharpness

Comparison off/32(top-left half) andf/5(bottom-right half)

Shallow focus with a wide open lens

Depth of fieldincreases with f-number, as illustrated in the image here. This means that photographs taken with a low f-number (large aperture) will tend to have subjects at one distance in focus, with the rest of the image (nearer and farther elements) out of focus. This is frequently used fornature photographyandportraiturebecause background blur (the aesthetic quality known as 'bokeh') can be aesthetically pleasing and puts the viewer's focus on the main subject in the foreground. Thedepth of fieldof an image produced at a given f-number is dependent on other parameters as well, including thefocal length,the subject distance, and theformatof the film or sensor used to capture the image. Depth of field can be described as depending on just angle of view, subject distance, andentrance pupildiameter (as invon Rohr's method). As a result, smaller formats will have a deeper field than larger formats at the same f-number for the same distance of focus and sameangle of viewsince a smaller format requires a shorter focal length (wider angle lens) to produce the same angle of view, and depth of field increases with shorter focal lengths. Therefore, reduced–depth-of-field effects will require smaller f-numbers (and thus potentially more difficult or complex optics) when using small-format cameras than when using larger-format cameras.

Beyond focus, image sharpness is related to f-number through two different optical effects:aberration,due to imperfect lens design, anddiffractionwhich is due to the wave nature of light.The blur-optimal f-stop varies with the lens design. For modern standard lenses having 6 or 7 elements, thesharpestimage is often obtained aroundf/5.6–f/8,while for older standard lenses having only 4 elements (Tessar formula) stopping tof/11will give the sharpest image.The larger number of elements in modern lenses allow the designer to compensate for aberrations, allowing the lens to give better pictures at lower f-numbers. At small apertures, depth of field and aberrations are improved, butdiffractioncreates more spreading of the light, causing blur.

Light falloff is also sensitive to f-stop. Many wide-angle lenses will show a significant light falloff (vignetting) at the edges for large apertures.

Photojournalistshave a saying, "f/8and be there",meaning that being on the scene is more important than worrying about technical details. Practically,f/8(in 35 mm and larger formats) allows adequate depth of field and sufficient lens speed for a decent base exposure in most daylight situations.

Human eye

Computing the f-number of thehuman eyeinvolves computing the physical aperture and focal length of the eye. The pupil can be as large as 6–7 mm wide open, which translates into the maximal physical aperture.

The f-number of the human eye varies from aboutf/8.3in a very brightly lit place to aboutf/2.1in the dark.Computing the focal length requires that the light-refracting properties of the liquids in the eye be taken into account. Treating the eye as an ordinary air-filled camera and lens results in an incorrect focal length and f-number.

Focal ratio in telescopes

Diagram of thefocal ratioof a simple optical system where$f$is thefocal lengthand$D$is the diameter of theobjective

In astronomy, the f-number is commonly referred to as thefocal ratio(orf-ratio) notated as$N$.It is still defined as thefocal length$f$of anobjectivedivided by its diameter$D$or by the diameter of anaperturestop in the system:

$$N={\frac {f}{D}}\quad {\xrightarrow {\times D}}\quad f=ND$$

Even though the principles of focal ratio are always the same, the application to which the principle is put can differ. Inphotographythe focal ratio varies the focal-plane illuminance (or optical power per unit area in the image) and is used to control variables such asdepth of field.When using anoptical telescopein astronomy, there is no depth of field issue, and the brightness of stellar point sources in terms of total optical power (not divided by area) is a function of absolute aperture area only, independent of focal length. The focal length controls thefield of viewof the instrument and the scale of the image that is presented at the focal plane to aneyepiece,film plate, orCCD.

For example, theSOAR4-meter telescope has a small field of view (aboutf/16) which is useful for stellar studies. TheLSST8.4 m telescope, which will cover the entire sky every three days, has a very large field of view. Its short 10.3 m focal length (f/1.2) is made possible by an error correction system which includes secondary and tertiary mirrors, a three element refractive system and active mounting and optics.

