The Myth of Equivalent Aperture and other overly simplistic Camera Formulae

[Daniel Lauring]

I would say that pixel level size and quality are important, this would effect most aspects of image quality that are not lens based like field of view and depth of field. Let's take a great well performing sensor like the one in the Nikon D750 for example, take a slice of the exact same sensor and put it a compact camera with quality optics and the same processing engines and you will effectively get a image that is cropped from the D750.

The only problem is you would probably end up with 2mp, and 2mp just do not sell to the point and shoot crowd who believe megapixels are the be all an end all.

Pixel size, while important, is often overemphasized when people are discussing the improved performance of larger sensors. Having said that bigger pixels improve low light sensitivity and have a higher saturation point. For much of the shooting people do, they would notice the loss of resolution/sharpness much more than they would improved dynamic range. However, for those people that photograph in very low light (astrophotographers for example) or those that photograph scenes with huge dynamic ranges their would be some advantage to this tradeoff. The Sony A7s is becoming very popular in astrophotography for example.

 

[cesjr]

A bit confuse. If crop the image size to APSC or micro 4/3 from the fully captured image of FF size (fully utilize all the sensor area). Are that the image crop from full size ff is batter than the image crop by covering the sensor? Any body had done this experiment before?

When you crop you get the same performance as a sensor the size of the crop. If you crop a FF image to m43 size the performance is the same as if you had taken the photo with an m43 camera without cropping.

I realize your job is not to convince me but just for the record - not convinced.

 

[Daniel Lauring]

A bit confuse. If crop the image size to APSC or micro 4/3 from the fully captured image of FF size (fully utilize all the sensor area). Are that the image crop from full size ff is batter than the image crop by covering the sensor? Any body had done this experiment before?

When you crop you get the same performance as a sensor the size of the crop. If you crop a FF image to m43 size the performance is the same as if you had taken the photo with an m43 camera without cropping.

I realize your job is not to convince me but just for the record - not convinced.

You can lead a horse to water....

 

[Daniel Lauring]

A bit confuse. If crop the image size to APSC or micro 4/3 from the fully captured image of FF size (fully utilize all the sensor area). Are that the image crop from full size ff is batter than the image crop by covering the sensor? Any body had done this experiment before?

When you crop you get the same performance as a sensor the size of the crop. If you crop a FF image to m43 size the performance is the same as if you had taken the photo with an m43 camera without cropping.

I realize your job is not to convince me but just for the record - not convinced.

P.S. Just to confuse you more, when people talk of the advantage of a bigger sensor they often are erroneously talking about the advantage of a bigger lens. If you use truly equivalent lenses, the FF camera will have a much smaller advantage over an APSC camera. Unfortunately, truly equivalent lenses give up the weight advantage of APSC as well.

For example an F2.8 24mm APSC lens is equivalent to an F4 35mm FF lens and given sensors of similar efficiency will yield nearly identical results on both cameras (same field of view, same DOF, same signal to noise ratio.)

Fuji's new F2.8 50-140mm is equivalent to a FF F4 75-210mm. Unfortunately, to get this equivalent performance you end up with a lens that weighs about 30% more than Canon or Nikon's 70-200 F4.

 

[Daniel Lauring]

A bit confuse. If crop the image size to APSC or micro 4/3 from the fully captured image of FF size (fully utilize all the sensor area). Are that the image crop from full size ff is batter than the image crop by covering the sensor? Any body had done this experiment before?

When you crop you get the same performance as a sensor the size of the crop. If you crop a FF image to m43 size the performance is the same as if you had taken the photo with an m43 camera without cropping.

I realize your job is not to convince me but just for the record - not convinced.

Maybe this video will help you understand better.

 

[Daniel Lauring]

A bit confuse. If crop the image size to APSC or micro 4/3 from the fully captured image of FF size (fully utilize all the sensor area). Are that the image crop from full size ff is batter than the image crop by covering the sensor? Any body had done this experiment before?

When you crop you get the same performance as a sensor the size of the crop. If you crop a FF image to m43 size the performance is the same as if you had taken the photo with an m43 camera without cropping.

I realize your job is not to convince me but just for the record - not convinced.

One more thing while I'm on a roll.

The real limitation in systems often turns out to be the lenses.

For example people will claim they prefer a small sensor because it is better at getting everything in focus for macro photography. The reality is you could do the same thing with a FF camera if you could stop the lens down to F45 or F56. You would end up with the same diffraction softness that you get with the tiny sensor camera and the same DOF. But, there aren't many FF lenses that stop down that small.

