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F-number

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 Title: F-number Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

F-number

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

In

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

/16 and a shutter speed of 1/200 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. f An example of the use of f-numbers in photography is the

Sunny 16 rule

Lens transmittances of 60%–90% are typical,[7] so T-stops are sometimes used instead of f-numbers to more accurately determine exposure, particularly when using external light meters.[8] 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.

Since real lenses have transmittances of less than 100%, a lens's T-stop is always greater than its f-number.[6]

T = \frac{2.0}{\sqrt{0.75}} = 2.309...

For example, an f/2.0 lens with transmittance of 75% has a T-stop of 2.3:

T = \frac{f}{\sqrt{\text{transmittance}}}.

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 N projects an image of the same brightness as an ideal lens with 100% transmittance and an f-number of N. A particular lens' T-stop, T, is given by dividing the f-number by the square root of the transmittance of that lens:

T-stop

A 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 discs or sieve aperture found in Rodenstock Imagon lenses.

H-stop

Sometimes the same number is included on several scales; for example, f/1.2 may be used in either a half-stop[3] or a one-third-stop system;[4] sometimes f/1.3 and f/3.2 and other differences are used for the one-third stop scale.[5]

 AV f/N Minolta 5 5.25 5.5 5.75 6 6.25 6.5 6.75 7 7.25 7.5 7.75 8 8.25 8.5 8.75 9 9.25 9.5 9.75 10 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 5.6 5.61 5.62 5.63 8 8.01 8.02 8.03 110 111 112 113 160 161 162 163 220 221 222 223 320
 AV f/N Minolta 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 4.75 5 1 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 3.4 3.7 4 4.4 4.8 5.2 5.6 1 1.01 1.02 1.03 1.4 1.41 1.42 1.43 2 2.01 2.02 2.03 2.8 2.81 2.82 2.83 4 4.01 4.02 4.03 5.6

Typical one-quarter-stop f-number scale

 AV f/N −1 −0.7 −0.3 0 0.3 0.7 1 1.3 1.7 2 2.3 2.7 3 3.3 3.7 4 4.3 4.7 5 5.3 5.7 6 6.3 6.7 7 7.3 7.7 8 8.3 8.7 9 9.3 9.7 10 10.3 10.7 11 11.3 11.7 12 12.3 12.7 13 0.7 0.8 0.9 1 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 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

Typical one-third-stop f-number scale

 AV f/N −1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 0.7 0.8 1 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-half-stop f-number scale

 AV f/N calculated −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0.5 0.7 1 1.4 2 2.8 4 5.6 8 11 16 22 32 45 64 90 128 180 256 0.5 0.707… 1 1.414… 2 2.828… 4 5.657… 8 11.31… 16 22.62… 32 45.25… 64 90.51… 128 181.02… 256

/N = \sqrt{2^{AV}}

f

Including aperture value AV:

Standard full-stop f-number scale

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

In practice the maximum aperture of a lens is often not an integral power of \scriptstyle \sqrt{2} (i.e., \scriptstyle \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 \scriptstyle \sqrt{2}.

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

... 16/13°, 20/14°, 25/15°, 32/16°, 40/17°, 50/18°, 64/19°, 80/20°, 100/21°, 125/22°...

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

20/3×0.5, 21/3×0.5, 22/3×0.5, 23/3×0.5, 24/3×0.5 etc.

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

20/2×0.5, 21/2×0.5, 22/2×0.5, 23/2×0.5, 24/2×0.5 etc.

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

20×0.5, 21×0.5, 22×0.5, 23×0.5, 24×0.5 etc.

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

f/4.5, f/5, f/5.6, f/6.3, f/7.1, f/8, etc.

/4. The next few f-stops in this sequence are: f 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

Most old cameras had a continuously variable aperture scale, 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.

Fractional stops

Photographers sometimes express other 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 "half a stop".

In the same way as one f-stop corresponds to a factor of two in light intensity, shutter speeds 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. This is less true for extremely long or short exposures, where we have 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.

f/1 = {f/}(\sqrt{2})^0 , f/1.4 = {f/}(\sqrt{2})^1 , f/2 = {f/}(\sqrt{2})^2 , f/2.8 = {f/}(\sqrt{2})^3 ...

/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 Most modern lenses use a standard f-stop scale, which is an approximately

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 usually 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/\scriptstyle \sqrt{2} or about 0.7071, and hence a halving of the area of the pupil.

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.

A 35 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/2.0 to f/22.
A /0.95 f

Stops, f-stop conventions, and exposure

A T-stop is an f-number adjusted to account for light transmission efficiency.

A 100 mm focal length f/4 lens has an entrance pupil diameter of 25 mm. A 200 mm focal length f/4 lens has an entrance pupil diameter of 50 mm. The 200 mm lens's entrance pupil has four times the area of the 100 mm lens's entrance pupil, and thus collects four times as much light from each object in the lens's field of view. But compared to the 100 mm lens, the 200 mm lens 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.

Most lenses have an adjustable diaphragm, which changes the size of the aperture stop and thus the entrance pupil size. 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. Doubling the f-number decreases the relative brightness by a factor of four. To maintain the same photographic exposure when doubling the f-number, the exposure time would need to be four times as long.

/2. f is the f where

N = \frac{f}{D} \

The f-number N or f# is given by:

Contents

• Notation 1
• Stops, f-stop conventions, and exposure 2
• Fractional stops 2.1
• Standard full-stop f-number scale 2.1.1
• Typical one-half-stop f-number scale 2.1.2
• Typical one-third-stop f-number scale 2.1.3
• Typical one-quarter-stop f-number scale 2.1.4
• H-stop 2.2
• T-stop 2.3
• Sunny 16 rule 2.4
• Effects on image sharpness 3
• Human eye 4
• Focal ratio in telescopes 5
• Working f-number 6
• History 7
• Origins of relative aperture 7.1
• Aperture numbering systems 7.2
• Typographical standardization 7.3
• References 9