Noise Performance in an ISOless System

Started Mar 26, 2013 | Discussions
dosdan Contributing Member • Posts: 503
Noise Performance in an ISOless System
14

Conceptually, as far as noise is concerned, a DSLR signal path can be considered as:

Sensor -> PGA -> ADC

Each of these stages contributes noise. Beside the photonic noise inherent in light itself ("shot" noise), the most common noise is read noise. The contributions of read noise from the 3 stages above can be lumped together by combining the 3 noise components in quadrature (root-mean-square) into a value called the Total Read Noise.

However since some of these noise components are affected by ISO gain, the total read noise changes as gain is applied. It is important to understand this and its effect on overall system noise performance.

The PGA (Programmable Gain Amplifier) is used to apply stepped amounts of analogue gain (increasing the ISO sensitivity) when the signal from the sensor is weak i.e. the exposure level is low. In this discussion, I'll generally omit its noise contribution. You would hope that an amp used to reduce the total noise level was of a low-noise design itself. Some of the PGA noise will come from the input stage of the PGA, and therefore increase as you boost the analogue gain. Another part of the PGA noise will come from the output stage, so it will be of a constant level and not affected by analogue gain changes.

The sensor read noise will be boosted as the analogue gain is increased.

The ADC read noise, coming after the PGA stage, is constant in level, regardless of the amount of analogue gain.

So the simplified signal path becomes:

Sensor (analogue gain influenced) -> ADC

Since noise is coming from different parts of the signal path, the noise is either "input referenced" (photo-electrons or e-) or "output referenced" (DN - Digital Numbers, or ADU - Analogue to Digital Units).

I'll be using www.sensorgen.info data, which is input referenced. This means that the noise is considered as if it was another signal coming from the sensor. So the sensor read noise level (I'll call it just "sensor") might be 3e-. Since the ADC noise is after the PGA, we need to reverse the effect of ISO boost, if we are to think of it as another sensor signal. For example, an ADC has a read noise level of 16e-. At base ISO100 we'll consider the PGA gain to be 1x (it will probably be different from this, but we're interested in relative gain changes in this discussion). So at ISO1600 the PGA gain is 16x, and our ADC noise needs to be divided by 16. Therefore, with input-referencing, the ADC noise is seen at ISO100 as an 16e- signal from the sensor, and at ISO1600, as if it was a 1e- sensor signal. So the the input-referenced total read noise value tends to fall as ISO increases.

The formula for the simplified total read noise we'll be discussing here is:

Total = sqrt(Sensor^2 + ADC^2)

The shape of the graph of this equation vs ISO is very important. We'll be considering the ISOs of ISO100 & ISO1600. Generally, with modern sensors, we're still within the ISO range were analogue gain is applied and any in-camera raw NR is not yet enabled.

Let's look at the K-5 total read noise within this range (Manufacturers ISO used):

http://www.sensorgen.info/PentaxK-5.html

ISO Total e-
100 3.5
200 3.1
400 2.6
800 2.4
1600 1.9

The "16x" ratio (ISO1600/ISO100) of the change in the total read noise as ISO increases is 1.4:1, or just 1.4x. If you play around in a spreadsheet you can roughly get the corresponding values that produce this curve. The values are: sensor=2e- & ADC=2.8e-.

So the K-5 values are:
Sensor: 2e-
ADC: 2.8e-
16x: 1.4x

Other APS-C:

60D:
Sensor: 3e-
ADC: 13e-
16x: 4.3x

550D
Sensor: 2.7e-
ADC: 11.6e-
16x: 4.3x

7D
Sensor: 2.8e-
ADC: 8e-
16x: 2.9x

A77
Sensor: 2.7e-
ADC: 3.5e-
16x: 1.3x

D5200
Sensor: 2e-
ADC: 3e-
16x: 1.5x

FF sensors:

D600
Sensor: 3.7-
ADC: 6.3-
16x: 1.7x

D800
Sensor: 2.9e-
ADC: 3.6e-
16x: 1.2x

D4
Sensor: 2.4e-
ADC: 18.5e-
16x: 7.7x

5D III
Sensor: 4.2e-
ADC: 33e-
16x: 7.9x

1D X
Sensor: 2.6e-
ADC: 38e-
16x: 14.6x

The sensel read noise value will be affected by its size. Here we're not interested in its absolute value, but the way it contributes to the total read noise value.

The "16x" figure shows how effective the use of analogue gain is in improving the total read noise value, as the sensor output level decreases (i.e. at lower exposure levels). Sensors where this value is <2 are approaching ISOless operation. You can also get some idea how bad an idea it would be to operate a camera like the 1D X at base ISO and rely on much boosting of the rendering brightness afterwards in PP. Operating in a suitable ISO range is much better for this camera.