On the other side, you could get just as narrow a DOF with a APSC or m43 camera as a FF camera, if you had really fast glass but they are often not available or prohibitively expensive. The best you can get for m43 is a $1000 F0.95 (F1.9 equivalent) or $1300 F1.2 (F2.4 equivalent.)

It was nice that Fuji release their 56mm F1.2 but we should remember it is only equivalent to a FF 85mm F1.8 which costs half as much. Likewise when you compare the speed of Fuji's F2.8-F4 kit lens to the typical F3.5-F5.6 FF lens (they are equivalent.)

People are funny about this too. For example they rave about the constant aperture 12-40mm F2.8 Olympus m43 lens but they complain that F5.6 is too slow on FF and they would never consider buying a constant aperture F5.6 FF 24-80mm lens (even though it would yield the same results) and offer the same size advantage.

 

[Fraulain Uebermueller]

"under most circumstances the larger sensor outperformas the smaller one"

Sure but the debate is why. Is it the dimensions of the sensor.

Yes. It is because a big sensor can collect more light than a small one. Noise is almost entirely a function of light because light particles, photons play by the rules of quantum mechanics - their position in the capturing device (the sensor) is random and follows the poisson distribution. Any other sources of noise are neglible under most situations.

The light collecting efficiency of the sensors out there are is aout 50% give or take a bit (ignoring the colour filer array losses etc. which are also similar in all cameras with CFA).

If the technology used is similar, as is the case for all the big-sensor cameras on sale today, apart from Foveon, and the sensor size is by far the biggest differentiator when it comes to image quality from the sensor point of view.

Or is it something else. It seems to me the best explanation (stated above) is that you could make an aps-c sensor with the same high ISO as the best FF but you'd have to cut back too much on the megapixels to do it.

No, this is false. You are thinking in a pixel centric way. A forest is made of lots of trees, so basing a comparison of forests on a sample of one tree don't tell much of the forest.

Pixel size has mostly influence in the resolution of the device. It's incluence in the SNR is minute over allmost all of the dynamic range.

Let's imagine very simple two black and white sensors:

Sensor A has 1 pixel.

Sensor B is twice the size of A, and has 2 pixels, so the pixel of the same size.

Each pixel has full well capacity of 30.000 electrons and the read noise is 3 electrons. These numbers are perfectly normal by today's standards.

(Noise of light (standard deviation of the number of photons) is interestingly the square root of the signal in poisson distribution.)

For a full saturation A has noise of sqr(3^2 + sqrt(30.000)^2). B has noise of sqrt(2*3^2 + 2*sqrt(30.000)^2). A has signal of 30.000, B 60.000. Thus A has SNR of 173 at full saturation, while B has 245. Different by sqrt(2).

Here's a small graph showing the difference:

SNR comparison of sensors

 

[Fraulain Uebermueller]

"I have a scientific grade chilled, monochrome, back-illuminated 1" CCD with a resolution of 1024x1024 that has an order of magnitude better s/n and dynamic range than any prosumer camera. That technology cannot be manufactured and sold in a pocketable camera costing $500 no matter how hard they try."

Can one of the "equivalence" defenders address this? Because it seems to blow a big hole in your argument.

Well, the person who wrote that offered zero evidence for his claim, did he? And the claim is rather extraordinary, thus he should offer evidece - underneath the points below I ask some for simple metrics he should provide.

Some points no notice:

• Cooling the imager reduces sensor generated noise and increases the engineering dynamic range (not really the DR which is relevant for most photography as the influence is in really deep shadow range). This is not relevant for image quality equivalence. Also going down from 3 electrons per pixel to 2 is not awfully relevant.
• Backside illumination improves quantum efficiency somewhat - the only large sensor camera which uses it is Samsung NX1. Other than that camera, it's not relevant for image quality equivalency. Also FF is 7 or 8 times larger than 1", thus QE would need to be some 400% on the 1" to equal FF.
• It's monochrome, thus the effective quantum efficiency will be higher as our cameras lose about 50% of light to the colour filter array. So now the QE would only need to 200%
• The poster of the article thinks in pixel-centric way instead of whole images, ignoring in the case of Nikon D800 about 97% of light which hits the D800 sensor is not intellectually honest.
• Unless exposure is limited, QE is not relevant for DR and SNR.

If we compare intellectually honestly the whole sensors we will end up in quite different conclusion. Of course if he'd provide information on the sensor, like FWC, QE and read noise, I'd be happy to do some quick calculations.

Anyhow, his "order of magnitude" better SNR and DR claim is false to the point of being ridicilous.

 

[Fraulain Uebermueller]

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.

