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Equivalence theory

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Miranda F View Drop Down
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Post Options Post Options   Quote Miranda F Quote  Post ReplyReply Direct Link To This Post Posted: 08 January 2019 at 10:51
It is disappointing to see the same old lies, half-truths and misunderstandings being perpetuated in a document that purports to be scientific. An example:

"Equivalent photos are produced using the same amount of light. However, a larger format has the capability of collecting more light than a smaller format. This offers additional photographic capability such as a shallower possible DoF (for the same perspective, AFoV and shutter speed). When this additional capability is utilized, the smaller format will be unable to produce an equivalent photo. Therefore, equivalence theory can be used to determine the maximum photographic capability of a smaller format in relation to a larger one"]

This is simply not true as a comparison of formats (sensor/film sizes). The amount of light collected, and the amount of blur caused away from the focal plane is determined only by the lens entrance pupil (mechanical aperture) and the lens to subject distance, as explained by Harold Merklinger decades ago. If you keep these the same then the results are identical whatever sensor size you use.

When you change the sensor size you have to change the optical strength of the glass in the lens to concentrate the same amount of light on a smaller area of sensor, while maintaining the same entrance pupil. And yes, this does mean changing the focal length and numerical aperture according to the equivalence formula. When you do that, the results are the same.

What *is* true is that you might not be able to find a suitable lens off the shelf to give the same effect on APS-C or micro 4/3 as a your favourite FF portrait lens on 35mm film or an FF sensor.

What *might* be true is that designing and manufacturing such a lens may be more difficult or may be not always be possible. But nobody ever seems to phrase the statement in terms of what is possible in lens design (at least until after I've complained), and even then this claimed without any kind of proof (as indeed it is done later in the article referenced). But the next time the subject is raised out come the same old misleading half-truth headlines as if nothing had been learned.

What *is* true is that the lens manufacturers think they can make much more money from selling FF cameras and lenses than APS-C ones, so they put the majority of their R&D effort into FF. Therefore there is a real difference in what can be achieved by you or me in different sensor sizes using available lenses. But this is a commercial consequence and little to do with basic optics.


Edited by Miranda F - 08 January 2019 at 11:05
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Post Options Post Options   Quote pegelli Quote  Post ReplyReply Direct Link To This Post Posted: 08 January 2019 at 11:15
Originally posted by Miranda F Miranda F wrote:


This is simply not true as a comparison of formats (sensor/film sizes). The amount of light collected, and the amount of blur caused away from the focal plane is determined only by the lens entrance pupil (mechanical aperture) and the lens to subject distance, as explained by Harold Merklinger decades ago. If you keep these the same then the results are identical whatever sensor size you use.
For the image on the sensor you are right, but when the resulting total image is printed on the same paper size (or viewed on the same screen) there will be quite a difference between the pictures from the different sensor sizes (because the image from the smaller sensor needs to be enlarged more).


Originally posted by Miranda F Miranda F wrote:

What *is* true is that you might not be able to find a suitable lens off the shelf to give the same effect on APS-C or micro 4/3 as a your favourite FF portrait lens on 35mm film or an FF sensor.
Agree, it's at the extremes that certain sensor sizes produce results that cannot be achieved with smaller sensors.

Originally posted by Miranda F Miranda F wrote:

What *might* be true is that designing and manufacturing such a lens may be more difficult or may be not always be possible. But nobody ever seems to phrase the statement in terms of what is possible in lens design (at least until after I've complained). And the next time the subject is raised out come the same old misleading half-truths as if nothing has been learned.
Since these lenses are not made it might be true, but also until they are made it's a moot point.

Originally posted by Miranda F Miranda F wrote:

What *is* true is that the lens manufacturers think they can make much more money from selling FF cameras and lenses than APS-C ones, so they put the majority of their R&D effort into FF. Therefore there is a real difference in what can be achieved by you or me in different sensor sizes using available lenses. But this is a commercial consequence and little to do with basic optics.
This I wholeheartedly disagree with as a general statement, Fuji is a clear example which is building a comprehensive high quality APS-C system without any FF offering.
Same is true for Olympus which does the same on M43, without trying anything in FF. So your statement *might* be true for *some* manufacturers but as far as I'm concerned there is no proof for that.


And as always in equivalence discussions for me the most important thing is to define what is kept constant and what is being varied when making statements about the effect of different formats. Examples of these variables (that can either be kept constant or varied are (and some are interdependent): focal length, entry pupil, angle of view, viewing size, aperture value, iso, shutter speed, EV etc. etc.)

