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Author Topic: Sensor and Sensibility  (Read 17616 times)
Ray
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« Reply #20 on: August 10, 2006, 07:14:26 PM »
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One important point not mentioned in the article is the relationship between pixel size and lens resolution.  Increasing the pixel count of a sensor of a given size by making smaller pixels provides little improvement in image quality once the pixels become smaller than the lens resolution.  At this point, image quality is dominated by the lens rather than the sensor.  This consideration has nothing to do with noise.

We're a long way from DSLR pixels being smaller than good 35mm lenses can resolve. These Airy Disk diameters and diffraction spot sizes can be misleading. The question should be, 'Is the pixel sensitive enough, efficient enough and sufficiently protected from extraneous noise, to record fine detail that has lost most of its contrast?'; because that's what happens as you try to record finer and finer detail. The detail is there, it's resolved by the lens, but it loses a lot of its original contrast as a result of lens diffraction, opacity of the glass, reflections and other aberrations.

A lens that is truly diffraction limited at F4 has awesome resolving power. Even at 50% MTF it would resolve way beyond the capabilities of current sensors.

To get things in perspective, old-fashioned B&W film such as T-Max 100 is (was) capable of recording 50 lp/mm without any loss of contrast. (Ie, what the lens delivered, the film recorded at 100% MTF, up to 50 lp/mm). Above 50 lp/mm the film began to lose contrast, but at 100 lp/mm it could still record detail at 60% MTF.

Consider the result of using a lens diffraction limited at f4 with T-Max 100. At the Rayleigh's limit of 9% MTF, lens resolution is about 800 lp/mm; at 50% MTF it's about 200 lp/mm; at 75% MTF it's about 100 lp/mm (figures off the top of my head).

100 lp/mm at 75% MTF from the lens gets recorded at (60% x 75%=45%) on the film. That's quite a good result in my view.

Now, I don't want to get into a debate of film versus digital. We know that these results are going to be somewhat spoiled by clumps of grain and subjected to further degradation in the scanning process. The point I make here is, a sensor that could record 100 lp/mm with a loss of only 40% in contrast would finally be on a par with the best B&W film in terms of absolute resolution (but not in terms of over all image quality, obviously. Resolution isn't everything.)
« Last Edit: August 10, 2006, 07:16:35 PM by Ray » Logged
Ray
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« Reply #21 on: August 10, 2006, 09:01:32 PM »
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Wow, that paragraph got really mangled; I must have deleted part of the sentence.  Let me try again:

However, shot noise is not the most immediate obstacle to greater DR with current sensors; sloppy readout noise at low ISOs is.  Shot noise affects mainly the highlights at low ISOs, and highlights and midtones at high ISOs.
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No you didn't. You just missed a full stop. I understood you perfectly because this is not a computer program   .

I tend to agree that lowering read noise of small pixels is a major obstacle to further imrovement in digital image quality. We appear to be stuck with photonic shot noise, as we are with lens diffraction (although this is something that nanotechnology is already addressing in the laboratory). Thermal noise seems to be more of a problem with the larger pixels and/or the longer exposure, which, for equal DoF the larger format also needs. Extremes of temperature difference might also produce a noticeable difference with short exposures, as Boku has found, so there's probably some scope for thermal noise reduction technology even in the small camera.

The quantum efficiency factor is also an avenue for further improvement. We can never reach 100% efficiency, but technological progress seems to be directed at improving the efficiency of just about everything. The 2 litre engine in my Daewoo wagon is both more powerful and less gas hungry than the 2.4 litre engine in my previous car.
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bjanes
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« Reply #22 on: August 13, 2006, 05:59:14 PM »
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Consider the result of using a lens diffraction limited at f4 with T-Max 100. At the Rayleigh's limit of 9% MTF, lens resolution is about 800 lp/mm; at 50% MTF it's about 200 lp/mm; at 75% MTF it's about 100 lp/mm (figures off the top of my head).

100 lp/mm at 75% MTF from the lens gets recorded at (60% x 75%=45%) on the film. That's quite a good result in my view.

