What Is F-ratio

[Oliverio Gallman]

Anf-number is a measure of the light-gathering ability of an optical system such as a camera lens. It is calculated by dividing the system's focal length by the diameter of the entrance pupil ("clear aperture").[1][2][3] The f-number is also known as the focal ratio, f-ratio, or f-stop, and it is key in determining the depth of field, diffraction, and exposure of a photograph.[4] The f-number is dimensionless and is usually expressed using a lower-case hooked f with the format .mw-parser-output span.fnumber,.mw-parser-output .fnumber-fallbackdisplay:inline-block;white-space:nowrap;width:max-content.mw-parser-output span.fnumber::first-letter,.mw-parser-output .fnumber-fallback .first-letterfont-style:italic;font-family:Trebuchet MS,Candara,Georgia,Calibri,Corbel,seriff/N, where N is the f-number.

The f-number is also known as the inverse relative aperture, because it is the inverse of the relative aperture, defined as the aperture diameter divided by focal length.[5] 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 the numerical 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 the refractive index of the medium in which the system is working, while the f-number does not.

where f \displaystyle f is the focal length, and D \displaystyle D is 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 of f \displaystyle f and N.[1] For example, if a lens's focal length were 10 mm and its entrance pupil's diameter were 5 mm, the f-number would be 2. This would be expressed as "f/2" in a lens system. The aperture diameter would be equal to f / 2 \displaystyle f/2 .

Most lenses have an adjustable diaphragm, which changes the size of the aperture stop and 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. A 100 mm focal length f/4 lens has an entrance pupil diameter of 25 mm. A 100 mm focal length f/2 lens has an entrance pupil diameter of 50 mm. Since the area is proportional to the square of the pupil diameter,[6] the amount of light admitted by the f/2 lens is four times that of the f/4 lens. To obtain the same photographic exposure, the exposure time must be reduced by a factor of four.

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 f/4 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.

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.

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".

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.

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

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[7]or a one-third-stop system;[8]sometimes f/1.3 and f/3.2 and other differences are used for the one-third stop scale.[9]

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 discs or sieve aperture found in Rodenstock Imagon lenses.

Photographic film's and electronic camera sensor's sensitivity to light is often specified using 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 to a doubling of sensitivity. Doubling or halving the sensitivity is equal to a difference of one T-stop in terms of light transmittance.

Most electronic cameras allow to amplify the signal coming from the pickup element. This amplification is usually called gain and is measured in decibels. Every 6 dB of 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.

Photojournalists have a saying, "f/8 and 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.[16]

The f-number of the human eye varies from about f/8.3 in a very brightly lit place to about f/2.1 in the dark.[17] 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.

Even though the principles of focal ratio are always the same, the application to which the principle is put can differ. In photography the focal ratio varies the focal-plane illuminance (or optical power per unit area in the image) and is used to control variables such as depth of field. When using an optical telescope in 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 the field of view of the instrument and the scale of the image that is presented at the focal plane to an eyepiece, film plate, or CCD.

For example, the SOAR 4-meter telescope has a small field of view (about f/16) which is useful for stellar studies. The LSST 8.4 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.[18]

The f-number accurately describes the light-gathering ability of a lens only for objects an infinite distance away.[20] This limitation is typically ignored in photography, where f-number is often used regardless of the distance to the object. In optical design, an alternative is often needed for systems where the object is not far from the lens. In these cases the working f-number is used. The working f-number Nw is given by:[20]

where N is the uncorrected f-number, NAi is the image-space numerical aperture of the lens, m \displaystyle is the absolute value of the lens's magnification for an object a particular distance away, and P is the pupil 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 a bellows factor. This is of particular importance in macro photography.

Although he did not yet have access to Ernst Abbe's theory of stops and pupils,[23] which was made widely available by Siegfried Czapski in 1893,[24] Dallmeyer knew that his working aperture was not the same as the physical diameter of the aperture stop:

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.[22]

3a8082e126