Definition of f-stop?
It has been brought to my attention that the Court has asked what the “f”
means in f-stop. Hopefully, this might help.
Q.
What, exactly, is the meaning of the term "f-stop"?
A.
This is the number one question asked via email to F-Stop. Basically every thing that has to do
with photography can be grasped by the newcomer except for the subject of the "f-stop"(and
'reciprocity failure'... but that's another issue).
You've seen f-stops if you've ever looked at a camera lens that had them imprinted or observed
an enlarger lens. In these photos (left to right are three camera lenses: a 35mm, 6x6cm, 4x5" and
one enlarging lens).
You will notice that they all share something in common: they all have numbers which are fstop indicators. Many photographers believe these numbers to be directly related to the amount
of light that is allowed to strike the emulsion of the film and that this is the sole purpose of the fstop. Well, it isn't.
And the "f" in f/stop, what specifically is the letter about?
The f number is the ratio between the size of the aperture and the focal length of
the lens. The f "stop" is determined by taking the focal length of the lens divided
by the diameter of the aperture in millimeters. An example of this would be on a
50 mm lens where the aperture measures 25 mm in diameter, the f/stop would be
f/2. Each f/stop, regardless of the focal length, film format, etc., means that the
same measurement of light is reaching the film. Each change in f/stop indicates
either a doubling or halving of the amount of light passing through the aperture of
the lens. Therefore, f/11 is half as much as f/8, and f/5.6 is twice as much light as
f/8.
The average 35 mm camera lens will show f/stops similar to this:
2.8
4
5.6
8
11
16
22
"Stop" is a term generically used to refer to the measurement of light reaching the
film. (However, as you read further, I have a somewhat different take on all what
an f/stop is.) A one stop change is halving or doubling of light by one point
change in either f/stop, shutter speed, film speed or even light output if using
artificial lighting.
It is true, though, that as the f-stop is set to a high number (f/22, for example), less light will be
allowed to reach the film emulsion — and, likewise, if the f-stop is set to the lowest number
(f/1.2, for example) the maximum amount of light will be allowed through the lens. But this is
not the primary purpose of the f-stop. F-stops are used in lenses to resolve the sharpness of a
photographic scene. Like our own eye, the camera lens can be made to focus on a primary
subject object. The question is, with the lens opening set at a specific aperture, how much of the
scene will be in crisp focus and how much will be blurry? By adjusting the opening of the metal
iris in a lens, the photographer can specifically control how much of the scene will and will not
be in focus. This control of what is referred to as the "depth of field" of focus in a scene allows
the photographer to exercise considerable creativity.
Let's start at the beginning with a simple definition of f-stop. F-stop (Focal stop) is a terminology used
for the specific measurement of light loss or gain in relationship to lenses. One f-stop gain is equivalent
to a one hundred percent (100%) gain in light passage in a lens. One f-stop loss is equivalent to fifty
percent (50%) light loss. To help explain how we can have a 100% gain or 50% loss think of the
following scale of numbers:
1248
What is the relationship of one to two? 100% gain. The relationship of two to four? 100% gain. Four to
eight? 100% gain. On the retrospect, what is the relationship of eight to four? 50% decrease. Four to
two? 50% decrease, et cetera. This explains how we can have a 100% increase or a 50% decrease in any
factor scale.
The next step is to understand the f-stop scale. We start (under normal lens conditions) with f1.4 and go
up from there. The larger the number, the more light loss we will have within a lens. The scale is easy to
build if you remember the first two numbers of f1.4 and f2. From this point it is a matter of doubling
each number in alternating progression.
f-Stop Scale I:
f-1.4 f-2 f-2.8 f-4 f-5.6 f-8 f-11 f-16 f-22
Ok, now let's take a level of light and work it up and down the scale.... 8 foot candles (fc) at f-2 will
become 4fc at f-2.8, 2fc at f4, 1fc at f-5.6, .5fc at f-8, et cetera..... Going the opposite way, up the scale,
it's 100% gain.
Cats and owls can see in dim light better than we can, in part, because the lenses of their eyes allow in more
light. We could say the "speed" of the lenses in their eyes is faster than that of our eyes.
We define lens speed as the maximum amount of light that can pass through the lens to end up on the target.
However, it's generally not desirable to transmit the maximum amount of light through the lens, so we need a way
of governing the amount.
Like the pupil of an eye automatically adjusting to varying light levels, the iris of the camera lens controls the
amount of light passing through the lens.
Under very low light conditions, the pupils of our eyes open up almost completely to allow in maximum light.
Conversely, in bright sunlight, the pupil contracts in an effort to avoid overloading the light-sensitive rods and
cones in the back of the eye.
In the same way, the amount of light falling on the light-sensitive target of a TV camera must be controlled with
the aid of an iris in the middle of the lens (shown above on the left).
Too much light will overexpose and wash out the picture; too little will cause the loss of detail in the darker areas.
We can smoothly adjust an iris from a tiny to a large opening, and we
refer to the various specific numerical points throughout this range as
f-stops.
The "f" stands for factor. An f-stop is the ratio between the lens
opening and the lens focal length. More specifically, the f-stop equals the focal length divided by the size of the
lens opening.
f-stop = focal length / lens opening
This math explains the strange set of numbers used for f-stop designations, as well as the fact that the smaller the
f-stop number the more light the lens transmits.
That's worth repeating: the smaller the f-stop number the more light the lens transmits.
