How Does One Calculate F-Number For The Longest Focal Length Of A Varifocal Lens?

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The "f" in f-stop actually stands for "focal length"; the format f/x is a simple radio of focal length to aperture diameter. So if your aperture is f/4 and your focal length is 10mm, your aperture diameter is 10/4, or 2.5mm.

Yes, I'm aware of that, but I'm trying to determine what the f-stop is at the far end of a vari-focal lens. In photographic lenses, the f-stop-range is usually provided along with the focal length range.

This doesn't seem to be the usual case for CCTV lenses. Take a 4mm-12mm for example. It might be listed at f/2.0, which assumedly applies only to the short side of the zoom.

Which would give a exit pupil diameter of 2mm.

But it is really legitimate to continue and back into f/6 for the long side, the 12mm?

Unless it's a fixed-aperture design (highly unlikely, as that tends to be a feature of only a few higher-end photographic lenses), I'd say that's a reasonable assumption.

Manufacturer spec sheets may have it listed, although f-number seems to be a relatively unimportant spec when it comes to CCTV lenses in general - I rarely see anyone ask about it or talk about it, and it often appears to be included "just because".

It can make a great difference with PTZs. A PTZ may be marketed with an f/1.4 or f/1.6 lens but at the longest focal length that could be f/4 or f/5.4 etc. That will make a big difference in worse low light performance at the far / long end.

That said, most PTZs show the f stop at both sides.

1, what lens or camera are you looking at specifically?

True, the wider the zoom range, the bigger factor it becomes.

1, what lens or camera are you looking at specifically?

Lets take a look at the new award winning hik 4k ptz. Focal length ranges from 6 to 202 mm. Aperture range is from f1.55 to f4.8.

So do you and Matt think that the f number at 202mm is f4.8 or something like f55.8 (1.55 x 36)

I hate to be a negative influence but calculating the exit pupil has very little meaning in reality. The lens or camera manufacturer's specification is what has meaning. If not listed one should inquire.

That said for general information the traditional "f" stop should only be a guideline. It tells one which lens is more likely to pass more or less light to the front of the sensor.

There is another factor that lens makers no longer publish and that is the "t" stop. This is a true measurement of the light passing thru the lens. Every lens has multiple elements and each element has a light loss. The more efficient the lens ( element) design the higher percentage of light will arrive at the sensor. Thus a lower "t" stop the more light at the sensor.

As we all know the lens is only one part of the equation and the total sensitivity of the lens / camera should be a deciding factor.

The safest way to know if your camera lens will do the job in a low light situation is still to take it out to the site and try it.

I hate to be a negative influence but calculating the exit pupil has very little meaning in reality. The lens or camera manufacturer's specification is what has meaning.

I'm trying to get a rough sense of how much the f-number varies from the short end to the long.

I'm not talking about a particular lens, but want to apply a calculation to all CCTV lenses so as to filter them for further research.

Even if the calculation were to be off 50% it would still be useful. See the example above with the Hik PTZ.

Is it closer to 5 or 55? If that can't even be inferred thru calculation, then I admit all hope is lost.

btw, this has nothing per se to do with low-light capabilities.

I am not a "Scientist" per say but rather a person that has dealt with lenses as a camera manufacturer for many years. Why I mentioned low light is that is the area that the "f" stop becomes critical. From my knowledge the "f" stop is really the opening of the iris that allows the light to pass. It is simple on a fixed lens, but with a zoom or varifiocal all the elements loose light, therefore the lower "f" stop at the telephoto setting. I really think this may be a technical misnomer as the iris opening does not change. The "t" stop I mentioned earlier is what is really happening. The light at the rear of the lens decreases in the telephoto setting by the loss of the various lens elements. I don't believe there is a calculation that will work here as all lens designs, the efficiency of the light passage for each element, is up to the lens designer.

The only real way I have been able to determine the real "f" or 't" stop was by actually measuring the light coming out of the lens that reaches the sensor.

Why I mentioned low light is that is the area that the "f" stop becomes critical. From my knowledge the "f" stop is really the opening of the iris that allows the light to pass.

All I'm interested is the ratio of effective length to width, or f-number.

T-stops are a more accurate measure of light, but are not important to me because I am trying to estimate the size of airy discs and circles of confusion.

Again, I am not interested in the magnitude of light, rather it's degree of collimation.

Even a general guideline here would help me from having to research lenses one by one.

But seeing as no one will even take a stab at the order of magnitude Hik example I gave, I'm guessing people (besides the mfr) just don't know what the f-stop is at the far end.

f/number is simply the ratio of the len's focal length to its entrance pupil diameter.

