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Ray

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« Reply #120 on: July 16, 2008, 11:24:39 am »

Okay! Enough theory! Time for real world experiments!

Today was a dull day in Brisbane. I wondered what might be a good scene for checking the DR variation between the cropped format 40D and a full frame sensor consisting of 40D pixels.

I decided to remove a 24"x36" print from the wall and place it in the centre of the window, through which is a view of the Brisbane river and grey skies. The dynamic range is great, but not excessive.

The print is a 15mm shot of Ta Prohm in the Angkor Wat area (taken with the 5D and Sigma lens). It actually looks a lot more vibrant than the crops in this experiment would suggest.

I used the Canon 24-105mm zoom, initially at 24mm amd F8. To simulate a doubling of sensor area, I would need to multuply that focal length by 1.4, ie. 33.6mm. To simulate a full frame 35mm sensor, I would need to multiply the focal length by 1.6, ie. 38.4mm. I can't get such precision with zoom adjustments and/or ACR read-outs, so I settled for a compromise of 35mm. That's the first approximation.

To adjust F stop for equal DoF, I would need F11.2 with double the sensor area and F12.8 with FF 35mm. I used F13, so that's the second approximation.

The conclusion first. Doubling sensor area containing same size and same quality pixels seems to increase DR by close to one F stop but probably not quite one F stop in view of the above stated approximations.

Immediately below is the over all scene with a bit of adjustment, so it doesn't appear totally flat, followed by 200% and 100% comparison crops of totally flat conversions with zero settings in ACR, no sharpening and linear tone curve.

[attachment=7470:attachment]

First, F8 at 1/30th (24mm) compared with F13 at 1/10th (35mm). Perhaps that's the third approximation. I can't get any more precise than that.

[attachment=7471:attachment]  [attachment=7472:attachment]

For the benefit of Mark, who seems a bit skeptical about this relationship between sensor size and DR, the Full Frame 40D clearly has less noise. There's no doubt about it. The only doubt is, by just how much?

The next crops compare the 24mm shot overexposed by one stop, with the correctly exposed 35mm shot. To my eyes, they are about equal. But this is extreme pixel peeping. How such differences relate to real world prints  is another experiment.

[attachment=7473:attachment]  [attachment=7474:attachment]

In the final crop comparisons, the crop of the cropped format shot has been upsmapled to the same size as the full frame shot.

[attachment=7475:attachment]
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joofa

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« Reply #121 on: July 16, 2008, 11:45:06 am »

Quote
you might want to refer to actual examples.

And,

Quote
I think the thrust of bjanes' reply and my previous post is that dark current is a negligible component of the output noise in all but very long time exposures (several seconds or more).

It all depends upon what sensor and what integration time you are using. As I mentioned before that in some of the sensors we have tried, we have not found dark current to be insignificant for exposures as small as ~30 milli seconds, when signal is captured right off the sensor without any calibration. Where as typically people will acquire "raw" after all the calibrations, adjustments, etc. have been made.

It may be possible that for really small integration times one may not observe a lot of dark current, but as I mentioned above, for ~30 milli seconds we have not found that with at least those sensors we tested.

Quote
What is the utility of using input-referred quantities?
I'm also puzzled why one would want to extrapolate this back to a hypothetical input noise which, as far as I can tell, is not any actual noise of any actual component of the capture process.

Input level quantities may be used to derive equations for DR, SNR, etc. and give a good comparison of noise with dark current, etc.

BTW, the whole discussion on this input thingy started from a side remark of mine and originally I had no intention of going into the details of it as it is indeed irritating for some users.
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Mark D Segal

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« Reply #122 on: July 16, 2008, 04:23:55 pm »

Quote
Okay! Enough theory! Time for real world experiments!

Today was a dull day in Brisbane. I wondered what might be a good scene for checking the DR variation between the cropped format 40D and a full frame sensor consisting of 40D pixels.

I decided to remove a 24"x36" print from the wall and place it in the centre of the window, through which is a view of the Brisbane river and grey skies. The dynamic range is great, but not excessive.

The print is a 15mm shot of Ta Prohm in the Angkor Wat area (taken with the 5D and Sigma lens). It actually looks a lot more vibrant than the crops in this experiment would suggest.

I used the Canon 24-105mm zoom, initially at 24mm amd F8. To simulate a doubling of sensor area, I would need to multuply that focal length by 1.4, ie. 33.6mm. To simulate a full frame 35mm sensor, I would need to multiply the focal length by 1.6, ie. 38.4mm. I can't get such precision with zoom adjustments and/or ACR read-outs, so I settled for a compromise of 35mm. That's the first approximation.

