In which ways, and why, are smaller sensors more efficient than larger? Part 2

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Anders W
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In which ways, and why, are smaller sensors more efficient than larger? Part 2
9 months ago

In a recently expired thread (whose OP is summarized here), some of us discussed (among other things) the extent to which the greater efficiency of smaller sensors compared to larger generalizes across different measures of efficiency. In order to answer some questions that still remain in that regard, I proposed here that I supplement the three indicators I have previously used to index efficiency by a fourth one. I am happy to present the results of so doing in this new thread.

The idea behind the four measures is as follows: The efficiency of a sensor can vary depending on which light level we consider (shadows versus highlights) as well as the ISO range we are looking at (low versus high ISOs). The three measures I previously used considered shadow rendering separately for low and high ISOs but highlights at a single point along the ISO range only. Since the efficiency with regard to highlight rendering turns out to vary a bit across the ISO range as well, my new set of indicators consider all four combinations, shadows as well as highlights at low as well as high ISOs.

How the measures are defined is described in detail in the technical appendix at the end of the post. The two indictors that index the efficiency with regard to shadow rendering, i.e., those that focus on dynamic range (DR), are the same as before. Those that index the efficiency with regard to highlight rendering, i.e., those that focus on max SNR, are both new although the first of them can be seen as slightly modified version of the single measure focusing on max SNR used in earlier analyses. The sample of bodies/sensors is the same as that used in the previous thread, i.e., that described here supplemented by the Canon 6D (since I already happened to have entered the data for that body as well). The data source is also unchanged (DxOMark).

As in the previous thread, I capture the relationship between efficiency and sensor size by a set of regression analyses with each of the four efficiency indicators as the dependent variable and sensor size as the independent. The measure of sensor size used is the square root of the square root of the sensor area (as expressed in millimeters squared). In all four cases, this provides a better fit (as measured by the adjusted R-square) than using the sensor area or the square root of the sensor area. The results are as follows (the regression coefficient, its standard error, and the adjusted R-square).

Normed ISO-100 DR: -18.21, 2.63, 0.723

Normed High-ISO DR: -102.59, 13.70, 0.754

Normed ISO-100 max SNR: -1.84, 0.27, 0.710

Normed High-ISO max SNR: -2.42, 0.67, 0.404

The coefficients show that the expected negative relationship with sensor size obtains in all four cases. If we choose to regard the sample as simple random, all effects are statisticially significant at the .01-level or better. Consequently, the conclusion that smaller sensors are more efficient than larger generalizes to all four efficiency measures.

Comments and questions welcome, especially, of course, from some of those who participated in the thread to which this is a continuation.

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Technical appendix

Normed ISO-100 DR: This is the unlogged "print-mode" (8 MP) DR at a DxOMark measured ISO of 100 divided by the sensor area. Before unlogging and performing the division described, the logged DR at ISO 100 was extra- or interpolated from the closest observations available using the following formula:

Logged DR at ISO 100 = BIDR + (LOG10(100) - LOG10(BI))*(BIDR - NIDR) / (LOG10(BI) - LOG10(NI))

where BIDR is the logged DR at the base measured ISO, NIDR the logged DR at the next measured ISO, BI is the base measured ISO, and NI is the next measured ISO.

Normed High-ISO DR: This is the unlogged "print-mode" (8 MP) DR obtained for equivalent photos (same amount of total light on the sensor, same DoF, same shutter speed) at a higher measured ISO given by

12,800 * SA/864

where SA is the sensor area and 864 is the sensor area of real FF, i.e., 24 x 36 mm.

Before unlogging, the DR at that particular ISO was interpolated from the closest observations available using a formula similar to the one used for "normed ISO-100 DR".

Normed ISO-100 Max SNR: This is the unlogged max SNR at a DxOMark measured ISO of 100 multiplied by the square root of MP/8 (where MP is the number of sensor megapixels) and divided by the square root of the sensor area (as expressed in millimeters squared).

Before unlogging and performing the multiplication and division described, the logged max SNR (expressed in decibels) at ISO 100 was extra- or interpolated from the closest observations available using a formula similar to the one used for "normed ISO-100 DR".

Normed High-ISO Max SNR: This is the unlogged max SNR obtained for equivalent photos (same amount of total light on the sensor, same DoF, same shutter speed) after multiplication by the square root of MP/8 and at a higher measured ISO given by

12,800 * SA/864

where SA is the sensor area and 864 is the sensor area of real FF, i.e., 24 x 36 mm.

Before unlogging and performing the multiplication described, the logged max SNR (expressed in decibels) at that particular ISO was interpolated from the closest observations available using a formula similar to the one used for "normed ISO-100 DR".

