267 replies to this topic

[sharkmelley]

How can you represent more than 12 bits of data with just 12bits? Maybe all my advanced degrees were a waste, I should just have come and learnt from you.

Yes, but you are limited to 12 bits in the ADC output. In fact in this scenario quantization error will have an impact because you have more dynamic range than you can represent using the ADC. Could lead to posterisation. For faint deep sky objects e.g nebulae this is unlikely to be an issue but if you have bright stars you could see artifacts.

Very few cameras have read noise of less than 1DN, so it can be quite counterintuitive seeing a dynamic range of 12.4EV when the bit depth is 12bits.  However I'm sure with modern CMOS sensors this will become more and more commonplace. So let's see if we can get some intuition on this using a consumer camera as an example.

 

The Olympus OM-D E-M1 Mark II is a consumer camera with a 12bit sensor and read noise of less than 1DN.The read noise is 0.85DN at ISO 200:

https://www.photonst...E-M1 Mark II_12

 

Here is a crop of the raw green channel from DPReview's Exposure Latitude test at ISO 200:

 

 

I measured the read noise in PixInsight and it is definitely 0.85DN. Now dynamic range is the ratio of the brightest and dimmest recordable light intensity.  But in the image above which step on the step wedge should we choose as the dimmest?  By convention we choose the one where the signal-to-noise ratio is 1 - I've marked this one with an arrow.  Equivalently we can simply divide the saturation level by the read noise.  Either way, we end up with a dynamic range of around 12.3EV which is obviously greater than 12.  To the right of the arrowed wedge you can clearly see dimmer steps on the wedge (i.e. a lot dimmer than 1DN) until they become lost in the noise.  So obviously there is a greater range of intensities in the data than suggested by the dynamic range of 12.3EV.  

 

Since we are astronomers, we know we could take multiple exposures of this scene then stack them and stretch the stack to make these dimmer steps on the wedge visible.  You are absolutely right that the ADC is giving us only 12 bits of data.  But the range of signal intensities sitting in the image data is far more than the simplistic assumption of 12EV suggested by those 12bits - they are just obscured by read noise.

 

Mark

Edited by sharkmelley, 26 November 2020 - 06:46 PM.

[Astrojedi]

I am not sure how your response is relevant to the discussion. You also don’t need to explain any of this to me. I understand it very well. I was referring to the discussion above regarding the SharpCap sensor analysis. The reason the output dynamic range is 12 stops even though the sensor is capturing a higher dynamic range is because the ADC is limited to 12 bits. 
 

Also yes, stacking can bring signal over the noise and vastly increase the dynamic range, we all know that here. Nothing new there. You don’t need to produce charts and figures to make that point. But discussion is not about stacking.

Edited by Astrojedi, 26 November 2020 - 06:50 PM.

[Scott Mitchell]

I am not sure how your response is relevant to the discussion. You also don’t need to explain any of this to me. I understand it very well. I was referring to the discussion above regarding the SharpCap sensor analysis. The reason the output dynamic range is 12 stops even though the sensor is capturing a higher dynamic range is because the ADC is limited to 12 bits. 
 

Also yes, stacking can bring signal over the noise and vastly increase the dynamic range, we all know that here. Nothing new there. You don’t need to produce charts and figures to make that point. But discussion is not about stacking.

Wow, I actually appreciated the explanation, and I don't think it was done in any sort of condescending way. Thanks for the explanation Mark.

[Astrojedi]

No one is saying it is not a good explanation but it does not address the discussion. You simply cannot achieve more than 12 stops of dynamic range in a single exposure with a 12 bit ADC. Saying otherwise absolutely false. I was just answering the question above on the SharpCap sensor analysis when Mark decided to jump in educate us.

Edited by Astrojedi, 26 November 2020 - 08:08 PM.

[sharkmelley]

No one is saying it is not a good explanation but it does not address the discussion. You simply cannot achieve more than 12 stops of dynamic range in a single exposure with a 12 bit ADC. Saying otherwise absolutely false.

Yes you can achieve more than 12 stops of dynamic range in a single exposure with a 12 bit ADC and my explanation attempted to show how.  