To adjust F stop for equal DoF, I would need F11.2 with double the sensor area and F12.8 with FF 35mm. I used F13, so that's the second approximation.

The conclusion first. Doubling sensor area containing same size and same quality pixels seems to increase DR by close to one F stop but probably not quite one F stop in view of the above stated approximations.

Immediately below is the over all scene with a bit of adjustment, so it doesn't appear totally flat, followed by 200% and 100% comparison crops of totally flat conversions with zero settings in ACR, no sharpening and linear tone curve.

[attachment=7470:attachment]

First, F8 at 1/30th (24mm) compared with F13 at 1/10th (35mm). Perhaps that's the third approximation. I can't get any more precise than that.

[attachment=7471:attachment]  [attachment=7472:attachment]

For the benefit of Mark, who seems a bit skeptical about this relationship between sensor size and DR, the Full Frame 40D clearly has less noise. There's no doubt about it. The only doubt is, by just how much?

The next crops compare the 24mm shot overexposed by one stop, with the correctly exposed 35mm shot. To my eyes, they are about equal. But this is extreme pixel peeping. How such differences relate to real world prints  is another experiment.

[attachment=7473:attachment]  [attachment=7474:attachment]

In the final crop comparisons, the crop of the cropped format shot has been upsmapled to the same size as the full frame shot.

[attachment=7475:attachment]
[a href=\"index.php?act=findpost&pid=208670\"][{POST_SNAPBACK}][/a]

I think what's happening in the comparisons where one can see a difference is the effect of diffraction between f/8 (less) and f/11 (more).
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Mark D Segal (formerly MarkDS)
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BJL

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« Reply #123 on: July 16, 2008, 05:25:35 pm »

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Furthermore, DR and SNR are not the same things -- sensors typically quote 2 different numbers for these two.
[a href=\"index.php?act=findpost&pid=208516\"][{POST_SNAPBACK}][/a]
True, and there are also at least two different meanings of each phrase, some of which overlap.

Sensor spec. sheets do indeed often state both a dynamic range (in dB) and a signal to noise ratio (in a form like 1000:1), but these are different statements of the same information: the ratio between maximum output signal (well capacity) to dark noise level. The DR in dB is computed as 20*log10(SN), so that for example 1000:1 given 60dB. I call this S/N ratio the "global" one.

But most often the noise measure that we care about is the "local S/N ratio" at various parts of the image: the ratio of signal level at a particular part of the image to the noise level there. Then the relevant signal level is usually far less than maximum, and the noise is often more, as it includes photon shot noise as well as dark noise. So local S/N ratio is far lower, and a Kodak document suggests that about 40:1 is excellent and 10:1 is barely acceptable.

For comparison the "global" S/N ratio probably needs to be about 1000:1 (60dB) or more for decent dynamic range, and MF sensors offer about 4000:1 (72dB).

By the way, Dalsa's spec's for DR in stops are simply the log base 2 of the S:N ratio, so 12.5 stops means a S/N ratio of about 5600:1 or 75dB. This is a valid engineering spec. if understood correctly,  but the bottom three or so stops of that range will have excessive visible noise levels.
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joofa

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« Reply #124 on: July 16, 2008, 05:58:18 pm »

Thanks BJL, you explained it very well. I could not have done that.
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Ray

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« Reply #125 on: July 16, 2008, 08:22:08 pm »

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I think what's happening in the comparisons where one can see a difference is the effect of diffraction between f/8 (less) and f/11 (more).
[a href=\"index.php?act=findpost&pid=208747\"][{POST_SNAPBACK}][/a]

Mark,
It's true that the simulated 26mp full frame image (at 35mm) appears only marginally more detailed than the smaller format image at 24mm. This is probably due to a number of factors such as zero sharpening and a linear tone curve which tends to reduce accutance differences; diffraction effects at F13, and the degraded nature of image quality in dark shadows which are not ideal targets for displaying resolution. However, here I was not trying to demonstrate resolution differences but noise differences.

It's clear on my monitor (a Sony 19" CRT at 1600x1200) that the 24mm correctly exposed F8 shot has a lot more noise in the shadows than the 35mm F13 shot which has been exposed by the same standards within the accuracy limitations of the camera's exposure values, ie. F8 at 1/30th = F13 at 1/10th.

