The Myth of Equivalent Aperture and other overly simplistic Camera Formulae

I am not tired of these threads. The original post is exactly right. What matters is the s/n ratio. There is nothing inherent in a larger sensor that means better high ISO. It may be that larger sensors typically have better high ISO but that's not because the sensor is bigger. It's because the pixels have better S/N ratio. Why? Because you can fit more larger pixels on the sensor for a given megapixel. But you could cram 75mp on there using smaller pixels with a lower S/N ratio. Then high ISO would be worse.
Absolutely not true. I repeat my simple question - the 16Mpx APS-C sensor in Sony NEX-3N has a very similar pixel size to the full frame 36Mpx one in A7R. Do you really think they have identical high ISO performance?

Check it out for yourself:

Nex-3N vs A7R
Pixel size is not the only factor affecting the s/n ratio, as the original post made clear. The question is the s/n ratio. I don't doubt that most FF cameras have higher s/n ratio pixels but there is nothing that says that is necessarily the case. How do you explain differences in high ISO among FF cameras? They should all be the same if sensor size is everything. Obviously that's not true. Also older FF don't fare better than some newer aps-c
 
I am not tired of these threads. The original post is exactly right. What matters is the s/n ratio. There is nothing inherent in a larger sensor that means better high ISO. It may be that larger sensors typically have better high ISO but that's not because the sensor is bigger. It's because the pixels have better S/N ratio. Why? Because you can fit more larger pixels on the sensor for a given megapixel. But you could cram 75mp on there using smaller pixels with a lower S/N ratio. Then high ISO would be worse.
Absolutely not true. I repeat my simple question - the 16Mpx APS-C sensor in Sony NEX-3N has a very similar pixel size to the full frame 36Mpx one in A7R. Do you really think they have identical high ISO performance?

Check it out for yourself:

Nex-3N vs A7R
Pixel size is not the only factor affecting the s/n ratio, as the original post made clear. The question is the s/n ratio. I don't doubt that most FF cameras have higher s/n ratio pixels but there is nothing that says that is necessarily the case. How do you explain differences in high ISO among FF cameras? They should all be the same if sensor size is everything. Obviously that's not true. Also older FF don't fare better than some newer aps-c
No one said it was "the only factor." We said it was a factor and that "all things being equal" a larger sensor will ALWAYS have better signal to noise ratio than a smaller one. This is a fact caused by 4 times the area to collect light. In fact, if you look at sensors of similar technology, the FF sensors have about 3 times the dynamic range of APSC ones. Smaller sensors are a bit more efficient which is why it isn't 4 times.
 
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I am not tired of these threads. The original post is exactly right. What matters is the s/n ratio. There is nothing inherent in a larger sensor that means better high ISO. It may be that larger sensors typically have better high ISO but that's not because the sensor is bigger. It's because the pixels have better S/N ratio. Why? Because you can fit more larger pixels on the sensor for a given megapixel. But you could cram 75mp on there using smaller pixels with a lower S/N ratio. Then high ISO would be worse.
Absolutely not true. I repeat my simple question - the 16Mpx APS-C sensor in Sony NEX-3N has a very similar pixel size to the full frame 36Mpx one in A7R. Do you really think they have identical high ISO performance?

Check it out for yourself:

Nex-3N vs A7R
Pixel size is not the only factor affecting the s/n ratio, as the original post made clear. The question is the s/n ratio. I don't doubt that most FF cameras have higher s/n ratio pixels but there is nothing that says that is necessarily the case. How do you explain differences in high ISO among FF cameras? They should all be the same if sensor size is everything. Obviously that's not true. Also older FF don't fare better than some newer aps-c
No one said it was "the only factor." We said it was a factor and that "all things being equal" a larger sensor will ALWAYS have better signal to noise ratio than a smaller one. This is a fact caused by 4 times the area to collect light. In fact, if you look at sensors of similar technology, the FF sensors have about 3 times the dynamic range of APSC ones. Smaller sensors are a bit more efficient which is why it isn't 4 times.
If "all things are equal," then the s/n ratio is the same and the high ISO is the same. Since the pixels are the same size - all thing equal right -- then the only thing you get with FF is more of them and thus greater resolution.
 
