The myth of the large sensor "high ISO advantage"

I have been waffling back and forth between moving to a Sony A7 or A6000, and looking at DxOMark's low light sensor rating I think I realized something kind of interesting.
Interesting, yes. But not really new. This topic has actually been beaten to death here on dpreview. To summarize:
  1. At any given combination of DOF, FOV, subject distance and scene light, the sensor will receive the same total amount of light*, no matter what your sensor size is.
  2. With the same total amount of light, most modern sensors will have roughly the same noise in the final photo, no matter what the sensor size is. But if there is a difference, it is often slightly in favor of the smaller sensors.
  3. Consequently, if you are limited by a minimum required DOF which all your cameras are able to reach, there is not really a low light noise advantage to the larger sensor.
*: Of course assuming that the light path to the sensor have the same transmission loss. So if you use an ND filter or an SLT camera, the rule doesn't hold up.

So the question is: Are you in reality limited by a minimum required DOF in low light situations?

I know that I am usually not. In low light, I will almost always open up my aperture as much as I can. If I stop down a bit, it is only to get better general sharpness (because my lenses perform worse fully open), not to get more DOF.

In most of the situations where I need long DOF, I have plenty of light for base ISO. And then the tables are turned. Now the larger sensor can receive more total light before it saturates, and that means that it will end up with less noise in the final photo.

So in reality, the larger sensor will very often win the noise contest.
First of all, correct me if I'm wrong, but sensitivity across formats is not really equivalent, and smaller sensors are inherently more sensitive than larger sensors for a given DoF & shutter speed length. I.e. if you have the same ISO, aperture diameter & shutter speed in front of two different size sensors, the larger sensor will have a dimmer exposure due to the given volume of light being spread over a larger area.

With that in mind, FF has 1.2 stops/2.36 times more sensor area than APS-C. So correct me if I'm wrong, but if an APS-C sensor is rated at ISO1000 for some low light S/N metric, a FF sensor with equivalent performance per unit of area will be rated at ISO2360 for the same metric, correct?
Correct. But the A7 does not have the same area performance as the a6000. And that is the main problem with your comparison: The A7 does not have typical FF performance.

Sony's first three cameras with OSPDAF - a99, NEX-6 and A7 - did all have worse low light performance than comparable non-OSPDAF cameras with Sony sensors, even when compensating for the SLT mirror in the a99. I have never seen a good reason for this, but it is quite clear when you compare DxO numbers. With the a6000, Sony seems to have made an OSPDAF sensor without this OSPDAF penalty.

So if you compare the a6000 to any other newer FF camera with Sony sensor and redo your math, you will see that you get roughly the same noise at the same DOF. The a6000 will not have a noise advantage. (But it will have a DR disadvantage in good light.)
This is the most correct post in this thread. discussion should ended right here if people were reading.
 
This is the most correct post in this thread. discussion should ended right here if people were reading.
LOL! If people start reading, this site would go bankrupt within a month or so.

Just one small detail. Equivalent shots close to the wide open end do not really mean the same amount of light because of lens vignetting. For example, 25/1.7 on m43 would likely vignette much more than 50/3.5 on FF. That vignetting is not just dark corners - it affects the overall brightness a lot. Also, at f/1.7, some light would be lost due to microlens vignetting. The FF advantage then is more light, better resolution, and stronger bokeh because vignetting and loss of light affect bokeh as well.

On the other hand, a 50/1.8 lens would not be really two stops better on FF than itself compared to f/3.5 because of the same problems. The 2 stop difference is still preserved in that sense.
 
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it's basically the same argument HTC made, larger pixels allow you to catch more light for the same resolution, a larger sensor makes it easier to do this, but it's not the sensor size causing the cleaner ISO, it's the size of the pixels

f958c1df3f294b739e1d285105236dba.jpg.png
If HTC really believed in "ultra pixel" why did it not follow it up with another one? why is it the latest One M9 uses a 20mp sensor?
Because people are still pixel whores.

Same reason why I want lenses with 0 distortion, but the masses cared far more about other things like megapixels and sharpness, and now you have lenses with massive distortion getting good reviews simply because they're sharp.