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Re: In which ways, and why, are smaller sensors more efficient than larger? Part 2
In reply to Anders W, 9 months ago

This is a response to Chris's (cpw's) post here in a recently expired thread on the same topic as the present one.

cpw wrote:

Anders W wrote:

As already acknowledged, yes, although I'd express it slightly differently: My normed SNR data takes the negative impact of PRNU noise on the SNR into account whereas a QE figure doesn't.

cpw wrote:

If you do a series of calculations of your normedSNR vs. ISO for the D4, you will see the number monotically increase as you go up in ISO. This is because the PRNU noise is becoming less influential, and you are moving closer to your normedSNR becoming proportional to sqrt(QE). (If you go up really high in ISO, I guess the read noise would start to be involved). But it's not as if any QE number was changing. Bob's peak QE evaluations look solid to me, and show modern sensors holding steady in the 50-60 % region. Also, remember if you want to use your normedSNR data for comparisons, for equivalent comparisons of say a crop x4 sensor at ISO 100, that more properly gets compared to a FF at ISO 100*4^2 = ISO 1600.

Well, those are my thoughts on this.

Chris

I will attempt to cover yours and Joe's points at the same time. The end of my post says what I was getting at. You have obviously not continued evaluating your normedSNR data for D4 at higher ISOs, so I will:

I certainly have. It's just that I didn't have the opportunity to post the results of that evaluation before the previous thread expired.

for D4 I get a number of 140 at ISO 1600. Also, from Bob's QE estimate, it's peak QE = 0.53. Now I'll use S100 data, because it has a known QE of 0.52 (I don't think Bob did the S120 yet), but this is ok. For S100 at ISO 100, I get a normedSNR of 130 from your equation.

In what way can you claim a higher efficiency for the smaller sensor?

While I am glad that you like the idea I introduced in my reply to Joe (Great Bustard) here and presented in greater detail in the OP of the present thread, illustrative examples like the one you provide above can be slightly misleading. First, they have to be done right and this one isn't. The ratio of the D4 sensor area to the S100 sensor area is about 21 whereas the ratio of the ISOs for the SNRs you are comparing (DxO measured ISOs of 1192 and 85, respectively) is only about 14. It follows that the comparison is biased against the smaller sensor. Furthermore, the difference between the S120 and the S100 isn't entirely negligible (more than a dB with the measured ISO kept constant at a point close to 100), which introduces additional bias against the smaller sensor. Second, a systematic analysis across the entire sample of sensors/bodies is of course preferable to a single illustration. You find such an analysis in the OP of the present thread.

What the data really says is: When comparing sensors at equivalent operating points (higher ISO for the FF and near base ISO for the smaller sensor as I wrote above), both large and small sensors with similar QEs operate with similar SNRs.

The question of QE aside, smaller sensors do better for SNR in this case too (although that may be because they have higher QE). See the results presented in the OP of this thread.

When we try to operate the large sensored camera at its lower ISO, an operating point that the small sensored camera can't operate at, then it's achievable SNR, while being larger than at high ISO, is not as high as it could be due to PRNU. This last point, of PRNU limitations, can be ameorilated by use of flat-fielding, which would allow the sensor to operate at its shot noise limit.

It's an ameliorative procedure all right, but would you say it is easily accomplished (and worth doing) for the ordinary photographer (and outside special applications like astrophotography)?

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Re: In which ways, and why, are smaller sensors more efficient than larger? Part 2
In reply to Anders W, 9 months ago

This is a response to Joe's (Great Bustard's) post here in a recently expired thread on the same topic as the present one.

Great Bustard wrote:

Anders W wrote:

You aren't off at all. What I wanted to say in general (apart from the comparison between the D4 and the E-M5 already discussed above) is the following:

The difference figures in the last column indicate that for both cameras, and especially the D4, the difference in SNR as we half the exposure (going to the next higher ISO) is significantly less than the 3 dB figure we would expect under the premise I mentioned (constant QE, no fixed pattern noise, trifling impact of read noise), especially in the lower part of the ISO range. Since we know read noise to have a trifling impact in that range, it follows that either QE isn't constant across ISOs and/or there is significant fixed pattern noise. This may be at least part of the explanation why my results for normed max SNR differ from Bob's QE figures.

