The fallacy of 35mm "equivalent focal lengths"

Started 5 months ago | Discussions
OP Tony Beach Forum Pro • Posts: 11,967
Re: Definition of "reach", and an example/comparison

gardenersassistant wrote:

Is your essential point here that, depending on optics, pixel density and output size, you may get better results for a particular field of view from a crop on one camera using a shorter equivalent focal length than from the full frame on another camera using a longer equivalent focal length?

My point is that "equivalent focal length" is a misnomer, the widespread reliance on it to understand the FOV notwithstanding. In practice, I could mount a Sigma 18-35/1.8 DX lens on a D500 or D7200 and get the same results with it as the stated "equivalent 28-105" range of the S95 -- so given that, why not say the Sigma 18-35/1.8 has an "equivalent focal length" of 28-105mm?

And where that was the case the "reach" of the shorter equivalent focal length would be greater than the reach of the longer equivalent focal length? Hence your point that there is more to reach than equivalent focal length?

It's really deliberately misleading for camera manufactures to use "equivalent focal lengths." No focal length is really equivalent to another, and a knowledgeable photographer can make the actual focal length of a lens on her camera equivalent to any number of focal lengths on any number of cameras as long as certain conditions are met (none of which are spelled out when manufacturers use the term "equivalent focal length").

So, for example, the full frame from a ZS70 at 129mm (720mm equivalent focal length) might not be as good as a crop from a D800 with a 28-70 at 70mm (70mm equivalent focal length).

I didn't postulate that.

I just did an experiment along somewhat similar lines. I captured an image using 720mmm equivalent with a TZ90 (ZS70). I then captured the same scene, focused on the same area (the notice board) with an A7ii with 24-240 at 70mm. I then cropped the A7ii image to match the TZ90 full frame. Here is the extent of the crop. It measured 609 x 456 pixels.

I did the same at 105mm on the A7ii, with this crop, which was 901 x 676 pixels.

I then output all three at 1080 pixels high.

TZ90, full frame

A7ii, cropped from 70mm

A7ii, cropped from 105mm

For these particular cameras, focal lengths, pixel densities and output size it seems to me that the TZ90 has greater reach than the A7ii with 24-240 at 70mm and 105mm focal length.

Postscript.

With the 24-240 at 240 it was closer, but I think the TZ90 was still a little better.

Thank you for that. My expectation, as stated in my OP, is that camera will resolve more than anything I currently have (and that was one factor in why I chose it for my girlfriend), and in good or decent light it should hold up reasonably well (such as the middle "web size" crops I showed) up to about what can be done with a 350mm on a D800 with a good lens.

OP Tony Beach Forum Pro • Posts: 11,967
Re: Needs definitions

hesbehindyou wrote:

hesbehindyou wrote:

Hi Tony, skimmed through it twice but got hopelessly confused.
I'd recommend re-writing it to make more concise and also to add in the definitions of the various terms you're using.

Hi again,

I read through the replies and it looks like you think that it would be less confusing if equivalent focal length stopped being used to refer to a field of view that's equivalent to full frame camera, and instead changing its meaning to refer to something like:

'the equivalent image quality taking into account the sensor too'.
I think that would confuse everyone

Another poster wanted to do a similar thing with redefining aperture as he objected to an f1.8 lens on a smaller sensor giving a different image quality & depth of field to an f1.8 lens on a larger sensor.

Essentially, we've got a fairly simple and limited concept that tells part of the story and some people want to divorce that figure and definition from its current, limited, logical meaning and confuse it into a single number that defines what, for want of a better word, I'll call 'image quality'.

It's not possible as things like focal length compression and exposure mean there is no equivalence-in-all-respects for you to attach a single number to. Attaching a number to what things you can (or think you can) leaves you back where we are now (with multiple factors to take into account) but with a system that's arbitrary, difficult to measure and impossible to be objective about.
Best we accept the limitations of what is meant by equivalence and be aware of what it doesn't take into account.

