F/STOPS AND T/STOPS

F/Stops and T/Stops

f/stops are a bit more confusing because the numbers appear so arbitrary. This is the standard sequence of f/stops from f/1.4 to f/22. Although it may not seem intuitive at first, in this sequence the f/1.4 setting lets in the most light while the f/22 setting lets in the least. Also, each of these f/stops has precisely the same halving/doubling relationship as the shutter speed sequence.

1.4 2.0 2.8 4 5.6 8 11 16 22

On the face of it, going from f/4 to f/5.6 doesn't sound like halving the amount of light. What's more, 5.6 is a larger number and sounds like it ought to be more light, not less. Neither does f/4 to f/2.8 sound like doubling the amount of light. In fact, each of the numbers in this sequence is a halving/doubling of the amount of light from its immediate neighbours, just like the shutter speed settings are. Not only that, but it makes sense, as I shall show below.

The reason that both the halving and doubling and the smaller numbers mean more light things make sense is that the f/stop is a ratio. The ratio is between the diameter of the aperture in the lens and the focal length of the lens. The focal length is generally measured in millimeters, so we'll stick with those as our unit of measure. On a 50mm lens, f/2 is saying that the diameter of the aperture is 25mm. The ratio is: 50/25 = 2. That seems pretty straightforward. A good question might be, what is the area of that aperture? Well, the aperture is usually a set of five to fifteen blades which form a roughly circular hole, so we'll use the formula for the area of a circle, which as I'm sure you'll recall is &pi * radius2. For π I'll use 3.14159265. On our 50mm lens, the aperture at f/2 has a diameter of 25mm which is a radius of 12.5mm. The area of the aperture is thus π X 12.52, or 3.14159265 X 156.25, or 490.9 square millimetres.

This fact by itself isn't all that useful. It is useful in relation to the adjacent f/stops. What is the area of the aperture at f/2.8? Well, because the f/stop is a ratio of the focal length to diameter, our 50mm lens at f/2.8 would have a diameter of 50/2.8 = 17.86mm. Remember, we have to divide that by 2 to get the radius of 8.93mm, so the area of the circle thus formed would be π X 8.932, or 250.5 square mm. Rounding off a bit, that's about 250 sq. mm at f/2.8 and 500 sq. mm at f/2, a double/half relationship. Aha! So that's it! The area of the hole doubles and halves, it's just represented by a ratio on the lens! No wonder it's so darn confusing.

The F-Stop is a theoretical value, while the T-Stop is an actual tested value. So while both the Zeiss Otus 55mm f/1.4 and 85mm f/1.4 lenses have a wide-open F-Number of 1.4, they actually transmit different values. According to DxOMark’s tests, the 55mm Otus transmission is T1.5 while the 85mm Otus transmission is T1.7.

Which brings us to the question you’re probably asking yourself right now: why do most photography lenses use F-Stop and cinema lenses use T-Stop? Wolfcrow explains this as well.

According to him, there are three reasons photography lens manufacturers don’t bother with T-Stops:

In-camera light metering will compensate for the minor exposure difference between two different lenses with the same F-Stop but different T-Stops.

The biggest transmission difference you’ll get is about 1/3 of a stop, which is no problem to fix in post-processing.

T-Stop testing every new lens is expensive and time consuming; because of reasons 1 and 2, it’s not worth the investment for photography lenses.

Cinematography, on the other hand, is more complicated. Multiple scenes, sometimes captured on multiple days, and often consisting of multiple angles shot with multiple lenses means correcting exposure in post can be expensive. Plus, even if new tech means all you’re saving is minutes per day, those minutes can cost thousands on a huge production.

Modern camera technology makes F-Stops a viable option for today’s filmmakers, but the top cinema lenses still guarantee the real-world exposure of T-Stops.