For the purpose of measuring sensor efficiency, I think the implication is that we should move away from the simplified view provided by a focus on QE (as a constant for each sensor) and read noise. Instead I would suggest, that we use four measures to capture that efficiency. The three measures I have already constructed plus a fourth focusing on "normed max SNR" at higher ISOs. As I hope/think you agree, the two DR measures are good indicators of efficiency with regard to shadow rendering at low and high ISO and the two SNR measures are good indicators of highlight rendering at low and high ISO. So we cover variations in efficiency across the ISO range as well as between shadow and highlight rendering. What do you think?

I think we need to discuss PRNU, as Chris discussed below. For example, consider the EM5 at ISO 107 (42.2 dB) and ISO 394 (37.4 db). These exposures are 1.88 stops apart, which should correspond to a noise differential of 5.66 dB vs the measured 4.8 dB, where this discrepancy is due to PRNU.

In other words, PRNU prevents not only the one stop noise advantage of FF over mFT for the same exposure, but the one stop noise advantage of ISO 100 over ISO 400 for exposures two stops apart.

I have now addressed that problem in a systematic fashion in the manner I already outlined. See the OP of this thread.

As Chris states downthread:

http://www.dpreview.com/forums/post/53174252

"What the data really says is: When comparing sensors at equivalent operating points (higher ISO for the FF and near base ISO for the smaller sensor as I wrote above), both large and small sensors with similar QEs operate with similar SNRs. When we try to operate the large sensored camera at its lower ISO, an operating point that the small sensored camera can't operate at, then it's achievable SNR, while being larger than at high ISO, is not as high as it could be due to PRNU. This last point, of PRNU limitations, can be ameorilated by use of flat-fielding, which would allow the sensor to operate at its shot noise limit."

See my reply to Chris here.

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DPR exposure
In reply to Anders W, 9 months ago

This is a response to Steen Bay's post here in a recently expired thread on the same topic as the present one.

Steen Bay wrote:

P.S. - Eksamples of how the exposure can vary (quite a bit) in DPR's new comparison tool :

http://www.dpreview.com/forums/post/52346197

Have you tried to check, for those examples, how the ADU levels in the RAW files match those we'd expect on the basis of DxO "measured ISOs" if the exposure were the same (i.e., same amount of light on the sensor per area unit). What I think Richard Butler has said is that they have better means of controlling the light level for the new studio scene than for the old. But that doesn't necessarily mean that the light level doesn't vary at all (whether intended or not). I wouldn't take anyone words for it but just check the RAW files. When I have done so in the past (for the old studio scene rather than the old), I have never found exposure to differ by more than 1/3 EV between two cameras, and the difference has usually been less than that.

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DPR exposure
In reply to Anders W, 9 months ago

This is a response to Joe's (Great Bustard's) post here in a recently expired thread on the same topic as the present one.

Great Bustard wrote:

Steen Bay wrote:

P.S. - Examples of how the exposure can vary (quite a bit) in DPR's new comparison tool :

http://www.dpreview.com/forums/post/52346197

This makes DPR's studio comparison test all but useless. Well, thanks for that. Now I know.

I wouldn't jump to conclusions about this. See my reply to Steen here.

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Re: In which ways, and why, are smaller sensors more efficient than larger? Part 2
In reply to Anders W, 9 months ago

Just in case you haven't noticed... not quite sure why since you don't normally have a signature, but both here and in the previous thread large parts of your OP is hidden below 'show signature'.

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Re: In which ways, and why, are smaller sensors more efficient than larger? Part 2
In reply to Steen Bay, 9 months ago

Steen Bay wrote:

Just in case you haven't noticed... not quite sure why since you don't normally have a signature, but both here and in the previous thread large parts of your OP is hidden below 'show signature'.

Signatures are signaled by '--' at the beginning of a line and Anders is using '--------' as a separator.

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Re: In which ways, and why, are smaller sensors more efficient than larger? Part 2
In reply to richarddd, 9 months ago

richarddd wrote:

Steen Bay wrote:

Just in case you haven't noticed... not quite sure why since you don't normally have a signature, but both here and in the previous thread large parts of your OP is hidden below 'show signature'.

Signatures are signaled by '--' at the beginning of a line and Anders is using '--------' as a separator.

Yes, that's in all likelihood the explanation. I should have used dots or something like that as a separator instead. Not much to do about it at this stage. Hopefully, people will see these posts about the matter and click on show signature.

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ALERT: IMPORTANT NOTE ON HOW TO SEE THE ENTIRE OP
In reply to Anders W, 9 months ago

Unfortunately, I used a dash rather than something else to separate the technical appendix of my OP from the rest. This means that the appendix isn't visible unless you click on "show signature". Please do so if you want to read it.

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Re: DPR exposure
In reply to Anders W, 9 months ago

Anders W wrote:

This is a response to Joe's (Great Bustard's) post here in a recently expired thread on the same topic as the present one.