Once the amplified sensor read noise is much bigger then the ADC read noise, there is little reason to apply further analogue gain, as sensor read noise dominates the total read noise, and the total read noise now increases at the same rate as the amplified signal increases. So the SNR due to the read noise remains the same. Therefore for high-ISO operation, cameras switch to digital gain.

With some cameras, particularly the D600 & D800, there are difficulties in getting reasonable curve fits using just Sensor & ADC read noise values. Since the sensorgen info is derived by solving a curve fit of the DxOMark Full SNR graph, and since DxoMark is known to smooth the curves, this is possibly the reason. It could also be that PGA noise does need to be considered in some cases. Or it could be that Nikon is doing something unusual.

The 7D is unusual in having a relatively low 16x ratio compared to the other Canon cameras. It looks like the ADC read noise level is unusually low for a Canon camera.

Some camera have such low 16x values that it seems no change of analogue gain is being used at all: D7000; RX100. Perhaps the unusual results from the D800 should also be considered this way.

Note: just because a camera is ISOless, does not means it's a low-noise design. Some P&S cameras used only digital gain to change ISO. This may have been done just for simplicity.

Why worry about ISOless operation?  Boosting ISO can be done in either an analogue or digital manner. Doing so digitally only improves the rendered image brightness. Using analogue gain at low ISO helps with reducing the contribution of ADC noise to the total read noise, as well as increasing the brightness of a rendered image. However both forms of gain have a negative effect: they decrease the DR (Dynamic Range).

The max. level is determined by the saturation level, either the sensel become full of photo-electrons i.e. reaching FWC (Full-Well Capacity) or reaching FS (Full Scale) in the ADC output level (running out of bits). FWC is only a consideration at base ISO. Once you need to apply extra gain (i.e. due to a low exposure level), FS clipping is the main consideration. Since FS is fixed, as you further amplify the signal, the distance between the noise floor and max. level decreases. If total read noise was constant with ISO, DR would decrease 1 stop for every doubling of gain/ISO. However, since total read noise usually changes in systems using analogue gain, DR decrease steps tend to be smaller at low ISO and increase in size, up to a max. of 1 stop per doubling of gain, at mid ISO. At high-ISO, where digital gain is used, the DR decrease should be exactly 1 step. However two thing can cause the DR value to be different.

1. High ISO involve small sensor signals do it becomes more difficult to get accurate measurements.

2. Cameras may apply raw-level NR.

The problem with decreasing DR as ISO increases, is that it also increases the likelihood of a highlight or specular reflection being clipped. If you're shooting raw, and the total read noise is relatively low, it becomes feasible to shoot at either base ISO (ISOless), or at a relatively low max. ISO, e.g. ISO400 (semi-ISOless), and then increase the rendered image brightness afterwards in PP.

So instead of, in a low-exposure situation, shooting at ISO1600, you instead shoot at ISO100 and afterwards apply 4-stops boost (16x) in PP, or in an auto-ISO setup, shoot at ISO400 (your set max. ISO), and later apply 2 stops boost in PP.

This means that relatively low levels have been recorded and it is unlikely that any highlights will be blown in the capturing phase. Of course, if you just applied the same boost in PP to reach the same rendered brightness level, you run the same chance of blowing a highlight. But since the highlight, as captured, is not yet blown, you still have an opportunity to fiddle with the tone curve to successfully render the image within the limited DR of a print or display screen. So this form of operation becomes like a superior form of highlight protection/recovery.

The disadvantage for the raw shooter is that the review image is darkish. But if cameras & raw file formats were set up to accommodate this type of operation, the review image need not be darkish at all. As the relative contribution of ADC read noise to the total read noise keeps decreasing, it is rather frustrating to see that no manufacturer has yet offered this mode.

Dan.

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Pentax K100D Super Pentax K20D Pentax K-5 Pentax K-01 Pentax K-3 +1 more
Great Bustard Forum Pro • Posts: 39,705
My name is Joseph James, and I endorse this post. : )

Well done, Dan! Combine this with gollywop's post:

http://forums.dpreview.com/forums/post/51136862

and Daniel Browning's six-part treatice:

http://forums.dpreview.com/forums/post/32064270

and you'll have a good understanding of the technical aspects of the digitally captured photo.

EDIT:  Dan's post is not meant to teach you how to take "good photos" -- it's simply to help you understand how the digital capture works, with the hope that the competent photographer might be able to improve the IQ of at least some photos in some circumstances, not unlike a race car driver understanding the mechanics of their car.  That is, you don't have to know how a car works to be a good driver, but it doesn't hurt to know why and how the car works, and sometimes helps.

dosdan wrote:

Conceptually, as far as noise is concerned, a DSLR signal path can be considered as:

Sensor -> PGA -> ADC

Each of these stages contributes noise. Beside the photonic noise inherent in light itself ("shot" noise), the most common noise is read noise. The contributions of read noise from the 3 stages above can be lumped together by combining the 3 noise components in quadrature (root-mean-square) into a value called the Total Read Noise.