 

Mark

[Astrojedi]

Yes you can achieve more than 12 stops of dynamic range in a single exposure with a 12 bit ADC and my explanation attempted to show how.  

 

Mark

 

Ok I see what you mean... 12 stops of brightness but that does not represent dynamic range alone. An extreme example... by that logic I can use 1 bit to represent any n number of stops with 0 representing the lowest brightness level and 1 representing the highest brightness level... let’s say 13 stops or 14 stops brighter. But this does not mean that you are representing 13 or 14 stops of dynamic range. The number of levels matter.

[Dimperev]

If we are talking about one pixel, then yes, with 12 bits we have 12 degrees of brightness.
If we consider a 4x4 bit pad, then with 12 bits of each pixel we can get 65535 steps of brightness and a depth of 16 bits of brightness.
That is, to increase the depth of brightness, we can integrate several pixels, of course with a loss of resolution. Or we can add a stack of several frames (as everyone knows).
In theory, only random reading noise will act as a limitation. For example, if we quantize the signal with a 12-bit ADC with an error of 0.1 bit, then in the end we can achieve a brightness depth of more than 15 bits.
In my opinion, in practice, the sky noise will act as a limitation.

[sharkmelley]

Ok I see what you mean... 12 stops of brightness but that does not represent dynamic range alone. An extreme example... by that logic I can use 1 bit to represent any n number of stops with 0 representing the lowest brightness level and 1 representing the highest brightness level... let’s say 13 stops or 14 stops brighter. But this does not mean that you are representing 13 or 14 stops of dynamic range. The number of levels matter.

That's right, 1 bit can be used to represent a large range of brightnesses. Jack Hogan muses on that fact here:

https://www.strollsw...-and-bit-depth/

 

So it's important not to confuse dynamic range (technically called engineering dynamic range) with bit depth.  Signal levels lower than 1 least significant bit (LSB) of the ADC can certainly be detected and seen in an image, as the real world example of the step wedge using the Olympus camera in post #605 demonstrates.  However, as you say, it is preferable to have a few more bits to encode those extremely low signal levels. 

 

Emil Martinec has some great examples in his article here:

http://theory.uchica...3.html#bitdepth

He shows how the noise dithers the discrete steps in the quantization to allow a continuum of brightness to be represented and he also addresses the posterization issue, which is something you hinted at earlier.

 

Mark

Edited by sharkmelley, 27 November 2020 - 04:38 AM.

[Astrojedi]

That's right, 1 bit can be used to represent a large range of brightnesses. Jack Hogan muses on that fact here:

https://www.strollsw...-and-bit-depth/

 

So it's important not to confuse dynamic range (technically called engineering dynamic range) with bit depth.  Signal levels lower than 1 least significant bit (LSB) of the ADC can certainly be detected and seen in an image, as the real world example of the step wedge using the Olympus camera in post #605 demonstrates.  However, as you say, it is preferable to have a few more bits to encode those extremely low signal levels. 

 

Emil Martinec has some great examples in his article here:

http://theory.uchica...3.html#bitdepth

He shows how the noise dithers the discrete steps in the quantization to allow a continuum of brightness to be represented and he also addresses the posterization issue, which is something you hinted at earlier.

 

Mark

Mark, yes of course you can. The bit is a logical construct and can represent any piece of information. That is my point. That is not dynamic range alone when we talk about imaging. If that was the case you could just build a sensor with a 1 bit ADC - why bother with 12bits or 16 bits. I could easily design an ADC which has very coarse gain. But the key point is that the analog information gets quantized so ultimately you can only represent 12 bits of information.

 

My point is different as I am answering the specific question on the SharpCap analysis. You can only represent 12^2 levels using a 12 bit ADC and that matters in a single exposure but is irrelevant when you are stacking (a point I have made many times on these forums). What you are sharing holds true if we stack as the variability will bring that information out. 

 

Also I respect you but you don’t need to educate me on this. I understand all this. My technical background is Information theory and I have designed many ADCs. Please don’t take this the wrong way.