People are free to do whatever makes them comfortable. When I want an idea of what a camera can do (i.e., what it is equivalent to) I look at its actual focal lengths and apertures, and then the size and pixel density of its sensor. The only limitation actually described by "equivalent focal length" is how wide a FOV you can capture in the file. Many consumers (and even some participants in the forums here at DPR) falsely think that when the camera is sold to them with some extraordinary "equivalent focal length" that they would need an enormous lens to replicate that, and that's misleading and fallacious.

OP Tony Beach Forum Pro • Posts: 11,967
Re: The fallacy of 35mm "equivalent focal lengths"

thinkinginimages wrote:

Tony Beach wrote:

Preface

Ironically, even here at DPR equivalent focal lengths are often divorced from a complete understanding of what is or isn't equivalent. There is this idea that if a lens covers a certain FOV on a given format then it is somehow equivalent to whatever focal length that would cover that FOV on a 35mm format camera.

[This is a good place to suggest to anyone that doesn't want to read a long post (I usually don't like reading long posts) that you might want to skip to the picture below and take a long look at it and draw your own conclusions. Just be prepared for me alluding back to the "Getting into the weeds" portion of this post if you have any questions or concerns about what I'm presenting.]

The reason for this post is that I got to thinking about "reach" the other day as I was researching a compact camera to give my girlfriend for her upcoming birthday. “Reach” is one of the factors I was considering, and I’ve settled on a Panasonic Lumix DC-ZS70 with (among other features I think will be valuable to have) its 20 MP sensor and a 30x zoom. However, I don’t for a minute buy into the “24-720 mm equivalent focal length” which is how the camera is marketed (for instance, here and here). Will this new camera get more reach than the Canon PowerShot S95 it will be replacing? Undoubtedly, but I will have more to say about that later this week when I have the new camera in hand. Will it get more reach than I have with my D800, NIKKOR 70-200/2.8 VR and TC-14eII? I'm thinking it should, but that too remains to be seen.

Getting into the weeds

There are three things that add up to reach:

1.) Optics -- which includes the actual focal length (and not the equivalent focal length), and just how good the optics are (I looked at a 70-300mm lens for my D800 and it was sent back because it didn't have any more resolution at 300mm than the 200mm lens focal length I already had).

2.) Pixel density -- which is essentially how many linear pixels in a mm of the image circle covered.

3.) Aperture diameter -- which is what true equivalence is all about. As it relates to reach small apertures have more diffraction, and because smaller apertures restrict light coming to the sensor the exposure ends up being noisier which in turn negatively effects resolution.

Given all of that, what is the actual “equivalent” focal length of the Canon PowerShot S95 compared to what I routinely get with my D800? After some testing with various lenses I concluded that at 35mm my NIKKOR 28-70/2.8D matches the longest focal length of my S95, so it's a third of the published 105mm "equivalent" focal length of that compact camera. I expect the DC-ZS70 to do better than the S95 with its 129mm lens rather than the 22.5mm lens on the S95, and with its 840 pixels per linear millimeter rather than the 490 pixels per linear millimeter on the S95.

Will the DC-ZS70 do better than what I get from my D800 with my longest current focal length? Well here's the math so far for the D800 compared to the S95:

At 35mm my D800 with its 204 pixels per linear millimeter beats my S95 at 22.5mm with its 490 pixels per linear millimeter. That's not true of all the lenses I tested, and some could possibly do even better, but I did test my old NIKKOR 18-70 DX kit lens and at 50mm it barely matched the S95. One might have expected the S95 having 2.4x as much linear resolution as my D800 at the sensor level would translate to its 22.5mm lens being equivalent to a 54mm lens, and while reasonably close to that it's only 65% of the way there (35mm rather than 54mm). Some of this is about optics, for sure; but as I will show in the visual examples below diffraction is also a factor.