Great Bustard wrote:

Steen Bay wrote:

P.S. - Examples of how the exposure can vary (quite a bit) in DPR's new comparison tool :

http://www.dpreview.com/forums/post/52346197

This makes DPR's studio comparison test all but useless. Well, thanks for that. Now I know.

I wouldn't jump to conclusions about this. See my reply to Steen here.

Wouldn't call the comparison tool useless either. The exposure can sometimes vary a bit between cameras (and in a few cases more than a bit), but at least we know if it varies now if we remenber to check the EXIF data (the 'i' below the 100% crops). Assuming, of course, that the lighting actually is held constant now..

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The practical utility of sensor efficiency
In reply to Anders W, 9 months ago

This is a response to Sergey_Green's post here in a recently expired thread on the same topic as the present one.

Sergey_Green wrote:

Anders W wrote:

While that example was posted to show that and why shadow noise is a problem rather than to show the greater efficiency of one sensor size than another, it works for the latter purpose too. You could not have used the same f-stop on FF without making the DoF too shallow and (as I hope you agree) this is a shot where'd you'd want everything to be sharp across the frame.

Many of the images you post (most of) are shot from a distance. There are no close foregrounds, with the main objective further away, and there are no depths to capture.

You got that wrong. While the images I post here on DPR are certainly not a representative sample of my photography, most of them are nevertheless either such that I am at the limit in terms of DoF or they are shot in scenarios where light is abundant or shutter speed not a problem (and the question of sensor efficiency for equivalent images therefore not of much interest). If you think you can show systematic evidence that the above claim of mine is not correct, let me know what that evidence is. Links please.

The particular example we are discussing (originally posted here) is a case in point. That was shot with my Minolta MD 85/2 on my E-M5, either wide open or at f/2.8 (I don't remember which but I remember trying to go as wide as I could) at a distance of about 20 meters. That gives me a DoF of three to five meters, and I certainly needed that in this case to get both the cupola and the ceiling beneath it (sloping downwards on all sides) as sharp as I wanted them, particularly since I prefer to set focus in a scene like this on the central point of the image (the ceiling inside the cupola) rather than somewhere inbetween the most distant and the most proximate point (which would compromise the sharpness of the central point somewhat). So an FF user would have had to stop down to f/4 or f/5.6 to get the same.

Like most of the images in bad light that people post.

What evidence can you muster in support of that sweeping generalization? Links please.

Which means you could use say f/5.6 with standard zoom on one camera as you could use exactly the same on the other. The only argument you could bring to this is which lens performs better at what stop. Which, in turn, makes this whole debate even more restrictive in real shoot situation then it first appears.

For reasons already explained, you are wrong about that.

I do for reasons already explained: Provided that we don't clip the highlights (and it seems we agree that we shouldn't), the shadows are the most problematic part of the image with regard to signal-noise performance. The highlights will look just fine.

No, not really, the shadows are hardly problematic in most cases.

I am not saying that the shadows are a problem in most cases. What I am saying is that if you have problems, they'll show up most strongly in the shadows (provided that you have exposed correctly so as not to clip any important highlights).

But if you start pushing things around, the blue sky will show signs of posterization well sooner (and show real problems in most cases) and well before the viewer start even looking at shadows.

Please give us an example, including a link to the associated RAW file, of the situation you describe on the preceding two lines.

Shadows is a problem, or it can be a problem, but it is not as big a problem as you are trying to make it.

See above.

But this is not a premise with regard to the efficiency issue since my analyses show smaller sensors to be more efficient with regard to the highlights too (greater normed max SNR).

And for the reasons that no-one knows, and so what?

The reason that I show results not only for the shadows but also for the highlights is that some people appear to worry about the latter. You for example. Don't know why you would want to complain about the fact that I address your concerns.

Purely academic debate, you like this kind of stuff, don't you .

As I think most people on this forum are already aware, I like to discuss technical issues that have practical implications (e.g., for the choice of camera gear). The present discussion is but one example.

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Re: DPR exposure
In reply to Steen Bay, 9 months ago

Steen Bay wrote:

Anders W wrote:

This is a response to Joe's (Great Bustard's) post here in a recently expired thread on the same topic as the present one.

Great Bustard wrote:

Steen Bay wrote:

P.S. - Examples of how the exposure can vary (quite a bit) in DPR's new comparison tool :

http://www.dpreview.com/forums/post/52346197

This makes DPR's studio comparison test all but useless. Well, thanks for that. Now I know.

I wouldn't jump to conclusions about this. See my reply to Steen here.