Edited by pegelli - 08 January 2019 at 11:44
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Jonas A-R View Drop Down
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Post Options Post Options   Quote Jonas A-R Quote  Post ReplyReply Direct Link To This Post Posted: 08 January 2019 at 11:50
Originally posted by Miranda F Miranda F wrote:

It is disappointing to see the same old lies, half-truths and misunderstandings being perpetuated in a document that purports to be scientific. An example:

"Equivalent photos are produced using the same amount of light. However, a larger format has the capability of collecting more light than a smaller format. This offers additional photographic capability such as a shallower possible DoF (for the same perspective, AFoV and shutter speed). When this additional capability is utilized, the smaller format will be unable to produce an equivalent photo. Therefore, equivalence theory can be used to determine the maximum photographic capability of a smaller format in relation to a larger one"]

This is simply not true as a comparison of formats (sensor/film sizes). The amount of light collected, and the amount of blur caused away from the focal plane is determined only by the lens entrance pupil (mechanical aperture) and the lens to subject distance, as explained by Harold Merklinger decades ago. If you keep these the same then the results are identical whatever sensor size you use.


It is neither a lie or a half truth. For the same exposure, a larger format will produce an image with better signal-to-noise.
The amount of light is not only determined by the entrance pupil. It should be rather obvious that the exposure time is equally important.
The exposure is thus solely determined by three independent variables: Aperture, shutter speed and scene brightness. In natural light exposure can be controlled by changing the aperture and shutter speed. In artificial light, one can simply increase the scene brightness to normalize the exposure at the higher f-number required for the same entrance pupil diameter and AoV on the larger format.
Typically, the larger format offers lenses with larger apertures for the same AoV. That could be the usual f/1.4 FF lenses which is rather difficult to make equivalent on smaller formats. You therefore have a larger shooting envelope on larger formats where you can trade DoF and shutter speed for better SnR.





Originally posted by Miranda F Miranda F wrote:

When you change the sensor size you have to change the optical strength of the glass in the lens to concentrate the same amount of light on a smaller area of sensor, while maintaining the same entrance pupil. And yes, this does mean changing the focal length and numerical aperture according to the equivalence formula. When you do that, the results are the same.

What *is* true is that you might not be able to find a suitable lens off the shelf to give the same effect on APS-C or micro 4/3 as a your favourite FF portrait lens on 35mm film or an FF sensor.


Bingo! You agree that larger formats typically offers larger entrance pupils for the same AoV making the statement you initially objected against true

Originally posted by Miranda F Miranda F wrote:

What *might* be true is that designing and manufacturing such a lens may be more difficult or may be not always be possible. But nobody ever seems to phrase the statement in terms of what is possible in lens design (at least until after I've complained), and even then this claimed without any kind of proof (as indeed it is done later in the article referenced). But the next time the subject is raised out come the same old misleading half-truth headlines as if nothing had been learned.

What *is* true is that the lens manufacturers think they can make much more money from selling FF cameras and lenses than APS-C ones, so they put the majority of their R&D effort into FF. Therefore there is a real difference in what can be achieved by you or me in different sensor sizes using available lenses. But this is a commercial consequence and little to do with basic optics.


Whatever

Edited by Jonas A-R - 08 January 2019 at 13:27
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Phil Wood View Drop Down
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Post Options Post Options   Quote Phil Wood Quote  Post ReplyReply Direct Link To This Post Posted: 08 January 2019 at 20:21
Originally posted by Jonas A-R Jonas A-R wrote:

The exposure is thus solely determined by three independent variables: Aperture, shutter speed and scene brightness.


Not so, there is a fourth variable - sensor sensitivity or ISO. Take your three variables and use the same settings/scene to shoot with ISO 50 and ISO 400 film and you'll see a difference!

Larger digital sensors are more sensitive than smaller sensors using the same technology and pixel count - because the individual sensors recording each pixel are larger and thus receive more light (assuming equivalent lenses).

Of course sensor technology is evolving all the time - it is entirely possible that a FF sensor pixel of 10 years ago is less sensitive than an equivalent sized APS sensor pixel made today.