Thus:
1.4, 2.0, 2.8, 4.0, 5.6, 8, 11, 16, 22
<== more light
less light ==>
Occasionally, we see other f-stops, such as f/1.2, f/3.5, and f/4.5. These are mid-point settings between whole fstops, and on some lenses they represent the maximum aperture (speed) of the lens.
The figure at the right compares f-stop sizes.
We've noted that the speed of a lens is equal to its maximum (wide-open) f-stop. Here, f/l.4 is the speed of the
lens.
Opening the iris one f-stop (from f/22 to f/16, for example) represents a 100 percent increase in the light passing
through the lens. Conversely, "stopping down" the lens one stop (from f/16 to f/22, for example) cuts the light by
50 percent.
Put another way, when you open up one stop, you double the light going through the lens; when you stop down
one stop, you cut the amount of light going through the lens in half.
Wikipedia
Library > Reference > Wikipedia
f-number
The correct title of this article is f-number. The initial letter is capitalized due to technical
restrictions.
"F number" redirects here. For other uses, see F scale.
Diagram of decreasing apertures, that is, increasing f-numbers, in one-stop increments
In optics, the f-number (sometimes called focal ratio, f-ratio, or relative aperture[1]) of an
optical system expresses the diameter of the entrance pupil in terms of the effective focal length
of the lens. It is the quantitative measure of lens speed, an important concept in photography.
Notation
The f-number f/#, often notated as N, is given by
where f is the focal length, and D is the diameter of the entrance pupil. By convention, "f/#" is
treated as a single symbol, and specific values of f/# are written by replacing the number sign
with the value. For example, if the focal length is 16 times the pupil diameter, the f-number is
f/16, or N = 16. The greater the f-number, the less light per unit area reaches the image plane of
the system.
The literal interpretation of the f/N notation for f-number N is as an arithmetic expression for
the effective aperture diameter (input pupil diameter), the focal length divided by the f-number:
D = f / N.
The pupil diameter is proportional to the diameter of the aperture stop of the system. In a
camera, this is typically the diaphragm aperture, which can be adjusted to vary the size of the
pupil, and hence the amount of light that reaches the film or image sensor. Other types of optical
system, such as telescopes and binoculars may have a fixed aperture, but the same principle
holds: the greater the focal ratio, the fainter the images created (measuring brightness per unit
area of the image). Note that the common assumption in photography that the pupil diameter is
equal to the aperture diameter is not correct for all types of camera lens. A focal ratio of f/16
does not always mean that the physical aperture inside the camera lens has diameter equal to one
sixteenth the focal length.
Stops, f-stop conventions, and exposure
The term 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 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 one stop
meaning a factor of two, or one-half. The one-stop unit is also known as the EV (exposure
value) unit. On a camera, the f-number 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
, and hence a halving of the area of the pupil.
A 35mm 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
Modern lenses use a standard f-stop scale that corresponds to the sequence of the powers of
: 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.
The values of the ratios are rounded off to these particular conventional numbers, to make them
easy to remember and write down.
The slash indicates division. For example, f/16 means that the pupil diameter is equal to the
focal length divided by sixteen; that is, if the camera has an 80 mm lens, all the light that reaches
the film passes through a circle that is 5 mm (80 mm/16) in diameter. The location of this circle
inside the lens depends on the optical design. It may simply be the opening of the aperture stop,
or may be a magnified image of the aperture stop, formed by elements within the lens.
Shutter speeds are arranged in a similar scale, so that one stop in the shutter speed scale
corresponds to one stop in the aperture scale. 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, you
must have a shutter speed twice as fast (shutter open half as long). Alternatively, you could use a
film which is half as sensitive to light. This fundamental principle of photographic technique is
known as reciprocity.
Photographers sometimes express other exposure ratios in terms of 'stops'. If we ignore the fnumber markings, the f-stops make a logarithmic scale of exposure intensity. Given this
interpretation, you can then think of taking a half-step along this scale, to make an exposure
difference of "half a stop".
Fractional stops
Most old cameras had an aperture scale graduated in full stops but the aperture is continuously
variable allowing to select any intermediate aperture.
Click-stopped aperture became a common feature in the sixties; the aperture scale was usually
marked in full stops, but many lenses had a click between two marks, allowing a gradation of
half a 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 speeds. Half-stop steps are also seen on
some cameras. 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
f/4.5, f/5, f/5.6, f/6.3, f/7.1, f/8, etc.
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
... 16/13°, 20/14°, 25/15°, 32/16°, 40/17°, 50/18°, 64/19°, 80/20°, 100/21°, 125/22°...
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).
In practice the maximum aperture of a lens may not be an integral power of
it is usually a half or third stop above or below an integral power of
, in which case
.
Modern electronically-controlled interchangeable lenses, such as those from Canon and Sigma
for SLR cameras, have f-stops specified internally in 1/8-stop increments, so the cameras' 1/3stop settings are approximated by the nearest 1/8-stop setting in the lens.
Standard full-stop F-number scale
Including aperture value AV:
AV -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
f/# 0.7 1.0 1.4 2 2.8 4 5.6 8 11 16 22 32 45 64 90 128
Typical one-half-stop F-number scale
f/# 1.0 1.2 1.4 1.7 2 2.4 2.8 3.4 4 4.8 5.6 6.7 8 9.5 11 13 16 19 22
Typical one-third-stop F-number scale
f/# 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 8 9 10 11 12 14 16 18 20 22
Notice that sometimes a number is ambiguous; for example, f/1.2 may be used in either a halfstop[1] or a one-third-stop system; sometimes f/1.3 might be used instead for the one-third stop
scale[2]. There are other variations, such as 3.3 instead of 3.2.[3]