#### The maximum aperture of the diaphragm largely determines the performance of an optic, and the amount of light that the lens allows to be passed through. But why do some lenses open less than others? What is the difference between the values expressed in f/xx and TXX? We’ll explain all below.

Controlling exposure has already been discussed at length in a previous article. In order to go further and understand the mechanism, it is necessary to know both the physical and mathematical limits of a lens in order to choose it with full knowledge of its capabilities. The opening of a lens is managed by the diaphragm, which has the ability to open or close a lens and let more or less light in, meaning that it becomes the first tool to understand when it comes to the management of exposure.

#### Where does the aperture value come from?

Aperture is simply the relationship between the focal length and the maximum diameter of the diaphragm (i.e. the inner barrel of the lens). For example, a 50mm lens with a maximum diameter of 25mm, we obtain 50/25=2. To simplify the calculation, we annotate the aperture as f/2, f:2 or even 1:2. The calculation is completed beforehand, and allows the camera operator to have common reference values. Regardless of the lens, an f/2 will always give the same amount of light to the sensor – theoretically, at least.

However, via this rule, we realise that if we want an aperture at f/2 for a focal length of 150mm, we will need a diameter of 75mm! This explains why large focal lengths that “open” a lot are very large and very expensive. At this focal length, we will more generally find lenses that open at f/4 (37.5mm diameter). This is also why systems such as the m4/3 (GH5 etc.), which have a sensor smaller than full size, can have very bright optics without being bulky. Indeed, on this system, as a 50mm full frame lens corresponds to a 25mm full frame lens in m4/3, a 12.5mm diaphragm diameter is sufficient to open at f/2. This is why the lenses are much less cumbersome than on a Full Frame system.

#### f/1.4, f/2, f/2.8 – where do these numbers come from?

You will have noticed that whatever the lens, the camera, or the hybrid, the different diaphragm levels are made up of the same sequence of “numbers”. At the same time, increasing the opening by 1 “Stop”, or 1 “diaph” means bringing in twice as much light. Each increment is therefore twice the surface area of the previous one. The difference is that the smaller the value, the larger the surface area.

It is also important to know the famous formula to calculate the area of a circle: Surface of the disc =πr² where “r” symbolises the radius. Since the area of a circle decreases by half when the radius is divided by √2 (i.e. 1.4142), we move from one increment to the next by multiplying by √2 and rounding. Let’s try:

If r=1, 1 x √2 = 1.4

1,4 x √2 = 2

2 x √2 = 2.8

2.8 x √2 = 4

That’s the mystery solved. However, all you have to remember there is a ratio of 2 as to the amount of light sent each time.

#### The limits of F-Stops, and why T-Stops?

As we have just seen, the diaphragm values or F-Stops, are mathematical calculations that are accessible to anyone. Unfortunately, the lenses are not just lenses placed on tubes of such diameter and length. There are many parameters that disturb the theoretical calculation in the transmission of light.

First of all, for the same lens (same brand, same focal length, same “f”), we realise that there is always a slight difference because the lenses are never quite identical because of the coating, the complexity of the lenses etc., meaning that an f/2 will never really be an f/2. In photography, we don’t care so much because the difference is very small, and therefore more acceptable – particularly thanks to post-production.

In video however, it’s another story because in large productions, we often shoot with multiple cameras, and if there are differences in exposure between several cameras, post-production can very quickly become both complicated and expensive.

And this is where the T-Stops come in.

F-Stops are based on the ratio betweenFocal length and diameter. TheT-stops integrates the lightTransmittance value.

Starting from the F-Stops, manufacturers will calculate the loss of light due to the different disturbance parameters (radius lost against the drum, absorption of the coating, loss when passing through X lenses) and will therefore add around 85% to the transmittance factor calculation. By multiplying the theoretical value by this factor we obtain an actual value. An f/2.8 will therefore be a T3.3 according to our 85% transmittance.

#### So why don’t we just use T-Stops?

The answer to this question is quite simple: establishing the transmittance factor means that it must be calibrated to each lens that comes off the production line. To ensure that a T3.1 is exactly the same as another T3.1 implies tariffs that are often multiplied by 3 or 4 compared to a “simple” objective “f”. That’s why we reserve these lenses for cinema production by adding other functions: toothed focusing ring for follow-focus, longer strokes for precise movement, “declicked” diaphragm to switch from one level to the other smoothly – all of which brings the bill to a stratospheric level.

But do you really need these lenses? The answer is simply “yes”, if the simplification of post-production justifies this additional cost of renting the optics. The answer is no, for simpler productions: matching two cameras remains quite easy. It is all about balancing the budget.