Until recently there was not that much competition for canon and nikon for serious cameras, which was part of the problem. Even Sony has limited competition on the sensor front.

Not really. There a plenty of sensor manufacturers and if you put in the cash they're happy to make big sensors to you.

One should remember that it is not the big sensors whch drive the technology and have the most advances solutions, but the small ones (cell phone sensors etc.).

Nikon has to buy sensors from Sony.

No they don't. Over the recent years they have had no less than four (4) different sources for sensors:

• Sony (FF - D800, D810, APS-C, pocket cameras)
• Toshiba (APS-C)
• Aptina (Nikon-1)
• Nikon's own design team (FF - D3, D4)

Some pocket cameras may well have had sensors from other manufacturers as well.

A good example of a new manufacturer designing a FF sensor from scratch is CMOSIS for Leica.

Basically canon has been the only sensor producer competing with Sony.

Apart from a couple of dozen other competitors out there

And Sony has an incentive to keep full frame better than aps-c too

There is no such artificial incentive - the 2.25 times larger sensor is enough to quarantee better performance even if APS-C sensor had slightly better design. The fact of the matter is that the smallest sensors are far more advanced than the big ones.

And as an example, Canon uses much finer design geometries for their APS-C sensors than their FFs - their FFs are fabricated with ancient 500nm fabrication lines, whle the Canon APS-C chips are made with 180nm is I recall right. This is a pretty significant advantage for the APS-C designs.

, and indeed to withhold better sensors from nikon and others for some period of time. I think they've acknowledged they do that.

False. Sony sensors and cameras are manufacturerd by independent parts of Sony. The camera division is nothing but a customer for the sensor division. And the most important customer for the sensor division is...Nikon, not Sony. The sensor in Nikon D800 was not released to Sony cameras until a long delay for example.

Also if you look at the measurements of DxOMark, you notice that the tendency has been Nikon (and Pentax) cameras using Sony sensors have certainly not performed worse than Sonys using the same sensors, nor have the Sonys been out in the market earlier (at least by in any significant mount of time).

By far most sensors Sony sells are off-the-shelf parts - designed for good all-around performance. They're sold to anyone from the day they come available. Naturally there can also be some specialities manufactured for order, like the A7s-sensor which might never appear in any other camera. But just as well Sony could have made such sensor for Nikon to never be sold for others.

 

[klownshed]

But what is always conveniently ignored is at what point the noise level becomes significant or even noticeable. For many people, the situations in which a bigger sensor shows a clear advantage are not situations that tip the balance enough for it to be a significant issue.

Once an image is reduced in size for its intended output media, even an APS-C sensored image can show negligible noise under most circumstances.

For some, a larger sensor can indeed reap rewards. But for many people in many circumstances, the difference between APS-C sized sensors and 36x24mm sized sensors is insignificant in real world use.

 

[min32]

How you get that formula? In real world image capturing is that actual result as you graph? Had any body do the experiment on the FF system? Just compare the image crop fro full size image with the image capture by cover the ff sensor to APSC size or micro 4/3 or 1" size.

 

[cesjr]

A bit confuse. If crop the image size to APSC or micro 4/3 from the fully captured image of FF size (fully utilize all the sensor area). Are that the image crop from full size ff is batter than the image crop by covering the sensor? Any body had done this experiment before?

When you crop you get the same performance as a sensor the size of the crop. If you crop a FF image to m43 size the performance is the same as if you had taken the photo with an m43 camera without cropping.

I realize your job is not to convince me but just for the record - not convinced.

One more thing while I'm on a roll.

The real limitation in systems often turns out to be the lenses.

For example people will claim they prefer a small sensor because it is better at getting everything in focus for macro photography. The reality is you could do the same thing with a FF camera if you could stop the lens down to F45 or F56. You would end up with the same diffraction softness that you get with the tiny sensor camera and the same DOF. But, there aren't many FF lenses that stop down that small.

On the other side, you could get just as narrow a DOF with a APSC or m43 camera as a FF camera, if you had really fast glass but they are often not available or prohibitively expensive. The best you can get for m43 is a $1000 F0.95 (F1.9 equivalent) or $1300 F1.2 (F2.4 equivalent.)

It was nice that Fuji release their 56mm F1.2 but we should remember it is only equivalent to a FF 85mm F1.8 which costs half as much. Likewise when you compare the speed of Fuji's F2.8-F4 kit lens to the typical F3.5-F5.6 FF lens (they are equivalent.)