However since some of these noise components are affected by ISO gain, the total read noise changes as gain is applied. It is important to understand this and its effect on overall system noise performance.

The PGA (Programmable Gain Amplifier) is used to apply stepped amounts of analogue gain (increasing the ISO sensitivity) when the signal from the sensor is weak i.e. the exposure level is low. In this discussion, I'll generally omit its noise contribution. You would hope that an amp used to reduce the total noise level was of a low-noise design itself. Some of the PGA noise will come from the input stage of the PGA, and therefore increase as you boost the analogue gain. Another part of the PGA noise will come from the output stage, so it will be of a constant level and not affected by analogue gain changes.

The sensor read noise will be boosted as the analogue gain is increased.

The ADC read noise, coming after the PGA stage, is constant in level, regardless of the amount of analogue gain.

So the simplified signal path becomes:

Sensor (analogue gain influenced) -> ADC

Since noise is coming from different parts of the signal path, the noise is either "input referenced" (photo-electrons or e-) or "output referenced" (DN - Digital Numbers, or ADU - Analogue to Digital Units).

I'll be using www.sensorgen.info data, which is input referenced. This means that the noise is considered as if it was another signal coming from the sensor. So the sensor read noise level (I'll call it just "sensor") might be 3e-. Since the ADC noise is after the PGA, we need to reverse the effect of ISO boost, if we are to think of it as another sensor signal. For example, an ADC has a read noise level of 16e-. At base ISO100 we'll consider the PGA gain to be 1x (it will probably be different from this, but we're interested in relative gain changes in this discussion). So at ISO1600 the PGA gain is 16x, and our ADC noise needs to be divided by 16. Therefore, with input-referencing, the ADC noise is seen at ISO100 as an 16e- signal from the sensor, and at ISO1600, as if it was a 1e- sensor signal. So the the input-referenced total read noise value tends to fall as ISO increases.

The formula for the simplified total read noise we'll be discussing here is:

Total = sqrt(Sensor^2 + ADC^2)

The shape of the graph of this equation vs ISO is very important. We'll be considering the ISOs of ISO100 & ISO1600. Generally, with modern sensors, we're still within the ISO range were analogue gain is applied and any in-camera raw NR is not yet enabled.

Let's look at the K-5 total read noise within this range (Manufacturers ISO used):

http://www.sensorgen.info/PentaxK-5.html

ISO Total e-
100 3.5
200 3.1
400 2.6
800 2.4
1600 1.9

The "16x" ratio (ISO1600/ISO100) of the change in the total read noise as ISO increases is 1.4:1, or just 1.4x. If you play around in a spreadsheet you can roughly get the corresponding values that produce this curve. The values are: sensor=2e- & ADC=2.8e-.

So the K-5 values are:
Sensor: 2e-
ADC: 2.8e-
16x: 1.4x

Other APS-C:

60D:
Sensor: 3e-
ADC: 13e-
16x: 4.3x

550D
Sensor: 2.7e-
ADC: 11.6e-
16x: 4.3x

7D
Sensor: 2.8e-
ADC: 8e-
16x: 2.9x

A77
Sensor: 2.7e-
ADC: 3.5e-
16x: 1.3x

D5200
Sensor: 2e-
ADC: 3e-
16x: 1.5x

FF sensors:

D600
Sensor: 3.7-
ADC: 6.3-
16x: 1.7x

D800
Sensor: 2.9e-
ADC: 3.6e-
16x: 1.2x

D4
Sensor: 2.4e-
ADC: 18.5e-
16x: 7.7x

5D III
Sensor: 4.2e-
ADC: 33e-
16x: 7.9x

1D X
Sensor: 2.6e-
ADC: 38e-
16x: 14.6x

The sensel read noise value will be affected by its size. Here we're not interested in its absolute value, but the way it contributes to the total read noise value.

The "16x" figure shows how effective the use of analogue gain is in improving the total read noise value, as the sensor output level decreases (i.e. at lower exposure levels). Sensors where this value is <2 are approaching ISOless operation. You can also get some idea how bad an idea it would be to operate a camera like the 1D X at base ISO and rely on much boosting of the rendering brightness afterwards in PP. Operating in a suitable ISO range is much better for this camera.

Once the amplified sensor read noise is much bigger then the ADC read noise, there is little reason to apply further analogue gain, as sensor read noise dominates the total read noise, and the total read noise now increases at the same rate as the amplified signal increases. So the SNR due to the read noise remains the same. Therefore for high-ISO operation, cameras switch to digital gain.