Camera equation (G#)

The camera equation, or G#, is the ratio of theradiancereaching the camera sensor to theirradianceon the focal plane of thecamera lens:

$$G\#={\frac {1+4N^{2}}{\tau \pi }}\,,$$

whereτis the transmission coefficient of the lens, and the units are in inversesteradians(sr⁻¹).

Working f-number

The f-number accurately describes the light-gathering ability of a lens only for objects an infinite distance away.This limitation is typically ignored in photography, where f-number is often used regardless of the distance to the object. Inoptical design,an alternative is often needed for systems where the object is not far from the lens. In these cases theworking f-numberis used. The working f-numberN_wis given by:

$$N_{w}\approx {1 \over 2\mathrm {NA} _{i}}\approx \left(1+{\frac {|m|}{P}}\right)N\,,$$

whereNis the uncorrected f-number,NA_iis the image-spacenumerical apertureof the lens,$|m|$is theabsolute valueof the lens'smagnificationfor an object a particular distance away, andPis thepupil magnification.Since the pupil magnification is seldom known it is often assumed to be 1, which is the correct value for all symmetric lenses.

In photography this means that as one focuses closer, the lens's effective aperture becomes smaller, making the exposure darker. The working f-number is often described in photography as the f-number corrected for lens extensions by abellows factor.This is of particular importance inmacro photography.

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 "1⁄24"is calculated as the ratio of 6 inches (150 mm) to1⁄4inch (6.4 mm), corresponding to anf/24f-stop:

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 a1⁄4in. 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.

In 1874,John Henry Dallmeyercalled the ratio$1/N$the "intensity ratio" of a lens:

Therapidityof a lens depends upon the relation or ratio of the aperture to the equivalent focus. To ascertain this, divide theequivalent focusby the diameter of the actualworking apertureof 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.,1⁄3is the intensity ratio.

Although he did not yet have access toErnst Abbe's theory of stops and pupils,which was made widely available bySiegfried Czapskiin 1893,Dallmeyer knew that hisworking aperturewas not the same as the physical diameter of the aperture stop:

It must be observed, however, that in order to find the realintensity 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 insertedbetweenthe 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.

This point is further emphasized by Czapski in 1893.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."

J. H. Dallmeyer's son,Thomas Rudolphus Dallmeyer,inventor of the telephoto lens, followed theintensity ratioterminology in 1899.

Aperture numbering systems

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, theUniform System(U.S.) of apertures was adopted as a standard by thePhotographic Society of Great Britainin the 1880s. Bothamley in 1891 said "The stops of all the best makers are now arranged according to this system."U.S. 16 is the same aperture asf/16,but apertures that are larger or smaller by a full stop use doubling or halving of the U.S. number, for examplef/11is U.S. 8 andf/8is U.S. 4. The exposure time required is directly proportional to the U.S. number.Eastman Kodakused 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 thef/xsystem, and the diaphragms of all modern lenses of good construction are so marked. "

Here is the situation as seen in 1899:

Piper in 1901discusses five different systems of aperture marking: the old and newZeisssystems 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 likef/8the "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 off/4,f/5.6,f/8,f/11.3,etc.The R.P.S. had changed their name and moved off of the U.S. system some time between 1895 and 1902.

Typographical standardization

Yashica-D TLRcamera front view. This is one of the few cameras that actually says "F-NUMBER" on it.

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 termf-numberappeared in books both asF numberandf/number.In modern publications, the formsf-numberandf numberare more common, though the earlier forms, as well asF-numberare still found in a few books; not uncommonly, the initial lower-casefinf-numberorf/numberis set in a hooked italic form: ƒ.

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.

The 1961ASAstandard PH2.12-1961American Standard General-Purpose Photographic Exposure Meters (Photoelectric Type)specifies that "The symbol for relative apertures shall be ƒ/ or ƒ: followed by the effective ƒ-number." They show the hooked italic 'ƒ' not only in the symbol, but also in the termf-number,which today is more commonly set in an ordinary non-italic face.

See also

• Circle of confusion
• Group f/64
• Photographic lens design
• Pinhole camera
• Preferred number

External links

• Large format photography—how to select the f-stop