How do constant-f/stop zoom lenses exist?

JustinRebbert · Jan 16, 2019

There’s something I’ve been wondering about the theory and math behind constant f/stop zoom lenses. I apologize in advance that this is going to be a rather lengthy and technical post.

The f/stop value of a lens isn’t an actual measurement; rather, it’s a ratio. Specifically, the ratio of focal length to aperture diameter. So for example if you have a 100mm lens that has a maximum f/stop value of f/2, you can calculate that the actual maximum aperture diameter would be 50mm. You will sometimes see the f/stop value correctly presented as an actual ratio, such as 2.8:1, which means 2.8 units of focal length for one unit of aperture diameter.

If you do that math on an opening with a diameter of 50mm, you can calculate that the area of that aperture is around 1963.5mm^2.

Now consider the same 100mm lens at f/2.8. We can calculate that the aperture diameter would be around 35.71mm, the the area would be around 1001.8mm^2. This approximately corresponds to the concept that each whole f/stop value lets in half as much light as the previous one, since a hole of a particular size will let half as much light through as a hole that’s twice its size (in area). (Those two areas aren’t exactly double or half of each other probably due to rounding errors with the f/stop values.)

So far, all of this makes sense.

Here’s what I don’t understand: How can a zoom lens have a constant maximum f/stop value?

Remember that the f/stop value is the ratio of focal length to aperture diameter. If the focal length changes but the aperture remains the same, the ratio, the f/stop value, will change.

I would think that the aperture of a lens can open up to some particular maximum diameter, and I would further think that it can remain opened to that diameter regardless of the focal length of the lens. And mathematically, this means that the ratio of focal length to aperture diameter should change as the focal length changes while the aperture diameter remains the same. Consider a 70-200mm f/2.8 lens. 70mm at f/2.8 calculates to an aperture diameter of 25mm, and if that’s as wide as it can open, then at 200mm that would work out to f/8. On the other hand, 200mm at f/2.8 calculates to an aperture diameter of 71.4mm, and if it’s that wide at 70mm, that would work out to an astonishing f/0.98!

The concept of the f/stop value being the ratio of focal length to aperture diameter is correct. The math is correct, allowing for rounding errors. It does not make sense that the actual aperture diameter of a zoom lens would change as the lens is zoomed in or out. Yet zoom lenses with constant maximum f/stop values do exist.

How is this possible? What have I misunderstood?

Adrian Tung · Jan 16, 2019

JustinRebbert said:
The concept of the f/stop value being the ratio of focal length to aperture diameter is correct.

Not exactly. The f/stop is the ratio of focal length to entrance pupil, which is a projection of the physical aperture as seen/measured from the front of the lens.

Different types of zoom lenses may employ a different method of constant aperture, but if you look at telephoto zooms like the 70-200/2.8, when you zoom towards 200mm the elements in front of the physical aperture move in a way that makes aperture appear to grow in diameter as seen through the front element.

FrancoD · Jan 16, 2019

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JustinRebbert · Jan 16, 2019

If I understand what you’re saying correctly, and also using the graphic in the next reply down as an aid, a lens magnification effect makes the projected pupil size you mentioned appear to increase in size as the lens is zoomed in...just like moving a magnifying glass (a lens itself) closer to an object makes it appear larger...and this apparent, or projected, pupil size is what’s actually considered to be the aperture, rather than the physical size of the diaphragm opening, so as it appears to be enlarged by a lens magnification effect, the ratio of focal length to this apparent pupil size remains constant. Is that more or less what you’re saying?

Adrian Tung · Jan 16, 2019

JustinRebbert said:
If I understand what you’re saying correctly, and also using the graphic in the next reply down as an aid, a lens magnification effect makes the projected pupil size you mentioned appear to increase in size as the lens is zoomed in...just like moving a magnifying glass (a lens itself) closer to an object makes it appear larger...and this apparent, or projected, pupil size is what’s actually considered to be the aperture, rather than the physical size of the diaphragm opening, so as it appears to be enlarged by a lens magnification effect, the ratio of focal length to this apparent pupil size remains constant. Is that more or less what you’re saying?

