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T-stops vs f-stops Explained: Practical Differences and Math

T-stops vs f-stops Explained: Practical Differences and Math

Ever since I made my article on f-stops, I've been getting frequent requests for the T-stop version. So, that's what we're gonna be covering today.


So, what are T-stops?

Well, they're just like f-stops in the sense that they inform you of the effectiveness of your lens, but the calculation is different. If you remember from my previous article on the subject, f-stops, or more appropriately, f-numbers, are merely a ratio of the lens's focal length to the diameter of its entrance pupil.

Basically, you can figure out how large your entrance pupil is by dividing your focal length by your f-number.

And your entrance pupil is basically how the aperture appears when viewed through the front of your lens. So, a 70mm lens with the f-stop set to f/2.8 would have an entrance pupil diameter of 25mm. 70 divided by 2.8 equals 25.

As your entrance pupil gets smaller, less and less light will reach your sensor and your depth of field will get deeper and deeper and the same is true for T-stops, but rather than a ratio based on focal length, a T-stop is a measure of the transmission efficiency of your lens.

Or more simply, what percentage of the light makes it through the lens with 100% being a perfect score and zero light lost. This system is more useful when you want exposures to match more precisely and is the reason why cinema lenses used for movie production are usually measured in T-stops.

You don't want a sudden shift in exposure when switching angles during a scene, so you need to be able to fit your cameras with lenses that have the same transmittance.

F-numbers don't work for this because even if you were to adjust two different lenses to have the same entrance pupil size, it doesn't mean the quality of the elements inside the lens will be capable of the same light transmittance.

The way a T-stop is calculated is actually pretty easy. You just take the f-number of your lens and divide it by the square root of its transmittance score.

So, for instance, let's say that we have the same 70mm f/2.8 lens that we were using in our previous example, but in this lens, only 80% of the light that goes into it makes it out the other side. So, you would take your f-number of 2.8 and divide it by the square root of that 80% or 0.8. And the square root of 0.8 is .894. So, you take your f-number of 2.8 and divide it by .894 and you get your T-stop of 3.1-- rounded.

Now, the T-stop of a lens will always be a bigger number than its f-stop because you can't have a greater than 100% transmittance. In fact, it's almost impossible to have 100% transmittance because they're always will be some light lost when you put that much glass between the source and the destination.

But high-quality lenses can actually get you surprisingly close to 100%. For instance, I have a Sony 90mm Macro and it has an f-stop of 2.8 and a measured T-stop of 2.9. That means it has a light transmission efficiency of about 94% and would be considered a great performer.

Now, often when people learn that the differences between f-numbers and T-stops, they wonder why we use f-stops in the first place because it seems like an inferior system.

When it comes to maintaining exposure, it definitely is, but there are some applications where f-stops excel. If you need to calculate your depth of field, for example, then f-stops are much more useful, because as I said in my previous article, the diameter of your entrance pupil is a major contributing factor to your depth of field, where the transmission efficiency of your lens isn't.

So, the line typically gets drawn between photo and video, with video requiring a more consistent exposure between angles and shoot days, where photographers would require a more reliable sense of the depth of field because changes in exposure aren't as jarring from photo to photo as they are with video.

But another advantage to f-stops would be the reduced production lag and costs. Because in order to know the T-stop of a lens, it has to go through a much more rigorous testing process in order to measure the light transmission versus simply calculating a ratio based on f-number. This makes f-stop lenses cheaper on average and more widely available.

However, this is also the drawback to f-stops because you can usually safely estimate your f-stop if you know your T-stop, but the reverse is not true. Since we know that T-stops are always higher than f-stops, we can just move down to the nearest stop in order to take a guess at our f-number.

For instance, in our example of a quality lens with a T-stop of 2.9 or 3.0, it'll likely have an f-stop of 2.8 after accounting for lost transmission. But unfortunately, knowing that a lens has an f-stop of 2.8 does not allow us to safely assume its T-stop. That'll have to be measured precisely in order to be useful.


Conclusion

Finally, when it comes to approaching this topic, it's important to remember that this isn't a competition.

Often, these two terms are compared quite adversarially, but as you now know, they aren't separate concepts, and the T-stop formula is based in large part on the f-number.

T-stops should instead be looked at as an extra step that can be taken when exposure precision is necessary, and as usual, it's just about using the right tool for the job. But, that's gonna be it for me. I hope you found this article helpful or at least entertaining, and if you did, make sure you give it a share and comment below.

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