With some cameras, particularly the D600 & D800, there are difficulties in getting reasonable curve fits using just Sensor & ADC read noise values. Since the sensorgen info is derived by solving a curve fit of the DxOMark Full SNR graph, and since DxoMark is known to smooth the curves, this is possibly the reason. It could also be that PGA noise does need to be considered in some cases. Or it could be that Nikon is doing something unusual.

The 7D is unusual in having a relatively low 16x ratio compared to the other Canon cameras. It looks like the ADC read noise level is unusually low for a Canon camera.

Some camera have such low 16x values that it seems no change of analogue gain is being used at all: D7000; RX100. Perhaps the unusual results from the D800 should also be considered this way.

Note: just because a camera is ISOless, does not means it's a low-noise design. Some P&S cameras used only digital gain to change ISO. This may have been done just for simplicity.

Why worry about ISOless operation? Boosting ISO can be done in either an analogue or digital manner. Doing so digitally only improves the rendered image brightness. Using analogue gain at low ISO helps with reducing the contribution of ADC noise to the total read noise, as well as increasing the brightness of a rendered image. However both forms of gain have a negative effect: they decrease the DR (Dynamic Range).

The max. level is determined by the saturation level, either the sensel become full of photo-electrons i.e. reaching FWC (Full-Well Capacity) or reaching FS (Full Scale) in the ADC output level (running out of bits). FWC is only a consideration at base ISO. Once you need to apply extra gain (i.e. due to a low exposure level), FS clipping is the main consideration. Since FS is fixed, as you further amplify the signal, the distance between the noise floor and max. level decreases. If total read noise was constant with ISO, DR would decrease 1 stop for every doubling of gain/ISO. However, since total read noise usually changes in systems using analogue gain, DR decrease steps tend to be smaller at low ISO and increase in size, up to a max. of 1 stop per doubling of gain, at mid ISO. At high-ISO, where digital gain is used, the DR decrease should be exactly 1 step. However two thing can cause the DR value to be different.

1. High ISO involve small sensor signals do it becomes more difficult to get accurate measurements.

2. Cameras may apply raw-level NR.

The problem with decreasing DR as ISO increases, is that it also increases the likelihood of a highlight or specular reflection being clipped. If you're shooting raw, and the total read noise is relatively low, it becomes feasible to shoot at either base ISO (ISOless), or at a relatively low max. ISO, e.g. ISO400 (semi-ISOless), and then increase the rendered image brightness afterwards in PP.

So instead of, in a low-exposure situation, shooting at ISO1600, you instead shoot at ISO100 and afterwards apply 4-stops boost (16x) in PP, or in an auto-ISO setup, shoot at ISO400 (your set max. ISO), and later apply 2 stops boost in PP.

This means that relatively low levels have been recorded and it is unlikely that any highlights will be blown in the capturing phase. Of course, if you just applied the same boost in PP to reach the same rendered brightness level, you run the same chance of blowing a highlight. But since the highlight, as captured, is not yet blown, you still have an opportunity to fiddle with the tone curve to successfully render the image within the limited DR of a print or display screen. So this form of operation becomes like a superior form of highlight protection/recovery.

The disadvantage for the raw shooter is that the review image is darkish. But if cameras & raw file formats were set up to accommodate this type of operation, the review image need not be darkish at all. As the relative contribution of ADC read noise to the total read noise keeps decreasing, it is rather frustrating to see that no manufacturer has yet offered this mode.

Dan.

Detail Man
Detail Man Forum Pro • Posts: 16,688
Re: Noise Performance in an ISOless System

Good stuff, Dan (as is always the case from you). Just one thought. Something raised by Jack Hogan a while back on another thread. Poisson and (ADC Quantization Noise) Gaussian distributions are not directly combinable in the typical "vector summation" when the population sizes are small.

Was searching a few days ago, finding only papers that pretty much snow me mathematically.

The gist of it seems to be that Poisson distributions approach Gaussian when very large population sizes exist. I wonder if this (might, possibly) become something of an issue in cases of per-photosite analysis where relatively small numbers of photons/electrons are involved per  analysis time-period ?

Great Bustard Forum Pro • Posts: 39,705
So far as I'm aware...

Detail Man wrote:

Good stuff, Dan (as is always the case from you). Just one thought. Something raised by Jack Hogan a while back on another thread. Poisson and (ADC Quantization Noise) Gaussian distributions are not directly combinable in the typical "vector summation" when the population sizes are small.

Was searching a few days ago, finding only papers that pretty much snow me mathematically.