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Ray,

It is true that MTFs multiply, but not so simply as you show above. For details, see Norman Koren's website. Before you can perform the multiplication, you need to do a Fourier transform to convert from the spatial to frequency domain. You then multiply the components and then you must apply  a reverse Fourier transform via a complex convolution algorithm to go back from the frequency to spatial domain.  

[a href=\"http://www.normankoren.com/Tutorials/MTF.html]http://www.normankoren.com/Tutorials/MTF.html[/url]

For MTF at the Rayleigh limit, the equation 1/r = 1/r1 + 1/r2 is often used, where r = system resolution and r1 and r2 are system components (lens and film, for example).  If the lens resloved at 800 lp/mm and the sensor at 100 lp/mm at Rayliegh, the system resolution would be about 89 lp/mm.
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Ray
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« Reply #23 on: August 13, 2006, 07:30:34 PM »
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Bill,
Did I write 800 lp/mm as the Rayleigh's resolution limit of a lens diffraction limited at f4? You should have corrected me   . It is of course 400 lp/mm, but maybe still 200 lp/mm at MTF 50% and possibly 100 lp/mm at 75% MTF.

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For MTF at the Rayleigh limit, the equation 1/r = 1/r1 + 1/r2 is often used, where r = system resolution and r1 and r2 are system components (lens and film, for example).  If the lens resloved at 800 lp/mm and the sensor at 100 lp/mm at Rayliegh, the system resolution would be about 89 lp/mm.


I'm aware of this formula but don't know how to apply it for digital photography. Sensor manufacturers don't give us resolution and MTF details as film manufacturers do or used to. But generally, it seems to me that using that formula to generatet a lower sytem resolution than the component resolutions at the same  MTF is roughly equivalent to multiplying the MTF responses to generate the same system resolution as the component resolutions (if they are both equal) but at a lower MTF.

In other words, if lens and film independently both produce 100 lp/mm at 50% MTF, then the system resolution is 50 lp/mm at 50% MTF (1/100+1/100=1/50).

Multiply the MTFs and you get 100 lp/mm at (50%x50%)=25% MTF, which might be a good approximation if one is considering high MTFs and provided the MTF fall-off for both lens and sensor is fairly even. The straight line MTF response for the 10D system resolution, on Norman Koren's site, would suggest to me that multiplying MTFs of equal component resolutions is a good approximation.
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bjanes
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« Reply #24 on: August 13, 2006, 08:45:39 PM »
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Bill,
Did I write 800 lp/mm as the Rayleigh's resolution limit of a lens diffraction limited at f4? You should have corrected me   
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Ray, you mentioned the figure 800 lp/mm and I assumed incorrectly that you were referring to Rayleigh. Using the correct figure of 400, the system resolution becomes 80 lp/mm rather than 88. At such high lens resolutions, one is reaching the point of dimishing returns and the system is primarily limited by the sensor.

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I'm aware of this formula but don't know how to apply it for digital photography. Sensor manufacturers don't give us resolution and MTF details as film manufacturers do or used to. But generally, it seems to me that using that formula to generatet a lower sytem resolution than the component resolutions at the same  MTF is roughly equivalent to multiplying the MTF responses to generate the same system resolution as the component resolutions (if they are both equal) but at a lower MTF.

In other words, if lens and film independently both produce 100 lp/mm at 50% MTF, then the system resolution is 50 lp/mm at 50% MTF (1/100+1/100=1/50).