Maybe I should break out my D300 and crop its final output to 4:3 aspect ratio, which would work out to 10.8 MP and be a bit closer to the 9.98 MP for the S95, but at 181 pixels per linear millimeter that's only a difference in linear resolution per millimeter of 12.5% more for the D800 (i.e., it's barely noticeable). The thing is when it comes to focal length equivalence (if you define that as reach rather than FOV coverage area) is that it's not about the sensor's format or aspect ratio, it's about the relative pixel densities -- so if I put one of my 105mm focal length lenses on my D300 you're going to have a hard time at the pixel level telling the difference between its output on that camera and its output on my D800 (the one thing that will be obviously different will be the FOV, but that's not reach).

Given all of that, I'm expecting the reach of the ZS70 at about 105mm to beat my current longest lens on my D800. I'll try to test that hypothesis next week. In the meantime...

A picture is worth a 1000 words (if not more)

Okay, so now comes the visual evidence to back up what I'm writing about here:

As always, it's important to view this at its "original size" or "100% zoom."

My final thoughts (for this post)

For me that upper right crop at f/22 says a lot. Why? Because the aperture diameter at f/22 for a 90mm lens is 4.09mm, and that's (essentially) the same aperture diameter as f/5.6 for the 22.5mm lens used on the S95 (4.02mm). The middle crops are basically "web size," which in this context is the full frame of the S95 file and the equivalent FOV of the D800 file both sized to 1080 vertical pixels in height -- and for all practical purposes that's enough for a lot of people, and if that's the case I could probably have taken a good 20mm lens and gotten "good enough" results on my D800 under these conditions.

Well written. In a big overview I think "equivalence" created more confusion than it was worth. Taking the sensor and "mechanics" out of the equation, it's more about magnifications, and angles of view, the optics. What does 20X mean in common terms? Why equivalence in 35mm terms? It's such an old point of reference. (Been there.)

I use MFT. I don't think "2X (or 1/2) equals 35mm, so...". 14mm is wider, 150mm is narrower, 20mm is close to the human eye, etc. I'd lose my train of thought if I had to calculate every sensor size.

Thank you for that. My proposal would be to simply say in degrees the AOV of the lens.

OP Tony Beach Forum Pro • Posts: 11,967
Re: The fallacy of 35mm "equivalent focal lengths"

hesbehindyou wrote:

thinkinginimages wrote:

Why equivalence in 35mm terms? It's such an old point of reference. (Been there.)

Because it was a common frame of reference for those coming from 35mm.

The truth is that most don't actually know the AOV of any 35mm lens in degrees. Ask them to quick tell you which lens captures a vertical or horizontal 90° AOV.

Ilfotografo Regular Member • Posts: 341
Re: The fallacy of 35mm "equivalent focal lengths"
1

Tony Beach wrote:

The truth is that most don't actually know the AOV of any 35mm lens in degrees. Ask them to quick tell you which lens captures a vertical or horizontal 90° AOV.

True, but who said anything about aOV in degrees?

Lee Jay Forum Pro • Posts: 54,507
Even though you're right, you're actually wrong
7

35mm-equivalent focal length isn't about "reach", it's about "field of view".

"Reach", is about resolving power - the smallest angle which an object can occupy and be resolved.

You correctly stated the major parameters that control "reach", but "35mm-equivalent focal length" isn't about reach, it's about FOV. When I crop, my 35mm-equivalent FOV changes but the resolving power obviously doesn't.

Think of 35mm-equivalent focal length as just a different way of stating "angle-of-view". In fact, they are directly related by a simple formula:

Angle-of-view = 2*arctan(sensor size/(focal length*2))

If you fix sensor size to 36mm, then horizontal angle-of-view gives 35mm-equivalent focal length using the above formula.  You can use a different measurement if you prefer vertical or diagonal angle-of-view.

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sybersitizen Forum Pro • Posts: 13,146
Okay. What now?
3

Tony Beach wrote:

When I want an idea of what a camera can do (i.e., what it is equivalent to) I look at its actual focal lengths and apertures, and then the size and pixel density of its sensor. The only limitation actually described by "equivalent focal length" is how wide a FOV you can capture in the file. Many consumers (and even some participants in the forums here at DPR) falsely think that when the camera is sold to them with some extraordinary "equivalent focal length" that they would need an enormous lens to replicate that, and that's misleading and fallacious.