Wouldn't call the comparison tool useless either. The exposure can sometimes vary a bit between cameras (and in a few cases more than a bit), but at least we know if it varies now if we remenber to check the EXIF data (the 'i' below the 100% crops). Assuming, of course, that the lighting actually is held constant now..

As I said, I wouldn't make any assumptions about the light and wouldn't rely on the EXIF to tell me what the exposure (actual amount of light on the sensor per area unit) was like. I'd just check out what the RAWs in conjunction with the DxOMark "measured ISOs" tell me. When I have tried to do that (as I have on quite a few occasions), I have never found a greater difference at the same ISO than 1/3 EV (and usually less than that). But of course, I can't guarantee that there is never a problem on this score.

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Re: In which ways, and why, are smaller sensors more efficient than larger? Part 2
In reply to richarddd, 9 months ago

richarddd wrote:

Steen Bay wrote:

Just in case you haven't noticed... not quite sure why since you don't normally have a signature, but both here and in the previous thread large parts of your OP is hidden below 'show signature'.

Signatures are signaled by '--' at the beginning of a line and Anders is using '--------' as a separator.

Boo. On Usenet the separator was dash dash space on a single line, something less likely to be used by accident.

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Re: In which ways, and why, are smaller sensors more efficient than larger? Part 2
In reply to Anders W, 9 months ago

Anders W wrote:

In a recently expired thread (whose OP is summarized here), some of us discussed (among other things) the extent to which the greater efficiency of smaller sensors compared to larger generalizes across different measures of efficiency. In order to answer some questions that still remain in that regard, I proposed here that I supplement the three indicators I have previously used to index efficiency by a fourth one. I am happy to present the results of so doing in this new thread.

The idea behind the four measures is as follows: The efficiency of a sensor can vary depending on which light level we consider (shadows versus highlights) as well as the ISO range we are looking at (low versus high ISOs). The three measures I previously used considered shadow rendering separately for low and high ISOs but highlights at a single point along the ISO range only. Since the efficiency with regard to highlight rendering turns out to vary a bit across the ISO range as well, my new set of indicators consider all four combinations, shadows as well as highlights at low as well as high ISOs.

How the measures are defined is described in detail in the technical appendix at the end of the post. The two indictors that index the efficiency with regard to shadow rendering, i.e., those that focus on dynamic range (DR), are the same as before. Those that index the efficiency with regard to highlight rendering, i.e., those that focus on max SNR, are both new although the first of them can be seen as slightly modified version of the single measure focusing on max SNR used in earlier analyses. The sample of bodies/sensors is the same as that used in the previous thread, i.e., that described here supplemented by the Canon 6D (since I already happened to have entered the data for that body as well). The data source is also unchanged (DxOMark).

As in the previous thread, I capture the relationship between efficiency and sensor size by a set of regression analyses with each of the four efficiency indicators as the dependent variable and sensor size as the independent. The measure of sensor size used is the square root of the square root of the sensor area (as expressed in millimeters squared). In all four cases, this provides a better fit (as measured by the adjusted R-square) than using the sensor area or the square root of the sensor area. The results are as follows (the regression coefficient, its standard error, and the adjusted R-square).

Normed ISO-100 DR: -18.21, 2.63, 0.723

Normed High-ISO DR: -102.59, 13.70, 0.754

Normed ISO-100 max SNR: -1.84, 0.27, 0.710

Normed High-ISO max SNR: -2.42, 0.67, 0.404

The coefficients show that the expected negative relationship with sensor size obtains in all four cases. If we choose to regard the sample as simple random, all effects are statisticially significant at the .01-level or better. Consequently, the conclusion that smaller sensors are more efficient than larger generalizes to all four efficiency measures.

Comments and questions welcome, especially, of course, from some of those who participated in the thread to which this is a continuation.

......................................................................................................................................

Technical appendix

Normed ISO-100 DR: This is the unlogged "print-mode" (8 MP) DR at a DxOMark measured ISO of 100 divided by the sensor area. Before unlogging and performing the division described, the logged DR at ISO 100 was extra- or interpolated from the closest observations available using the following formula:

Logged DR at ISO 100 = BIDR + (LOG10(100) - LOG10(BI))*(BIDR - NIDR) / (LOG10(BI) - LOG10(NI))

where BIDR is the logged DR at the base measured ISO, NIDR the logged DR at the next measured ISO, BI is the base measured ISO, and NI is the next measured ISO.

Normed High-ISO DR: This is the unlogged "print-mode" (8 MP) DR obtained for equivalent photos (same amount of total light on the sensor, same DoF, same shutter speed) at a higher measured ISO given by

12,800 * SA/864

where SA is the sensor area and 864 is the sensor area of real FF, i.e., 24 x 36 mm.

