### DIAPHRAGM AND APERTURE

Inside the photographic lenses there is a device called the **diaphragm** which has the purpose of controlling the amount of light that reaches the sensor (or in the case of non-digital cameras, the film).

The diaphragm is made up of a series of metal lamellae arranged in a fan shape which, when moving, create a hole of variable size.

It is also called an **iris diaphragm** because just like in the human eye it allows a variation of aperture.

By closing the diaphragm, the number of lamellae increases and the greater are the sides of the polygon that delimit the hole. For example, a diaphragm with 6 lamellae creates a hexagonal shaped hole, while one with 8 lamellae creates an octagonal shaped hole. More lamellae there are, the more the polygon resembles a circle.

The polygonal shape that the hole in the diaphragm assumes influences the shape of the circles of confusion in the out-of-focus air of the image, the so-called **Bokeh** effect (blur). When we talk about bokeh quality, we are referring to the quality of the out-of-focus areas of the image.

Regardless of the shape, the greater the width of the hole is, the greater is the amount of light that can pass.

**The position of the diaphragm** inside the lens barrel **is approximately halfway between the entrance pupil and the exit pupil of the lens**, a position carefully designed and optimized to ensure the highest overall optical quality.

The purpose of the diaphragm is to control the amount of light that passes through the lens barrel by varying the size of the hole.

In most modern lenses this variation is directly controlled by one of the rings on the camera body as these do not have physical controls. On older or particular lenses, however, there is a dedicated ring on the lens barrel that allows for adjustment of the aperture.

The light intensity that reaches the sensor does not depend exclusively on the aperture of the diaphragm but also on the focal length of the lens.

With the same aperture of the diaphragm, if the focal length doubles, the light intensity is halved. To get the same amount of light, if the focal length increases, the aperture must also increase.

This is why long focal length lenses have larger lenses, and still barely reach very large apertures.

The aperture value, called **f-stop**, was defined using the so-called **relative aperture ƒ** as the **ratio between the focal length of the lens and the diameter of the entrance pupil*** and expresses the amount of light that *theoretically (read the T-Stop section below)* reaches the sensor rather than the actual aperture size.

**f-stop = ****f****/D**

**f-stop =****f**

**/D**where

**ƒ-stop** = relative aperture of the diaphragm

**f** = focal length

**D** = diameter of the entrance pupil of the lens

Since this is a ratio, a smaller f-stop number (e.g. f /1.4) corresponds to a larger **entrance pupil diameter***, while a larger f-stop number (e.g. f/8) corresponds to a smaller entrance pupil diameter.

*** The size of the entrance pupil is the virtual size of the aperture as seen through the front element of the lens.** Considering that the diaphragm is located approximately in the middle of the barrel lens and considering all the optical elements that are present between the front element and the physical position of the diaphragm, the visible aperture (which can be calculated using mathematical formulas) will be larger than the physical one.

The f-stop number **does not represent** the ratio between the focal length of the lens and the diameter of the diaphragm aperture, but the ratio between the focal length of the lens and the diameter of the diaphragm aperture as seen from the front element of the lens.

What is shown on the barrel lens, around the front lens, is always the maximum f-stop number, with the diaphragm fully open. In the case of a fixed focal length lens, the number will always and only be one. In the case of a zoom lens there may be one or two numbers depending on whether it is a zoom with a fixed or variable maximum aperture. In the first case the aperture remains constant as the focal length varies, in the second case the aperture varies as the focal length varies.

The *maximum possible aperture* of the diaphragm is indicated on each lens with the words **1: f**.

If we take, for example, the lens in the image above on the left, it is possible to read 1.2 so the maximum aperture will be f/2.

In the lens of the photo above on the right it is possible to read 24-90mm 1: 2.8-4. This means that at 24mm the maximum aperture will be f/2.8 while at 90mm it will drop to f /4.

Constant aperture zoom lenses are more complex and expensive than variable aperture lenses. This is in order to keep the ratio at all focal lengths constant, the design and construction of the lens are more complex and require more expensive materials and production processes.

The minimum aperture of a lens, regardless of whether it is a fixed lens or a zoom, is not usually indicated on the barrel lens but only on the data sheet and usually it has minimum f-stop values between f/16 and f/32 .

Any camera that can be used in manual mode has the ability to set the aperture, and consequently the amount of light that passes through the optical system and reaches the sensor.

### F-STOP

There is a standard values scale that indicates the aperture used by all camera manufacturers such as Leica, Hasselblad, Phase One, Canon, Nikon, Sony, etc .: **the f-stops scale**.

Having a minimum of knowledge of the **exposure triangle**, i.e. the correlation between **ISO sensitivity**, **exposure time** and **aperture**, for ISO values and times, if you want to increase or decrease the exposure by one stop, it may be necessary to multiply or divide the set value by two, depending on the case..

However, the aperture does not follow a linear trend as for ISO and exposure times. The f-stop scale is:

The amount of light that passes through the lens and reaches the sensor depends on the size of the diaphragm aperture, or the area of the hole, which is approximately circular, as mentioned above.

Wanting to halve its area – in photographic terms, reduce by one stop – it is not possible to simply halve the value, but you must use a factor that is approximately the square root of 2.

To double or halve the value, as is usual to do with ISO at times, the distance, for example, from f/2 to f/4 is 2 f-stops.

This is simply because the f-stop scale is, mathematically, a geometric progression with a square root factor of 2 as demonstrated below.