 

Edit: another clarification on this article: www.strollswithmydog.com/dynamic-range-and-bit-depth/

I have seen many junior engineers think this way but this is incorrect. If you are using adjacent pixels to increase dynamic range then you have to include their bit depth in the total bit calculation as well. There is no free lunch here. You are trading spatial information for bit depth. Similar concept to software binning.

Edited by Astrojedi, 27 November 2020 - 12:47 PM.

[sharkmelley]

My point is different as I am answering the specific question on the SharpCap analysis. You can only represent 12^2 levels using a 12 bit ADC and that matters in a single exposure but is irrelevant when you are stacking (a point I have made many times on these forums). What you are sharing holds true if we stack as the variability will bring that information out. 

 

Also I respect you but you don’t need to educate me on this. I understand all this. My technical background is Information theory and I have designed many ADCs. Please don’t take this the wrong way.

 

I don't claim to be an expert and I certainly have never designed an ADC.  But in my mind there is still an outstanding question about the Sharpcap analysis since the column called "dynamic range" is clearly calculated from the ratio of full well capacity to read noise. 

 

In your opinion is that a legitimate way of calculating "dynamic range"?  If so, why is it not permissible to do the same calculation at gain 0, just because the read noise happens to be less than the least significant bit of the ADC?  The resulting figure of 12.38 stops must have some meaning, does it not?

 

Mark

[Astrojedi]

I don't claim to be an expert and I certainly have never designed an ADC.  But in my mind there is still an outstanding question about the Sharpcap analysis since the column called "dynamic range" is clearly calculated from the ratio of full well capacity to read noise. 

 

In your opinion is that a legitimate way of calculating "dynamic range"?  If so, why is it not permissible to do the same calculation at gain 0, just because the read noise happens to be less than the least significant bit of the ADC?  The resulting figure of 12.38 stops must have some meaning, does it not?

 

Mark

Not sure what your point is. Sharpcap seems to be showing the correct dynamic range at gain 0 which is 12 bits. As a very practical matter I am not sure how it can exceed 12 bits. Sharpcap has no way of bypassing the ADC. The ADC performs quantization of the analog signal and it only has 12 bit depth. I know this for a fact from my experience with ADC design. Maybe the ZWO driver is manipulating / stuffing the bits before outputting it as 16 bits to Sharpcap or it may have something to do with how Sharpcap measures / estimates those values. I am not sure.

 

But either way Sharpcap is definitely not using the approach you describe above of using information from adjacent pixels to increase dynamic range beyond the bit depth of the ADC. Actually that is very flawed reasoning for many reasons.

 

Lets take the example of DPReview's Exposure Latitude test that you reference above.

 

1. How many pixels do you need to infer the different levels of gray? In the DPreview image above it is definitely more than 1. Say for example you need at minimum 5x5 pixels (although the image slices seem much larger in the DPReview image). Then you are talking a required bit depth of log (102,400) = 16.64 bits (assuming full dynamic range is being used). If 10x10 then you need 18.64 bits.

 

2. Another reason that DRReview is incredibly flawed (at least for our purposes) is that while imaging I just cannot use such large number of pixels to increase dynamic range (i.e. x5 bin or x10 or whatever slice is being used here). Many small galaxies would fit in that image slice that DPReview is using. It just does not make sense for our purposes.

 

As an aside this is how software binning increases SNR and dynamic range. It is the same process at play.

Edited by Astrojedi, 27 November 2020 - 09:56 PM.

[sharkmelley]

Not sure what your point is. Sharpcap seems to be showing the correct dynamic range at gain 0 which is 12 bits. As a very practical matter I am not sure how it can exceed 12 bits. Sharpcap has no way of bypassing the ADC. The ADC performs quantization of the analog signal and it only has 12 bit depth. I know this for a fact from my experience with ADC design. Maybe the ZWO driver is manipulating / stuffing the bits before outputting it as 16 bits to Sharpcap or it may have something to do with how Sharpcap measures / estimates those values. I am not sure.

 

But either way Sharpcap is definitely not using the approach you describe above of using information from adjacent pixels to increase dynamic range beyond the bit depth of the ADC. Actually that is very flawed reasoning for many reasons.