Multiply the MTFs and you get 100 lp/mm at (50%x50%)=25% MTF, which might be a good approximation if one is considering high MTFs and provided the MTF fall-off for both lens and sensor is fairly even. The straight line MTF response for the 10D system resolution, on Norman Koren's site, would suggest to me that multiplying MTFs of equal component resolutions is a good approximation.
[a href=\"index.php?act=findpost&pid=73274\"][{POST_SNAPBACK}][/a]

As I understand things, the simplified formula only works for MTF around 10% or less, and it is using spatial resolution in lp/mm not the MTF. For MTF of 50%, you would have to use the Fourier transform and convolution in the case of unequal component resolutions, but if the resolutions are similar perhaps you can multiply the MTFs as you suggest. This is beyond my expertise, and perhaps an expert can reply.  
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Olivier_G
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« Reply #25 on: August 15, 2006, 07:22:09 PM »
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I am quite worried about this article because when reading it, one will believe that a 20MP 35mm sensor will have inherently more noise than a 20MP 645 sensor... which is not true, of course (this is the usual 'Sensor centric' or 'Same ISO comparison' bias).
A better picture is that Signal/Noise Ratio implies the sensor AND THE LENS... and the consequence is that for a given Field Of View, it is the lens' diameter that set the Signal/Noise Ratio, not the Sensor's size (ie: where are the 35mm f/1.4; 85mm f/1.2; 200mm f/1.8; 600mm f/4.0... equivalents in the 645 world???).

Bottom line: "The larger the sensor, the better" is probably worse than "The more MP, the better"!

Olivier
PS: I am not saying that MF backs don't make sense. On the contrary, I believe they deliver because they are optimized for quality: CCD Full Frame, Sensor design, no microlenses, Dynamic Range, etc...
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Ray
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« Reply #26 on: August 15, 2006, 08:08:22 PM »
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Bottom line: "The larger the sensor, the better" is probably worse than "The more MP, the better"!
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I've never seen a satisfactory explanation as to why large format digital backs perform relatively poorly at high ISOs, compared with FF 35mm sensors just half the size. Join 2x1Ds2 sensors together and you have a 32MP digital back which would be very usable at ISO 800. At ISO 1600, noise is slightly greater (in the 1Ds2) than the 5D, but resolution is better. Higher ISO does slightly degrade resolution and I imagine this also applies to the large sensor digital MF backs.
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jani
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« Reply #27 on: August 16, 2006, 03:24:22 AM »
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I am quite worried about this article because when reading it, one will believe that a 20MP 35mm sensor will have inherently more noise than a 20MP 645 sensor... which is not true, of course (this is the usual 'Sensor centric' or 'Same ISO comparison' bias).
Given the same manufacturing process technology, this is most likely true.

If you have evidence that suggests otherwise, you should definitely produce documentation for it, because your claim goes against generally accepted knowledge in the field.

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A better picture is that Signal/Noise Ratio implies the sensor AND THE LENS... and the consequence is that for a given Field Of View, it is the lens' diameter that set the Signal/Noise Ratio, not the Sensor's size (ie: where are the 35mm f/1.4; 85mm f/1.2; 200mm f/1.8; 600mm f/4.0... equivalents in the 645 world???).
This has nothing to do with signal/noise ratio in the sensor.

This has something to do with signal/noise ratio in the system.

If you want to compare systems, you have to take that into account, yes, but if you want to compare sensors, you have to try to eliminate the system dependent issues.

Fortunately, there are ways of comparing different sensors in the same sensor generation on systems that otherwise are very similar, because camera manufacturers occasionally release models within the same model line at the same time.

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I've never seen a satisfactory explanation as to why large format digital backs perform relatively poorly at high ISOs, compared with FF 35mm sensors just half the size.
I've never seen a comparison, even, because medium format digital backs don't seem to offer ISO 800, 1600 or 3200.

ISO 400 comparisons are possible, however, and they do show a relatively poor performance vs. CMOS based 135 format sensors.

Then again, Nikon's CCD sensors also show relatively poor high ISO performance compared to Canon's CMOS sensors.

It appears that it's CCD vs. CMOS all over again, doesn't it?
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Jan
Ray
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« Reply #28 on: August 16, 2006, 05:51:47 AM »
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I've never seen a comparison, even, because medium format digital backs don't seem to offer ISO 800, 1600 or 3200.

