[dosdan]

For an image from an 18% reflective surface to be "excellent" from a noise standpoint, each display pixel must correspond to the collection of at least 1600 photons (40^2).

Dave, yes, but the number of display pixels, say in a A4-sized printout, is not the same as the number of image pixels. Say, with a very larger number of image pixels, we had 4x as many as in the final printed/displayed image. Then we'd be root-mean-squaring every block of 4 noisy image pixels into 1 less-noisy display pixel.

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Last edited by dosdan; 09-04-2009 at 06:59 AM.

[newarts]

Dave, yes, but the number of display pixels, say in a A4 printout, is not the same as the number of image pixels. Say, with a very larger number of image pixels, we had 4x as many as in the final printed/displayed image. Then we'd be root-mean-squaring every block of 4 noisy image pixels into 1 less-noisy display pixel.

I agree, but it is not necessary to consider the number of sensor pixels at all. For a particular display, viewed at a particular distance one must have collected 1600 photons per displayed pixel.

For example, a typical requirement for an 8x10" display viewed at 14" is a print pixel size of 0.1mm. The total number of print pixels is about

(8*25.4/0.1)(10*25.4/0.1)~5mp

For "excellent noise quality", a perfect sensor must collect, on average, 1600 photons for each of these display pixels.

The sensor therefore must be divided into 5 million logical subdivisions, each of which must collect a total of 1600 photons (by binning or whatever); the total number of photons collected must be 8000E6 photons

Say the sensor is 1/2.3", 6.16E3umx4.32E3um = 26.6E6umsquared. (um means micrometer.)

This is 8000E6photons/26.6umsquared = 300photons/umsquared, which is about 1/4-1/3 the saturation limit for silicon. A perfect 1/2.3" P&S camera is just theoretically sufficient to take an "excellent" 8x10" photo.

Dave

[WMBP]

Dave, yes, but the number of display pixels, say in a A4-sized printout, is not the same as the number of image pixels. Say, with a very larger number of image pixels, we had 4x as many as in the final printed/displayed image. Then we'd be root-mean-squaring every block of 4 noisy image pixels into 1 less-noisy display pixel.

Well, obviously. :-)

[falconeye]

Simply put, this puts a lower limit on sensor size for an "excellent" image of a particular scene for display at a particular size with constant f-number and exposure time (even in the absence of "equivalence" requirements.)

Dave, you seem to completely miss the heart of this entire thread (and I am glad to repeat my answer to your previous post ) ...

In the equivalence we are discussing here, the point is that f-number is not kept constant. The physical size of lens aperture (not f-stop), noise and DoF is kept constant.

This means that when going to smaller sensors, f-stop and ISO setting both decrease. And decreasing ISO makes your argument entirely void. The number of photons hitting the sensor simply doesn't change.

[JonPB]

Since Dave brings up the theoretical limits of a 1/2.3" sensor, I thought I'd look at noise levels of compact cameras. The DxO Mark website has analyzed the Nikon P6000, which should be using sensor technology comparable to the D90 and D700.

Using this calculator, I figure that the 1/1.72" sensor on the P6000 is about 4.5 stops different from a 135-size sensor. That is, with 21mm at f/3.3, a 1/1.72" sensor has a comparable FOV and DOF to 100mm at f/16 on a 135-size sensor.

At ISO 64, the P6000 has a SNR of 29.2 dB; at ISO 1600, the D700 has a SNR of 30.7 dB. At ISO 400, the P6000 has 20.9 dB; at 12800, the D700 has 21 dB. That's about 4.5 stops of difference at a given noise level. So you could claim that there is no noise benefit to the D700 over the P6000. (The DxO measured ISOs come out at about 4.5 stops, too.) The DxO chart can be seen here.

Dave has a valid point, that larger sensors have a higher theoretical signal-to-noise limits. However, I think Haakan's point needs to be taken to heart: with current technology, larger sensors capturing the same image will have no less noise. (This assumes that we can extrapolate Nikon's sensor technology to other brands.) In the future, larger sensors probably will produce lower noise in the same image, but technology hasn't reached that point yet.

The noise-related benefit of larger formats, then, may be stated as not having fast-enough lenses for smaller formats. An image produced by a lens at f/2.8 on a 135-size camera would require an f/0.5 lens on a 1/2.3" camera--without such a lens, the smaller sensor cannot produce a comparable image. (Or, a lens at f/5.6 on a 4x5 camera would require f/1.8 on a 135-size camera.) But with such a lens, on similar-technology sensors, the noise results would be about the same. Buying a 200mm/2.8 for your APS-C-size camera probably makes more sense than buying a 300mm/4 and a 135-size camera.

Alternately, if you desire (or are willing to have) a shallower depth of field than the available lenses for smaller sensors permit, larger sensors will have less noise. But using a different DOF will capture a different image, and Haakan reasonably wants to compare images with the same optical attributes.