Yes, that's basically the gist of it, though the exact definition of "entrance pupil" is a bit more technical than how I had described it.

Some reading material for reference:

https://software.canon-europe.com/files/documents/EF_Lens_Work_Book_10_EN.pdf

https://lenspire.zeiss.com/photo/app/uploads/2018/04/Article-Bokeh-2010-EN.pdf

Do note that Canon calls it the "effective aperture" whereas Zeiss uses the term "entrance pupil".

John Sheehy · Jan 18, 2019

JustinRebbert said:
How is this possible? What have I misunderstood?

The weakness you perceive is very real; from the perspective of the subject, as you stand in one spot, and (un-)zoom your lens from 200mm in to 70mm, the area of the visible entrance pupil PLUMMETS.

That increases subject-level noise (with the same shutter speed), subject-level diffraction, and subject-relative DOF, even if your f-ratio and exposure and ISO are unchanged.

This constant "feature" is highly over-rated, as just about any camera lets you set Av value to be either fixed or maximum (or switch in the middle of the range), regardless of whether the f-ratios wide open are constant or not.

John Sheehy · Jan 18, 2019

Adrian Tung said:
Different types of zoom lenses may employ a different method of constant aperture, but if you look at telephoto zooms like the 70-200/2.8, when you zoom towards 200mm the elements in front of the physical aperture move in a way that makes aperture appear to grow in diameter as seen through the front element.

Of course, we say "appears" because we know that the physical size of the opening inside the camera may be different, but the "apparent" entrance pupil is very real in determining how much of the light from a subject is captured.

lilBuddha · Jan 18, 2019

John Sheehy said:
This constant "feature" is highly over-rated, as just about any camera lets you set Av value to be either fixed or maximum (or switch in the middle of the range), regardless of whether the f-ratios wide open are constant or not.

Uum, what? The constant aperture is about the max aperture. And it is very useful to some phtographers to have that max aperture be as large as it can be.

In other words, it isn't so much about the aperture being constant as it is about more light when zoomed in.

Tell, events, action and wildlife photographers that they don't need that large aperture when zoomed in because they can have a smaller constant one.

Any feature can feel over-rated if one doesn't use it. Unnecessary for a particular individual ≠ over-rated

John Sheehy · Jan 18, 2019

lilBuddha said:
John Sheehy said:

This constant "feature" is highly over-rated, as just about any camera lets you set Av value to be either fixed or maximum (or switch in the middle of the range), regardless of whether the f-ratios wide open are constant or not.

Click to expand...

Uum, what? The constant aperture is about the max aperture. And it is very useful to some phtographers to have that max aperture be as large as it can be.

In other words, it isn't so much about the aperture being constant as it is about more light when zoomed in.

Tell, events, action and wildlife photographers that they don't need that large aperture when zoomed in because they can have a smaller constant one.

Any feature can feel over-rated if one doesn't use it. Unnecessary for a particular individual ≠ over-rated

I don't think that you have read what I thought that I wrote.

The larger the entrance pupil on the long end, the better; no argument; that is a superset of capabilities, at the cost of a larger front end. The "feature" of the open f-ratio staying the same as you zoom out to the wide end does nothing for you that camera settings can't do, though, and if you are after minimal DOF, diffraction, and subject-level noise, though, you are better off if the f-ratio drops as you zoom out, because that means that the entrance pupil size is plummeting slower than if the f-ratio remained the same.

IOW, a zoom that is 70/2.2 to 200/2.8 is better than a 70-200/2.8, except for it's heft. If you want constant f/2.8, you just zoom to 200mm, set the Av value explicitly to 2.8, and zoom away; it will always be at 2.8. However, if you zoom to 70mm and set the Av value explicitly to 2.2, the camera will always use the largest aperture at every focal length as you zoom in and out and in and out again.

lilBuddha · Jan 18, 2019

John Sheehy said:
lilBuddha said:

John Sheehy said:

This constant "feature" is highly over-rated, as just about any camera lets you set Av value to be either fixed or maximum (or switch in the middle of the range), regardless of whether the f-ratios wide open are constant or not.