I am not tired of these threads. The original post is exactly right. What matters is the s/n ratio. There is nothing inherent in a larger sensor that means better high ISO. It may be that larger sensors typically have better high ISO but that's not because the sensor is bigger. It's because the pixels have better S/N ratio. Why? Because you can fit more larger pixels on the sensor for a given megapixel. But you could cram 75mp on there using smaller pixels with a lower S/N ratio. Then high ISO would be worse.
Absolutely not true. I repeat my simple question - the 16Mpx APS-C sensor in Sony NEX-3N has a very similar pixel size to the full frame 36Mpx one in A7R. Do you really think they have identical high ISO performance?

Check it out for yourself:

Nex-3N vs A7R
Pixel size is not the only factor affecting the s/n ratio, as the original post made clear. The question is the s/n ratio. I don't doubt that most FF cameras have higher s/n ratio pixels but there is nothing that says that is necessarily the case. How do you explain differences in high ISO among FF cameras? They should all be the same if sensor size is everything. Obviously that's not true. Also older FF don't fare better than some newer aps-c
No one said it was "the only factor." We said it was a factor and that "all things being equal" a larger sensor will ALWAYS have better signal to noise ratio than a smaller one. This is a fact caused by 4 times the area to collect light. In fact, if you look at sensors of similar technology, the FF sensors have about 3 times the dynamic range of APSC ones. Smaller sensors are a bit more efficient which is why it isn't 4 times.
If "all things are equal," then the s/n ratio is the same and the high ISO is the same. Since the pixels are the same size - all thing equal right -- then the only thing you get with FF is more of them and thus greater resolution.
Pixel size is a secondary factor in determining noise. Sensor size is primary, assuming the same technology in both sensors.

For your reading pleasure: What is equivalence and why should I care?

--
Jeff
Leave it in the ground!
 
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I am not tired of these threads. The original post is exactly right. What matters is the s/n ratio. There is nothing inherent in a larger sensor that means better high ISO. It may be that larger sensors typically have better high ISO but that's not because the sensor is bigger. It's because the pixels have better S/N ratio. Why? Because you can fit more larger pixels on the sensor for a given megapixel. But you could cram 75mp on there using smaller pixels with a lower S/N ratio. Then high ISO would be worse.
Absolutely not true. I repeat my simple question - the 16Mpx APS-C sensor in Sony NEX-3N has a very similar pixel size to the full frame 36Mpx one in A7R. Do you really think they have identical high ISO performance?

Check it out for yourself:

Nex-3N vs A7R
Pixel size is not the only factor affecting the s/n ratio, as the original post made clear. The question is the s/n ratio. I don't doubt that most FF cameras have higher s/n ratio pixels but there is nothing that says that is necessarily the case. How do you explain differences in high ISO among FF cameras? They should all be the same if sensor size is everything. Obviously that's not true. Also older FF don't fare better than some newer aps-c
No one said it was "the only factor." We said it was a factor and that "all things being equal" a larger sensor will ALWAYS have better signal to noise ratio than a smaller one. This is a fact caused by 4 times the area to collect light. In fact, if you look at sensors of similar technology, the FF sensors have about 3 times the dynamic range of APSC ones. Smaller sensors are a bit more efficient which is why it isn't 4 times.
If "all things are equal," then the s/n ratio is the same and the high ISO is the same. Since the pixels are the same size - all thing equal right -- then the only thing you get with FF is more of them and thus greater resolution.
Wrong. The facts are right there. Staring you in the face. Click on any one of the DXO links I put in earlier posts. For example, the comparison of the Nikon D4s to the Nikon D610 to the Nikon D800. These all have very different pixel sizes and therefore pixel performance yet their high ISO performance is very close and it is 3 times better than the best APSC sensor.

How do you account for that?
 
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I am not tired of these threads. The original post is exactly right. What matters is the s/n ratio. There is nothing inherent in a larger sensor that means better high ISO. It may be that larger sensors typically have better high ISO but that's not because the sensor is bigger. It's because the pixels have better S/N ratio. Why? Because you can fit more larger pixels on the sensor for a given megapixel. But you could cram 75mp on there using smaller pixels with a lower S/N ratio. Then high ISO would be worse.
Absolutely not true. I repeat my simple question - the 16Mpx APS-C sensor in Sony NEX-3N has a very similar pixel size to the full frame 36Mpx one in A7R. Do you really think they have identical high ISO performance?