The gist of it seems to be that Poisson distributions approach Gaussian when very large population sizes exist. I wonder if this (might, possibly) become something of an issue in cases of per-photosite analysis where relatively small numbers of photons/electrons are involved per analysis time-period ?

...the population sizes are not a factor.  The condition for the quadrature sum is that the samples  are uncorrelated, not sample size.

For example, if Noise Source 1 is 2 electrons and Noise Source 2 is 5 electrons, then the combined noise is sqrt (2² + 5²) ~ 5.4 electrons so long as Noise Source 1 and Noise Source 2 are uncorrelated.

If the noise sources are correlated, then we have to add in an extra term that includes the correlation between the two noise sources.

For example, if the correlation between Noise Source 1 and Noise Source 2 is 50%, then the combined noise would be sqrt (2² + 5² + 2 · 0.5 · 2 · 5) ~ 6.2 electrons.  As an aside, note that a 100% correlation means that the quadrature sum will be the same as the linear sum.

OP dosdan Contributing Member • Posts: 503
Re: Noise Performance in an ISOless System

I was computing the 16x value (total read noise, input-referenced, at ISO100 vs ISO1600) incorrectly. It does not make a great difference to the results. I'll use the sensorgen total read noise values. Measurement & curve-fit blips will affect these values (I think the 7D is affected), but the groupings are still similar.

K-5:
1.8x

60D:
4.6x

550D
4.5x

7D
2.5x

A77
1.6x

D5200
1.6x

D600
2x

D800
0.9x

D4
8.1x

5D III
8.5x

1D X
10.9x

Dan.

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Pentax K100D Super Pentax K20D Pentax K-5 Pentax K-01 Pentax K-3 +1 more
Detail Man
Detail Man Forum Pro • Posts: 16,688
Re: So far as I'm aware...

Great Bustard wrote:

Detail Man wrote:

Good stuff, Dan (as is always the case from you). Just one thought. Something raised by Jack Hogan a while back on another thread. Poisson and (ADC Quantization Noise) Gaussian distributions are not directly combinable in the typical "vector summation" when the population sizes are small.

Was searching a few days ago, finding only papers that pretty much snow me mathematically.

The gist of it seems to be that Poisson distributions approach Gaussian when very large population sizes exist. I wonder if this (might, possibly) become something of an issue in cases of per-photosite analysis where relatively small numbers of photons/electrons are involved per analysis time-period ?

...the population sizes are not a factor. The condition for the quadrature sum is that the samples are uncorrelated, not sample size.

For example, if Noise Source 1 is 2 electrons and Noise Source 2 is 5 electrons, then the combined noise is sqrt (2² + 5²) ~ 5.4 electrons so long as Noise Source 1 and Noise Source 2 are uncorrelated.

If the noise sources are correlated, then we have to add in an extra term that includes the correlation between the two noise sources.

For example, if the correlation between Noise Source 1 and Noise Source 2 is 50%, then the combined noise would be sqrt (2² + 5² + 2 · 0.5 · 2 · 5) ~ 6.2 electrons. As an aside, note that a 100% correlation means that the quadrature sum will be the same as the linear sum.

Have done some reading, and yes, it seems that you are correct. Also, the Poisson distribution seems to be considered to begin to fairly closely approach a Gaussian distribution when the Mean is on the order of 10 or so - which is not all that large of a number. So, if we can convince ourselves that these sources are indeed truly uncorrelated (covariance=0), it works.

Great Bustard Forum Pro • Posts: 39,705
Re: So far as I'm aware...

Detail Man wrote:

Great Bustard wrote:

Detail Man wrote:

Good stuff, Dan (as is always the case from you). Just one thought. Something raised by Jack Hogan a while back on another thread. Poisson and (ADC Quantization Noise) Gaussian distributions are not directly combinable in the typical "vector summation" when the population sizes are small.

Was searching a few days ago, finding only papers that pretty much snow me mathematically.

The gist of it seems to be that Poisson distributions approach Gaussian when very large population sizes exist. I wonder if this (might, possibly) become something of an issue in cases of per-photosite analysis where relatively small numbers of photons/electrons are involved per analysis time-period ?

...the population sizes are not a factor. The condition for the quadrature sum is that the samples are uncorrelated, not sample size.

For example, if Noise Source 1 is 2 electrons and Noise Source 2 is 5 electrons, then the combined noise is sqrt (2² + 5²) ~ 5.4 electrons so long as Noise Source 1 and Noise Source 2 are uncorrelated.

If the noise sources are correlated, then we have to add in an extra term that includes the correlation between the two noise sources.

For example, if the correlation between Noise Source 1 and Noise Source 2 is 50%, then the combined noise would be sqrt (2² + 5² + 2 · 0.5 · 2 · 5) ~ 6.2 electrons. As an aside, note that a 100% correlation means that the quadrature sum will be the same as the linear sum.