It's also clear that an F8 shot overexposed by one stop (ie. 1/15th instead of 1/30th) has about the same degree of shadow noise as the F13 shot correctly exposed.

Below are two sets of 3 smaller shadow crops showing, from left to right; (1) the correctly exposed F8 shot, (2) the F8 shot overexposed by one stop, (3) the correctly exposed F13 shot.

Of course I've had to lighten the shadows a lot using 'levels' in order for such differences to be apparent. The excessive noise in the first image of both sets hits me in the face at this high degree of magnification. Do you see a flaw in the methodology? It was an overcast day with even lighting. All shots were taken within a 5 minute time frame.

[attachment=7491:attachment]  [attachment=7490:attachment]
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Mark D Segal

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« Reply #126 on: July 16, 2008, 08:42:23 pm »

Ray, yes I know you were demonstrating differences in noise - it's all part of the same package I had in mind in the sense that more diffraction means less apparent resolution and less apparent noise.

Your examples are consistent with this generality. At f/8 you are getting less diffraction, more resolution and more apparent noise than you are at f/13. By increasing the exposure of the f/8 shot, you are adding light which improves the S/N hence reducing apparent noise toward the lower level of the f/13 (versus the f/8) shot. Of course lightening shadows with Levels simply "shines a light" on the noise that is there. I don't see any methodological issues so far, except that I probably would have chosen a real scene with the appropriate ingredients rather than a print for generating the scene data. But what you are using seems to be working for the purpose at hand.
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Mark D Segal (formerly MarkDS)
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Ray

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« Reply #127 on: July 16, 2008, 09:26:24 pm »

Quote
Ray, yes I know you were demonstrating differences in noise - it's all part of the same package I had in mind in the sense that more diffraction means less apparent resolution and less apparent noise.

Your examples are consistent with this generality. At f/8 you are getting less diffraction, more resolution and more apparent noise than you are at f/13. [a href=\"index.php?act=findpost&pid=208802\"][{POST_SNAPBACK}][/a]

Mark,
I don't see it that way. The F8 shot is a cropped format 10mp shot and actually has slightly less resolution than the F13 shot which is 26mp full frame (simulated). If I had used F8 with the 26mp full frame at 35mm, then instead of a barely perceptable increase in resolution, I would have got a significant increase in resolution in the plane of focus, which was the print, and therefore, according to your reasoning, the improvement in noise (and DR) would have been even greater than one stop.

By the way, I've just realised that my monitor is set at 1800x1440, not the 1600x1200 that it used to be. The crops are probably unnecessarily large.

Actually, I've just got myself confused, so I'll rephrase that point I was trying to make. At F13 the image is already marginally sharper than the F8 image because it's effectively a 26mp full frame image comprised of more pixels, so the lower noise of the F13 shot would seem to have little to do with resolution. The loss of resolution due to diffraction is largely compensated by the effectively larger sensor.

Since no sharpening or contrast enhancement has been applied to any of these crops, I don't see how increasing resolution by using F8 instead of F13 at 35mm FL would increase noise
« Last Edit: July 16, 2008, 09:47:18 pm by Ray »
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Mark D Segal

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« Reply #128 on: July 16, 2008, 09:33:27 pm »

Oops - several things happening at the same time. It gets confusing. I think the testing should isolate one variable at a time and see what happens.
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Mark D Segal (formerly MarkDS)
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Ray

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« Reply #129 on: July 16, 2008, 09:51:07 pm »

Quote
Oops - several things happening at the same time. It gets confusing. I think the testing should isolate one variable at a time and see what happens.
[a href=\"index.php?act=findpost&pid=208809\"][{POST_SNAPBACK}][/a]

Okay! If the target is 2-dimensional, then DoF is not an issue. I'll repeat a similar experiment using F8 with all shots,  
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ejmartin

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« Reply #130 on: July 16, 2008, 10:39:18 pm »

Quote
Ray, yes I know you were demonstrating differences in noise - it's all part of the same package I had in mind in the sense that more diffraction means [...] less apparent noise.

Your examples are consistent with this generality. [...]
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Diffraction has zero effect on noise.  There are two classes of noise, one due to the sensor electronics, and the other is the photon noise that is intrinsic to the light hitting the sensor.  The former couldn't care less whether there is diffraction or not, since it's a property of the sensor independent of whether it's receiving a light signal or not.  The latter also couldn't care less whether there is diffraction; it's dependent only on how many photons are collected by a given photosite, and it doesn't matter whether or not those photons arrived at that photosite through diffraction, it just matters that they arrived at that photosite and not another one.