Check it out for yourself:

Nex-3N vs A7R
Pixel size is not the only factor affecting the s/n ratio, as the original post made clear. The question is the s/n ratio. I don't doubt that most FF cameras have higher s/n ratio pixels but there is nothing that says that is necessarily the case. How do you explain differences in high ISO among FF cameras? They should all be the same if sensor size is everything. Obviously that's not true. Also older FF don't fare better than some newer aps-c
No one said it was "the only factor." We said it was a factor and that "all things being equal" a larger sensor will ALWAYS have better signal to noise ratio than a smaller one. This is a fact caused by 4 times the area to collect light. In fact, if you look at sensors of similar technology, the FF sensors have about 3 times the dynamic range of APSC ones. Smaller sensors are a bit more efficient which is why it isn't 4 times.
If "all things are equal," then the s/n ratio is the same and the high ISO is the same. Since the pixels are the same size - all thing equal right -- then the only thing you get with FF is more of them and thus greater resolution.
Wrong. The facts are right there. Staring you in the face. Click on any one of the DXO links I put in earlier posts. For example, the comparison of the Nikon D4s to the Nikon D610 to the Nikon D800. These all have very different pixel sizes and therefore pixel performance yet their high ISO performance is very close and it is 3 times better than the best APSC sensor.

How do you account for that?
Easy - pixel size is not the only determinant of s/n ratio. Just like the original poster said. It just makes no sense what you are saying. If you take a given pixel technology and size - you have a given s/n ratio. Spread those pixels across 1" and you have the same s/n ratio. Spread them across 5" and you have the same s/n ratio. You just have more pixels hence more resolution. You can't improve the high ISO of those pixels by spreading them across a larger sensor Or at least nobody has explained to me how that could be the case.
 
I am not tired of these threads. The original post is exactly right. What matters is the s/n ratio. There is nothing inherent in a larger sensor that means better high ISO. It may be that larger sensors typically have better high ISO but that's not because the sensor is bigger. It's because the pixels have better S/N ratio. Why? Because you can fit more larger pixels on the sensor for a given megapixel. But you could cram 75mp on there using smaller pixels with a lower S/N ratio. Then high ISO would be worse.
Absolutely not true. I repeat my simple question - the 16Mpx APS-C sensor in Sony NEX-3N has a very similar pixel size to the full frame 36Mpx one in A7R. Do you really think they have identical high ISO performance?

Check it out for yourself:

Nex-3N vs A7R
Pixel size is not the only factor affecting the s/n ratio, as the original post made clear. The question is the s/n ratio. I don't doubt that most FF cameras have higher s/n ratio pixels but there is nothing that says that is necessarily the case. How do you explain differences in high ISO among FF cameras? They should all be the same if sensor size is everything. Obviously that's not true. Also older FF don't fare better than some newer aps-c
No one said it was "the only factor." We said it was a factor and that "all things being equal" a larger sensor will ALWAYS have better signal to noise ratio than a smaller one. This is a fact caused by 4 times the area to collect light. In fact, if you look at sensors of similar technology, the FF sensors have about 3 times the dynamic range of APSC ones. Smaller sensors are a bit more efficient which is why it isn't 4 times.
If "all things are equal," then the s/n ratio is the same and the high ISO is the same. Since the pixels are the same size - all thing equal right -- then the only thing you get with FF is more of them and thus greater resolution.
Wrong. The facts are right there. Staring you in the face. Click on any one of the DXO links I put in earlier posts. For example, the comparison of the Nikon D4s to the Nikon D610 to the Nikon D800. These all have very different pixel sizes and therefore pixel performance yet their high ISO performance is very close and it is 3 times better than the best APSC sensor.