Typically, the "published" f/number is the very fastest f/number the lens is capable of, which occurs at the lowest zoom (the shortest focal length).

I hear that you want to know how to find the f/number for that same lens when it is at maximum zoom (longest focal length).

I assume that the entrance pupil is the same at all focal lengths. This may not be a 100% accurate assumption -- one can imagine aspects of zooming that might change the len's entrance pupil diameter a little -- but it's not likely to be way out to lunch.

With this assumption, the math falls out automatically.

entrance pupil diameter = shortest focal length / published f/number

Now that you know the entrance pupil diameter at lowest zoom, assuming diameter doesn't change much throughout the zoom, you can calculate f/number for longest zoom:

f/number = longest focal length / entrance pupil diameter

summarizing:

long focal length f/number = published f/number x longest focal length / shortest focal length

This looks a bit messy in paragraph form, so let's abbreviate:

SFL = shortest focal length

SFN = f/number at shortest focal length (the published f/number)

LFL = longest focal length

LFN = f/number at longest focal length

Summarizing,

LFN = SFN x LFL / SFL

Hope this helps.

f-stop is simply the ratio of the len's focal length to its entrance pupil diameter.

Typically, the "published" f-stop is the very lowest f-stop the lens is capable of, which occurs at the lowest zoom (the shortest focal length).

I hear that you want to know how to find the f-stop for that same lens when it is at maximum zoom (longest focal length).

I assume that the entrance pupil is the same at all focal lengths. This may not be a 100% accurate assumption -- one can imagine aspects of zooming that might change the len's entrance pupil diameter a little -- but it's not likely to be way out to lunch.

With this assumption, the math falls out automatically.

entrance pupil diameter = shortest focal length / published f-stop

Now that you know the entrance pupil diameter at lowest zoom, assuming diameter doesn't change much throughout the zoom, you can calculate f-stop for longest zoom:

fstop = longest focal length / entrance pupil diameter

summarizing:

long focal length f-stop = published f-stop x longest focal length / shortest focal length

This looks a bit messy in paragraph form, so let's abbreviate:

SFL = shortest focal length

SFS = f-stop at shortest focal length (the published f-stop for that lens)

LFL = longest focal length

LFS = f-stop at longest focal length

Summarizing,

LFS = SFS x LFL / SFL

Hope this helps.

IPVM edit functions occasionally surprise, as now when it seems my edit becomes a double post.

My motivation to edit is this:

f/number can be thought of as a fraction such as 1/1.4, or as a number such as 1.4. This creates space for confusion when describing larger or smaller f/numbers.

f-stops are the denominator term, e.g. 1.4 not 1/1.4.

If you assume the formula I initially provided applies to the f/number as fraction such as 1/1.4, the answer comes out wrong. If you use f/number as simply a number such as 1.4, it works as intended.

To eliminate that element of confusion, I substituted f-stop for f/number.

Because of my great skill leaving messages on IPVM, that wound up as a nearly duplicate message instead of an edit.

Sorry for all the noise... Best of luck with your project.

No worries.

Thanks for the formula. I think I am doing essentially the same thing you describe, up above in my second post:

Take a 4mm-12mm for example. It might be listed at f/2.0, which assumedly applies only to the short side of the zoom.

Which would give a diameter of 2mm.

But it is really legitimate to continue and back into f/6 for the long side, the 12mm?

Do you agree the formulas are similar?

The only thing that gives me pause is looking at photographic lenses, (only because they list aperture sizes right on the lens for both sides of the zoom range), since the formula clearly wouldn't work for them:

The one on the far right is > 10x yet the f-number doesn't even double.

Yes I know these are much higher quality lenses with more optical parts and so they might not work with the same formula. But just to note these lenses above are the low-end Nikons, and the focal does physically extend when you zoom on these (unlike some of the higher end ones with near constant aperture though out their range.), so I guess the entrance pupil is getting significantly bigger as you zoom.

Also, if you apply the straight line formula you can get some pretty high f-numbers, for instance the calculated f/55 of the Hik PTZ above a bit.

Not that it couldn't be that, but it would be nice to know.

I'm just gonna do some tests on some lenses I have lying around, maybe with a c-mount adapter into a Nikon to use the meter.

Thanks!

Thanks, you're right, that is the same approach. Sorry for the redundancy.

One point that's fairly arcane is that the aperture of a complex lens is typically internal -- that is, the point of restriction to aperture diameter cannot be determined by measuring the entrance or exit lens diameter. In ignorance, I suppose that aperture may change throughout the zoom, which would invalidate the linear assumption. If that is the case, then in the absence of fact, we are left with very little other than to guess at full zoom f/number.

I'd very much like to hear how your assessment ultimately works out.