Ppl never understood the idea of larger pixels. Hell even in this forum, focused on photography, ppl don't understand the benefit.
 
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it's basically the same argument HTC made, larger pixels allow you to catch more light for the same resolution, a larger sensor makes it easier to do this, but it's not the sensor size causing the cleaner ISO, it's the size of the pixels

f958c1df3f294b739e1d285105236dba.jpg.png
If HTC really believed in "ultra pixel" why did it not follow it up with another one? why is it the latest One M9 uses a 20mp sensor?
Because people are still pixel whores.
Then why did HTC get into this idea in the first place? is it not possible that it came and gone because it was wrong?
Same reason why I want lenses with 0 distortion, but the masses cared far more about other things like megapixels and sharpness, and now you have lenses with massive distortion getting good reviews simply because they're sharp.
Distortion correction results in only one penalty - resolution. If the lens was very sharp and provided tons of resolution to begin with, then overall resolution loss may well be less than a zero distortion lens that cost the same to produce - i.e. the bulk of manufacture cost went into reducing distortion rather than increasing sharpness.
Ppl never understood the idea of larger pixels. Hell even in this forum, focused on photography, ppl don't understand the benefit.
People understood the fallacy of larger pixel argument, manufactures did too long ago. That is why there is very little IQ difference between D7000 and D7100 despite significant pixel size difference.
 
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Not really. Again microlenses overcome this to the point where it barely matters, if at all.
Are you talking fill factor or full well capacity? Fill factor is the amount of total area available to collecting light. The more area you mask off/cover with source followers the lower the fill factor.
And microlenses overcome this to the point where it doesn't really matter. How long are you going to ignore their contribution?
I don't agree that it's really pixel size dependent at all when we're comparing two sensors of identical size. As for available signal, if you're talking about incoming light we should always assume that that is a constant in discussions like this otherwise we'll be mixing up our variables.
Then, given a constant available light level the smaller pixel will have a lower SNR for the same size sensor.
Look, what you seem to be saying is that a sensor with a higher pixel density collects less light because its fill factor is compromised. And you went on to imply (at least the way I saw it) that this is the reason for its poorer low-light performance.

I am saying that the fill factor is not compromised because microlenses collect light that would otherwise fall onto a non-photosensitive area and direct it onto the photosensitive area. And I am saying that in the case of two sensors of the same size but different pixel counts it is read noise that impacts the low-light performance of the higher resolution sensor and not some photon shortage induced by an inferior fill factor.
 
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Equivalence all over again -- for the millionth time. You'd think people would take the trouble to think about this before jumping in with their own "fresh" arguments.

I explained to you the flaw in your argument. Smaller sensors have to be magnified more. You were too interested in my other comments to respond, yet you want me to show you "facts" you won't understand, comprehend, or reply to.

Good bye!
 
This is why the A6000 was close to the FF camera and why when you look at all the measurements (take an average to be fair) the E-M1 performs better than expected compared to the A6000.
For the avoidance of doubt, when you say "better than expected compare to" you mean "worse than, but not as bad as expected compared to", right?
No, for example, at ISO 120 and 200 the E-M1 would have more DR, or when using the same DOF it would not be "worse" at even more ISOs. It simply depends. This is the topic. When considering DoF, smaller sensors often perform a bit better than larger ones. Not always, but pretty often.

Let's stick to the same brand here so no one can get us off topic and turn it in to bashing as then tend to do.

So take the A6000 and see how it performs favorably against the new A7ii. Both have the latest sensors. If you account for DoF, the A6000 beats the A7ii at almost every ISO. If you prefer more DOF, the A6000 is the better option.
So everyone should shoot with RX100 which is even more efficient, right?
um, that was already addressed in this thread. If you think one size fits all, then you need to start another thread.
You introduced "more DoF" as some kind of arbitrary limitation for photos (no idea why this would be the only consideration, but ok...), I am asking where your reductio ends.
Are you asking if there are situations where wider DoF is preferred? If so please start another thread.
No I'm asking why you arbitrarily introduced it as your main parameter. Why not talk about subject isolation instead? Or maybe both (aka DoF control)?
If you want to learn more, go to this thread (I get bored repeating things)....