 

 

In post #584 it can be clearly seen that Sharpcap is calculating the sensor gain, sensor read noise and full well using image data. It then calculates dynamic range by dividing full well by read noise and converting to photographic stops:

 

dynamic_range(stops) = log(full_well/read_noise)/log(2)

 

The above formula is no doubt based on the ISO 15739 definition of dynamic range, which is the ratio of the maximum luminance to the lowest luminance for which the SNR is at least 1.0  For the avoidance of any doubt, it's obvious that the calculation of noise will require multiple pixel values.

 

You seem to think that the gain 0 calculated dynamic range of 12.38 has no meaning because it exceeds the 12bit of the ADC.  On the other hand I think it provides useful information and it's a pity Sharpcap suppresses the result of this calculation, especially since it separately reports "Measured Sensor Bit Depth" as 12.

 

For what it's worth, if you take the example Olympus OM-D E-M1 Mark II camera that I used earlier, which also has read noise less than the least significant bit of the ADC, DXOMark happily reports dynamic range figures higher than the 12bits of the ADC - click on the "Dynamic Range" tab here:

https://www.dxomark....---Measurements

 

We obviously won't come to agreement on this so let's not discuss it further.  In the end it's just a minor technical detail that won't affect imaging.  Any reader sufficiently interested in dynamic range can read the arguments and evidence on both sides of the discussion and can come to their own conclusions. 

 

Mark

Edited by sharkmelley, 28 November 2020 - 07:34 AM.

[Astrojedi]

Mark,

 

We know for a fact that the 12 bit ADC cannot output more than 4096 levels in a single exposure for a single pixel. Do we agree on this?

 

The sensor can be capable of a much larger dynamic range than the ADC can handle. This is not uncommon and is what the SharpCap analysis is suggesting to me.

 

To take advantage of that you can bin the output or stack subexposures.

Edited by Astrojedi, 28 November 2020 - 11:35 AM.

[Astrojedi]

Once we agree on the above I will now layer in some additional complexity.

 

The read noise value you see from the SharpCap analysis is an RMS value averaged over the full sensor. Unlike CCD, in CMOS each pixel has its own readout architecture so read noise varies from pixel to pixel. When you average that and the levels across the sensor you can come up with a dynamic range that potentially looks like it exceeds the ADC bit depth but that is not a correct interpretation.

 

At any single pixel the bit depth cannot exceed 12 bits or 12 stops. If read noise varies across adjacent pixels (likely in CMOS) you can SW bin to create a super pixel which has much higher dynamic range. A secondary impact (or primary depending on how you look at it) that SW binning has is that it also averages out the shot noise. I have seen increases of as much as 2x in SNR from SW binning.

Edited by Astrojedi, 28 November 2020 - 12:04 PM.

[Astrojedi]

Everyone, I am following this discussion with great interest, since I have a 294mm on the way. I have been shooting with a 294MC pro for the last year, so I am already used to the 4.63um Pixel size. I image with several different telescopes ranging from about 250mm focal length up to 1280mm. I have really enjoyed the 294mc pro, and look forward to the mono version.
But here is my question. Under what circumstances would it be a good idea to use the unlocked bin 1 mode with the smaller pixels? What is a good use case for that mode, as opposed to using the 4.63um bin 2 mode? I would appreciate your practical feedback on that. Thanks.

Chris

Chris,

The unlocked x1 bin mode makes the most sense with small refractors or lenses when you want to maximize resolution. The only caveat is that the optical quality of the scope / lens should be sufficient to deal with the resolution.

[Astrojedi]

In post #584 it can be clearly seen that Sharpcap is calculating the sensor gain, sensor read noise and full well using image data. It then calculates dynamic range by dividing full well by read noise and converting to photographic stops:

 

dynamic_range(stops) = log(full_well/read_noise)/log(2)

 

The above formula is no doubt based on the ISO 15739 definition of dynamic range, which is the ratio of the maximum luminance to the lowest luminance for which the SNR is at least 1.0  For the avoidance of any doubt, it's obvious that the calculation of noise will require multiple pixel values.