How do you account for that?
Easy - pixel size is not the only determinant of s/n ratio. Just like the original poster said. It just makes no sense what you are saying. If you take a given pixel technology and size - you have a given s/n ratio. Spread those pixels across 1" and you have the same s/n ratio. Spread them across 5" and you have the same s/n ratio. You just have more pixels hence more resolution. You can't improve the high ISO of those pixels by spreading them across a larger sensor Or at least nobody has explained to me how that could be the case.
You aren't increasing the high ISO performance of individual pixels anymore than you are increasing the resolution of individual pixels. You are getting more ISO performance from having more pixels, just like you are getting resolution by having more pixels.

Signal to noise ratio consists of signal and noise. Think of the pixels as little buckets that collect light. More buckets more light. More light, more signal.

Size of the buckets has something to do with it to, but it is a lesser effect with all the rest of the technology being equal.

So imagine it's raining. Your job is to collect as much water as possible. You have 4 buckets. You go out and set them down. Now imagine I have 16 buckets of the same size and I go out and lay mine down. Guess who is going to collect more water (more signal.)

Here is a good article but it is in German.

http://sacherkhoudari.de/Artikel/Ueber_Sensorgroessen_und_Rauschen_von_Digitalkameras

What might also be confusing you is you are putting those two different size sensors behind the same imaginary lens. They can't be. The larger sensor requires a bigger lens to put light over it's larger angle of view. That bigger lens collects more light.

Let's look at another example, that might help you understand the Metabones Speed Booster adapter. When you use an F4 FF lens on a smaller field of view APSC sensor, the smaller sensor is collecting less light because a lot of the light the lens collected is being projected onto space where a larger sensor would be. If, you add the Metabones adapter to the lens it will concentrate that light over the smaller sensor and change the F4 to an F3.5 which effectively improves the systems high ISO performance.

To say it another way, all things being equal, a larger sensor requires a larger lens (for the same aperture) which in turn, collects more light (signal.)

Here is a camerasize/lens size comparison to help illustrate.

http://camerasize.com/compact/#290.353,482.411,464.356,ha,t

Both cameras have F1.8 lenses. Both cameras capture the same field of view of the subject. But look how much bigger the Nikon lens is. It is necessarily grabbing more light because it has to distribute that light over a larger area to produce the same results. Also in there is the Pentax Q with it's F1.8 50mm equivalent lens to illustrate it's even smaller light gathering ability.

This is the part of equivalence that is usually overlooked by people that argue against using it. In the end, it is all about the lens that collects the light. Bigger lenses collect more light (everything else being equal.) So you don't really save anything in size, with a smaller sensor, if you want to collect the same amount of light and achieve the same signal to noise ratio because the smaller sensor will require a larger aperture lens to be equivalent in light gathering ability.
 
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Looks like over-simplification rules.
Why is that surprising? Looking at the voters one can easily conclude that close to 50% of the population are complete idiots. The simpler the formula the easier to sway the masses, doesn't matter how stupid it is -- every politician knows that.
 
As somebody said,

The trouble ain't what people don't know, it's what they know that ain't so.

Let me throw a wrench in all your speculations. The equivalence isn't about the sensor at all, it's about the lenses. There is only one parameter of the sensor, which participates in the equivalence calculations, namely it's area. The equivalence will work exactly the same way if instead of a modern sensor you would have a film, a CCD, or any other device registering photons, e.g. a human eye.

Equivalence is a mathematical abstraction, which assumes the recording media is ideal. It answers the question what the lens parameters should be for the different image sizes to achieve the same FOV, DOF, and shot noise. As such equivalence works the same way with any crop, not just different size sensors. So you can as well experiment with the equivalence by cropping your images in PP. You can also experiment with teleconverters and focal reducers as those are converting one equivalent lens to another.

If you don't like the idea of applying the abstract models, like equivalence, to the imperfect reality then you must have the same problem with f-stop, focal length, exposure time, ISO, etc. -- which are all abstractions as well.

I don't want to search for the links now as it was explained so many times before, so if anybody is interested to learn about this subject can easily find the references.
 