http://www.dpreview.com/forums/post/52452668
You didn't read later in the the thread such as here. Why so selective?
btw, it is kind of funny how you thumbs you every post of yours the second after you post. Obviously that means a lot to you.
It's not me doing that.
 
it's basically the same argument HTC made, larger pixels allow you to catch more light for the same resolution, a larger sensor makes it easier to do this, but it's not the sensor size causing the cleaner ISO, it's the size of the pixels

f958c1df3f294b739e1d285105236dba.jpg.png
If HTC really believed in "ultra pixel" why did it not follow it up with another one? why is it the latest One M9 uses a 20mp sensor?
Because people are still pixel whores.
Then why did HTC get into this idea in the first place? is it not possible that it came and gone because it was wrong?
Because the HTC engineers know it increases low light performance. They picked that in favor of higher resolution.

Just like Sony engineers know that their triluminos TV are able to give a wider and more accurate color gamut. They chose that in favor of 4k.

Yet both companies are struggling, and both had to change their course and follow what samsung did, HTC with their phone, Sony with their TV.

Why did they do it, because underestimated people's herd mentality of preferring pixels density over pixel accuracy.
 
Why did they do it, because underestimated people's herd mentality of preferring pixels density over pixel accuracy.
Not really. HTC were just engaging in the same basic style of marketing nonsense from the other direction. In other words they were trying to cash in on a new emerging herd mentality based on ill-conceived notions about how rising pixel counts are destroying IQ.

If you pull both the HTC One and iPhone 5 sample from here, which are the closest in terms of exposure, and then downsample the iPhone 5 image to match (which you can do automagically in-camera if you like), this is what you get:

HTC One
HTC One

iPhone 5
iPhone 5

To my eyes the iPhone 5 image is simply much nicer since IQ is not just about noise it's also about detail. And the noise difference isn't drastic anyway. In fact when you've captured more detail you have additional processing latitude when it comes to noise anyway since most intelligent noise reduction methods work best when detail is well defined.

(and please note that I didn't cherry pick an example; I went straight to the challenging low-light high ISO scene)

As someone who cares about IQ the choice here would be clear. And it wouldn't be the HTC. And I reach this conclusion with my own eyes rather than by waiting to see what the rest of the "herd" is doing. That's what most discerning photographers who appreciate the benefits of additional resolution do. It's an informed choice, and it's a good one.



iPhone 5, NeatImage (Luminance NR = 50), 4MP, +1EV just to show that we're not trying to hide noise behind a brightness difference.
iPhone 5, NeatImage (Luminance NR = 50), 4MP, +1EV just to show that we're not trying to hide noise behind a brightness difference.

Understand though that I'm not suggesting that PP is even necessary. I'd still prefer the iPhone 5 image even without it.
 
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The A7r probably uses the older sensor from the Nikon D800 while the a6000 probably got a completely new sensor.

So the 3% difference you have found can probably be adequately explained by the age difference. (We got a one stop improvement in 6-8 years, but it has slowed down now because we are closer to the theoretical limit).
So the A6000 uses the latest technology. So how does the old E-M1 with a smaller sensor match it for DR at almost every ISO?

e31a0225ccc843f58ef9c0359bf89caa.jpg
You're comparing apples to oranges (what relevance does DR have in a thread about SNR?), and in any case the A6000 has an advantage in maximum DR about equal to its advantage in sensor size, which for ISOless sensors like the Sonys in both of these cameras is all that matters.
Well, DR will determine the amount of shadow noise more the SNR18%. Also, I love the "max DR" argument. If you shoot at ISO100 the A6000 wins, BUT if you use too high a shutter speed and ISO changes to 120 or god forbid 200, then magically the E-M1 wins. The truth is, with real word use they are equal.
Now I have seen everything.

A day ago, in your comments in the A7s review you "helpfully" pointed out that the a7s LOW ISO DR is not as good as other cameras (never mind that it is still better at 13.2 stops than the EM-1 12.7 Max DR).....in reply to my pointing out this very thing (which matter more for the a7s as it IS a low light camera while the EM-1 is not so much).