The ONLY thing that diffraction affects is the resolution.
« Last Edit: July 16, 2008, 10:40:40 pm by ejmartin »
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emil

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« Reply #131 on: July 16, 2008, 10:55:54 pm »

Quote
Diffraction has zero effect on noise.  There are two classes of noise, one due to the sensor electronics, and the other is the photon noise that is intrinsic to the light hitting the sensor.  The former couldn't care less whether there is diffraction or not, since it's a property of the sensor independent of whether it's receiving a light signal or not.  The latter also couldn't care less whether there is diffraction; it's dependent only on how many photons are collected by a given photosite, and it doesn't matter whether or not those photons arrived at that photosite through diffraction, it just matters that they arrived at that photosite and not another one.

The ONLY thing that diffraction affects is the resolution.
[a href=\"index.php?act=findpost&pid=208821\"][{POST_SNAPBACK}][/a]

Yes, but doesn't diffraction scatter light between photosites, and doesn't the reduction of resolution somehow also reduce the apparent definition of the noise eventhough it is not the primary cause? How else would you interpret the results Ray was showing, or do you not think the methodology is sufficiently fine-tuned or the information provided sufficient to come to any robust conclusions about cause and effect here?
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ejmartin

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« Reply #132 on: July 17, 2008, 12:33:42 am »

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Yes, but doesn't diffraction scatter light between photosites, and doesn't the reduction of resolution somehow also reduce the apparent definition of the noise eventhough it is not the primary cause? How else would you interpret the results Ray was showing, or do you not think the methodology is sufficiently fine-tuned or the information provided sufficient to come to any robust conclusions about cause and effect here?
[a href=\"index.php?act=findpost&pid=208824\"][{POST_SNAPBACK}][/a]

Well, here's a little thought experiment -- do you think there is no noise or less noise in OOF areas of images, or that the noise is somehow less 'grainy'?  It is not, as you will see by looking through your images.

Perhaps you have in mind that, if the lens is defocussed, or loses resolution due to diffraction, that the noise will somehow also get defocussed and averaged out.  This is not the case, because the noise is a property of the light that gets to a particular photosite, as well as the electronics of that photosite; it doesn't care what the other photosites are receiving, whether the image they are making is focussed or not, whether the optics are diffraction limited.  A signal of N photons has sqrt(N) amount of photon noise, no matter where those photons came from, whether or how they were reflected/refracted/diffracted.  It's true that diffraction and also defocussing will rearrange the pattern of photons hitting the sensor, but then the new distribution of photons will have a new pattern of photon noise that still only cares about how many photons are collected in each photosite.  And of course the read noise is happening independent of what the photons are doing, and contributing the same no matter what.
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« Reply #133 on: July 17, 2008, 05:59:44 am »

Quote
Well, here's a little thought experiment -- do you think there is no noise or less noise in OOF areas of images, or that the noise is somehow less 'grainy'?  It is not, as you will see by looking through your images.

Perhaps you have in mind that, if the lens is defocussed, or loses resolution due to diffraction, that the noise will somehow also get defocussed and averaged out.  This is not the case, because the noise is a property of the light that gets to a particular photosite, as well as the electronics of that photosite; it doesn't care what the other photosites are receiving, whether the image they are making is focussed or not, whether the optics are diffraction limited.  A signal of N photons has sqrt(N) amount of photon noise, no matter where those photons came from, whether or how they were reflected/refracted/diffracted.  It's true that diffraction and also defocussing will rearrange the pattern of photons hitting the sensor, but then the new distribution of photons will have a new pattern of photon noise that still only cares about how many photons are collected in each photosite.  And of course the read noise is happening independent of what the photons are doing, and contributing the same no matter what.
[a href=\"index.php?act=findpost&pid=208833\"][{POST_SNAPBACK}][/a]

Emil,
This is more or less what I would have thought. I just repeated a similar experiment this afternoon, to prove Mark wrong, but was surprised at the results.

Using F8 for all shots, the approximately 1 stop advantage I saw at F13 has almost disappeared. It's most puzzling.

What I see at F8 is a more obvious resolution advantage for the simulated larger sensor, which is evident across the board, in both highlights and shadows, but the obviously lower shadow noise I saw previously in the F13 shot, has virtually disappeared.

Consider the following 200% crops at F8 and 1/4 sec exposure.