Jani,
The Leaf Aptus 75 has ISO 800, but it's a pretty degraded image compared to ISO 50 and 100. The CCD sensor must have some qualitative advantage over CMOS at low ISOs, I guess. Two joined 1Ds2 sensors would produce a sensor of the same size as the Dalsa 33mp sensor in the Aptus 75, which I believe actually consists of 2 joined smaller sensors which occasionally reveal the join line vertically down the middle, according to a current thread on this very problem.
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Olivier_G
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« Reply #29 on: August 16, 2006, 06:45:48 AM »
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This has nothing to do with signal/noise ratio in the sensor. This has something to do with signal/noise ratio in the system.
You can't talk about Signal/Noise in the sensor independantly from the whole system, as there is no Signal in the sensor considered separately.
You can talk about Noise generated in the sensor, but Noise alone doesn't provide any information about the noise in your picture.

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If you have evidence that suggests otherwise, you should definitely produce documentation for it, because your claim goes against generally accepted knowledge in the field.
The 'generally accepted knowledge' is that under the same illumination, a larger photosite will receive more photons and have a better Signal/Noise.
I agree: the Signal will be higher while the Noise will have little variation. I would even say that smaller photosites have actually LESS Noise generated in the sensor (more about noise here) and this is exactly why I consider that saying "a bigger pixel will have less noise" is not true... (an oversimplification, at best).

As I said, there is little meaning in comparing different systems without taking into account the optics (current lenses and/or optical limitations implied by the system).
I will make a comparison: people now understand that resolution cannot be determined by Sensor's definition (MP) alone and that the lens has to be factored in. The big difference here is that the theorical resolution based on sensor's definition has a meaning... whereas the Signal/Noise considered independantly for the sensor alone has NO meaning at all.

Now, about that 'Same ISO comparison bias': people tend to compare Signal/Noise under a same illumination and say "everything else being equal". What this really mean is considering an Olympus 150mm f/2.0 on '4/3', a Nikon 200mm f/2.0 on DX, a 300mm f/2.0 on 24x36 (huh? where is this one???) and a 450mm f/2.0 on 645!!!
That "everything else being equal"(ISO/Illumination) is in reality the most absurd way to compare things: weight, price, Depth Of Field and even existence of products is not even comparable due to optics consideration.

Olivier
PS: in addition, here is an excerpt of an email I sent to Michael after reading his article "Industry Push Pull" 1 year ago:
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Your articles are very interesting and refreshing. However, I see a bias about sensors' size issues in some of them: you seem to consider separately the sensor and the lenses when talking about noise... whereas it is mostly a result of the quantity of light captured (and necessarily involves the lens). As an example: a 150mm f/2.0 on '4/3' gives the same quantity of light on the sensor as a 300mm f/4.0 on 24x36 (therefore the same Signal to start from), as well as the same Depth Of Field. And those lenses should be pretty close in diameter (150mm/2.0 = 75mm = 300mm/4.0) as well as in weigth and manufacturing cost.

It is possible to give a more accurate picture than just "a smaller sensor has more noise" and "a larger sensor needs larger lenses"... you can actually compare various systems with different sensors' size (and this theoritical comparison will get more accurate as we reach the Photon Noise limit, which is not that far away with the 20D, for example. You may consider this as a pretty good approximation in the mid/long term). If you are more interested in this comparison, please have a look at this excel sheet: http://olivier.gallen.mageos.com/Temp/Sens...Equivalence.xls
A quick summary could be: for a given angle of view (or zoom range), the larger the diameter, the lower the noise (...and sensor's size can be completely factored out).
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jani
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« Reply #30 on: August 16, 2006, 06:53:09 AM »
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Jani,
The Leaf Aptus 75 has ISO 800, but it's a pretty degraded image compared to ISO 50 and 100.
Duh, it was right there in the review I linked to, too.

The quality at ISO 800 isn't bad, just not up to the standards that medium format photographers might like. It seems to be useful at approximately the same level as ISO 800 is on the 20D (where image quality is pretty degraded, too), but it's hard to tell without a side-by-side comparison. Unfortunately, other system differences might get in the way of testing this properly.

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The CCD sensor must have some qualitative advantage over CMOS at low ISOs, I guess.
It could also be that CCD sensors are easier to produce at such a large size.