Nevertheless, the way to increase sensitivity is to increase pixel size in the sensor - hence we have the Sony A7S range.
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Post Options Post Options   Quote sybersitizen Quote  Post ReplyReply Direct Link To This Post Posted: 09 January 2019 at 03:31
Originally posted by Phil Wood Phil Wood wrote:

Originally posted by Jonas A-R Jonas A-R wrote:

The exposure is thus solely determined by three independent variables: Aperture, shutter speed and scene brightness.
Not so, there is a fourth variable - sensor sensitivity or ISO.

Not so.

Sensor sensitivity is one thing. ISO adjustment is a completely separate thing. Neither has any bearing on exposure.

Larger digital sensors are more sensitive than smaller sensors using the same technology and pixel count - because the individual sensors recording each pixel are larger and thus receive more light (assuming equivalent lenses).

Nothing guarantees that larger sensors are more sensitive. What is guaranteed is that more light can impinge on them because they're larger.

Nevertheless, the way to increase sensitivity is to increase pixel size in the sensor

A sweeping statement that does not hold up in actuality.

- hence we have the Sony A7S range.

That's one specific case, not representative of a universal truth.

See, this thread can be fun after all. :)
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Post Options Post Options   Quote Miranda F Quote  Post ReplyReply Direct Link To This Post Posted: 09 January 2019 at 11:57
Originally posted by pegelli pegelli wrote:

Originally posted by Miranda F Miranda F wrote:


This is simply not true as a comparison of formats (sensor/film sizes). The amount of light collected, and the amount of blur caused away from the focal plane is determined only by the lens entrance pupil (mechanical aperture) and the lens to subject distance, as explained by Harold Merklinger decades ago. If you keep these the same then the results are identical whatever sensor size you use.

For the image on the sensor you are right, but when the resulting total image is printed on the same paper size (or viewed on the same screen) there will be quite a difference between the pictures from the different sensor sizes (because the image from the smaller sensor needs to be enlarged more).


This may be true for film but not for digital sensors. If the pixel count is the same (and the exposure time too, Jonas A-R ) then the total light reaching each pixel is the same in each format. The shorter focal length lens in APS-C focusses the same amount of light in a smaller area.

The larger sensor does not collect more light if the lens is adjusted to suit it as per the equivalence formula. If you forget the equivalence formula and just stick the same lens on both cameras then yes, but that's not what we're talking about here. My complaint is the comment often made that 'larger format senors collect more light' - they don't - it is the lens that collects the light.
Miranda F & Sensorex, Sony A58, Nex-6, Dynax 4, 5, 60, 500si/600si/700si/800si, various Sony & Minolta lenses, several Tamrons, lots of MF primes and *far* too many old film cameras . . .
 



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Post Options Post Options   Quote Miranda F Quote  Post ReplyReply Direct Link To This Post Posted: 09 January 2019 at 12:07
Originally posted by Phil Wood Phil Wood wrote:

Originally posted by Jonas A-R Jonas A-R wrote:

The exposure is thus solely determined by three independent variables: Aperture, shutter speed and scene brightness.


Not so, there is a fourth variable - sensor sensitivity or ISO. Take your three variables and use the same settings/scene to shoot with ISO 50 and ISO 400 film and you'll see a difference!

Larger digital sensors are more sensitive than smaller sensors using the same technology and pixel count - because the individual sensors recording each pixel are larger and thus receive more light (assuming equivalent lenses).

No, this assumes the *same* lens. If you use equivalent lenses, they collect the same amount of light.




Originally posted by Phil Wood Phil Wood wrote:


Of course sensor technology is evolving all the time - it is entirely possible that a FF sensor pixel of 10 years ago is less sensitive than an equivalent sized APS sensor pixel made today.

Nevertheless, the way to increase sensitivity is to increase pixel size in the sensor - hence we have the Sony A7S range.


I think the noise benefit of the A7s is mostly attributable to the lower pixel count, and if you process a comparable A7 or A7R image to get the same end pixel count the benefit mostly disappears, and any remaining difference is down to construction.

The question whether a smaller or a larger sensor will produce more noise with a given quantity of incident light focused on it is a nuanced one. I suspect the larger cell would produce more shot noise but would have a higher maximum light capability (though this depends on the ADC as well). But whatever the answer to this question is, it again has nothing to do with basic optics.

And no offense to any of you personally, but this gets to the heart of my complaint about this subject. People keep making sweeping statements about one format being better than another without any qualification, then when you argue the point they always seem to resort either to unproven claims about semiconductor device physics or insist on comparing how the same lens behaves in each format!