[attachment=7496:attachment]

One might wonder why I'm shooting a back-lit print. This print has excellent shadow detail because I used fill flash when I took the shot in 1995. There's lots of detail in them thar shadows.

Below is a comparison with the original file from which the print was produced. Would you say that something has been lost in the reproduction   ?

[attachment=7498:attachment]  [attachment=7497:attachment]
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madmanchan

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« Reply #134 on: July 17, 2008, 07:32:48 am »

Diffraction and noise are completely independent at the physical level (in terms of underlying causes and contribution to the recorded image) but not necessarily at the visual results level. This is because diffraction affects the overall frequency content of the recorded signal -- i.e., it makes the image blurrier. Noise is typically more visible, and hence objectionable, in blurry images.

A thought experiment: consider taking an image of a detailed colorful rug. Lots of fine detail and texture. You take a perfectly-focused image at ISO 1600 with, say, a Rebel XSi. There is noise in the image but it is largely masked by the actual image detail. The noise is generally not objectionable and perhaps even invisible in a print.

Retake the same image with the same capture parameters, except this time defocus the lens. So the capture noise is the same, but now the image is completely blurry. The noise suddenly becomes extremely visible and easy to pick out.

Diffraction is related to this example in that it creates a blur and hence can make noise more visible, just not to the same degree as grossly misfocusing.

Cheers,
Eric
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Ray

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« Reply #135 on: July 17, 2008, 09:32:54 am »

Quote
Diffraction is related to this example in that it creates a blur and hence can make noise more visible, just not to the same degree as grossly misfocusing.
Cheers,
Eric
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Eric,
You seem to have got this the wrong way round. I produced an image at F13 which had clearly less noise than another image at F8.

Mark claimed that the lower noise might have been due to the blurring effect of diffraction at F13.

I retook similar shots (albeit in slightly different circumstances) and found that F8 with all shots had an effect of equalising noise, despite different pixel counts.

More test shots are required, I think.
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Mark D Segal

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« Reply #136 on: July 17, 2008, 09:54:08 am »

I'm not convinced more tests are needed. I'm not arguing with the theory so ably explained by Emil and Bill in this thread and on websites such as Imatest/Norman Koren, Cambridgeincolour, etc. Also please note that when I speak of noise I usually qualify it with the word "apparent" specifically because I'm talking about what we see rather than what may be embedded in the image but we don't see for reasons Eric explains ( which BTW jusstifies use of selective noise reduction in image processing).

At the end of my previous post I asked Emil if he could explain what's happening in Ray's tests, or if for some reason that is not possible. Perhaps that question got overlooked by accident. Then Eric came in with a correct set of propositions which point to the "apparent" opposite of what's happening in Ray's images, as Ray pointed out.

Hence, I'm thinking that what's needed is a better explanation of an obvious disconnect between what we're all seeing in those images and what the theory says we should be seeing. There may be a missing variable or two which would clarify why Ray's results are what they are.
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Mark D Segal (formerly MarkDS)
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bjanes

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« Reply #137 on: July 17, 2008, 11:30:17 am »

Quote
I'm not convinced more tests are needed. I'm not arguing with the theory so ably explained by Emil and Bill in this thread and on websites such as Imatest/Norman Koren, Cambridgeincolour, etc. Also please note that when I speak of noise I usually qualify it with the word "apparent" specifically because I'm talking about what we see rather than what may be embedded in the image but we don't see for reasons Eric explains ( which BTW jusstifies use of selective noise reduction in image processing).

At the end of my previous post I asked Emil if he could explain what's happening in Ray's tests, or if for some reason that is not possible. Perhaps that question got overlooked by accident. Then Eric came in with a correct set of propositions which point to the "apparent" opposite of what's happening in Ray's images, as Ray pointed out.

Hence, I'm thinking that what's needed is a better explanation of an obvious disconnect between what we're all seeing in those images and what the theory says we should be seeing. There may be a missing variable or two which would clarify why Ray's results are what they are.
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As [a href=\"http://www.imatest.com/docs/noise.html#spectrum]Norman Koren[/url] points out, the visual appearance of noise is rather difficult to quantify and depends on more than the standard deviation. A noise spectrum plot may help to some extent. Your qualification of "apparent" is quite appropriate.