Before unlogging, the DR at that particular ISO was interpolated from the closest observations available using a formula similar to the one used for "normed ISO-100 DR".

Normed ISO-100 Max SNR: This is the unlogged max SNR at a DxOMark measured ISO of 100 multiplied by the square root of MP/8 (where MP is the number of sensor megapixels) and divided by the square root of the sensor area (as expressed in millimeters squared).

Before unlogging and performing the multiplication and division described, the logged max SNR (expressed in decibels) at ISO 100 was extra- or interpolated from the closest observations available using a formula similar to the one used for "normed ISO-100 DR".

Normed High-ISO Max SNR: This is the unlogged max SNR obtained for equivalent photos (same amount of total light on the sensor, same DoF, same shutter speed) after multiplication by the square root of MP/8 and at a higher measured ISO given by

12,800 * SA/864

where SA is the sensor area and 864 is the sensor area of real FF, i.e., 24 x 36 mm.

Before unlogging and performing the multiplication described, the logged max SNR (expressed in decibels) at that particular ISO was interpolated from the closest observations available using a formula similar to the one used for "normed ISO-100 DR".

It struck me that logging the sensor area rather than taking the square root of the square root of it (as I originally did) might be a more "natural" solution to the problem of finding the best-fitting functional form (given the restriction of a single parameter). Since logging additionally turned out to improve the fit one notch further, I present the results of this slightly revised analysis below. The independent variable is now the log2 of the sensor area. Everything else is unchanged. The regression coefficients now all have a very simple interpretation. They indicate the expected decline in sensor efficiency per doubling of the sensor area.

Normed ISO-100 DR: -11.98, 1.45, 0.788

Normed High-ISO DR: -65.37, 8.44, 0.766

Normed ISO-100 max SNR: -1.20, 0.16, 0.757

Normed High-ISO max SNR: -1.65, 0.39, 0.480

All relationships are now statistically significant at the 0.001 level or better (if we choose to regard the sample as simple random).

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Re: In which ways, and why, are smaller sensors more efficient than larger? Part 2
In reply to Anders W, 9 months ago

Anders W wrote:

...

While I am glad that you like the idea I introduced in my reply to Joe (Great Bustard) here and presented in greater detail in the OP of the present thread, illustrative examples like the one you provide above can be slightly misleading. First, they have to be done right and this one isn't. The ratio of the D4 sensor area to the S100 sensor area is about 21 whereas the ratio of the ISOs for the SNRs you are comparing (DxO measured ISOs of 1192 and 85, respectively) is only about 14. It follows that the comparison is biased against the smaller sensor. Furthermore, the difference between the S120 and the S100 isn't entirely negligible (more than a dB with the measured ISO kept constant at a point close to 100), which introduces additional bias against the smaller sensor. Second, a systematic analysis across the entire sample of sensors/bodies is of course preferable to a single illustration. You find such an analysis in the OP of the present thread.

What the data really says is: When comparing sensors at equivalent operating points (higher ISO for the FF and near base ISO for the smaller sensor as I wrote above), both large and small sensors with similar QEs operate with similar SNRs.

The question of QE aside, smaller sensors do better for SNR in this case too (although that may be because they have higher QE). See the results presented in the OP of this thread.

Hi Anders,

Ok cool.  I only chose S100 because that's all I could find!  Unfortunately I am user impaired, and can't see your results yet.  Is there a way to see it?

When we try to operate the large sensored camera at its lower ISO, an operating point that the small sensored camera can't operate at, then it's achievable SNR, while being larger than at high ISO, is not as high as it could be due to PRNU. This last point, of PRNU limitations, can be ameorilated by use of flat-fielding, which would allow the sensor to operate at its shot noise limit.

It's an ameliorative procedure all right, but would you say it is easily accomplished (and worth doing) for the ordinary photographer (and outside special applications like astrophotography)?

It takes alot of work and only in its infancy yet for photography, but I could see it incorporated as a button if found to be worth doing.  I have tried it for the raw green CFA in my D40 and can eliminate the PRNU so I know it's possible, but to answer your question about its necessity, I don't really know.  It might help for low contrast details and it also eliminates the corner rolloff.  I am of the opinion though, that we pay good money for sensors, and we deserve to have maximum IQ :).  Thanks for all your hard work,

Chris

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Re: In which ways, and why, are smaller sensors more efficient than larger? Part 2
In reply to cpw, 9 months ago

cpw wrote:

Anders W wrote:

...