Have done some reading, and yes, it seems that you are correct.

That reminds me of a story.

One morning, my son was fighting with me because I wouldn't let him wear sandles.  My wife jumps in and says to let him wear what he wants.  Whatever.  I tell him he can wear whatever he wants when mama is around.

So, as we all drive off, my wife starts to lay into me about being too strict with him, and the "entertainment" begins.  So, here's my son in the back of the car listening to us argue about this insanely stupid thing, and when there's a pause, he says, "Papa's right.  Papa's always right."

My wife explodes.  "WTF?!  I'm defending you, and you are saying 'papa's right'?!  'Papa's always right'?!  I'm never going to help you again!"  To which my son calmly replies, "Papa, you're always right, right?"

Now, what would someone give to have a son like that? 

Also, the Poisson distribution seems to be considered to begin to fairly closely approach a Gaussian distribution when the Mean is on the order of 10 or so - which is not all that large of a number. So, if we can convince ourselves that these sources are indeed truly uncorrelated (covariance=0), it works.

Well, "uncorrelated" might be a bit too strong, let's just say "weakly correlated", so far as I'm aware.

Tom Axford Veteran Member • Posts: 3,640
Re: Noise Performance in an ISOless System

dosdan wrote:

The disadvantage for the raw shooter is that the review image is darkish. But if cameras & raw file formats were set up to accommodate this type of operation, the review image need not be darkish at all. As the relative contribution of ADC read noise to the total read noise keeps decreasing, it is rather frustrating to see that no manufacturer has yet offered this mode.

Agree completely. Let's hope the manufacturers are listening.

Detail Man
Detail Man Forum Pro • Posts: 16,688
Re: So far as I'm aware...

Great Bustard wrote:

Detail Man wrote:

Great Bustard wrote:

Detail Man wrote:

Good stuff, Dan (as is always the case from you). Just one thought. Something raised by Jack Hogan a while back on another thread. Poisson and (ADC Quantization Noise) Gaussian distributions are not directly combinable in the typical "vector summation" when the population sizes are small.

Was searching a few days ago, finding only papers that pretty much snow me mathematically.

The gist of it seems to be that Poisson distributions approach Gaussian when very large population sizes exist. I wonder if this (might, possibly) become something of an issue in cases of per-photosite analysis where relatively small numbers of photons/electrons are involved per analysis time-period ?

...the population sizes are not a factor. The condition for the quadrature sum is that the samples are uncorrelated, not sample size.

For example, if Noise Source 1 is 2 electrons and Noise Source 2 is 5 electrons, then the combined noise is sqrt (2² + 5²) ~ 5.4 electrons so long as Noise Source 1 and Noise Source 2 are uncorrelated.

If the noise sources are correlated, then we have to add in an extra term that includes the correlation between the two noise sources.

For example, if the correlation between Noise Source 1 and Noise Source 2 is 50%, then the combined noise would be sqrt (2² + 5² + 2 · 0.5 · 2 · 5) ~ 6.2 electrons. As an aside, note that a 100% correlation means that the quadrature sum will be the same as the linear sum.

Have done some reading, and yes, it seems that you are correct.

That reminds me of a story.

One morning, my son was fighting with me because I wouldn't let him wear sandles. My wife jumps in and says to let him wear what he wants. Whatever. I tell him he can wear whatever he wants when mama is around.

So, as we all drive off, my wife starts to lay into me about being too strict with him, and the "entertainment" begins. So, here's my son in the back of the car listening to us argue about this insanely stupid thing, and when there's a pause, he says, "Papa's right. Papa's always right."

My wife explodes. "WTF?! I'm defending you, and you are saying 'papa's right'?! 'Papa's always right'?! I'm never going to help you again!" To which my son calmly replies, "Papa, you're always right, right?"

Now, what would someone give to have a son like that?

Also, the Poisson distribution seems to be considered to begin to fairly closely approach a Gaussian distribution when the Mean is on the order of 10 or so - which is not all that large of a number. So, if we can convince ourselves that these sources are indeed truly uncorrelated (covariance=0), it works.

Well, "uncorrelated" might be a bit too strong, let's just say "weakly correlated", so far as I'm aware.

Yeah, "Papa's always right ... so far as I am aware .. especially when he always gets outgunned".

TheMartyGuy Regular Member • Posts: 181
Posterization might be a problem

Your noise analysis seems well thought out.  However one needs to also consider spatial correlation between pixels in darker areas of the image  due to low values on the AD converter.  It might happen that shot noise between pixels keeps a low AD output at the same count over a spatial region.  This spatially correlated noise can cause posterization in darker areas of the image.