Regarding lenses I will readily admit that making a very short focal length lens with a given entrance pupil is very difficult to do, which means that in practical terms FF ultra-wide lenses will usually work better than APS-C ones do, but this is not in general true for longer lenses.

In particular, a 300mm f4 FF lens has about the same entrance pupil and light collecting power as a 200mm f2.8 does on APS-C, and gives roughly the same FOV. The 200mm lens is shorter and lighter for the same light collecting power. So if you're comparing the formats for birding or sports shooting, what do you choose to keep constant to make the comparison valid?

I would suggest that the lens diameter is a good choice, as this relates both to entrance pupil and to physical size. (and don't forget that the large format portrait lenses of distant past were massive - not a valid comparison!).

If you do that then I would suggest that for long-focus lenses there is no advantage in the FF format at all, and indeed smaller-format sensors can give equal image results with less lens weight.

Miranda F & Sensorex, Sony A58, Nex-6, Dynax 4, 5, 60, 500si/600si/700si/800si, various Sony & Minolta lenses, several Tamrons, lots of MF primes and *far* too many old film cameras . . .
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Post Options Post Options   Quote pegelli Quote  Post ReplyReply Direct Link To This Post Posted: 09 January 2019 at 12:56
Originally posted by Miranda F Miranda F wrote:

This may be true for film but not for digital sensors. If the pixel count is the same (and the exposure time too, Jonas A-R ) then the total light reaching each pixel is the same in each format. The shorter focal length lens in APS-C focusses the same amount of light in a smaller area.

The larger sensor does not collect more light if the lens is adjusted to suit it as per the equivalence formula. If you forget the equivalence formula and just stick the same lens on both cameras then yes, but that's not what we're talking about here. My complaint is the comment often made that 'larger format senors collect more light' - they don't - it is the lens that collects the light.
Thanks for giving several factors what you are keeping constant and what the variables are. Without that any statement on equivalence cannot be evaluated.
And if they can make the smaller pixels of the same pixel count smaller sensor camera the same S/N efficiency as the larger pixels on the larger sensor camera (another variable you need to specify when making equivalence comparisons) the pictures will indeed look similar, assuming you use lenses that can meet the equivalence criteria, which is more and more difficult as lenses get shorter and brighter.

Your example above about a 300/4 on FF vs. a 200/2.8 on APS-C is very valid, but finding an APS-C or M43 equivalent for a FF 35/1.2 (a voigtlander lens I like and use a lot on my A7) is near impossible.   

Edited by pegelli - 09 January 2019 at 13:06
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Post Options Post Options   Quote Jonas A-R Quote  Post ReplyReply Direct Link To This Post Posted: 09 January 2019 at 15:03
Originally posted by Phil Wood Phil Wood wrote:

Originally posted by Jonas A-R Jonas A-R wrote:

The exposure is thus solely determined by three independent variables: Aperture, shutter speed and scene brightness.


Not so, there is a fourth variable - sensor sensitivity or ISO. Take your three variables and use the same settings/scene to shoot with ISO 50 and ISO 400 film and you'll see a difference!


That is incorrect. ISO is not part of the exposure. It is a mapping from a pixel value to display lightness. It can be adjusted after the image has been acquired in contrast to the exposure which is fixed once you take the picture.
And btw, it is the same with film: the ISO rating is only valid for a specific development condition. Change the development, and the ISO might change (aka push and pull processing)

Exposure is measured in luxseconds which is the image plane illumination. ISO can obviously not change that.

Check this article out: You probably don't know what ISO means and that's a problem

Originally posted by Phil Wood Phil Wood wrote:

Larger digital sensors are more sensitive than smaller sensors using the same technology and pixel count - because the individual sensors recording each pixel are larger and thus receive more light (assuming equivalent lenses).


Another common, but incorrect myth.
I recommend this great write-up from 2009. Myth busted: small pixels bad, 4 legs good

Alternatively, you can check out Emil Martinec's famous piece on noise. It is maintained at Bill Claff's site: Noise, Dynamic Range, and Bit Depth

Or you could simply compare some images from Sonys FF cameras with various pixel sizes using dpreviews studio scene widget to bust the myth for yourself

Originally posted by Phil Wood Phil Wood wrote:

Of course sensor technology is evolving all the time - it is entirely possible that a FF sensor pixel of 10 years ago is less sensitive than an equivalent sized APS sensor pixel made today.

