In photography and video, the relative amount of light is usually measured by light steps (stops or f-stops in English). Here we explain what the light steps are and how they are used.
What is a passage of light
In photography we need to measure in some way the amount of light that reaches the photographic film or the sensor.
The total amount of light collected by the camera determines the exposure: how light or dark the image as a whole comes out (with respect to the scene for example)
A light path indicates a two-fold increase or one-half decrease with respect to a certain amount of light.
For example, going up a light step is equivalent to having twice the light compared to the previous state.
Lowering one step of light means that we will have half the light.
Most of the information on the internet on this topic simply talks about how the steps are used: aperture (aperture), exposure time (shutter speed) and ISO, how to compensate for exposure, etc. but without going into the basic concepts or the origin of the criteria that are still used today in photography. I like to know the why of things, so the explanations can be a bit technical. If you just want to know the practical part, I recommend this other article where we talk about light management in photography: aperture, exposure and ISO
Why that double and half criterion?
On the one hand, we have that most human senses, including sight, work in a logarithmic way, following the Weber-Fechner Law .
The perception of the brain is not linear with respect to the variations of the external stimulus. For example, in the case of human vision, the perceived illumination does not correspond to the actual light incident on the eye .
There are many factors involved, but in general it follows a more or less logarithmic function, or at least non-linear: small changes in light intensity in a dark environment are perceived as large variations in lighting, and large changes in intensity in an environment very bright we perceive them as small variations.
When working with light steps we are using a logarithmic / exponential scale that fits very well with the way our own brain works .
Furthermore, although we could use any other logarithmic scale (for example, the logarithm in base 10 is used for sound, and it is measured in decibels), in the case of light the power scale of 2 is probably the simplest and most intuitive.
Light steps and diaphragm aperture
Historically, the concept of light passage is closely related to the operation of the diaphragm .
The diaphragm works like the iris of the eye. It is a more or less circular opening that can be made larger or smaller at will. Opening is the action of opening or closing that gap. In photography the word aperture is usually used in general, perhaps due to the similarity with the English term ‘aperture’.
The amount of light that can pass through this gap (per unit of time) depends on the area.
The bigger the gap: the more light will pass through, the smaller it is: the less light. The amount of light that passes through the hole is proportional to its area .
As a curiosity, in the first cameras there was no diaphragm as such, a disk or a plate was simply placed with the necessary hole for the type of photography. For example, if there was a lot of lighting, a plate with a small gap was placed (initially by disassembling the camera and screwing the disc with the aperture, later using plates as in the Waterhouse Stop system ) and if there was little light, a plate with the gap was placed larger or simply the entire entry surface of the target was left free.
Modern diaphragms are made up of blades or fins positioned in such a way that their rotation generates a more or less spherical hole in the center:
What is the f-number (F-stop in English)?
To understand the number f (the number that defines the openings of a lens) let’s go step by step.
First we are going to see what relationship there is between the radius of the inner hollow of the diaphragm and its area.
As we can see, to get the hole to have twice the area, we must open the radius (or diameter) by applying a root factor of 2 (that is, we must multiply or divide by approximately 1.41)
Now we are going to see another important question:
Is all the light that passes through the diaphragm reaching the sensor? No
Think that from every point in the scene rays of light start (or bounce) in all directions. The lens focuses part of those rays to build the corresponding point in the image.
Rays with paths that do not pass through the entrance of the objective do not reach the sensor (the objective is an opaque tube, the light can only enter through the entrance hole).
The same goes for the diaphragm. It is an opaque element that prevents the passage of light except for its central hole. The rays of light paths that do not pass through the central hole do not reach the sensor .
When we interpose a diaphragm we are not altering the image that is formed in the sensor (*), we are simply building it from a smaller number of rays (photons), that is, the same image is formed but with fewer photons the more we close the hollow of the diaphragm .
*) Closing or opening the diaphragm does have an effect on the range of the scene that appears in focus, that is, it influences the depth of field , but for what we are trying to explain here that effect does not matter to us.
To look at it another way: light ray paths that do not reach the sensor for whatever reason will not contribute to image formation. That is, none of those photons will reach the sensor and therefore do not count or have an effect on exposure.