Now it is the other way around????
Lab D will always pick whatever he thinks is the weakest point about a camera's measurements and harp on it ad nauseum. Even if it means contradicting himself across different lines of argument.

His basic MO is like trying to test drive a Ferrari and a hatchback in a carpark to prove the hatchback is superior. But when he wants to test a hatchback against his own car, suddenly he'll be all about the trunk space and 4 doors.

The best part is no matter how bad Canon's dynamic range is, the 7Dii (1.6x crop) still beats his beloved Olympus cameras (or was it Panasonic) at image noise. Yet he thinks MFT are able to match a FF camera.

pjLCKAS.png
 
Nobody buys FF and shoots f/2 with a f/1.4 lens. Equivalency was invented by some guy, who can't open his cropped f/1.4 lens to f/1.0.
 
Nobody buys FF and shoots f/2 with a f/1.4 lens. Equivalency was invented by some guy, who can't open his cropped f/1.4 lens to f/1.0.
NOT TRUE ! I have an FF camera and an f/1.4 lens ! I tried -once- to use it at f/5.6 and guess what ? It worked: I got a superb image !

....maybe my lens has a problem ?

;-)

Photo Galleries at http://www.pbase.com/scherrer
Spherical Panoramas at http://www.360cities.net/profile/jps or http://www.viewat.org/?sec=pn&id_aut=2489
 
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Equivalence all over again -- for the millionth time. You'd think people would take the trouble to think about this before jumping in with their own "fresh" arguments.

I explained to you the flaw in your argument. Smaller sensors have to be magnified more. You were too interested in my other comments to respond, yet you want me to show you "facts" you won't understand, comprehend, or reply to.

Good bye!
 
The discussion was about how DPR found Sony misled about the A7s. DPR and several other people pointed out old Nikon APS bodies with lower prices and smaller sensors have more DR at ISO 100 even though Sony said the A7s is better.

Remember how vocal you were about how the A7 cameras were "weather sealed"? This is similar. What Sony said is not true. Unfortunately, several people damaged their cameras thinking there was some real sealing on them. This is why it is so important to get the word out and let people know the truth.

It is strange you think explaining how a companies marketing is false is "bashing". You think Consumer reports and the BBB are "bashers" too.

Here is what DPR said about the A7s DR issue (And we both agree the A7R is the real deal):

If Sony should've been bragging about the dynamic range of any of its cameras, it should've been the a7R, not the a7S. Sony marketing claimed 15.3 EV dynamic range for the a7S, which appears to be approximately exaggerated by 2 EV according to DXO tests. The a7R appears to be 1 EV ahead of the a7S in those tests. To put this in perspective, though, both cameras are well ahead of offerings from Canon, but if you're looking for dynamic range for landscapes, or exposure latitude for flexibility in post-processing (or because you've simply mis-exposed a shot), the a7R is the winner here. Even in non-normalized, full-resolution comparisons, where the a7R continues to offer both more resolution and more pixel-level dynamic range than the a7S.
 
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This is why the A6000 was close to the FF camera and why when you look at all the measurements (take an average to be fair) the E-M1 performs better than expected compared to the A6000.
For the avoidance of doubt, when you say "better than expected compare to" you mean "worse than, but not as bad as expected compared to", right?
No, for example, at ISO 120 and 200 the E-M1 would have more DR, or when using the same DOF it would not be "worse" at even more ISOs. It simply depends. This is the topic. When considering DoF, smaller sensors often perform a bit better than larger ones. Not always, but pretty often.

Let's stick to the same brand here so no one can get us off topic and turn it in to bashing as then tend to do.

So take the A6000 and see how it performs favorably against the new A7ii. Both have the latest sensors. If you account for DoF, the A6000 beats the A7ii at almost every ISO. If you prefer more DOF, the A6000 is the better option.
So everyone should shoot with RX100 which is even more efficient, right?
um, that was already addressed in this thread. If you think one size fits all, then you need to start another thread.
You introduced "more DoF" as some kind of arbitrary limitation for photos (no idea why this would be the only consideration, but ok...), I am asking where your reductio ends.
Are you asking if there are situations where wider DoF is preferred? If so please start another thread.