People are funny about this too. For example they rave about the constant aperture 12-40mm F2.8 Olympus m43 lens but they complain that F5.6 is too slow on FF and they would never consider buying a constant aperture F5.6 FF 24-80mm lens (even though it would yield the same results) and offer the same size advantage.

Dude you're hardly on a roll. You're dug in and your arguments are not convincing a lot of folks. You can blame that on them sure. But maybe it's your arguments? Shudder, can't be I guess

 

[Jeff Charles]

But what is always conveniently ignored is at what point the noise level becomes significant or even noticeable. For many people, the situations in which a bigger sensor shows a clear advantage are not situations that tip the balance enough for it to be a significant issue.

Once an image is reduced in size for its intended output media, even an APS-C sensored image can show negligible noise under most circumstances.

For some, a larger sensor can indeed reap rewards. But for many people in many circumstances, the difference between APS-C sized sensors and 36x24mm sized sensors is insignificant in real world use.

Thanks for bringing a sensible perspective to this discussion.

 

[Jeff Charles]

A bit confuse. If crop the image size to APSC or micro 4/3 from the fully captured image of FF size (fully utilize all the sensor area). Are that the image crop from full size ff is batter than the image crop by covering the sensor? Any body had done this experiment before?

When you crop you get the same performance as a sensor the size of the crop. If you crop a FF image to m43 size the performance is the same as if you had taken the photo with an m43 camera without cropping.

I realize your job is not to convince me but just for the record - not convinced.

One more thing while I'm on a roll.

The real limitation in systems often turns out to be the lenses.

For example people will claim they prefer a small sensor because it is better at getting everything in focus for macro photography. The reality is you could do the same thing with a FF camera if you could stop the lens down to F45 or F56. You would end up with the same diffraction softness that you get with the tiny sensor camera and the same DOF. But, there aren't many FF lenses that stop down that small.

On the other side, you could get just as narrow a DOF with a APSC or m43 camera as a FF camera, if you had really fast glass but they are often not available or prohibitively expensive. The best you can get for m43 is a $1000 F0.95 (F1.9 equivalent) or $1300 F1.2 (F2.4 equivalent.)

It was nice that Fuji release their 56mm F1.2 but we should remember it is only equivalent to a FF 85mm F1.8 which costs half as much. Likewise when you compare the speed of Fuji's F2.8-F4 kit lens to the typical F3.5-F5.6 FF lens (they are equivalent.)

People are funny about this too. For example they rave about the constant aperture 12-40mm F2.8 Olympus m43 lens but they complain that F5.6 is too slow on FF and they would never consider buying a constant aperture F5.6 FF 24-80mm lens (even though it would yield the same results) and offer the same size advantage.

Dude you're hardly on a roll. You're dug in and your arguments are not convincing a lot of folks. You can blame that on them sure. But maybe it's your arguments? Shudder, can't be I guess

What "arguments"? He just posted facts.

 

[cesjr]

I would say that pixel level size and quality are important, this would effect most aspects of image quality that are not lens based like field of view and depth of field. Let's take a great well performing sensor like the one in the Nikon D750 for example, take a slice of the exact same sensor and put it a compact camera with quality optics and the same processing engines and you will effectively get a image that is cropped from the D750.

The only problem is you would probably end up with 2mp, and 2mp just do not sell to the point and shoot crowd who believe megapixels are the be all an end all.

Pixel size, while important, is often overemphasized when people are discussing the improved performance of larger sensors. Having said that bigger pixels improve low light sensitivity and have a higher saturation point. For much of the shooting people do, they would notice the loss of resolution/sharpness much more than they would improved dynamic range. However, for those people that photograph in very low light (astrophotographers for example) or those that photograph scenes with huge dynamic ranges their would be some advantage to this tradeoff. The Sony A7s is becoming very popular in astrophotography for example.

This camera seems to be a good illustration of the points being made here in opposition to "equivalence". Better high ISO was achieved by increasing the pixel size and lowering the megapixels. Not increasing the sensor size. Look FF is currently better at high ISO. What I'm saying is it seems unproven and a stretch to say that necessarily will remain the case because there's some kind of law of physics that says a bigger sensor will always be lower noise. I do think a bigger sensor will always have more resolution - up to the resolving power of the lens I guess. But I don't see the rest of the claims being solid at this point re FF will necessarily be lower noise than smaller sensors (assuming same sensor tech). For one thing, if the noise gets low enough at high ISO in the future, the differences may become way too small to matter even if they still exist.