Now imagine that you have two lenses with different focal lengths. Also imagine that both have the diaphragm open to exactly the same diameter. Therefore, the same intensity of light passes through the two diaphragms.
Will the same light intensity reach the sensor in both cases?
As the focal length increases, if we keep the diameter of the hole fixed, the cone of light that actually reaches the sensor becomes narrower and therefore the light intensity will be less.
That is, when comparing the amount of light that two lenses will deliver to the sensor, it is not enough to know the diameter of the hole in its diaphragm, we also have to take into account the focal length .
To take this effect into account and ‘normalize’ the diaphragm opening, a very simple formula is used:
N (f number) = F (focal length) / D (hole diameter)
With the f number to describe the aperture we will have a more precise idea of the amount of light that actually reaches the sensor.
The scale of numbers f corresponds to the scale of light steps (so that each step corresponds to letting double or half the light pass).
We take as reference f number 1 (N = 1)
To get an additional light path (twice the amount of light) you have to double the area, which is equivalent to multiplying the diameter by the root of 2 as we saw above.
But the number f is inversely proportional to the diameter of the hole, therefore the larger the aperture of the diaphragm, the smaller the number f .
That is, small f-numbers indicate a large aperture , while large f-numbers indicate a small aperture.
The aperture scale, already normalized with the number f, would look like this (1.41 is approximately the root of 2, each step that we close the diaphragm corresponds to multiplying by the root of 2):
1.4 (1 x 1.41)
2 (1.4 x 1.41)
2.8 (2 x 1.41)
4 (2.8 x 1.41)
Effective f-number / entrance pupil / T-number
In a real objective, made up of a combination of lenses and groups of lenses, the f-number is not determined by the physical diameter of the diaphragm aperture, but by the diameter of the entrance pupil .
The entrance pupil is the image of the physical aperture of the diaphragm , seen from the front of the objective, through the lenses that are between that position and the physical diaphragm.
To put it simply: the light in the scene does not ‘see’ the actual aperture of the diaphragm, it sees an image of that aperture.
The effective f-number or effective aperture, which is the one that really indicates a certain objective, is calculated taking the aperture diameter of the entrance pupil:
N (f-number) = F (focal length) / D (entrance pupil diameter)
For practical purposes it does not matter because the f number gives us in any case the reference on the amount of light that this objective is capable of collecting .
Therefore 99.9% of the time, if not always, we are going to talk about diaphragm aperture or f-number, and not effective f-number or entrance pupil.
It should also be borne in mind that the f number only takes into account the geometric part (effective area). It does not take into account that all physical lenses have losses due to absorption and unwanted internal reflections (impurities, reflections between lenses and groups, etc.)
From the point of view of the f-number, two lenses with the same aperture, for example f / 4, let exactly the same amount of light pass through.
But in reality the amount of light will depend on the optical transmittance of each of these objectives.
To measure more accurately, the T number is used , which takes into account both the effective aperture (f) and the optical transmittance. Two lenses with the same T-number do allow the same amount of light to pass through (at least with a very small difference)
In photography, the difference that may exist between two objectives with the same aperture is not important. In any case they are very small differences (we are talking about differences of 1/4 of a step or less) and they could be easily corrected from the camera itself or in editing.
In video it is more important because in a sequence created from different shots (with different lenses) you can notice these differences in exposure (remember that in video the shutter speed is usually a fixed parameter that depends on the number of frames per second ).
In film and video productions, specialized lenses are often used for video, which use the T number instead of the f number.
How does the f-number appear and how is it generally written?
The f-number has no units, the aperture is usually indicated following this format: f / N
For example: f / 2.8, f / 5.6, f / 22
This notation refers to the fact that if we solve for the diameter in the formula for the number f, it would be:
D = F / N
It is the notation that I like the most, because when the number is dividing, it becomes more intuitive to think that the larger that number is, the smaller the gap will be (D)
Another notation that is used a lot is as a 1: N ratio (it usually appears in the silkscreen of the objectives to indicate the maximum aperture of the same)
For example: 1: 2.8, 1: 5.6, 1:22
You can also find it as F2.8, F5.6 …
Working with steps of light
The light paths create a relative scale , not an absolute one.