Click to expand...

Uum, what? The constant aperture is about the max aperture. And it is very useful to some phtographers to have that max aperture be as large as it can be.

In other words, it isn't so much about the aperture being constant as it is about more light when zoomed in.

Tell, events, action and wildlife photographers that they don't need that large aperture when zoomed in because they can have a smaller constant one.

Any feature can feel over-rated if one doesn't use it. Unnecessary for a particular individual ≠ over-rated

Click to expand...

I don't think that you have read what I thought that I wrote.

John Sheehy said:
IOW, a zoom that is 70/2.2 to 200/2.8 is better than a 70-200/2.8, except for it's heft. If you want constant f/2.8, you just zoom to 200mm, set the Av value explicitly to 2.8, and zoom away; it will always be at 2.8. However, if you zoom to 70mm and set the Av value explicitly to 2.2, the camera will always use the largest aperture at every focal length as you zoom in and out and in and out again.

No one makes that lens. 2.8 seems a general ceiling for long lenses. I'm guessing it is a good balance between light transmitted, weight and cost.

There is no practical benefit for making the lens you propose. The people who want such large apertures at wider angles tend to buy shorter zooms or primes.

So whilst you might have a technical point, I do not think you have a practical one. You would be adding cost for no appreciable benefit to the target market.

PhotoFactor · Jan 18, 2019

JustinRebbert said:
If I understand what you’re saying correctly, and also using the graphic in the next reply down as an aid, a lens magnification effect makes the projected pupil size you mentioned appear to increase in size as the lens is zoomed in...just like moving a magnifying glass (a lens itself) closer to an object makes it appear larger...and this apparent, or projected, pupil size is what’s actually considered to be the aperture, rather than the physical size of the diaphragm opening, so as it appears to be enlarged by a lens magnification effect, the ratio of focal length to this apparent pupil size remains constant. Is that more or less what you’re saying?

I guess regardless of theory, what REALLY needs to be true is that as you zoom, the actual amount of light hitting the focal plane needs to be constant per unit area. So whatever tricks are employed in the lens/aperture to do it, as you zoom, the "brightness" on the focal plane has to stay constant. This provides for a constant exposure at a given shutter speed.

I thought the original question was quite a good one and I have the same curiosity, although I'm not sure I fully understand how it is done based upon the answers we have so far.

John Sheehy · Jan 18, 2019

lilBuddha said:
So whilst you might have a technical point, I do not think you have a practical one. You would be adding cost for no appreciable benefit to the target market.

You have an amazing ability to twist what other people write into something different for you to lampoon.

What I said is that there is no real practical value in a zoom lens having constant f-ratio as an end in itself, because the camera can do that, if you need that.

lilBuddha · Jan 18, 2019

John Sheehy said:
lilBuddha said:

So whilst you might have a technical point, I do not think you have a practical one. You would be adding cost for no appreciable benefit to the target market.

Click to expand...

You have an amazing ability to twist what other people write into something different for you to lampoon.

What I said is that there is no real practical value in a zoom lens having constant f-ratio as an end in itself, because the camera can do that, if you need that.

I'm not trying to twist anything, nor am I lampooning¹ anything. This site is replete with people who like to get technical and ignore the practical simply to make a point. I do realise that this is inference on my part, as I do not know your intent. But your post does miss thy why of constant zoom appreciation.

You began this with the constant aperture being over-rated.

And I replied that the constant part isn't why people buy those lenses.

Put into bold as this is the salient bit of the exchange.

I am not using irony or sarcasm. Ridicule would be an intent thing, but I do not think my words imply that, they were not meant to. Other than, possibly, the Um, what? And whilst, I suppose that could be considered ironic,² it was meant to emphasise the point.

¹lam·poon/lamˈpo͞on/

verb

1.publicly criticize (someone or something) by using ridicule, irony, or sarcasm.

²i·ro·ny1/ˈīrənē/

noun

the expression of one's meaning by using language that normally signifies the opposite, typically for humorous or emphatic effect.

And no, adding the definitions is not sarcastic. Just making sure we are operating under the same definitions.