If you want to learn more, go to this thread (I get bored repeating things)....

http://www.dpreview.com/forums/post/52452668
You didn't read later in the the thread such as here. Why so selective?
Did you read the next few posts after that? Obviously not because you were being selective again.

whether small pixels are more 'efficient' or not, that depends on the context. They are more efficient if comparing different sensor sizes with same MP count, because the best smaller pixels have higher QE and therefore better SNR at equivalent settings. But if discussing MP count on a given sensor size, then it seems that a higher resolution will come at the cost of a lower normalized DR, because the read noise of the small pixels ain't low enough, and the higher QE isn't enough to make up for that. Though, again it depends on what we're looking at. A FF sensor filled with SX50 pixels would have quite a bit better SNR 18% (print/8mp) and a higher 'Low-light ISO' score than the best FF sensors today.
 
The discussion was about how DPR found Sony lied about the A7s. DPR and several other people pointed out old Nikons like the D5200 with lower prices and smaller sensors have more DR at ISO 100 even though Sony said the A7s is better.
That's par for the course with manufacturer claims. They are based on different benchmarks, just like so-called 3-5 stop image stabilization that many manufacturers claim which is never true in actual practice. Or CIPA battery life, that you know you can always set your camera to exceed.

But that wasn't the point, though we know why you're so eager to shift attention away from the actual point. The actual point was that in one discussion you are hyping up DR at base ISO and in another suddenly you are insisting on looking at DR along the entire range of ISO, but you won't apply the same logic both ways, thus proving your disingenuousness and selectivity in looking to always frame things to make Sony look as bad as you can get away with. In this way, your trolling becomes obvious.
Remember how vocal you were about how the A7 cameras were "weather sealed"? This is similar. What Sony said is not true.
And they are. My A7 has survived shooting in rainy weather many times. There are also several Youtube videos of it showing it being dowsed in water with no problems. Why would that be possible, if they're not weather sealed to some degree? I bet you will selectively cut out pertinent facts in your replies as you always do. The real question is why you keep raising this red herring when you know I will either ignore it (for being a red herring) or rebut it (for being annoying why you keep being so disingenuous)? More evidence that your primary objective is trolling, rather than serious discussion.
 
First of all, correct me if I'm wrong, but sensitivity across formats is not really equivalent, and smaller sensors are inherently more sensitive than larger sensors for a given DoF & shutter speed length.
The sensor's "sensitivity" is not a function of the propertires of the image the lens draws, thus DoF and shutter speed are not relevant.

However, if the aim is to create the same output image, i.e. having an output image with the same DoF and shutter speed, then a larger format would use a smaller aperture than a smaller format would.

How efficient the sensor is in another topic - some small sensors have very high quantum efficiency, while some big ones also do. Iif the manufacturing geometries were the same and front side illumination were used, then with equal pixel count a bigger sensor would typically have higher quantum efficiency. In practise smaller sensors use finer manufacturing geomateries and backside illumination (BSI, BI) is often also used to compete.

So there is no hard rule.
I.e. if you have the same ISO, aperture diameter & shutter speed in front of two different size sensors, the larger sensor will have a dimmer exposure due to the given volume of light being spread over a larger area.
While I understand what you mean, what you say is written in a way which is bound to cause confusion.

First, let's ditch ISO as it's got no part in this context.

If we have the same aperture diameter, angle of view and shutter speed, the exposures of different sized sensors will be different, but this has nothing to do with being "dimmer". Exposure is a per are-concept and as bigger sensor has more area, the total amount of light collected will be ideantical.

Brightness is not a useful concept as it's a property of the output image, not the image and what the sensor samples is the image into data. Regardless of the sensor size the same amount of light is collected, thus the output image can have the same brightness with the same "apparent noise". If you consider two sensors with the same number of pixels, but different sizes, then with the "equivalent output image" settings the numeric information would be the same.