While I am glad that you like the idea I introduced in my reply to Joe (Great Bustard) here and presented in greater detail in the OP of the present thread, illustrative examples like the one you provide above can be slightly misleading. First, they have to be done right and this one isn't. The ratio of the D4 sensor area to the S100 sensor area is about 21 whereas the ratio of the ISOs for the SNRs you are comparing (DxO measured ISOs of 1192 and 85, respectively) is only about 14. It follows that the comparison is biased against the smaller sensor. Furthermore, the difference between the S120 and the S100 isn't entirely negligible (more than a dB with the measured ISO kept constant at a point close to 100), which introduces additional bias against the smaller sensor. Second, a systematic analysis across the entire sample of sensors/bodies is of course preferable to a single illustration. You find such an analysis in the OP of the present thread.

What the data really says is: When comparing sensors at equivalent operating points (higher ISO for the FF and near base ISO for the smaller sensor as I wrote above), both large and small sensors with similar QEs operate with similar SNRs.

The question of QE aside, smaller sensors do better for SNR in this case too (although that may be because they have higher QE). See the results presented in the OP of this thread.

Hi Chris,

See comments below.

Hi Anders,

Ok cool. I only chose S100 because that's all I could find!

Yes, I realize that you chose the S100 because your vantage point involved QE (and thus sensorgen data).

Unfortunately I am user impaired, and can't see your results yet. Is there a way to see it?

Not sure what you mean here. As indicated in some follow-up posts to my OP, the technical appendix that I included ended up as my "signature" by mistake (I used a dashed line to separate it from the rest). Just click on "show signature" to see it. Do you have any problems reading what I said other than that?

Also note that I updated the OP slightly in this post

http://www.dpreview.com/forums/post/53189207

which also includes the OP itself. So that's the best place to start.

When we try to operate the large sensored camera at its lower ISO, an operating point that the small sensored camera can't operate at, then it's achievable SNR, while being larger than at high ISO, is not as high as it could be due to PRNU. This last point, of PRNU limitations, can be ameorilated by use of flat-fielding, which would allow the sensor to operate at its shot noise limit.

It's an ameliorative procedure all right, but would you say it is easily accomplished (and worth doing) for the ordinary photographer (and outside special applications like astrophotography)?

It takes alot of work and only in its infancy yet for photography, but I could see it incorporated as a button if found to be worth doing.

It would be nice if it could be done automatically somehow but right now it seems like a whole lot of work (particularly since, if I understand things right, it would have to be done separately for each lens, FL, and f-stop, perhaps for each focus distance too if vignetting varies by that).

I have tried it for the raw green CFA in my D40 and can eliminate the PRNU so I know it's possible, but to answer your question about its necessity, I don't really know. It might help for low contrast details and it also eliminates the corner rolloff.

It would be interesting to see how much of a difference it makes, or equivalently, how much of a problem PRNU really is, from a perceptual (as opposed to SNR-measurement) point of view. Personally, as already indicated, I am more worried about shadow than highlight SNR (under the provision that we expose so as not to clip the highlights of course) and my provisional understanding is that PRNU is primarily (though perhaps not exclusively) a highlight concern. But perhaps that's an unwarranted simplification. What's your take on this?

I am of the opinion though, that we pay good money for sensors, and we deserve to have maximum IQ :).

Absolutely.

Thanks for all your hard work,

You are welcome. Glad you find it of some interest.

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Question about DR for various sensor sizes
In reply to Anders W, 9 months ago

Could you briefly explain why dynamic range for smaller sensors is often very close to what it is for larger ones?  For example, IIRC, the E-M1 at most ISOs has DR within 1 EV of D800 (And almost identical at ISO12800).  This goes against the myth that there should be a 2 stop difference between the M43 and FF sensors.  Is this due to pixel size?

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Re: Question about DR for various sensor sizes
In reply to Lab D, 9 months ago

Lab D wrote:

Could you briefly explain why dynamic range for smaller sensors is often very close to what it is for larger ones? For example, IIRC, the E-M1 at most ISOs has DR within 1 EV of D800 (And almost identical at ISO12800). This goes against the myth that there should be a 2 stop difference between the M43 and FF sensors. Is this due to pixel size?

What I have done in this thread so far is only to show that the premise of your question is largely correct, i.e., that the difference in DR between sensors of different sizes is often significantly smaller than the one we would expect if the sensors were equally efficient. Exactly why that is the case, is something I can't yet speak of with much certainty. So what I say below is at least partly speculative.