 

You seem to think that the gain 0 calculated dynamic range of 12.38 has no meaning because it exceeds the 12bit of the ADC.  On the other hand I think it provides useful information and it's a pity Sharpcap suppresses the result of this calculation, especially since it separately reports "Measured Sensor Bit Depth" as 12.

 

For what it's worth, if you take the example Olympus OM-D E-M1 Mark II camera that I used earlier, which also has read noise less than the least significant bit of the ADC, DXOMark happily reports dynamic range figures higher than the 12bits of the ADC - click on the "Dynamic Range" tab here:

https://www.dxomark....---Measurements

 

We obviously won't come to agreement on this so let's not discuss it further.  In the end it's just a minor technical detail that won't affect imaging.  Any reader sufficiently interested in dynamic range can read the arguments and evidence on both sides of the discussion and can come to their own conclusions. 

 

Mark

Hopefully my earlier post clarifies the error in this post. You are using read noise averaged over the entire sensor to argue for dynamic range at one pixel. Your argument misses the point that in CMOS read noise can vary across pixels hence you should not use RMS values for this calculation. SharpCap is actually correctly showing 12 bit of dynamic range. Propagating incorrect science does not help anyone on these forums. 

Edited by Astrojedi, 30 November 2020 - 11:35 AM.

[sharkmelley]

Hopefully my earlier post clarifies the error in this post. You are using read noise averaged over the entire sensor to argue for dynamic range at one pixel. Your argument misses the point that in CMOS read noise can vary across pixels hence you should not use RMS values for this calculation. SharpCap is actually correctly showing 12 bit of dynamic range. Propagating incorrect science does not help anyone on these forums. 

No, there was no error in that post but you do raise an interesting point. 

 

Certainly there are pixel to pixel variations which will affect the estimate of read noise obtained as an RMS across multiple pixels.  An alternative is to estimate the read noise of an individual pixel by taking the RMS of the value of that individual pixel over multiple exposures. But for approximately half the pixels this will result in a lower estimate of read noise (hence higher dynamic range).

 

Mark

Edited by sharkmelley, 30 November 2020 - 02:23 PM.

[Astrojedi]

No, there was no error in that post but you do raise an interesting point. 

 

Certainly there are pixel to pixel variations which will affect the estimate of read noise obtained as an RMS across multiple pixels.  An alternative is to estimate the read noise of an individual pixel by taking the RMS of the value of that individual pixel over multiple exposures. But for approximately half the pixels this will result in a lower estimate of read noise (hence higher dynamic range).

 

Mark

"Error" in the sense you did not consider the variation in read noise.

 

Also just to clarify and summarize, you are not wrong in that a larger dynamic range is possible with a 12 bit sensor but you have to either bin adjacent pixels (for a single exposure) or stack multiple exposures to achieve it. At each pixel you cannot exceed the bit depth of the ADC. it is a physical impossibility. If you think otherwise I would like to understand how (the examples you have presented so far involve including information from adjacent pixels).

[sharkmelley]

Also just to clarify and summarize, you are not wrong in that a larger dynamic range is possible with a 12 bit sensor but you have to either bin adjacent pixels (for a single exposure) or stack multiple exposures to achieve it. 

The usual definition of dynamic range for a digital sensor simply divides the max signal level by the read noise. It's obvious that a noise estimate relies on multiple pixel values (either values from adjacent pixels or multiple values from one pixel).  Also, if the noise estimate is less the the least significant bit of the ADC then the dynamic range (measured in stops) will be larger than the ADC bit depth.  No binning or stacking is required for this to be the case.

 

But I'm simply repeating myself, which is a waste of time really. 

 

Mark

Edited by sharkmelley, 30 November 2020 - 06:50 PM.

[Astrojedi]

The usual definition of dynamic range for a digital sensor simply divides the max signal level by the read noise. It's obvious that a noise estimate relies on multiple pixel values (either values from adjacent pixels or multiple values from one pixel).  Also, if the noise estimate is less the the least significant bit of the ADC then the dynamic range (measured in stops) will be larger than the bit depth.  No binning or stacking is required.

