What is T-number / T-stop?

Usually, when discussing aperture of a lens, F-stop and F-number are used for quantifying. But some photographers, and especially videographers, also mention T-stop. The concept and numbering used (e.g. T/3.4) seem to be similar to F-stops.

What is a T-stop, how is it related to F-stop, and what are the differences?

F-stops are purely geometrical, the ratio of aperture to focal length, regardless of actual light transmitted. But all lenses absorb a part of the light passing through them, and the amount being absorbed varies lens to lens. So, in situations where even the slightest change of lights being transmitted affect the output, i.e cinematography, where many images are seen in rapid succession and even small changes in exposure will be noticeable, T-Stop is used as an standard. Since all lenses absorb some light, the T-number of any given aperture on a lens will always be greater (less light transmission) than the f-number. For example, a lens with f-stop 2.8 can have a t-stop 3.2, meaning a small portion (about a quarter) of the transmitted light has been absorbed by the lens glass elements.

A real lens set to a particular T-stop will, by definition, transmit the same amount of light as an ideal lens with 100% transmission at the corresponding f-stop. A f/2.8 lens can have t/3.2 and another f/2.8 lens can have t/3.4, so the actual lights being transmitted are not the same though they both have the same f-stop.

An F-stop indicates how much light the lens could theoretically transmit - focal length divided by diameter of aperture. In practice, there are some losses each time a light ray enters or exits a glass surface. In a lens with many elements, these losses may sum into a considerable amount (like 25% loss in some old zoom lenses). This, naturally, affects exposure.

T-stop takes this transmittance into account and shows how much light a lens can really transmit. For example, a Nikkor 70-200mm f/2.8 VR II appears to be T/3.2 - it can transmit the same amount of light as an F/3.2 theoretical lens could. This discrepancy is not an engineering fault, but rather a fact of life.

The concept of T-stop is especially important for videography, as a person watching a video would notice the scene getting suddenly darker/lighter if changing lenses would result in a different T-stop not compensated adequately by shutter speed (even if F-stop stays the same).

Since there is always loss and never gain of light, T-stop of a lens is always slower than F-stop, almost equal in best cases. The difference between T-stops vs F-stops of lenses has declined with the evolution of coating technologies.

The T-stop is only important in context of exposure. When estimating depth of field, F-stop should be evaluated.