I don't think anyone here would choose to argue with those three sentences ... at least I wouldn't. Maybe this thread would be much shorter if you said exactly that in the first post.

Some (myself included) might feel that there is no guilty party at work intentionally trying to deceive or mislead the population of camera buyers; but rather it's just that many things are more complicated than can be easily presented and digested by the population of buyers of any complex product category, and this qualifies as one of them.

A question now is: Are you in favor of camera manufacturers describing and labeling products differently (replacing equivalent focal length with equivalent FOV) and including the many associated caveats in those descriptions and/or labels? And the same thing regarding camera reviews and forum discussions of equivalence?

Mark Scott Abeln
Mark Scott Abeln Forum Pro • Posts: 13,674
Diffraction

A Wingnut wrote:

My apologies if this was brought up, some of this is over my head.

At f/22, defraction is going to be an issue anyway, so heavy crops are generally out of the question. It’s difficult to compare IQ with f/5.6 and f/22. Most start at around f/13, give or take. I can get stupid good crops at f/8-f/13, and anything above that starts to deteriorate a bit. At f/22, my crop goes from being decent at even 125% to similar quality at 50%.

I am bringing this up because I wondered if it was even conclusive to have anything at over f/13.

One of the nice things about diffraction is that it is the same for all cameras and lenses at the same f/stop. The width of the diffraction blur—also known as the Airy Disk—is proportional to the f/stop value.

This proportionality means that f/22 will have double the diffraction blurring as will f/11, and f/8 will have double the blur of f/4, but half that of f/16. Please note that this width is the same on all sensors. So f/2 on a full frame will give the same diffraction blur—relatively speaking!—as f/4 on a micro 4/3rds sensor, which is half as wide. Likewise, f/64 on an 8x10 inch large format camera will give the same diffraction, as a percentage of image width, as would about f/9 on a 'full frame' camera.

Diffraction is also proportional to the wavelength of light. Red light will be diffracted a bit less than twice as much as blue light.

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Lee Jay Forum Pro • Posts: 54,507
Re: Diffraction
1

Mark Scott Abeln wrote:

A Wingnut wrote:

My apologies if this was brought up, some of this is over my head.

At f/22, defraction is going to be an issue anyway, so heavy crops are generally out of the question. It’s difficult to compare IQ with f/5.6 and f/22. Most start at around f/13, give or take. I can get stupid good crops at f/8-f/13, and anything above that starts to deteriorate a bit. At f/22, my crop goes from being decent at even 125% to similar quality at 50%.

I am bringing this up because I wondered if it was even conclusive to have anything at over f/13.

One of the nice things about diffraction is that it is the same for all cameras and lenses at the same f/stop. The width of the diffraction blur—also known as the Airy Disk—is proportional to the f/stop value.

Which means it's not the same for all cameras, because the size of the Airy Disk relative to the size of the sensor (which is what matters for resolution) changes with sensor size.

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Lee Jay

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tko Forum Pro • Posts: 12,880
the fallacy of fallacy posts
8

Anytime I see a post w/the word "fallacy" I'm going to assume it is a fallacy.

The thing is, when you do a comparison, you keep vary some things, keep others constant. Here, we've got things varying all over the place. Pixel density, lens quality, noise, different sensor generations, atmospheric distortions, subjective observations of image quality, wide range telephoto zooms compared to fixed zoom with telephotos.

Equivalence is a very simple thing. What you've done here is to use a lot of words to define it to your world view.

The explosive power of one atom bomb is equal to 50,000 pounds of TNT. Simple enough, right? But then the arguers come in. What? But you can't carry 50,000 pounds of TNT in a plane. TNT isn't radioactive. It has a different explosive time profile. The color is different. One is harder to obtain. All true, but irrelevant to the initial statement.

Lens equivalence is the simplest thing in the world. People like to make it complicated and confusing by throwing in other factors. Which, are of course important. But they don't change anything about equivalence.