This has been bugging me for a while and frequent discussions of lens f-number, crop factor and equivalent aperture have shown me that there's a broad misunderstanding of optics.
  1. The f-number for a lens is a mathematical constant that does not vary with sensor. The f-number is defined in optics as: focal length divided by aperture.
True. But since the field of view is different a larger sensor will require a larger focal length to capture the same image at the same distance.
  1. The amount of light (i.e. the number of photons) striking a fixed size area on the sensor does not change with different sensors. A full frame sensor is not necessarily less noisy than smaller sensors.
But the total amount of light is more and it is the total amount of light we care about when calculating signal to noise ratio.
  1. The effective ISO of a camera cannot be accurately predicted by the sensor size.
All things being equal, the larger the sensor, the larger the bucket that is collecting light.
  1. The size of the image on the sensor is determined only by the focal length of the lens. If an object projects a 3mm image on a full frame sensor, it will project the same 3mm image on any other sensor.
Yes.
  1. Because of 4, the only calculation one can make accurately based on the size of the sensor, is how much of the image will be captured. A Sensor 1" across will capture a field of view exactly twice that of a 1/2" wide sensor.
It will also capture twice the light (2.5 times actually because that is the area difference.)
 
Not to forget the cameras brain, the "processor" which is also a factor in determining noise performance etc.

Equivalence can be way over scrutinised, most of us only want to use it as a quick reference when understanding the focal length and d.o.f of various formats.
 
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Not to forget the cameras brain, the "processor" which is also a factor in determining noise performance etc.

Equivalence can be way over scrutinised, most of us only want to use it as a quick reference when understanding the focal length and d.o.f of various formats.
True...and how close one is when one views an image. Then there is the perception of noise...some people find it desirable in some cases, which is why there are editing filters that add noise.

The reality is, a larger sensor, all things being equal, is always capable of outperforming a smaller sensor, but the difference in performance, is much less noticeable when the capture light is good. It is also less noticeable the smaller the output image is viewed.

Having said all that, this is just an apples to apples comparison and we tend to forget how much better sensors and lenses have gotten over the last couple decades.

We have APSC sensors today that outperform FF sensors 5-6 years ago. We have zoom lenses today, with advanced coatings and computer generated profiles, that outperform prime lenses made 15-20 years ago.

Today we can take pictures that are technically every bit as good as pictures taken 20 years ago with much smaller and lighter equipment.

In the end, it still boils down to whether those images were artistically worth gathering.

Most people would benefit, me included, more from learning better photographic technique, than they ever would from any newer or better equipment.
 
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I can see how one can confuse these issues but it's still wrong. It's not the total amount of light on the whole sensor that makes for more sensitivity, it's the amount of light per pixel, combined with the single pixel's efficiency and depth, that determines signal to noise and dynamic range (= image quality). This is a physical and mathematical truth.

The issue of "overall image quality" gets complicated by the fact that most cameras we're using have a pixel count of approximately 20 million. If you put 20 million pixels on a FF sensor, they're going to be larger than 20 million pixels on a tiny sensor. Hence, the noise on the FF sensor will be lower. But don't try to say that a 50mm f1.8 lens is going to produce different results (other than field of view) on two different sized sensors with the same pixel size. The noise, DoF, bokeh, everything will be exactly the same. This is physics and it's invariant.
Could you please answer my question - APS-C 16Mpx vs FF 36Mpx
Different camera electronics, different sensors, different lens configurations render the comparison invalid (as pointed out by other posters).

The manufacturers (generally) put their best/most expensive chips and sensors in the high-end FF cameras, so the cameras perform better. I don't dispute that.

Here's a thought experiment that summarizes the argument.
  • Take an image with a FF camera
  • Mask off the sensor so it's the size of and APS-C sensor
  • Take another image with the FF camera
  • The *only* difference is the field
  • Noise, magnification, bokeh - everything but field is identical.
Therefore, some assertions made in other replies are obviously incorrect
  1. The image quality depends on the total light hitting the sensor - incorrect. In the example, the masked sensor sees a fraction of the light but the s/n is identical
  2. A FF camera always yields better images than one with a smaller sensor - incorrect. From the example, clearly the images are identical/same quality even though the effective sensor size changes
The simplest way of looking at it is to compare crops of an image from any camera. Cropping the image changes nothing but the field of view.

Q.E.D.
 