That was one of the arguments against CCD "full frame" 135 format sensors, before Canon proved them wrong.

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Two joined 1Ds2 sensors would produce a sensor of the same size as the Dalsa 33mp sensor in the Aptus 75, which I believe actually consists of 2 joined smaller sensors which occasionally reveal the join line vertically down the middle, according to a current thread on this very problem.
Well, maybe that explains one of the rumours for the 1Ds3 having a "double frame" size.
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Jan
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« Reply #31 on: August 16, 2006, 02:21:05 PM »
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Well, maybe that explains one of the rumours for the 1Ds3 having a "double frame" size.
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How many Canon lenses have a 60mm image circle?
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jani
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« Reply #32 on: August 16, 2006, 05:04:24 PM »
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How many Canon lenses have a 60mm image circle?
None, AFAIK.

But my (subtle) point wasn't that Canon would be making a "double" sensor for the 1Ds3; on the contrary, I was trying to point out that the rumour might have confused a few things.
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« Reply #33 on: August 16, 2006, 05:28:16 PM »
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You can't talk about Signal/Noise in the sensor independantly from the whole system, as there is no Signal in the sensor considered separately.
I beg to differ.

The sensor receives and converts a "signal" regardless of whether you have a lens cap, a lens or an AA/UV/IR filter.

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You can talk about Noise generated in the sensor, but Noise alone doesn't provide any information about the noise in your picture.
Yes, I -- and most of the regulars here -- are well aware of that.

However, when someone uses the term "noise" without any qualifiers in digital photography, he or she most likely means visible noise, which is an indicator of the signal/noise ratio.

While it's not technically precise, it's the generally accepted term.

I can rant and rave about how stupid the use of e.g. "pathetic" as a derogatory term is in today's English, but it doesn't mean that I'll get any sympathy.

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The 'generally accepted knowledge' is that under the same illumination, a larger photosite will receive more photons and have a better Signal/Noise.
I agree: the Signal will be higher while the Noise will have little variation.
So far, so good.

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I would even say that smaller photosites have actually LESS Noise generated in the sensor (more about noise here) and this is exactly why I consider that saying "a bigger pixel will have less noise" is not true... (an oversimplification, at best).
Well, considering that a pixel only has a physical size on a screen, it's not even an oversimplification, it's a meaningless statement.

However, given the common usage of "noise" I mention above, saying "a bigger photosite will, in the same process technology and generation, have less noise ((compared to signal))" is quite reasonable.

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As I said, there is little meaning in comparing different systems without taking into account the optics (current lenses and/or optical limitations implied by the system).
I will make a comparison: people now understand that resolution cannot be determined by Sensor's definition (MP) alone and that the lens has to be factored in. The big difference here is that the theorical resolution based on sensor's definition has a meaning... whereas the Signal/Noise considered independantly for the sensor alone has NO meaning at all.

Now, about that 'Same ISO comparison bias': people tend to compare Signal/Noise under a same illumination and say "everything else being equal". What this really mean is considering an Olympus 150mm f/2.0 on '4/3', a Nikon 200mm f/2.0 on DX, a 300mm f/2.0 on 24x36 (huh? where is this one???) and a 450mm f/2.0 on 645!!!
That "everything else being equal"(ISO/Illumination) is in reality the most absurd way to compare things: weight, price, Depth Of Field and even existence of products is not even comparable due to optics consideration.
You're missing my point.

Take two cameras with sensors from the same process technology and generation, with the same noise reduction system, but with different photosite sizes, from the same sensor manufacturer.

Use the same lenses, subject matter and conditions.

Compare.