If you have the time, can you address this issue?  Thanks.

OP dosdan Contributing Member • Posts: 503
Re: Posterization might be a problem

TheMartyGuy wrote:

Your noise analysis seems well thought out. However one needs to also consider spatial correlation between pixels in darker areas of the image due to low values on the AD converter. It might happen that shot noise between pixels keeps a low AD output at the same count over a spatial region. This spatially correlated noise can cause posterization in darker areas of the image.

As I understand it, the noise floor in 14-bit DSLR systems is sufficient to correctly dither the ADC so that posterisation is not an issue with low-level signals. It may be a problem with 12-bit systems.

Dan.

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jonas ar Regular Member • Posts: 398
Visual demo
2

I was discussing the concept of ISOlessness in another forum recently. A guy gave the advice to ETTR at high ISOs (because it will give lower noise) and I proposed it would be better shooting the same exposure at a lower ISO and adjusting the brightness in post processing. The specific subject was photography during surgical procedures, and I had some prior experience from a planned C-section where i completely screwed an otherwise great Kodak moment with blown highlights:

Since my advice was not well received, I created a little visual demonstration to illustrate:

This is ISO3200, f/2.4, 1/125:

This is the same exposure (f/2.4, 1/125) at ISO400:

And finally, the same exposure at ISO400 with adjusted brightness and compressed highlights. This was using Adobe lightroom and very quick adjustments:

Sony a900 by the way. I wish I had used a lower ISO in the first image.

Kind regards,

Jonas

John Sheehy Forum Pro • Posts: 19,131
Re: Posterization might be a problem

TheMartyGuy wrote:

Your noise analysis seems well thought out. However one needs to also consider spatial correlation between pixels in darker areas of the image due to low values on the AD converter. It might happen that shot noise between pixels keeps a low AD output at the same count over a spatial region. This spatially correlated noise can cause posterization in darker areas of the image.

If you have the time, can you address this issue? Thanks.

Shot noise in and of itself never causes posterization, except for zero populations, which are obviously going to be contiguous over large areas when the mean signal is much less than 1.  This isn't really an artifact, though; it is the reality that no photons were recorded there.

If the DN represents a scale of multiple photons, however, you could have posterization from the ADC, but in reality, it takes so little read noise to completely dither it that it isn't an issue (nor will you ever have large contiguous areas of zero/black, unless the firmware black-clips the digitized data well above mean black).

John Sheehy Forum Pro • Posts: 19,131
Re: Posterization might be a problem

dosdan wrote:

TheMartyGuy wrote:

Your noise analysis seems well thought out. However one needs to also consider spatial correlation between pixels in darker areas of the image due to low values on the AD converter. It might happen that shot noise between pixels keeps a low AD output at the same count over a spatial region. This spatially correlated noise can cause posterization in darker areas of the image.

As I understand it, the noise floor in 14-bit DSLR systems is sufficient to correctly dither the ADC so that posterisation is not an issue with low-level signals. It may be a problem with 12-bit systems.

There are a small number of 12-bit DSLRs with slightly posterized near-blacks at base-ISO, such as the Sony A900, the Nikon D300; mostly cameras that were still using 12 bits as the read noise got to new low levels.  Fortunately, this generally only affects the first few ADU above black, and this has absolutely no effect at higher levels.  For high DR scenes, there is usually enough flare for scene black to be a couple ADU, losing most of the posterized range in actual use, but for an "under-exposure", it could be an issue.

John Sheehy Forum Pro • Posts: 19,131
Re: So far as I'm aware...

Detail Man wrote:

Great Bustard wrote:

Have done some reading, and yes, it seems that you are correct. Also, the Poisson distribution seems to be considered to begin to fairly closely approach a Gaussian distribution when the Mean is on the order of 10 or so - which is not all that large of a number. So, if we can convince ourselves that these sources are indeed truly uncorrelated (covariance=0), it works.

It is reasonable to assume no correlation between the shot noise and the read noise, because one is signal dependent and the other is completely independent.

Read noise is very correlated, spatially, within itself, however.  The correlated components are weak, statistically, as a monolithic standard deviation, but can be quite strong visibly, as it exists in lower frequencies and in patterns and shapes.

Actually, 12 is the threshold where most Poisson generators switch to Gaussian for speed's sake (based on _Numerical Recipes in C_), and just to be safe, I have used higher values.

John Sheehy Forum Pro • Posts: 19,131
Re: Visual demo
2

jonas ar wrote:

I was discussing the concept of ISOlessness in another forum recently. A guy gave the advice to ETTR at high ISOs (because it will give lower noise) and I proposed it would be better shooting the same exposure at a lower ISO and adjusting the brightness in post processing.