Here's a thought experiment that summarizes the argument.
  • Take an image with a FF camera
  • Mask off the sensor so it's the size of and APS-C sensor
  • Take another image with the FF camera
  • The *only* difference is the field
  • Noise, magnification, bokeh - everything but field is identical.
Therefore, some assertions made in other replies are obviously incorrect
  1. The image quality depends on the total light hitting the sensor - incorrect. In the example, the masked sensor sees a fraction of the light but the s/n is identical
  2. A FF camera always yields better images than one with a smaller sensor - incorrect. From the example, clearly the images are identical/same quality even though the effective sensor size changes
The simplest way of looking at it is to compare crops of an image from any camera. Cropping the image changes nothing but the field of view.

Q.E.D.
That thought experiment highlights exactly where you are getting confused. When you crop the sensor like you did you effectively throw away the extra light the sensor and lens are gathering.

Here is the correct way to do your thought experiment.
  • Take an image with a FF camera and a zoom lens set manual F-stop and ISO and 24mm
  • Crop the image so it's the size of and APS-C sensor.
  • Take another image with the FF camera at the exact same F-stop and ISO and 35mm do not crop.
  • Downres the FF image to the same resolution as the APSC image.
  • The *only* difference is the amount of sensor area used.
  • Magnification (or field of view) is identical but DOF changes and output noise change per the equivalence rules.
By the way, you can do this as an actual experiment instead of just a thought experiment with the camera you have now. If you don't have a FF camera use your APSC camera and crop it down to m43 size.

Alternatively you could use a faster aperture on the cropped image set the ISO to half and the aperture to be double. This would equalize the DOF and noise (of course not exactly, but very close.)

P.S. Do you really believe that manufacturers aren't trying as hard with APSC sensor technology and that is why the sensors perform worse at high ISO? Doesn't that seem a bit implausible? Why would they would handicap themselves that way?
 
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I am not tired of these threads. The original post is exactly right. What matters is the s/n ratio. There is nothing inherent in a larger sensor that means better high ISO. It may be that larger sensors typically have better high ISO but that's not because the sensor is bigger. It's because the pixels have better S/N ratio. Why? Because you can fit more larger pixels on the sensor for a given megapixel. But you could cram 75mp on there using smaller pixels with a lower S/N ratio. Then high ISO would be worse.
Absolutely not true. I repeat my simple question - the 16Mpx APS-C sensor in Sony NEX-3N has a very similar pixel size to the full frame 36Mpx one in A7R. Do you really think they have identical high ISO performance?

Check it out for yourself:

Nex-3N vs A7R
Pixel size is not the only factor affecting the s/n ratio, as the original post made clear. The question is the s/n ratio. I don't doubt that most FF cameras have higher s/n ratio pixels but there is nothing that says that is necessarily the case. How do you explain differences in high ISO among FF cameras? They should all be the same if sensor size is everything. Obviously that's not true. Also older FF don't fare better than some newer aps-c
No one said it was "the only factor." We said it was a factor and that "all things being equal" a larger sensor will ALWAYS have better signal to noise ratio than a smaller one. This is a fact caused by 4 times the area to collect light. In fact, if you look at sensors of similar technology, the FF sensors have about 3 times the dynamic range of APSC ones. Smaller sensors are a bit more efficient which is why it isn't 4 times.
If "all things are equal," then the s/n ratio is the same and the high ISO is the same. Since the pixels are the same size - all thing equal right -- then the only thing you get with FF is more of them and thus greater resolution.
Wrong. The facts are right there. Staring you in the face. Click on any one of the DXO links I put in earlier posts. For example, the comparison of the Nikon D4s to the Nikon D610 to the Nikon D800. These all have very different pixel sizes and therefore pixel performance yet their high ISO performance is very close and it is 3 times better than the best APSC sensor.

How do you account for that?
Easy - pixel size is not the only determinant of s/n ratio. Just like the original poster said. It just makes no sense what you are saying. If you take a given pixel technology and size - you have a given s/n ratio. Spread those pixels across 1" and you have the same s/n ratio. Spread them across 5" and you have the same s/n ratio. You just have more pixels hence more resolution. You can't improve the high ISO of those pixels by spreading them across a larger sensor Or at least nobody has explained to me how that could be the case.
You aren't increasing the high ISO performance of individual pixels anymore than you are increasing the resolution of individual pixels. You are getting more ISO performance from having more pixels, just like you are getting resolution by having more pixels.