You can also improve noise by moving to a newer sensor technology: the P6000 is only 4 stops behind the D3, which is to say that the P6000 has about one-half stop less noise than the D3 when using the same DOF. See here. Likewise, the D90 appears to be about 1 stop better than the K20D, see here.

The upshot, I think, is that 135-size cameras are not improved APS-C-size cameras--nor are SLRs improved compact cameras. They are different formats with tradeoffs aside from cost, size, and weight. Moving to a larger format will not necessarily reduce the noise in your images.

[Haakan]

Hi JonPB
that is good input. So your analysis confirm that with todays "state of the art" sensors, the scaling in terms of noise according to area is valid even down to the small sensors of compact cameras.

So, as I stated before, where the scaling breaks down in practice is really in the lenses when you are getting close to f/1.0. But when comparing APS-C and FF there is also a practical size limit at the other end which means that for lenses in the order of 100-200mm focal lengths and above, it will be very hard to get a gain by using FF (in terms of noise)

An examples from the Canon lens set-up:

If you have a 200mm f/2.0 lens on your APS-C, there is actaully no lens in the Canon set-up (at least not on their home page) that will give a better performance on a FF (assuming you want the same FOV, i.e. around 300 mm on FF). The best you can get a 300 mm f/2.8, but then one have gained nothing in terms of low light performance. In order for the FF to give an advantage, one would have needed a 300mm f/2.0. I think Nikon had a 300mm f/2.0 lens in the early 80's, weighting 16 lbs with a list price (in those days) of $29,000 - quite a heafty price to be able to realize the noise gain of your FF (if you still can find it)

So in practise this means that in the telephoto range, it will be very hard and/or extremely costly (in many cases impossible) to benefit from a FF camera in terms of noise performance.

For wider lenses (where the scaling would require lenses with f/1.0 or larger apertures) you can get the noise benefit, provided you shoot at full aperture. At these focal lengths you can also get a thinner DOF on FF which is something some people are looking for - but there has been a full separate thread dedicated to that topic for those interested

I have come out of this discussion with a much better appreciation of the APS-C format for low light photography for e.g. sports, concerts, nature photography etc.

Best regards,
Haakan

[falconeye]

Nikon P6000 [...]
I figure that the 1/1.72" sensor on the P6000 is about 4.5 stops different from a 135-size sensor

Interesting consideration.

The 1/1.72" sensor is 7.40 x 5.55mm (9,25mm diameter, 4.68x crop) and this is 4.45 stops (2*log_2(4.68)) different from a 135-size sensor.

Its ISO range is 64-.... A Nikon D3X is ISO 100-..., a D700 is ISO 200-...

So, while Dave's point didn't hold true for APS-C vs. FF (you need the rather expensive D3X to have a better low ISO performance than ASP-C), it is a valid point in a comparison with P&S.

To have a comparable low ISO performance (and hence, the equivalent dynamic range), the P6000 would have to feature ISO 9 to compete with APS-C or a D700 and even ISO 5 to compete with a D3X.

It is a rather big degradation in dynamic range when going from ISO 5 to ISO 64! (this is like going from ISO 100 to 1400 ...)


So, the low ISO dynamic range advantage of a larger sensor (which isn't exploited in most current FF designs) makes a large difference if you compare with P&S.


We didn't consider this point earlier in the thread because we focussed on high ISO noise, not low ISO dynamic range. And we did so for a reason because of the lower low ISO setting normally available with APS-C. But it stops there. Already FourThirds has a disadvantage here, starting at ISO 100 rather than ISO 50.

[Haakan]

falconeye, if a sensor does not support ISO below e.g. 100, could one have a solution in the camera that takes e.g 4 images directly after each other and then add them in the camera to get an effective IS0 25 solution? One could even think of having some "pattern alignment" when adding the images to get some type of "shake reduction" to combat longer shutter times.

Best regards,
Haakan

[newarts]

Dave, you seem to completely miss the heart of this entire thread (and I am glad to repeat my answer to your previous post ) ...

In the equivalence we are discussing here, the point is that f-number is not kept constant. The physical size of lens aperture (not f-stop), noise and DoF is kept constant.

This means that when going to smaller sensors, f-stop and ISO setting both decrease. And decreasing ISO makes your argument entirely void. The number of photons hitting the sensor simply doesn't change.

Falconeye, thanks. I have watched the thread devolve from a discussion of sensor size being unimportant for equivalence (constant noise, constant f-number, time, FOV, etc) to its present state of large aperture lenses and variable ISO fixing the noise problem.

I'm sorry I did not state my point more clearly.