Since my advice was not well received, I created a little visual demonstration to illustrate:

People get trapped into that way of thinking, because they can not get rid of the notion that the ISO setting on the camera is the Exposure Index.  So, when they see good results at ISO 3200 with ETTR, they see it as a very good 3200, not the 1600 or 1250 or 1047.39 that it really is.

gollywop
gollywop Veteran Member • Posts: 8,237
Re: Noise Performance in an ISOless System

dosdan wrote:

I was computing the 16x value (total read noise, input-referenced, at ISO100 vs ISO1600) incorrectly. It does not make a great difference to the results. I'll use the sensorgen total read noise values. Measurement & curve-fit blips will affect these values (I think the 7D is affected), but the groupings are still similar.

K-5:
1.8x

60D:
4.6x

550D
4.5x

7D
2.5x

A77
1.6x

D5200
1.6x

D600
2x

D800
0.9x

D4
8.1x

5D III
8.5x

1D X
10.9x

Dan.

Whew, Dan, thanks for this.  I was going nuts trying to figure out how you were getting your figures in the OP.

By the way, let me take this opportunity to thank you for a fantastic post.  I hope you won't mind my including a link to it and some paraphrasing from it in the revision of Exposure vs. Brightening that I am undertaking now.

This brings together all the related strings to this topic from many directions. I have been looking for a source like this for some time.  Beautiful job.

-- hide signature --

gollywop

gollywop
gollywop Veteran Member • Posts: 8,237
Re: Noise Performance in an ISOless System

dosdan wrote:

The PGA (Programmable Gain Amplifier) is used to apply stepped amounts of analogue gain (increasing the ISO sensitivity) when the signal from the sensor is weak i.e. the exposure level is low. In this discussion, I'll generally omit its noise contribution. You would hope that an amp used to reduce the total noise level was of a low-noise design itself. Some of the PGA noise will come from the input stage of the PGA, and therefore increase as you boost the analogue gain. Another part of the PGA noise will come from the output stage, so it will be of a constant level and not affected by analogue gain changes.

Dan, as I said in my post above, this is a fantastic piece.  Many thanks for taking the trouble to put it together.

One very small suggestion relative to the above: when you say you'll "omit its noise contribution," I found a moment's ambiguity in determining whether the "its" referred to the PGA or the sensor.  The wrong resolution to that ambiguity clearly leads to problems in interpretation.

-- hide signature --

gollywop

Jack Hogan Veteran Member • Posts: 6,154
Re: Noise Performance in an ISOless System

dosdan wrote:

The disadvantage for the raw shooter is that the review image is darkish.

Excellent thread Dan. A couple more disadvantages are that one needs a well-behaved raw converter and zero blocking.

Apparently many raw-converters treat data differently depending on ISO. LR/ACR's treatment is anything but flat, for instance. So careful with that for extreme brightness corrections.

And as John mentioned, some cameras (e.g. most Nikons) do not bias their ADC, which means that the histogram of noise around zero is asymmetrical - it's blocked at zero level. Which means that when you pull brightness up digitally you end up with a 'hard' noise floor in the shadows, as opposed to a 'soft' one with cameras that bias the ADC. However, I have looked at many images thus recovered compared to ones of the same scene taken at 'classic' ISOs, and

1. It's mostly very hard to see a difference; and if one does see it
2. It's not clear what image would be preferable to the other.

So yes, set ISO for most information captured.

Jack

Allan Olesen Veteran Member • Posts: 3,391
Re: Noise Performance in an ISOless System
1

Tom Axford wrote:

dosdan wrote:

The disadvantage for the raw shooter is that the review image is darkish. But if cameras & raw file formats were set up to accommodate this type of operation, the review image need not be darkish at all. As the relative contribution of ADC read noise to the total read noise keeps decreasing, it is rather frustrating to see that no manufacturer has yet offered this mode.

Agree completely. Let's hope the manufacturers are listening.

It seems to me that Fuji has already listened - partially. Or perhaps I am just misinterpreting what I see at dxomark.com.

Look at the ISO Sensitivity measurements for the Fuji X100 here:

http://www.dxomark.com/index.php/Cameras/Compare-Camera-Sensors/Compare-cameras-side-by-side/%28appareil1%29/695|0/%28brand%29/Fujifilm

The measured ISO for camera ISO 1600, 3200 and 6400 is the same. Since dxomark's ISO definition is based on highlight headrom, we can conclude that these 3 ISO settings all have the same highlight headroom.

This leads me to believe that above ISO 1600 this camera does not use any additional gain, neither analogue gain nor digital gain. Instead I assume that the raw files have some embedded metadata telling the raw converter to make a +1 or +2 EV correction behind the scenes when treating a photo taken at ISO 3200 or 6400. Can anyone confirm this?

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