 

Mark

 

Mark,

 

Ok we seem to be going around in circles here. Couple points which may clarify this.

 

1) Formulas are only as good as the assumptions otherwise it is just math not physics. Why are you relying on other pixels for read noise estimate of a single pixel? It is definitely not obvious to me. If you do that you have to combine the signal as well which means you are effectively binning the pixels.

 

2) With regards to the sensor dynamic range exceeding the ADC, I have already addressed this multiple times but lets discuss it once more here. Yes, the sensor can exceed the dynamic range of the ADC but final output will always be constrained by the ADC otherwise why bother with 16bit or even 12bit ADCs.

 

If according to you Sharpcap is wrong and it should show 12.38 bits / stops that implies 5315 levels of brightness. I think what you are saying is that of this level 0 is mapped to level 0 of the ADC and level 5315 is mapped to level 4096 of the ADC output. So in fact you have that full brightness range in the output even though the ADC is outputting only 4096 levels.

 

If so, this is incorrect as dynamic range being measured here is not just the highest and lowest values but also the granularity of the representation otherwise all you would need is a 1 bit ADC and you map level 0 of brightness to level 0 of the ADC and level 5315 of brightness to level 1 of the ADC and voila! you have fantastic dynamic range.

 

Obviously that makes no sense and is not really a useful analysis.

Edited by Astrojedi, 30 November 2020 - 07:16 PM.

[brian_a_paden]

2^12 not 12^2.

[Dimperev]

Maybe this discussion goes a little in circles due to imprecise wording?
When we say read noise or RMS, it is both the sum of the ADC errors and the quantization error.
If we consider an ideal ADC, then we can have a maximum signal of 4095 ADU with an error of + - 0.5 ADU.
If we do not consider the distribution law, this gives the ratio of the signal magnitude to the error 2 to the power of 13.
This is the limit of 12-bit quantization, since the sampling error is not equal to 1 ADU, but + - 0.5 ADU.
Or am I misunderstanding?

[Astrojedi]

Maybe this discussion goes a little in circles due to imprecise wording?
When we say read noise or RMS, it is both the sum of the ADC errors and the quantization error.
If we consider an ideal ADC, then we can have a maximum signal of 4095 ADU with an error of + - 0.5 ADU.
If we do not consider the distribution law, this gives the ratio of the signal magnitude to the error 2 to the power of 13.
This is the limit of 12-bit quantization, since the sampling error is not equal to 1 ADU, but + - 0.5 ADU.
Or am I misunderstanding?

Each individual pixel in a single exposure is still limited to 2^12 or 4096 levels. Pretty much the definition of quantization. The ADC has to decide to round up or down for the lowest bit as it can only be 1 or 0.

Edited by Astrojedi, 30 November 2020 - 11:46 PM.

[sharkmelley]

If we consider an ideal ADC, then we can have a maximum signal of 4095 ADU with an error of + - 0.5 ADU.

That's right.  With a maximum error of 0.5 ADU an ideal ADC has an RMS noise of 1/sqrt(12).

 

This in turn means an ideal 12bit ADC has a dynamic range of 13.8 stops since log(4096*sqrt(12))/log(2) = 13.8

 

Mark

 

[Edit: fixed calculation to 12bits instead of 14bits]

Edited by sharkmelley, 01 December 2020 - 03:01 AM.

[Astrojedi]

That's right.  With a maximum error of 0.5 ADU an ideal ADC has an RMS noise of 1/sqrt(12).

 

This in turn means an ideal 12bit ADC has a dynamic range of 13.8 stops since log(4096*sqrt(12))/log(2) = 13.8

 

Mark

 

[Edit: fixed calculation to 12bits instead of 14bits]

But not in a single exposure and at a single pixel. That will always be limited to 12 bits. If you stack multiple exposures or bin pixels you can take advantage of this variability. The ADC cannot output half bits. All output is quantized 1 or 0.

 

At this point I feel this is a waste of time. At least I tried.

Edited by Astrojedi, 01 December 2020 - 09:43 PM.