It does not matter how big the lens is, or how you define ISO, or how long the exposure takes, one must collect something like 300 photons per square micrometer of planar silicon to meet the requirement of "excellent" S/N ratio for a reasonably sized display (8x10" @ 0.1mm/pixel)

As the 300 photons/square micrometer needed is for 18% of the saturation level (say1200 photons/square micron) for planar silicon the maximum linear dynamic range of such a small sensor would be not many stops.

These considerations put an independent floor on performance for planar collectors (the maximum photon density has to do with the the breakdown strength of the collector material I think.)

Dave

[falconeye]

Dave, IMHO you're both correct and wrong. This makes a proper response difficult. I'll try again.

one must collect something like 300 photons per square micrometer of planar silicon to meet the requirement of "excellent" S/N ratio for a reasonably sized display (8x10" @ 0.1mm/pixel)

There is no such constraint. Only total number of photons per entire sensor surface matters. Please, check your sources.

the maximum linear dynamic range of such a small sensor would be not many stops.

I already conceded this above.
But this fact is better expressed by the fact that the low ISO limit isn't low enough for small sensors (the well capacity doesn't increase sufficiently).
But in practice, the low ISO limit currently scales ok when going from FF to APS-C.

the maximum photon density has to do with the the breakdown strength of the collector material I think.

Of course, there is a floor when the equivalence scaling (on the low ISO end) breaks down. And as I pointed out, it is already broken at FourThirds.

There is an ultimate floor when the sensor would simply melt due to high photon density (*)


(*) I am actually wondering what is happening when using a tripod and LV imaging the sun with a sharp and fast wide angle lens (manually fully opened as LV would stop it down). It would probably be possible to melt parts of the sensor down (if camera electronics doesn't shut the shutter down due to overheat what it is supposed to do).

[falconeye]

if a sensor does not support ISO below e.g. 100, could one have a solution in the camera that takes e.g 4 images directly after each other and then add them in the camera to get an effective IS0 25 solution?

This is stacking and you can always do this (I do it regularly in software. PhotoAcute is great for doing this).

But it applies to any sensor size.

Point is that at the low ISO end (where the dynamic range problem occurs) exposure times may be as short as 1/8000s.

To fully emulate ISO 25 at this point (for full equivalence), you would have to be able to take 4 shots within 1/8000s which is the equivalent of 32,000 fps. It may be somewhat hard to achieve this (You would certainly need an electronic shutter ...)

And on the low ISO end where 5fps would probably be just fine, you don't have the well capacity problems.


So, the remaining fact is:
- no low noise benefit from FF vs APS-C when maintaining same big glass.
- no dynamic range benefit from FF vs APS-C for all but expensive FF cameras featuring ISO 100.
- but huge low noise and dynamic range benefit from FF/APS-C over much smaller sensors due to inavailaibity of very big glass and very low ISO for the smaller sensors.

[newarts]

Dave, IMHO you're both correct and wrong. This makes a proper response difficult. I'll try again.

There is no such constraint. Only total number of photons per entire sensor surface matters. Please, check your sources.

Yes, that's what I said. Further I used the criterion that each pixel of an "excellent quality" 8x10" display with 0.1mm pixels (see the wikipedia reference I gave earlier quoting from ISO 12232:2006 regarding photographic speed) requires 1600 captured photons per pixel at the 18% level.

This requirement (about 8E9 photons total) must be distributed over the collection area of a sensor, but a planar silicon or similar semiconductor sensor saturates at about 1000-1200 photons collected per square micrometer. This puts a minimum size requirement on the sensor to achieve the specified level of noise.

Using a 1000 photon per square micron at saturation for the sensor material & 18% of saturation results in a minimum sensor size of 8E6/0.18 square microns, or about 44 square mm.

Probably the 1600 photons per display pixel is tighter than needed, & maybe the saturation limit is 1200 rather than 1000, but my purpose was to show the principle.

But this fact is better expressed by the fact that the low ISO limit isn't low enough for small sensors (the well capacity doesn't increase sufficiently).
But in practice, the low ISO limit currently scales ok when going from FF to APS-C.

You are likely right about that as the area of an APS-C sensor is around 432 square mm, ten times larger than the limits I estimated, but given the realities of technology, I suspect there's not a lot of room for improvement.

Of course, there is a floor when the equivalence scaling (on the low ISO end) breaks down. And as I pointed out, it is already broken at FourThirds.

Sorry, I missed that and was aware that there's some noise room to spare for APS-C...that's why I mentioned the 1/2.3" sensor which is pushing the absolute limits. I intend to go a little further with this to see what it implies about full equivalence and saturation type ISO definitions.

Dave

ON Edit - I apologize for hijacking the thread

[cbaytan]

I've read everything and being no engineer, I found all confusing. I have to chip in and blow every my mislead information here, correct my mistakes if you can. Please.