As Emil has explained, if you take two sensors with the same total sensing area and double the pixel count of one, keeping all other characteristics unchanged, the signal:noise of the higher resolution sensor will be lower. If you examine the images at 100% on screen, the noise in the higher resolution sensor will be higher. However, if you print the two images at the same print size, there may not be any difference in the perceived noise. Intuitively, one may explain this by the fact that the noise in the higher resolution sensor is finer grained (the frequency distribution is shifted to the right).

However, as the pixel size decreased there may be problems with fill factor and with the microlenses, as explained here. If you carry a thought experiment on decreasing pixel size to the point of Reductio ad absurdum, S:N falls to zero when the pixel count approaches infinity.

Imatest does supply a noise spectrum. Noiseware does also, as you so ably demonstrated in your essay. However, interpreting the plot of the spectrum is problematic.

Due to the subjective quality of noise, I think some testing such as Ray is undertaking is helpful, but as his efforts show, it is difficult to control all the variables. Results that defy the laws of physics are doubtful. It would be interesting to apply Dr. Wandell's image simulator to some real world cameras.

Bill
« Last Edit: July 17, 2008, 11:33:14 am by bjanes »
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Mark D Segal

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« Reply #138 on: July 17, 2008, 06:27:14 pm »

Quote
As Emil has explained, if you take two sensors with the same total sensing area and double the pixel count of one, keeping all other characteristics unchanged, the signal:noise of the higher resolution sensor will be lower. If you examine the images at 100% on screen, the noise in the higher resolution sensor will be higher. However, if you print the two images at the same print size, there may not be any difference in the perceived noise. Intuitively, one may explain this by the fact that the noise in the higher resolution sensor is finer grained (the frequency distribution is shifted to the right).

''''''''''''''''''''''''''

Due to the subjective quality of noise, I think some testing such as Ray is undertaking is helpful, but as his efforts show, it is difficult to control all the variables. Results that defy the laws of physics are doubtful. It would be interesting to apply Dr. Wandell's image simulator to some real world cameras.

Bill
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I think you are tending toward the nub of the matter. I have seen from my 1Ds3 what you are mentioning - the "character" of the noise is different compared with the original 1Ds. It is "finer-grained", lighter and tighter, so less disturbing to look at.

Looking at Ray's last set of results in post 134 (wow, this is getting up there - maybe we'll make a L-L "Book of Records" for longest thread!) both shot at f/8, the 40 result has better overall definition than the 24 result, and as he says there appears to be very little difference of visible noise between these two images. If I remember correctly, his "40" designation is the simulated higher pixel count sensor; this would seem to indicate that between the two cameras being tested, perhaps within the range of pixel sizes on test, the lower S/N which physics tells us should be doming from the 40 is having less of an effect degrading quality than is the higher resolution increasing it.
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Mark D Segal (formerly MarkDS)
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Ray

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1DS3 vs 5D CoC shootout in MFDB forum
« Reply #139 on: July 18, 2008, 03:13:01 am »

So much for pixel peeping!

Part of the confusion here is due to the fact I made a mistake with regard to my initial comparison. I compared F13 at 1/10th sec exposure with F8 at 1/30th sec exposure. By doing so, I've given the simulated full frame sensor approximately a 1/3rd stop advantage. I should have been comparing F13 at 1/13th sec exposure with F8 at 1/30th. There's a 1 & 1/3rd stop difference between F8 and F13.

Below are the ACR windows showing the histograms. As you can see, the histogram for the F13 shot at 1/13th indicates underexposure whereas the F8 shot looks more correctly exposed. That's as it should be because the shot at 35mm has excluded areas of sky which would have been included if the sensor had been full frame.

[attachment=7505:attachment]

I won't bore you with additional examples of degraded images. Suffice it to say, it's mostly a storm in a tea cup. Comparing F8 at 24mm and 1/30th, with F13 at 35mm and 1/13th, does change the result and diminish the perceived differences to the point where it's all largely irrelvant, in my opinion.

However, a doubling (or more) of pixel count does produce a worthwhile increase in resolution and detail at the optimal aperture of the lens, whether F8 or F5.6.

At F13, F16 and F22, I think we're getting into irrelevant pixel peeping areas of little significance, resolution-wise, for the practical photographer.

Having compared a few shots at the same focal length but different apertures, such as F13 at 1/13th with F8 at 1/30th, both at 35mm, there is a curious phenomena whereby the F8 shot really does appear very marginally noisier in the really deep shadows where greens seem to shift to magenta and there's a hint of greater banding.

But again, it's curious at the pixel peeping level and no doubt of interest to Physicists, but not of much practical concern to photographers.
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