Signal to noise ratio consists of signal and noise. Think of the pixels as little buckets that collect light. More buckets more light. More light, more signal.

Size of the buckets has something to do with it to, but it is a lesser effect with all the rest of the technology being equal.

So imagine it's raining. Your job is to collect as much water as possible. You have 4 buckets. You go out and set them down. Now imagine I have 16 buckets of the same size and I go out and lay mine down. Guess who is going to collect more water (more signal.)

Here is a good article but it is in German.

http://sacherkhoudari.de/Artikel/Ueber_Sensorgroessen_und_Rauschen_von_Digitalkameras

What might also be confusing you is you are putting those two different size sensors behind the same imaginary lens. They can't be. The larger sensor requires a bigger lens to put light over it's larger angle of view. That bigger lens collects more light.

Let's look at another example, that might help you understand the Metabones Speed Booster adapter. When you use an F4 FF lens on a smaller field of view APSC sensor, the smaller sensor is collecting less light because a lot of the light the lens collected is being projected onto space where a larger sensor would be. If, you add the Metabones adapter to the lens it will concentrate that light over the smaller sensor and change the F4 to an F3.5 which effectively improves the systems high ISO performance.

To say it another way, all things being equal, a larger sensor requires a larger lens (for the same aperture) which in turn, collects more light (signal.)

Here is a camerasize/lens size comparison to help illustrate.

http://camerasize.com/compact/#290.353,482.411,464.356,ha,t

Both cameras have F1.8 lenses. Both cameras capture the same field of view of the subject. But look how much bigger the Nikon lens is. It is necessarily grabbing more light because it has to distribute that light over a larger area to produce the same results. Also in there is the Pentax Q with it's F1.8 50mm equivalent lens to illustrate it's even smaller light gathering ability.

This is the part of equivalence that is usually overlooked by people that argue against using it. In the end, it is all about the lens that collects the light. Bigger lenses collect more light (everything else being equal.) So you don't really save anything in size, with a smaller sensor, if you want to collect the same amount of light and achieve the same signal to noise ratio because the smaller sensor will require a larger aperture lens to be equivalent in light gathering ability.
Sorry not buying the More Light explanation. That "more" light is just projecting on a larger area to capture a larger FOV and more pixels. No matter how many little buckets you have on the sensor and how much water they collect, you still have each one contributing the same amount of noise. Keeping with the buckets and water analogy, imagine you're trying to capture rainwater in buckets with no impurities (noise). If the buckets all are made of wood with some zinc in it, the water will get zinc added in each bucket. Add more buckets over a larger area and you collect more water. But you'll still gave the same ratio of water to zinc in that water.
 
Here's a thought experiment that summarizes the argument.
  • Take an image with a FF camera
  • Mask off the sensor so it's the size of and APS-C sensor
  • Take another image with the FF camera
  • The *only* difference is the field
  • Noise, magnification, bokeh - everything but field is identical.
Therefore, some assertions made in other replies are obviously incorrect
  1. The image quality depends on the total light hitting the sensor - incorrect. In the example, the masked sensor sees a fraction of the light but the s/n is identical
  2. A FF camera always yields better images than one with a smaller sensor - incorrect. From the example, clearly the images are identical/same quality even though the effective sensor size changes
The simplest way of looking at it is to compare crops of an image from any camera. Cropping the image changes nothing but the field of view.

Q.E.D.
That thought experiment highlights exactly where you are getting confused. When you crop the sensor like you did you effectively throw away the extra light the sensor and lens are gathering.

Here is the correct way to do your thought experiment.
  • Take an image with a FF camera and a zoom lens set manual F-stop and ISO and 24mm
  • Crop the image so it's the size of and APS-C sensor.
  • Take another image with the FF camera at the exact same F-stop and ISO and 35mm do not crop.
  • Downres the FF image to the same resolution as the APSC image.
  • The *only* difference is the amount of sensor area used.
  • Magnification (or field of view) is identical but DOF changes and output noise change per the equivalence rules.
By the way, you can do this as an actual experiment instead of just a thought experiment with the camera you have now. If you don't have a FF camera use your APSC camera and crop it down to m43 size.