What we know is that DR is by definition a matter of the strength of the signal (determined, up to the clipping point, by the total amount of light that falls on the sensor and its quantum efficiency) plus read noise. Differences in quantum efficiency is likely to be part of the explanation although primarily, I would guess, because the smallest sensors use BSI technology whereas the larger don't. However, read noise is likely to be the more important factor.

The data we have suggest that if pixel size is kept proportional to sensor size (as it is if we compare sensors of different size but with the same pixel count), it is difficult to keep the read noise constant as you increase the pixel size. The read noise tends to be bigger for bigger pixels, especially at low ISOs (where more of the FWC is utilized).

If instead the pixel size is kept constant as sensor size expands so that larger sensors have more pixels rather than bigger pixels, this problem can obviously be overcome. Imagine, for example, a 64 MP FF sensor made up of four 16 MP MFT sensors. The sensor technology would thus be the same. It's just the sensor area and the pixel count that varies. Now let's ask ourselves what the relative DR of these sensors would be like.

If we compare them at their original resolution, it would obviously be exactly the same at the same ISO/exposure. The FF sensor would in this case have higher resolution (at the plane in perfect focus) but less DoF. For equivalent images (same DoF, different exposure), the FF image would still have higher resolution but 2 EV worse DR (if we compare the sensors over that part of the ISO range where read noise stays constant as you change the ISO).

Now if we try to address the noisiness of the 64 MP FF image by downsampling it to 16 MP, one might at first be inclined to think that the two sensors would do equally well with regard to resolution and DR alike. Such isn't the case however. At the same ISO/exposure, the FF sensor would be one EV ahead with regard to DR and two EV behind with regard to DoF. For equivalent images, the MFT image would be one EV ahead with regard to DR and the two images the same with regard to DoF.

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Thanks for the prompt reply (nt)
In reply to Anders W, 9 months ago

Anders W wrote:

Lab D wrote:

Could you briefly explain why dynamic range for smaller sensors is often very close to what it is for larger ones? For example, IIRC, the E-M1 at most ISOs has DR within 1 EV of D800 (And almost identical at ISO12800). This goes against the myth that there should be a 2 stop difference between the M43 and FF sensors. Is this due to pixel size?

What I have done in this thread so far is only to show that the premise of your question is largely correct, i.e., that the difference in DR between sensors of different sizes is often significantly smaller than the one we would expect if the sensors were equally efficient. Exactly why that is the case, is something I can't yet speak of with much certainty. So what I say below is at least partly speculative.

What we know is that DR is by definition a matter of the strength of the signal (determined, up to the clipping point, by the total amount of light that falls on the sensor and its quantum efficiency) plus read noise. Differences in quantum efficiency is likely to be part of the explanation although primarily, I would guess, because the smallest sensors use BSI technology whereas the larger don't. However, read noise is likely to be the more important factor.

The data we have suggest that if pixel size is kept proportional to sensor size (as it is if we compare sensors of different size but with the same pixel count), it is difficult to keep the read noise constant as you increase the pixel size. The read noise tends to be bigger for bigger pixels, especially at low ISOs (where more of the FWC is utilized).

If instead the pixel size is kept constant as sensor size expands so that larger sensors have more pixels rather than bigger pixels, this problem can obviously be overcome. Imagine, for example, a 64 MP FF sensor made up of four 16 MP MFT sensors. The sensor technology would thus be the same. It's just the sensor area and the pixel count that varies. Now let's ask ourselves what the relative DR of these sensors would be like.

If we compare them at their original resolution, it would obviously be exactly the same at the same ISO/exposure. The FF sensor would in this case have higher resolution (at the plane in perfect focus) but less DoF. For equivalent images (same DoF, different exposure), the FF image would still have higher resolution but 2 EV worse DR (if we compare the sensors over that part of the ISO range where read noise stays constant as you change the ISO).

Now if we try to address the noisiness of the 64 MP FF image by downsampling it to 16 MP, one might at first be inclined to think that the two sensors would do equally well with regard to resolution and DR alike. Such isn't the case however. At the same ISO/exposure, the FF sensor would be one EV ahead with regard to DR and two EV behind with regard to DoF. For equivalent images, the MFT image would be one EV ahead with regard to DR and the two images the same with regard to DoF.

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Re: Question about DR for various sensor sizes
In reply to Lab D, 9 months ago

Lab D wrote:

Could you briefly explain why dynamic range for smaller sensors

look @ SNR beyond deep shadows, Anders likes to shoot black cats in lightless rooms - but in a real life 99% of your details are above that.

PS: and when it comes to DR, he dislikes to illustrate bigger sensor with Sony APS-C 16mp @ base ISO... always using some poor Canons to beat.

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