1-Noise is generated by all electronic systems.
2-dSLR'r are electronic systems so they all produce noise. We hear that noise in sound amplifiers as static.
3-Different dSLR's produce different noise levels, regardless of their sensor sizes are the same.
4-Electrical signal is generated when photons hitting pixels, but photon number must big enough to create a signal from sensor pixels. This is like, sound must be bigger than amplifiers static so you can hear the music.

So. Considering two cameras creates same amount of noise but hypothetically one of the cameras has FF size sensor other one is APS-C size sensor (practically impossible because different sensor sizes mean different electronic system. So this hypothetical system) also use same lens and same aperture when taking a same sample shot. To my information:

FF sensor camera will produce less noise because FF sensor will collect more photons, because it has more surface than than APS-C so signal/noise ratio will be bigger in FF system.

So when you keep all other variables constant FF sensor will have less noise, if I am not mistaken.

But I think what I read it here oppose to that.

[Haakan]

I agree it has been a lot of information and it is not esay to keep track. I think Marc in one of his final posts, as well as falconeye, did a very good summary. But I will give it a shot as well.

You are correct on noise if you look at same ISO, but ISO is not a image parameter, like FOV, DOF, shutter time. It is rather a consequence of these settings. And since you are comparing two different formats, you have to take also these factors into consideration. So I will use an example to try to explain the logic.

1. If you compare a shot with the same lens, at same aperture, same shutter speed and thus same ISO (e.g. use 200mm f/2.0 on both your APS-C and FF), then you will have less noise in the FF. But you will have a different image due to the difference in FOV.

2. So you need to use a 300 mm lens on the FF. And in order to use the same ISO on the FF you would need to get a 300mm f/2.0 (actually not available if I look at different manufacturers home pages). So you end up using a 300mm f/2.8 as your best alternative.

3. Thus the 1 EV benefit was lost in the 1 EV lower max aperture.

4. If you look at the front lens diameter, they are the same for a 200mm f/2.0 and 300mm f/2.8 (at least decently close).

5. Thus one conclusion is that the only factor that really gives you better noise performance is having a bigger front lens (or more exactly larger aperture in absolute number) (it was falconeye who pointed this out)

6. In addition, also for lens combinations where you have same f values on both the FF and APS-C. e.g. 85mm f/1.4 and 55mm f/1.4, any time you use the lens at less than max aperture (e.g. you go to 2.8 on your 85mm to gain DOF) you can get exactly the same image in terms of FOV, DOF, shutter speed, having equal amount of noise, on your APS-C (using an aperture of 2.0 on the 55mm lens). I.e. a FF will not give you a benefit in lower noise unless you shoot all full aperture.

This is really the reason for the thread. I had always thought that FF gives you 1 EV lower noise, thinking that this would be seen across all high ISO images if you compared the two formats, even for images not shot at max aperture. This thread has made me realize that for me, in practise there would be very few situations where the FF would give me a less noisy image.

I do not know if that helped as summary, there is a lot more details in the thread though.

Best regards,
Haakan

[Marc Sabatella]

So. Considering two cameras creates same amount of noise but hypothetically one of the cameras has FF size sensor other one is APS-C size sensor (practically impossible because different sensor sizes mean different electronic system. So this hypothetical system) also use same lens and same aperture when taking a same sample shot.

If you literally use the same lens and same aperture, you get two very different pictures, due to the crop factor. Why would you want to compare noise in two very different pictures? That's why we've been focusing on making sure to use lenses and apertures that yield the same picture, and comparing the noise that way. Hence the notion of "equivalence" - the idea of figuring out what lenses and settings on one camera will yield the same *results* are on another, rather than blindly using the same lenses and settings regardless of results.

FF sensor camera will produce less noise because FF sensor will collect more photons, because it has more surface than than APS-C so signal/noise ratio will be bigger in FF system.

So when you keep all other variables constant FF sensor will have less noise

See above. The problem, as has been described at length here, is that it is *impossible* to keep all other variables constant. If you use the same lens and aperture, you get very different FOV. If you keep FOV and aperture constant, you get very different DOF as well as a much larger lens on the FF system. So you've got to chosoe which variables make the most sense to keep constant, and let the others vary as necessary.

In my world, I'm either concerned with getting the *exact same image* - meaning same FOV, shutter speed, and DOF - or else I'm concerned with getting the same FOV, shutter speed, and cost/size/weight of lens.

And that's where the results we keep speaking of come in - it turns out if you want to keep DOF and/or size of lens constant, there is no difference between FF and APS-C. Only if you're willing to use a larger lens and accept shallower DOF does FF win. And if you are willing to use a larger lens and accept shallower DOF, you can often get the same improvement in noise on APS-C - but only if the equivalent lens actually exists. The problem is that in many cases, it doesn't.