Bill Ferris · Jan 18, 2019

lilBuddha said:
John Sheehy said:

This constant "feature" is highly over-rated, as just about any camera lets you set Av value to be either fixed or maximum (or switch in the middle of the range), regardless of whether the f-ratios wide open are constant or not.

Click to expand...

Uum, what? The constant aperture is about the max aperture. And it is very useful to some phtographers to have that max aperture be as large as it can be.

In other words, it isn't so much about the aperture being constant as it is about more light when zoomed in.

Tell, events, action and wildlife photographers that they don't need that large aperture when zoomed in because they can have a smaller constant one.

Any feature can feel over-rated if one doesn't use it. Unnecessary for a particular individual ≠ over-rated

If I'm reading you, correctly, your comments about the value of a constant f-stop zoom (e.g. 70-200 f/2.8) are made in the context of comparing that lens to consumer zoom (e.g. 70-300 f/4.5-5.6). The consumer glass may be longer and less expensive but the constant f-stop zoom - especially in a longer telephoto - often allows you to blow out the background and use a lower ISO. It also probably auto focuses better and has a better build quality.

Is that what you're getting at?

FrancoD · Jan 18, 2019

"This site is replete with people who like to get technical and ignore the practical simply to make a point".

Yes, worth repeating.

Ilfotografo · Jan 18, 2019

JustinRebbert said:
There’s something I’ve been wondering about the theory and math behind constant f/stop zoom lenses. I apologize in advance that this is going to be a rather lengthy and technical post.

The f/stop value of a lens isn’t an actual measurement; rather, it’s a ratio. Specifically, the ratio of focal length to aperture diameter. So for example if you have a 100mm lens that has a maximum f/stop value of f/2, you can calculate that the actual maximum aperture diameter would be 50mm. You will sometimes see the f/stop value correctly presented as an actual ratio, such as 2.8:1, which means 2.8 units of focal length for one unit of aperture diameter.

If you do that math on an opening with a diameter of 50mm, you can calculate that the area of that aperture is around 1963.5mm^2.

Now consider the same 100mm lens at f/2.8. We can calculate that the aperture diameter would be around 35.71mm, the the area would be around 1001.8mm^2. This approximately corresponds to the concept that each whole f/stop value lets in half as much light as the previous one, since a hole of a particular size will let half as much light through as a hole that’s twice its size (in area). (Those two areas aren’t exactly double or half of each other probably due to rounding errors with the f/stop values.)

So far, all of this makes sense.

Here’s what I don’t understand: How can a zoom lens have a constant maximum f/stop value?

Remember that the f/stop value is the ratio of focal length to aperture diameter. If the focal length changes but the aperture remains the same, the ratio, the f/stop value, will change.

I would think that the aperture of a lens can open up to some particular maximum diameter, and I would further think that it can remain opened to that diameter regardless of the focal length of the lens. And mathematically, this means that the ratio of focal length to aperture diameter should change as the focal length changes while the aperture diameter remains the same. Consider a 70-200mm f/2.8 lens. 70mm at f/2.8 calculates to an aperture diameter of 25mm, and if that’s as wide as it can open, then at 200mm that would work out to f/8. On the other hand, 200mm at f/2.8 calculates to an aperture diameter of 71.4mm, and if it’s that wide at 70mm, that would work out to an astonishing f/0.98!

The concept of the f/stop value being the ratio of focal length to aperture diameter is correct. The math is correct, allowing for rounding errors. It does not make sense that the actual aperture diameter of a zoom lens would change as the lens is zoomed in or out. Yet zoom lenses with constant maximum f/stop values do exist.

How is this possible? What have I misunderstood?

I am glad that you asked the question, which had never occurred to me, and I'm happy to see the excellent answers.

To weigh in on the controversy, I have long placed a little value on the fast constant-aperture zoom lenses.

FrancoD · Jan 18, 2019

Ilfotografo said:
To weigh in on the controversy, I have long placed a little value on the fast constant-aperture zoom lenses.

If you had a choice , would you opt for ,say, a 28-105mm f 2.8-f 4 or a 28-105mm f 2.8 ?