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SirPeepsalot Contributing Member • Posts: 550
Re: the fallacy of fallacy posts

tko wrote:

Anytime I see a post w/the word "fallacy" I'm going to assume it is a fallacy.

The thing is, when you do a comparison, you keep vary some things, keep others constant. Here, we've got things varying all over the place. Pixel density, lens quality, noise, different sensor generations, atmospheric distortions, subjective observations of image quality, wide range telephoto zooms compared to fixed zoom with telephotos.

Equivalence is a very simple thing. What you've done here is to use a lot of words to define it to your world view.

The explosive power of one atom bomb is equal to 50,000 pounds of TNT. Simple enough, right? But then the arguers come in. What? But you can't carry 50,000 pounds of TNT in a plane. TNT isn't radioactive. It has a different explosive time profile. The color is different. One is harder to obtain. All true, but irrelevant to the initial statement.

Lens equivalence is the simplest thing in the world. People like to make it complicated and confusing by throwing in other factors. Which, are of course important. But they don't change anything about equivalence.

This.

Mark Scott Abeln
Mark Scott Abeln Forum Pro • Posts: 13,674
Re: Diffraction

Lee Jay wrote:

Which means it's not the same for all cameras, because the size of the Airy Disk relative to the size of the sensor (which is what matters for resolution) changes with sensor size.

Same as in same, actual, physical, width, in real life, on the sensor. That's a basic principle and it is easy to remember.

Once you realize that, then you can simply figure it out for various sensor sizes. Double the sensor width and you have to double the f/stop to get the same relative amounts of diffraction.

Lots of intermediate photographers, who read the older film literature, often try to duplicate the camera settings of the old masters of photography, and so they may use f/22 or even try to reach f/64, but end up being quite disappointed in the softness of their images. Simply remembering the basic rule, that the diffraction width is equal for all cameras and all lenses at the same f/stop, then they can calculate what setting to use on their particular camera.

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Mark Scott Abeln
Mark Scott Abeln Forum Pro • Posts: 13,674
Re: the fallacy of fallacy posts
1

Agreed.

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Fresch Senior Member • Posts: 1,821
Re: The fallacy of 35mm "equivalent focal lengths"

I just put black tape over all the numbers and shoot what looks like I want in the view finder.

SirPeepsalot Contributing Member • Posts: 550
Re: The fallacy of 35mm "equivalent focal lengths"
1

Fresch wrote:

I just put black tape over all the numbers and shoot what looks like I want in the view finder.

A true master black-tapes the viewfinder as well.

Lee Jay Forum Pro • Posts: 54,507
Re: Diffraction

Mark Scott Abeln wrote:

Lee Jay wrote:

Which means it's not the same for all cameras, because the size of the Airy Disk relative to the size of the sensor (which is what matters for resolution) changes with sensor size.

Same as in same, actual, physical, width, in real life, on the sensor.

Right, but that's not a particularly interesting thing because it defines basically nothing about the final image.  It doesn't define either total resolution or angular resolving power.

That's a basic principle and it is easy to remember.

Once you realize that, then you can simply figure it out for various sensor sizes. Double the sensor width and you have to double the f/stop to get the same relative amounts of diffraction.

I just don't think this is an easy way to understand the impact of diffraction on the final image.  In fact, I don't think there is an "easy" way because it depends on what you're trying to achieve (total image resolution or angular resolving power).

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Mark Scott Abeln
Mark Scott Abeln Forum Pro • Posts: 13,674
Re: The fallacy of 35mm "equivalent focal lengths"

SirPeepsalot wrote:

Fresch wrote:

I just put black tape over all the numbers and shoot what looks like I want in the view finder.

A true master black-tapes the viewfinder as well.

And always uses manual exposure. And adjusts focus by only using the focus scale on the lens (which is really hard to do these days!).