There is much more on this concept here in three articles.
With that in mind, FF has 1.2 stops/2.36 times more sensor area than APS-C. So correct me if I'm wrong, but if an APS-C sensor is rated at ISO1000 for some low light S/N metric, a FF sensor with equivalent performance per unit of area will be rated at ISO2360 for the same metric, correct?
ISO is an output image metric (JPG and such), not a metric for image sensors. It's best to ignore them for most part when considering raw-data or sensor performance, unless we're considering how changing the ISO influences the performance curve of the image sensor (typically increasing ISO reduces the influence of ADC/PGA noise up to a point).
Well when you apply that math to the A6000 and A7
A7 sensor design (at least for most part) is quite old, probably older than the sensor in A6000, and the latter is likely made with finer manufacturing geometry (to negate the pixel pitch difference inflluence) thus the relative efficiency of the latter is likely to be better. Thus for "equivalent images" it would perform better.
What's the practical impact of that? If you have a low light scene and two equivalent lenses wide open on the two cameras (i.e. the 24 1.8 & the 35 2.8), the A7 will have half a stop more noise.
Indeed it is not the sensor size itself which is the reason why the big sensor cameras are usually considered to have less noise, but the amount of light which is captured. After all, noise is almost entirely a function of light itself. Thus as f/1,8 on APS-C roughly equals f/2,8 on full frame, the sensor which is more efficient in capturing light (and for the lowest exposures has the lowest read noise) will have less noise.
Does this mean I won't get the A7? Probably not though I might go for the A7R as it somehow claws back most of that missing half a stop.
A7r has a more modern sensor than the A7 sensor. Nothing odd at all it being a better performer in this context.
This has other implications as well. A little 1/2.3 sensor at ISO100 is operating at a sensitivity equivalent to ISO3500 on a full frame.
I think II do understand what you mean and that would be right (assuming the math of yours is right), but what you say is wrong.

First, ISO is not a sensor metric.

Second, it's about light, not about ISO - if you want to crease the "equivalent image" (i.e. same output image), then the exposure parameters of the cameras would be very different and one might or might not use the ISOs you say.

I highly recomment to read the articles I pointed to earlier . They are about this very concept.

--
Abe R. Ration - amateur photographer, amateur armchair scientist, amaterur camera buff
http://aberration43mm.wordpress.com/
 
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This is why the A6000 was close to the FF camera and why when you look at all the measurements (take an average to be fair) the E-M1 performs better than expected compared to the A6000.
For the avoidance of doubt, when you say "better than expected compare to" you mean "worse than, but not as bad as expected compared to", right?
No, for example, at ISO 120 and 200 the E-M1 would have more DR, or when using the same DOF it would not be "worse" at even more ISOs. It simply depends. This is the topic. When considering DoF, smaller sensors often perform a bit better than larger ones. Not always, but pretty often.

Let's stick to the same brand here so no one can get us off topic and turn it in to bashing as then tend to do.

So take the A6000 and see how it performs favorably against the new A7ii. Both have the latest sensors. If you account for DoF, the A6000 beats the A7ii at almost every ISO. If you prefer more DOF, the A6000 is the better option.
So everyone should shoot with RX100 which is even more efficient, right?
um, that was already addressed in this thread. If you think one size fits all, then you need to start another thread.
You introduced "more DoF" as some kind of arbitrary limitation for photos (no idea why this would be the only consideration, but ok...), I am asking where your reductio ends.
Are you asking if there are situations where wider DoF is preferred? If so please start another thread.

If you want to learn more, go to this thread (I get bored repeating things)....

http://www.dpreview.com/forums/post/52452668
You didn't read later in the the thread such as here. Why so selective?
Did you read the next few posts after that? Obviously not because you were being selective again.