A 70-200mm f 2.8 -4 or a 70-200mm f 2.8 ?

BJL · Jan 18, 2019

Roughly, the method is to place the aperture diaphragm behind the movable elements that do the zooming. The f-stop is then determined only by the part of the lens behind the diaphragm.

I believe that one definition of aperture ratio is:

(optical distance from the aperture to the focal plane)/(diameter of the aperture)

so it is not affected by anything happening in front of the aperture diaphragm.

Historically the first zoom lenses were for cinema and consisted of a "zoom unit" added in front of an exiting fixed focal length lens, called the "prime lens" [that is where the weird jargon "prime lens" come from]. This used the aperture system of the prime lens, so that zooming did not change the f-stop: very important with moving pictures!

tony field · Jan 18, 2019

John Sheehy said:
lilBuddha said:

John Sheehy said:

This constant "feature" is highly over-rated, as just about any camera lets you set Av value to be either fixed or maximum (or switch in the middle of the range), regardless of whether the f-ratios wide open are constant or not.

Click to expand...

Uum, what? The constant aperture is about the max aperture. And it is very useful to some phtographers to have that max aperture be as large as it can be.

In other words, it isn't so much about the aperture being constant as it is about more light when zoomed in.

Tell, events, action and wildlife photographers that they don't need that large aperture when zoomed in because they can have a smaller constant one.

Any feature can feel over-rated if one doesn't use it. Unnecessary for a particular individual ≠ over-rated

Click to expand...

I don't think that you have read what I thought that I wrote.

The larger the entrance pupil on the long end, the better; no argument; that is a superset of capabilities, at the cost of a larger front end. The "feature" of the open f-ratio staying the same as you zoom out to the wide end does nothing for you that camera settings can't do, though, and if you are after minimal DOF, diffraction, and subject-level noise, though, you are better off if the f-ratio drops as you zoom out, because that means that the entrance pupil size is plummeting slower than if the f-ratio remained the same.

IOW, a zoom that is 70/2.2 to 200/2.8 is better than a 70-200/2.8, except for it's heft. If you want constant f/2.8, you just zoom to 200mm, set the Av value explicitly to 2.8, and zoom away; it will always be at 2.8. However, if you zoom to 70mm and set the Av value explicitly to 2.2, the camera will always use the largest aperture at every focal length as you zoom in and out and in and out again.

The 70/2.2 to 200/2.8 would be a definite value to me when I shoot theater and dance in low light. If I choose Auto exposure in TV mode with auto ISO, the extra 2/3 next stop exposure (all other things being equal) would on occasion yield better images technically.

it might also be useful for some of my low light portraits and provide a slightly more restricted depth of field when at 70mm.

This would be useful but not a mandatory option.

BJL · Jan 18, 2019

John Sheehy said:
JustinRebbert said:

How is this possible? What have I misunderstood?

Click to expand...

The weakness you perceive is very real; from the perspective of the subject, as you stand in one spot, and (un-)zoom your lens from 200mm in to 70mm, the area of the visible entrance pupil PLUMMETS.

That increases subject-level noise (with the same shutter speed), subject-level diffraction, and subject-relative DOF, even if your f-ratio and exposure and ISO are unchanged.

This constant "feature" is highly over-rated, as just about any camera lets you set Av value to be either fixed or maximum (or switch in the middle of the range), regardless of whether the f-ratios wide open are constant or not.

Agreed: almost any constant f/4 could become a f/2.8-4 by a redesign that moves the aperture diaphragm further forward, without any increase in weight or front element size. For me, lenses like f/2.8-4 and f/2.8-3.5 are wiser designs than constant f/4 — and these days, it can be f/2-2.8 instead of constant f/2.8.

Constant maximum aperture zooms used to be important with mechanically coupled aperture controls—especially when using external meters or zooming in cinematography—because with variable f-stop zooms, the actual f-stop deviated from the f-stop set on the lens, matching it only at minimum focal length and increasing as you zoomed in.

But none of that matters with modern lenses, since electronic coupling ensures that the actual f-stop always matches the setting.

How do constant-f/stop zoom lenses exist?

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