 

[Daniel Lauring]

I would say that pixel level size and quality are important, this would effect most aspects of image quality that are not lens based like field of view and depth of field. Let's take a great well performing sensor like the one in the Nikon D750 for example, take a slice of the exact same sensor and put it a compact camera with quality optics and the same processing engines and you will effectively get a image that is cropped from the D750.

The only problem is you would probably end up with 2mp, and 2mp just do not sell to the point and shoot crowd who believe megapixels are the be all an end all.

Pixel size, while important, is often overemphasized when people are discussing the improved performance of larger sensors. Having said that bigger pixels improve low light sensitivity and have a higher saturation point. For much of the shooting people do, they would notice the loss of resolution/sharpness much more than they would improved dynamic range. However, for those people that photograph in very low light (astrophotographers for example) or those that photograph scenes with huge dynamic ranges their would be some advantage to this tradeoff. The Sony A7s is becoming very popular in astrophotography for example.

This camera seems to be a good illustration of the points being made here in opposition to "equivalence". Better high ISO was achieved by increasing the pixel size and lowering the megapixels. Not increasing the sensor size. Look FF is currently better at high ISO. What I'm saying is it seems unproven and a stretch to say that necessarily will remain the case because there's some kind of law of physics that says a bigger sensor will always be lower noise. I do think a bigger sensor will always have more resolution - up to the resolving power of the lens I guess. But I don't see the rest of the claims being solid at this point re FF will necessarily be lower noise than smaller sensors (assuming same sensor tech). For one thing, if the noise gets low enough at high ISO in the future, the differences may become way too small to matter even if they still exist.

Actually, we got on a bad path there by suggesting a bigger sensor will always be better than a smaller one. While that is true, it isn't the biggest driver. The biggest driver is the total amount of light that is read by the entire sensor. If you put the same amount of total light on a smaller sensor it will do nearly as well as a larger one. To put the same amount of light on a smaller sensor you need a larger F-stop. That is what seems to be confusing people. They keep thinking in per pixel light vs. total sensor light.

 

[kolyy]

You can lead a horse to water....

+1

 

[Fraulain Uebermueller]

I had a question? If we just cover the ff sensor inside the camera to APSC size. The sensor performance will drop to aps-c sensor performance?

Yes. It doesn't matter how you crop. Cropping in the computer after the exposure will also cause the same effect.

It is (almost) all about how much light is collected. If you crop, you throw away part of the light.

 

[Daniel Lauring]

cesjr wrote;

Dude you're hardly on a roll. You're dug in and your arguments are not convincing a lot of folks. You can blame that on them sure. But maybe it's your arguments? Shudder, can't be I guess

You seem like the kind of "dude" who would benefit from watching this video seeing as you seem to totally ignore Fraulain's excellent explanations (which are much better written and scientifically backed up than my own.)

You could also read this but I suspect it isn't going to "take."

http://www.josephjamesphotography.com/equivalence/

The main thing to take away from that website is this statement, "The same total light will result in the same noise for equally efficient sensors (regardless of pixel count and regardless of the ISO setting."

 

[Fraulain Uebermueller]

How you get that formula? In real world image capturing is that actual result as you graph? Had any body do the experiment on the FF system? Just compare the image crop fro full size image with the image capture by cover the ff sensor to APSC size or micro 4/3 or 1" size.

If you crop, you throw away light. Noise is almost entirely because of the nature of light itself. thus if you crop, you decrease the both signal and the noise, but the signal goes down more, thus the signal-to-noise-ratio goes down.

About the formula - signals just add up. When you add pixels together, you just add the values.

When it comes to noise, uncorrelated sources of noise add up in quadrature, that is Noise(Total)^2 = Noise(A)^2 + Noise(B)^2 + Noise(C)^2 + ...

And since all the relevant noises are uncorrelated, that is how you calculate the relevant noise.

For more on this topic, please visit http://theory.uchicago.edu/~ejm/pix/20d/tests/noise/ - it's a site of Emil Martinec, a physics professor in University of Chicago.

The experiment you suggest is not needed as it would be pointless. All you need to know is the basic properties of one pixel and the number of pixels and you know the relevant properties of the whole image sensor. If you crop FF to APS-C, you lose performance. If you crop FF to iPhone size you lose even more performance. All this is because of loss of light (and resolution too, but that's a bit off topic) used to create the output image.

The link above teaches about nature of light and sources of noise, and how to measure it using a standard procedure. You'll learn that the standard deviation (or noise) of light is the square root of the number of captured photons. For reference on the relevant metrics (read noise and full well capacity) of many cameras, you can check out http://www.sensorgen.info/ - it has a couple of errors and the accuracy of the results is not great, but it is easily good enough to tell you what the ballpark is.