If you don't worry about comparing possibly different noise reduction systems, you should be able to find something. I suggest the following cameras:

 - Nikon D1H
 - Nikon D1X
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Jan
Olivier_G
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« Reply #34 on: August 16, 2006, 06:50:44 PM »
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I would even say that smaller photosites have actually LESS Noise generated in the sensor (more about noise here) and this is exactly why I consider that saying "a bigger pixel will have less noise" is not true... (an oversimplification, at best).
Well, considering that a pixel only has a physical size on a screen, it's not even an oversimplification, it's a meaningless statement. However, given the common usage of "noise" I mention above, saying "a bigger photosite will, in the same process technology and generation, have less noise ((compared to signal))" is quite reasonable.
Well... when I said "a bigger pixel will have less noise" I used the simpler 'joe average' vocabulary... but it is like "a bigger photosite will have less noise ((compared to signal))" and I agree that it should be compared at the same technology level. Therefore, your statement is equally wrong... (sorry).

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You're missing my point.
Well, I think exactly the same: it seems you focused on use of words, whereas my original message was about what's going on... and not nitpicking about vocabulary, really.

Before using real examples, we should first understand what we want to look for... and I believe the D1X is not exactly a good example of simplicity.
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Ray
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« Reply #35 on: August 16, 2006, 07:11:51 PM »
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That "everything else being equal"(ISO/Illumination) is in reality the most absurd way to compare things: weight, price, Depth Of Field and even existence of products is not even comparable due to optics consideration.
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Olivier,
I find your reasoning a little confused and don't quite know where to begin, but I see Jani has done a good job already   .

When comparing image quality and image quality alone, getting everything equal without exception is of course absurd. The only things we need to get equal (as far as possible) are the 'direct effects' on image quality, such as quality of lens, choice of f stop for equivalent DoF and choice of focal length for same field of view.

If the physical size of the sensors being compared are different, then it's not meaningful to use the same lens and the same f stop. Even after adjusting focal lengths and f stops to get the same DoF and FoV, it may not be appropriate to use the same ISO. The larger sensor will require use of a larger f stop # for equivalent DoF and consequently a slower shutter speed at the same ISO.

In situations where a fast shutter speed is required, one might then make the observation that the smaller sensor provided better image quality with less noise.
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Ray
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« Reply #36 on: August 16, 2006, 11:17:50 PM »
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Jani,
Below is a comparison of the leaf Aptus 75 at ISO 50 and ISO 800. The crops are very small crops from a much larger image at http://www.alpa.ch/en/focus/focus.html



The question arises, would a 1Ds2 shot of the same scene at ISO 400 provide better detail, bearing in mind that noise is reduced as downsampling takes place?
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Olivier_G
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« Reply #37 on: August 17, 2006, 04:45:11 AM »
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Olivier,
I find your reasoning a little confused and don't quite know where to begin, but I see Jani has done a good job already   .

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The only things we need to get equal (as far as possible) are the 'direct effects' on image quality, such as quality of lens, choice of f stop for equivalent DoF and choice of focal length for same field of view.
If the physical size of the sensors being compared are different, then it's not meaningful to use the same lens and the same f stop. Even after adjusting focal lengths and f stops to get the same DoF and FoV, it may not be appropriate to use the same ISO. The larger sensor will require use of a larger f stop # for equivalent DoF and consequently a slower shutter speed at the same ISO.
Ah... this is the 'Equivalence' I would like to see used (Equivalent Focal length, f-stop and ISO based on the crop factor => identical FOV, DOF, Shutter speed, Signal/Noise at the same level of technology and comparable lens weight/price).
The "new" thing I emphasize here is with that "fair" comparison, you get the same Signal/Noise Ratio whether you use a 20MP 24x36 sensor or a 20MP 645 sensor.

I am trying to communicate the message that a small format system is not inherently doomed with noise (cf: my "Noise is lower in a smaller photosite") and that it all depends on the Optics (available lenses or limitations). As an example, the 24x36 is probably the best performer regarding Signal/Noise due to the availability of very fast lenses.

Unfortunately, the flawed 'sensor centric'/'same ISO' point of view is widely spread and leads to wrong conclusions (like: superiority of large formats regarding noise and the evolutionary dead-end of smaller formats). Therefore I am trying to foster discussion and understanding about this very issue.