Knowing that the area of the circle is:

*where r is the radius and D the diameter*

By halving the area, the diameter of the entrance pupil D1 will become:

By further halving the area, the diameter of the entrance pupil D2 will become:

By further halving the area, the diameter of the entrance pupil D3 will become:

…

The values are obtained from the square root of 2 raised to n, an incremental number, 0, 1, 2, 3, etc.).

By halving the area, the diameter decreases by √2. By doubling the area, the diameter increases by √2. Starting from 1, and multiplying by √2, it is possible to obtain all the values of the scale:

\sqrt{2^0} | \sqrt{2^1} | \sqrt{2^2} | \sqrt{2^3} | \sqrt{2^4} | \sqrt{2^5} | \sqrt{2^6} | \sqrt{2^7} | \sqrt{2^8} | \sqrt{2^9} | \sqrt{2^{10}} |

\textbf{f/1} | \textbf{f/1.4} | \textbf{f/2} | \textbf{f/2.8} | \textbf{f/4} | \textbf{f/5.6} | \textbf{f/8} | \textbf{f/11} | \textbf{f/16} | \textbf{f/22} | \textbf{f/32} |

Assuming a lens with a 50mm focal length and aperture to f/2 and then to f/2.8, it is possible to concretely verify the greater size of the f/2 aperture, remembering that the radius and not the diameter must be entered in the formula, so the previously calculated value must be divided by two.

Knowing that

** f-stop = f / D** => **D = f / f-stop**

For a focal length of 50mm at f/2 the diameter will be 50mm/2 = 25mm and the radius 25mm/2 = 12.5mm.

For a focal length of 50mm at f/2.8 the diameter will be 50mm/2.8 = 17.86mm and the radius 17.86mm/2 = 8.9332mm.

By calculating the areas for the aperture on f/2 **A = π * 12.5mm² = 500mm²** and for the aperture on f/ 2.8 **A = π * 8.3932mm² = 250mm²**, it is clear that as the diameter changes, the area halves.

It is important to remember that:

1) The smaller the value, the larger the corresponding aperture. Therefore the greater the amount of light can pass through . On the contrary, the larger the value, the smaller the aperture will be, therefore the less the amount of light. For example: f/1.4 indicates an aperture larger than f/8, more light passes at f/1.4 than at f/8

2) The f-stops scale has been constructed in such a way that between one value and the next the amount of light doubles or halves (in photographic terms it is said to increase or decrease by **1 stop**).

For example, between f/5.6 and f/8 the amount of light is halved (-1 stop) and between f/8 and f/11 it is halved again (-1 stop). There are 2 stops of difference between f/5.6 and f/11 which represents a 4 times difference in light.

### T-STOP

It is important to make a clarification: the **f-stop** value is simply a geometric relationship between two dimensions, **f** and **D** and represents the amount of light that the lens is **theoretically able to convey** based on its physical dimensions (f and D) but **it doesn’t represent the light that actually manages to pass through**.

The ratio absolutely does not consider which and how many elements are present inside the lens and the light absorbed by the elements that compose it.

Even the most expensive and refined lenses are not completely transparent but absorb a small part of the light that passes through them, causing more or less marked differences in the final exposure.

For these reasons there is a scale similar to that of the f-stops, the **t-stop** scale, where the t stands for **transmission**, transmission of light. This scale derives from experimental measurements and indicates how much of the light entering the lens can actually reach the sensor.

But if the f-stops don’t indicate real light, why not use t-stops as the default in photo lenses? There are several reasons:

First of all, the greatest difference possible between the 2 values very rarely exceeds 1/3 stop. In photography it is not such a serious problem and can be easily corrected in shooting and/or in post-production.

In addition, the exposure meters of the cameras mark variations on 1/3 stop differences. Any minor differences are not considered and the t-stop value would still be reset to that of f-stop.

Finally, testing the actual t-stops values takes a lot of time and money. Precisely because the difference is minimal, it is not possible to use the t-stops and then provide a value that does not correspond (even if slightly) to the real one, so it is generally more sensible to use the f-stops directly which are, however, a precise value.

In cinematography the situation is different. Cinema lenses usually use the t-stop scale instead of the f-stop scale. Having to be used in different scenes, on different days and in different conditions, even small differences are visible. Being able to set them while shooting with the same effective exposure can save a lot of time and, consequently, a lot of money.

### INTERMEDIATE VALUES

Most modern cameras allow you to set the aperture scale with the intermediate values between one stop and another, at half-stop or one-third stop intervals (using the scale with thirds stops allows you more accurate settings).

Intermediate values in half stops (1.2, 1.7, 2.4, 3.3, 4.8, 6.7, 9.7, 13, 19, 27) or in thirds of stops (1.1, 1.3, 1.6, 1.8, 2.2, 2.5, 3.2, 3.5, 4.5 , 5, 6.3, 7.1, 9, 10, 13, 14, 18, 20, 25, 29) that can be set on the camera, mathematically are obtained in the same way described above for whole stops, adding or subtracting to the exponent of power (of the square root of 2) the values of 1/2, 1/3 or 2/3 as appropriate.

Below is an example of subtracting half stop and adding two thirds of stops to f /1.4.

**f/1.4**

**f/1.4 – 1/2 stop = f/1.2 **

**f/1.4 + 2/3 stop = f/1.8 **

The advice is to learn the entire f-stops scale or more simply, with a minimum of mental elasticity, memorize the first two values f/1 and f/1.4 and knowing that by multiplying or dividing by two we would have a jump of two stops, on the based on these two initial values it is possible to obtain all the others in alternating sequence.