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OP Tony Beach Forum Pro • Posts: 11,967
Re: The fallacy of 35mm "equivalent focal lengths"

Gerry Winterbourne wrote:

hesbehindyou wrote:

thinkinginimages wrote:

I think "equivalence" created more confusion than it was worth.

I've often wondered why we don't just go with field of view? I'm assuming that it's because it's not a property that's inherent to the lens but will also involve the sensor...

It's not just that although it is, of course, a factor. What do we mean by field of view? If we mean width there's the problem that it gets wider the further away the scene; so the FOV for portraits at a few metres away would be tiny compared to the FOV with the same lens used for a landscape. So we'd really have to mean angle of view.

But I've never come across anyone who thinks of scenes in terms of how many degrees (or radians) they cover. And angle of view isn't linear with focal length - especially at wide angles - so there's another complication to have to deal with.

It's not a complication at all, but rather an opportunity:

Many wrongly assume that if you double or halve the focal length the AOV (or FOV for a given distance) changes accordingly. It's easy to imagine the photographer saying she  wants to zoom twice as "close" to the subject and having the lens designating degrees instead of putative millimeters facilitates rather than hinders that.

There have always been different formats, going up to full plate. While it's silly to contemplate putting a full plate lens on a 35mm SLR there has always been some ability to swap lenses between formats. Now, it's easy to print the focal length of a lens on a body and it is a single number regardless of the body used. But printing the angle of view is tricky because you'd have to do it for every format the lens might be used on, as you say ...

For ILC lenses, and even on the front of compact cameras, the lens has its actual focal lengths printed on it. Now when I turn on my S95 the camera will display the "equivalent focal length" which I find marginally useful inasmuch as I know I'm fully or partially zoomed -- but seeing a number followed by a degree symbol rather than a misleading "mm" symbol would be more useful for me, and I am arguing here that others would find that more useful too.

tony field Forum Pro • Posts: 10,224
Re: Even though you're right, you're actually wrong

Lee Jay wrote:

35mm-equivalent focal length isn't about "reach", it's about "field of view".

"Reach", is about resolving power - the smallest angle which an object can occupy and be resolved.

You correctly stated the major parameters that control "reach", but "35mm-equivalent focal length" isn't about reach, it's about FOV. When I crop, my 35mm-equivalent FOV changes but the resolving power obviously doesn't.

Think of 35mm-equivalent focal length as just a different way of stating "angle-of-view". In fact, they are directly related by a simple formula:

Angle-of-view = 2*arctan(sensor size/(focal length*2))

If you fix sensor size to 36mm, then horizontal angle-of-view gives 35mm-equivalent focal length using the above formula. You can use a different measurement if you prefer vertical or diagonal angle-of-view.

Of course there is the third angle of view which is based upon the diagonal of the format. This is the standard by which "Equivalence" works.

I find it sadly amusing that some people in this thread, includng thet OP, use their own predilection definition of terms and ignore actual rigorously defined definitions. They like to play with equivalence because it is simply fun.

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Lee Jay Forum Pro • Posts: 54,507
Re: Even though you're right, you're actually wrong
3

tony field wrote:

Lee Jay wrote:

35mm-equivalent focal length isn't about "reach", it's about "field of view".

"Reach", is about resolving power - the smallest angle which an object can occupy and be resolved.

You correctly stated the major parameters that control "reach", but "35mm-equivalent focal length" isn't about reach, it's about FOV. When I crop, my 35mm-equivalent FOV changes but the resolving power obviously doesn't.

Think of 35mm-equivalent focal length as just a different way of stating "angle-of-view". In fact, they are directly related by a simple formula:

Angle-of-view = 2*arctan(sensor size/(focal length*2))

If you fix sensor size to 36mm, then horizontal angle-of-view gives 35mm-equivalent focal length using the above formula. You can use a different measurement if you prefer vertical or diagonal angle-of-view.

Of course there is the third angle of view which is based upon the diagonal of the format.

I said that (see above).

This is the standard by which "Equivalence" works.

I disagree, actually.  I always use horizontal and fix aspect ratio because I never frame diagonally.

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