Alternatively you could use a faster aperture on the cropped image set the ISO to half and the aperture to be double. This would equalize the DOF and noise (of course not exactly, but very close.)

P.S. Do you really believe that manufacturers aren't trying as hard with APSC sensor technology and that is why the sensors perform worse at high ISO? Doesn't that seem a bit implausible? Why would they would handicap themselves that way?
Your last bullet point in your "thought experiment" is circular. You've used your conclusion as part if it's "demonstration". That does not work. On trying hard for aps-c, i think Canon and Nikon at least have not gone all the way they could , preferring to reserve higher image quality for more expensive and likely more profitable FF.
 
Sorry not buying the More Light explanation. That "more" light is just projecting on a larger area to capture a larger FOV and more pixels. No matter how many little buckets you have on the sensor and how much water they collect, you still have each one contributing the same amount of noise. Keeping with the buckets and water analogy, imagine you're trying to capture rainwater in buckets with no impurities (noise). If the buckets all are made of wood with some zinc in it, the water will get zinc added in each bucket. Add more buckets over a larger area and you collect more water. But you'll still gave the same ratio of water to zinc in that water.
You are not doing the analogy correctly. You need to remember that it is signal to noise and resolution IS signal. You can chase that resolution with smaller pixels but then you give up signal to noise ratio at the pixel level.

It isn't just the total water in all the buckets that we care about. It is the type of water in the individual bucket mixed with that zinc and other impurities you talk about.

Look at it this way. Lets say we were collecting acid rain in 10 different countries (analogous to different areas of color and luminance information in a photo.) We collected it in buckets that have acid in their wood and leach that out into the bucket. The bigger the bucket the less acid from the wood gets into the bucket (less noise.) If I have 5 buckets I could only get information in 5 countries...but I'd still have the same amount of acid leaching out into the buckets. I could use bigger buckets, and get better data per country, but I'd still not have as many countries. I could use smaller buckets (APSC) in every country but then I would get more acid leaching in (noise.)

This is how light signal works. I can have more photocells and more signal, but I will be filtering that information with more noise. Or, I can increase the area and get more signal with no more noise. That is what a FF sensor does. But, in order to get the same signal over it's photocells the larger sensor needs a larger lens.

The main thing bigger pixels give you is a lower floor (darkest thing they can see) and higher dynamic range (store more photons.) This is why the D4S can perform better in the darkest conditions...it can "see" in the dark better. However, when you walk away from those end positions the D800 can perform nearly as well because you haven't overworked it's smaller pixels and it's extra pixels carry more signal along with their extra noise.
 
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By the way, you can do this as an actual experiment instead of just a thought experiment with the camera you have now. If you don't have a FF camera use your APSC camera and crop it down to m43 size.

P.S. Do you really believe that manufacturers aren't trying as hard with APSC sensor technology and that is why the sensors perform worse at high ISO? Doesn't that seem a bit implausible? Why would they would handicap themselves that way?
Your last bullet point in your "thought experiment" is circular. You've used your conclusion as part if it's "demonstration". That does not work.
Try the experiment yourself. It isn't hard to do. Look at the images and see which one looks noisier when viewed at the same output resolution.
On trying hard for aps-c, i think Canon and Nikon at least have not gone all the way they could , preferring to reserve higher image quality for more expensive and likely more profitable FF.
It isn't just Canon and Nikon. Sony makes sensors to and it has to compete with other companies at every size sensor. Manufacturers would not handicap themselves against their competition.

The reality is there is actually more technology being thrown at smaller sensors to get them to perform as well as FF.
 
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Are you mean that join together few iphone sensors until same size of ff sensor than the performance will be equal to ff perfomance?
 
Are you mean that join together few iphone sensors until same size of ff sensor than the performance will be equal to ff perfomance?
You won't get the same sensitivity to low light (high ISO performance) and you will have a lower light saturation point (lower dynamic range) but your signal to noise ratio will be very close away from those extreme ends of the lighting spectrum.
 

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