Nevertheless, the way to increase sensitivity is to increase pixel size in the sensor - hence we have the Sony A7S range.


We have the a7s range in order to be able to read the full chip for video
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Post Options Post Options   Quote ifreedman Quote  Post ReplyReply Direct Link To This Post Posted: 10 January 2019 at 14:59
Nice article. Thank you. I'm enjoying the debate... er, discussion... as well.
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Post Options Post Options   Quote addy landzaat Quote  Post ReplyReply Direct Link To This Post Posted: 10 January 2019 at 18:48
Originally posted by Jonas A-R Jonas A-R wrote:

Originally posted by addy landzaat addy landzaat wrote:

Hmmm, this thread is disappointing. When equivalence is off topic you guys keep going on about it and here, in a dedicated thread, nothing. Just a popcorn worthy thread on dpreview


Well, so far nobody has said that equivalence is a hoax and the earth is flat. Maybe you wish to start the entertainment?


Good to see the discussion is going. I keep on taking and looking at pictures

Oh, and I would like to call it hoax, but just like a flat earth, I do not believe that to be the case.
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Post Options Post Options   Quote Jonas A-R Quote  Post ReplyReply Direct Link To This Post Posted: 11 January 2019 at 10:10
Originally posted by addy landzaat addy landzaat wrote:

Originally posted by Jonas A-R Jonas A-R wrote:

Originally posted by addy landzaat addy landzaat wrote:

Hmmm, this thread is disappointing. When equivalence is off topic you guys keep going on about it and here, in a dedicated thread, nothing. Just a popcorn worthy thread on dpreview


Well, so far nobody has said that equivalence is a hoax and the earth is flat. Maybe you wish to start the entertainment?


Good to see the discussion is going. I keep on taking and looking at pictures


I don't have time taking pictures. Too busy explaining why objectives with the same AoV and aperture happens to project the same amount of light on the sensor (regardless of the sensor size) if you care to point the lens at the same scene. The word photography, might help people think about why the amount of light recorded might be of importance :)

Originally posted by addy landzaat addy landzaat wrote:

Oh, and I would like to call it hoax, but just like a flat earth, I do not believe that to be the case.


That's ok. We now have lies and half truths thrown at it, so things are rolling
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Post Options Post Options   Quote QuietOC Quote  Post ReplyReply Direct Link To This Post Posted: 11 January 2019 at 15:25
It is easy to forget about equivalence. It is easy to get mislead by flat test targets and using the same exposure settings. I just bought another FE 50 F1.8 and was again a bit disappointed with its sharpness wide-open. It is certainly nowhere near as sharp as the Zeiss Touit 32 F1.8 for example. The inexpensive AF Rokinons are also not the sharpest lenses wide-open. And I am feeling--why did I spend $1000 on 2.34x larger sensor?

But the image from the Touit wide-open on the A6000 looks like stopping down the FE to F2.8 on the A7II--that's what I should compare. For similar images on the different formats the FE 50 F1.8 looks very good compared to the Touit--while also allowing up to 2.34x more light/shallower depth-of-field than the Touit allows on the smaller format.

Edited by QuietOC - 11 January 2019 at 15:29
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Post Options Post Options   Quote pegelli Quote  Post ReplyReply Direct Link To This Post Posted: 11 January 2019 at 15:40
Originally posted by QuietOC QuietOC wrote:

It is easy to forget about equivalence. It is easy to get mislead by flat test targets and using the same exposure settings. I just bought another FE 50 F1.8 and was again a bit disappointed with its sharpness wide-open. It is certainly nowhere near as sharp as the Zeiss Touit 32 F1.8 for example. The inexpensive AF Rokinons are also not the sharpest lenses wide-open. And I am feeling--why did I spend $1000 on 2.34x larger sensor?

But the image from the Touit wide-open on the A6000 looks like stopping down the FE to F2.8 on the A7II--that's what I should compare. For similar images on the different formats the FE 50 F1.8 looks very good compared to the Touit--while also allowing up to 2.34x more light/shallower depth-of-field than the Touit allows on the smaller format.


Don't know about the UK but here the Touit 35/1.8 is 3.3 times more expensive than the FE50/1.8. So it's not a full apples-apples comparison taking into account the price (and resulting quality) of the lens. And if then they give "comparable" results at the equivalent aperture I don't think the 50/1.8 is such a bad deal quality wise vs. the Touit on an APS-C camera.
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