photographic lens apertures

and f-stops

>See also: Uniform system of lens apertures and T-stops.

Almost all consumer lenses have iris diaphragms. Changing the size of the hole made by the diaphragm adjusts exposure. Currently this adjustment is almost always calibrated in f-stops or f-numbers, which, roughly speaking, are the diameter of the glass at the front of the lens divided by the diameter of the hole made by the iris diaphragm. The smaller the f-number, the more light will be admitted. The great advantage of f-stops is that they apply equally to lenses of any focal length; f/8 at ยน⁄50th of a second will produce the same exposure with a 24mm lens as it will with a 200mm lens.

Because shutter speed scales are chosen so that the duration of every shutter speed is either twice or half the durations of the settings next to it, it is convenient if adjacent “whole stops” (the marked f-stops) also represent a doubling or halving of the amount of light reaching the film. That way a photographer who increases the shutter speed by one click can compensate by opening the aperture by one click. To double the amount of light passing through the lens, the area of the aperture must double, and for that the new diameter of the aperture must be the square root of 2 (1.414…) times the old diameter, because the area of a circle varies as the square of its radius.

With the steps defined, a set point must be chosen to establish a scale. After World War II, standards groups decided the set point would be f/2. An earlier standard sequence, (3.2, 4.5,…) was often used in continental Europe before World War II.

All the f-stops that aren't a multiple of 2 are rounded off, which leads to a curious effect. F/11, for example, would be f/11.3 if the calculation were carried out to one more decimal place. Two stops farther on, f/22 would be f/22.6, which rounds off to 23. But that spoils the instructive pattern of the numbers doubling every second stop. As a result, f-stop numbers are conventional, not calculated.

The table below shows, in the first four lines, conventional f-numbers in quarter stops. On each line, a number differs from those next to it on the same line by a whole stop, and from those next above and below it by a quarter stop. The final three lines depict the third-of-a-stop f-numbers. Numbers in boldface are those that differ from the calculated values.

By quarter stops

0.5···0.71···1···1.4···2···2.8···4···5.6···8···11···16···22···32···45···64
·0.55···0.77···1.1···1.5···2.2···3···4.4···6.2···8.7···12···17···25···35···49···
··0.59···0.84···1.1···1.6···2.3···3.3···4.7···6.6···9.5···13···19···26···38···54··
···0.65···0.92···1.3····1.8····2.6···3.8···5.2···7.3···10.4···15···21···29···41···59·

By one-third stops

0.5··0.71···1··1.4··2··2.8··4··5.6··8··11··16··22··32··45··64·
·0.56··0.79··1.1··1.5··2.2··3.1··4.4··6.3···8.9···12··17··25··36··51··
··0.63··0.89··1.2··1.7··2.5··3.5··5··7.1···10··14··20··28··40··57·

A lens has its maximum possible resolution at its widest aperture, but in practice, as a rule of thumb a lens is sharpest about 2 whole stops below its widest aperture.

ANSI PH3.29-1979 (R1989)
Measuring Apertures and Related Quantities Pertaining to Photographic Objectives and Projection Lenses.

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