whether small pixels are more 'efficient' or not, that depends on the context. They are more efficient if comparing different sensor sizes with same MP count, because the best smaller pixels have higher QE and therefore better SNR at equivalent settings. But if discussing MP count on a given sensor size, then it seems that a higher resolution will come at the cost of a lower normalized DR, because the read noise of the small pixels ain't low enough, and the higher QE isn't enough to make up for that. Though, again it depends on what we're looking at. A FF sensor filled with SX50 pixels would have quite a bit better SNR 18% (print/8mp) and a higher 'Low-light ISO' score than the best FF sensors today.
As usual, you throw out a red herring and try to get everyone to follow you down that garden path to avoid discussion of your flawed claims. As you conveniently cut out my actual response to your question:
You introduced "more DoF" as some kind of arbitrary limitation for photos (no idea why this would be the only consideration, but ok...), I am asking where your reductio ends.
Are you asking if there are situations where wider DoF is preferred? If so please start another thread.
No I'm asking why you arbitrarily introduced it as your main parameter. Why not talk about subject isolation instead? Or maybe both (aka DoF control)?
You're avoiding the main question, which is why do you arbitrarily insist on making statements based on maximizing DoF. As I said, it seems to me you want to test drive a Ferrari and a hatchback but the restriction is they never leave the carpark so that you can "prove" the hatchback is better.

Maximal DoF is elementary to achieve with a FF sensor (f/8 and up is generally hyperfocal in the normal focal range). For DoF to be a limitation, you also need shutter speed to be a limitation, so that then equivalent ISO and DoF must be used. That's akin to locking the cars in the carpark because there are so few real life situations where such a condition is the case.

So why are you so desperate to do this, and insist this is the only way we compare the sensors? It goes back to the original question I asked you, which you fudged with this nonsense above, which is
This is why the A6000 was close to the FF camera and why when you look at all the measurements (take an average to be fair) the E-M1 performs better than expected compared to the A6000.
For the avoidance of doubt, when you say "better than expected compare to" you mean "worse than, but not as bad as expected compared to", right?
Is it really so hard for you to admit a FF sensor is better than an APS-C sensor, which is better than a MFT sensor? I mean, you do shoot a FF camera right? Your gear list says you do, but you seem to understand DoF limitations (hardly any, and where they are there, they are the same for crop sensors) of FF so poorly that it makes it hard to believe you actually have shot a FF camera. Or have the first clue how to use it to its potential, anyway.
 
Let me break it down for you even more:

Put a 50mm on D810, set aperture to F10, you now have a 5 mm aperture diameter, set shutter speed to 1/50s and iso to 100, take the picture.

Now put a 35mm on a APS-C, set aperture to F7.1, you now have a 5 mm aperture diameter, set shutter speed to 1/50s and iso to 100, take the picture.

It should be abundantly clear that the APS-C image is brighter.

Again, the issue of "exposure" is complicated because it depends on one's understanding of what exposure means.
You've added another factor into the discussion, FL. It is primarily the longer FL, and the greater distance the light has to travel that causes the difference in exposure.
It's not due to the aperture diameter...that's why aperture settings equate to different aperture diameters for different focal lengths; to compensate for the longer light path and keep the exposure constant.
How about if you crop an image replicating a smaller sensor with the same pixel density...does the exposure change? (No) Or if you put your camera into crop mode? (No)
No idea what you are on about. in both scenario you are changing the FOV thus render comparison inappropriate.
You've assigned another factor of a fixed distance/composition here... The relevant factor in exposure is the lens' FOV/image circle, not the sensor's FOV.

I think you are overcomplicating the scenario/original question. Yes, if you change FL (light path distance), lens FOV, and aperture setting, then the exposure will change. But it's not "due to" the sensor size.
First. D4/D4s are not better except that they did not have purple glow, more of a problem with Sony sensor rather than result of smaller pixels.Secondly, between D4s, D750 and D810, it is a wash, more or less. Despite pixel difference of 50% jum each step. You can check DXO and DPR's samples.
I don't need to check... I own the D4/D810/V2. I've also owned the D200/300/3/3s/7000/800. In every case the larger pixel sensor (of same/similar generation) has better low light/high ISO performance on a pixel level. You *can* get similar/comparable results by "normalizing" a higher MP sensor of the same size. But then what's the point of using it? That's why I don't use the D810 much above ISO 1000 (unless it's the only camera I have with me).

If the light is good enough to where "normalizing" for equivalent IQ isn't necessary, then normalizing (oversampling) gives the higher MP (same size) sensor an advantage. And it can be significant. That's part of why I own the D810.
 

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