Olivier
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Ray
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« Reply #38 on: August 17, 2006, 07:43:42 AM »
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I am trying to communicate the message that a small format system is not inherently doomed with noise (cf: my "Noise is lower in a smaller photosite") and that it all depends on the Optics (available lenses or limitations). As an example, the 24x36 is probably the best performer regarding Signal/Noise due to the availability of very fast lenses.
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It depends on how small you want to compare with how big. For me there's a sense of deja vu here because some time ago I irritated a few people with my views on big versus small and got into trouble. I'm not sure I want to revisit this issue.

Anyway, here's what I still think, whether right or wrong.

1. A lens is most efficient when it's used at a diffraction limited aperture because at that aperture no further improvement is possible.

2. For equal FoV and DoF of the same scene under the same lighting conditions, the smaller sensor receives less light. Ie. fewer photons to describe the scene being captured.

3. There are many sources and types of noise that affect sensors, but the one type we can do nothing about, apparently, is photonic shot noise, the random arrival of the photons at a particular location (the photodiode), which apparently has a Poisson distribution. (I just threw in that to give the impression I know what I'm talking about   ).

4. The amount of photonic noise in a given exposure is calculated as the square root of the total number of photons impinging upon the sensor.

5. The image that is 'comprised of, results from' the smaller number of photons (the image from the smaller sensor) contains a greater proportion of the one type of noise we can do nothing about.

Conclusion: If we were able to eventually reduce all types of noise to virtually zero, except photonic shot noise which seems to be in the same category as diffraction in lenses, we would find that the smaller sensor has an inherent disadvantage with regard to noise and image quality.

There are also other issues of dynamic range and resolution where we can come to an impasse earlier (determined by the laws of Physics) with the smaller sensor. The size of photodiodes is limited by the wave length of light. You can always fit more pixels on a larger sensor.
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Olivier_G
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« Reply #39 on: August 17, 2006, 09:34:42 AM »
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2. For equal FoV and DoF of the same scene under the same lighting conditions, the smaller sensor receives less light. Ie. fewer photons to describe the scene being captured.
I'll focus on this one...

Let's consider formats A and B where B has a 2.0 cropping factor (24x36 and '4/3' are quite close, except aspect ratio):
- To get the same Field of View, you need to use a 2x longer focal on A compared to B.
- To get the same Depth of Field, you need to use a f-number x2 (close 2 stops) on A compared to B (you can use DOFMaster to check that. It is based on the fact that DoF formula is proportional to f-number, Circle of Confusion (which is proportional to the format for identical critera on output) and 1/(focal length)^2 => coef x coef / coef^2).
- We consider exactly the same scene/lightning and we use the same shutter speed.

So I put a 300mm f/4.0 on A, used at f/4.0, 1/500s and 400 ISO and a 150mm f/2.0 on B, used at f/2.0, 1/500s and 100 ISO.
=> FoV, DoF, Shutter speed are the same and I use the same Exposure Value as (1/500s & f/4.0 & 400 ISO) = (1/500s & f/2.0 & 100 ISO).

With the same number of pixels, each photosite of A is 4x larger compared to photosites of B. But to keep the same DoF, the lens on B is opened more by 2 stops (4x more photons per area) => photosites of B gets exactly the same amount of photons as photosites of A.
Bottom-line: settings used to get the same photo (FoV, DoF, Speed) imply that Signal will be identical in both formats.

About Noise: Read Noise and Dark Current Noise will be very similar for both formats (the previously linked document hints that the smaller photosites will have less of those Noises... this is actually supported by the Kodak CCD FFT sensors specs and by a friend Physicist/Researcher working in the energy/matter field). Shot Noise will be identical, as we have the same Signal for A and B.

=> If you compare different formats based on the same photographic criteria (FoV, DoF, Speed...) you end up with the same Signal/Noise ratio, and therefore the same noise in your picture, provided the same technology level and settings.
(This doesn't mean that all systems are equals: you need to find out their limitations. This is what I did in this excel sheet. You then have to include existing specifics: current level of technology, choices/orientations taken, etc...)

Olivier
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