What the #$!! are "T" stops?

WARNING: Part rant and all technical. If you simply enjoy taking photos without being a techno gearhead feel free to ignore this post. I promise to return to more readable posts after getting this out of my system.

On Facebook the other day one of my non-person friends (BorrowLenses) posted a link to a video about T stops vs f stops. Huh? I've been photographing for 57 years and never heard of T stops. I watched it and did a bit of further research. It seems some folks with lots of time on their hands (time that would have been better spent taking pictures IMO) compared the actual amount of light coming through a variety of lenses and learned that (allegedly) your lenses are lying to you. According to them f/2.8, for example, may actually be f/2.9 or even f/3.something depending on the lens. They are (accurately) surmising that some light is lost inside the lens, absorbed by the lens elements, reflection for lens surfaces, etc., which isn't being accounted for with the result that they believe the f/stops are mislabeled.

The only "mis" going on is a misunderstanding of what the f/# means. To arrive at the f/# the diameter of the diaphragm opening is divided into the distance between the lens when focused at infinity AKA the Focal Length (more on that later). The resulting number is the f/#, period, end of calculation. Thus a lens rated at f/2 has a diaphragm opening the is one half the focal length of the lens, an f/4 stop is one quarter the focal length. It's a simple ratio. The diameter of the opening:focal length with the focal length always being "1". It is not and never was a direct measure of the transitivity of the glass although it is a useful approximation for calculating exposure.

So why don't lens manufacturers measure the light each lens transmits? I'm not a lens engineer but I've been a practicing photographer for a looong time so here's my educated hard knocks school answer. They don't because light loss in the lens is only one factor in how much light will actually hit the film/sensor at any given f/stop. The nominal focal length of all lenses is the distance between the lens and the film/sensor plane when focused at infinity. That is the closest the lens can be to the film plane and have anything in focus. As you focus on anything closer than infinity you are moving the lens further from the film plane. You reach a 1:1 subject size to image size when your lens is smack in the middle between the subject and the film.

Yes, I know you can bend the light rays using a +diopter effect (basically a magnifying glass) and the distances won't exactly equal at 1:1 but that's not the point. The point is that as you move the lens further from the film plane the light on the film/sensor decreases because of the law of inverse squares. On an SLR (digital or otherwise) the diaphragm opening can be linked with the focusing helical to approximate the same amount of light to a point. The barrel of the lens however limits how far  the diaphragm can open. That's why the maximum aperture on most zoom lenses is marked as variable. When you zoom out, the lens barrel isn't big enough to accommodate the larger opening of the diaphragm at the longer focal length. It's the same size as at the shorter focal length but because it is a ratio of the two measurements, iris diameter:focal length, that same diameter is a smaller portion of the focal length. And yes, it does mean you get less light at any given spot on the focal plane, again because of the law of inverse squares (spread a given intensity of light over a large area and the light on any given part of the surface is less in inverse proportion to the increased distance). Although the effect is minor at subject distances closer to infinity, the light fall off increases as you focus on closer subjects and the progression of fall off is geometric.

There are other things that reduce the light at any given f/stop, notably filters. Before Photoshop allowed you to alter the relationship between values it was necessary to add a filter to the front of your lens. Obviously any filter you place in the light path will reduce the light reaching the film/sensor but that does not alter the ratio of the iris opening to the focal length of the lens. It is something the knowledgeable photographer has to compensate for to get accurate exposure. Or I should say had to compensate for.

All we are concerned about is correct exposure which is a mix of intensity of light and time. Modern cameras all have built in light meters coupled to computer chips to read the light actually falling on the sensor. The meter measures the light directly through the lens and doesn't give rat's patootie what the labeled f/stop is. If your camera has a histogram it tells you whether the light falls within the dynamic range that the sensor can interpret into a JPG based on the chosen exposure program (if you are shooting RAW the sensor will record a somewhat broader range that you can play with later). Even if the f/stop was intended to be a measure of actual light striking the sensor, which it isn't, there is no way the manufacturer could label the diaphragm ring on your lens with T numbers that accurately reflected the intensity since it is variable due to all sorts of  adjustments to focus, filtration, etc. that change with each and every image you shoot. A simple ratio of diaphragm diameter to nominal focal length, that is something they can label and that is all it is. So f/4 is f/4 no matter what other circumstances are reducing the light coming through the lens and no, the manufacturers aren't cheating to make you think the lens is faster than it actually is. Today's photographers have marvelously technological cameras that virtually eliminate the complex calculations needed to get accurate exposure 50 years ago. Be grateful, stop wasting time on silliness and go take pictures. Jeesh!

Update: I've since been told that "T" stops are important to videographers because they don't have in camera metering and they can't always trust an incident meter to read the correct f/stop because f/stops vary from lens to lens, thus the need for "T" stops. I'm not into video but the few times I've done it I never had exposure problems but hey, I suppose those who do it more are more likely to encounter such things. The point of my rant was that for still photographers (that's who I'm talking to here) it isn't something to get wrapped up in. Even when I was in the army and we had no light meters at all we never concerned ourselves over comparing the relative transivity (I don't think that is even a word) of  one lens vs another yet we somehow managed to get good exposure anyway. As the old saying goes "your mileage may vary".