That is, we always talk about going up N steps of light or going down N steps of light, we always refer to variations in the amount of light, not the absolute amount.
In an analog film camera there were only two parameters to regulate the amount of light that the frame collected:
- The aperture of the diaphragm
- Exposure time or shutter speed
Each film had its own sensitivity, once a roll of film was placed and that parameter could not be modified.
In digital cameras the sensitivity can be configured as one more parameter:
- Sensitivity (ISO) does not influence the amount of light the sensor receives, but it does affect the apparent exposure of the final image.
Playing with these three parameters we can get the exposure we need. Furthermore, each parameter has its own effect on the final result of the image.
Light steps in the diaphragm
To raise a light step we will have to lower an f number in the diaphragm
For example, if we are at f / 2.8 and we want to double the amount of light that the sensor receives, we would have to open at f / 2
Effect on Image: Depth of Field
Light steps on the shutter
This scale is much simpler and more intuitive:
If we want double the light we will simply have to keep the shutter open for twice as long .
For example, if we have the shutter in 1 second, to raise a light path we would have to pass it to 2 seconds.
The only thing to keep in mind is that in cameras, for shutter times less than 1 second, only the denominator of the fraction is usually indicated:
2 (1/2 seconds)
4 (1/4 seconds)
Light steps in ISO sensitivity
It is also very simple and intuitive:
To get double the light we just have to double the ISO value .
For example, if we are at ISO 100 and we want to raise a light step, we would have to go to ISO 200
Light steps and exposure value (EV)
Historically (when the ISO was fixed by the sensitivity of the photographic film) the concept of EV (Exposure Value ) was defined to relate the aperture (f number) with the shutter time to achieve a certain exposure.
The idea is that different combinations of shutter speed and aperture can be used to achieve a certain exposure value .
Logically, the formula was not used, for each ISO (that is, for each type of film) charts with exposure values (EV charts) were made that related the shutter speed to the aperture, for different typical lighting situations.
Bear in mind that the cameras did not have a built-in exposure meter and that using photographic film you have to try to get the correct exposure right the first time (the trial and error option as in digital cameras is not valid).
For example, a typical scene in broad daylight would be EV = 14 or EV = 15 . The photographer could then use the chart to see what combinations of aperture and speed achieved that exposure:
EV = 14 = log2 (8 * 8 / (1/250)): Aperture f / 8 | Speed 1/250
EV = 14 = log2 (11 * 11 / (1/125)): Aperture f / 11 | Speed 1/125
Really from a reference (for example f / 8 | 1/250) we would simply adjust aperture and speed to compensate and achieve that same exposure. For example, if we open the diaphragm one step to f / 5.6, we will have to compensate by lowering the exposure time to 1/500:
EV = 14 = log2 (5.6 * 5.6 / (1/500))
To give another example, a scene of a snowy landscape in broad daylight would correspond to EV = 16
Or for example in night photography of the sky (stars, Milky Way, etc.) the exposure value would be EV = -8, that is, we would need large apertures (small f-number) and long exposure times.
Nowadays, all cameras incorporate an exposure meter and also in digital photography we can play with trial and error, and compensate the exposure when necessary.
These exposure charts and the EV absolute value scale are no longer commonly used.
However, as each step of the exposure value ( EV ) corresponds to a light step, that notation is widely used as a synonym for light step or f-stop.
What is measured with light steps?
In photography and video the scale of light steps is used a lot to compare or to have a reference of characteristics.
We have already seen that the basic parameters are adjusted by light steps:
- Shutter speed
What other parameters are measured in light steps:
- The dynamic range (of a camera, a sensor, a medium …) is measured in light steps
For example, they can tell us that such a sensor has a dynamic range of 12 EV (12 steps)
- The effectiveness of an image stabilizer
That is, how many steps can we lower the shutter speed with that stabilizer compared to not using any to obtain an image without jitter. They can tell us for example: this objective achieves a stabilization of 4 EV (4 steps)