Albert, I think also the photon shot noise should be added in the DR calculation. If the noise at dark is 4e and the saturation signal is 4ke, one would define the DR=60dB. At 4 electrons signal level (same as noise level) there are 2e of photon shot noise which will further lower the real DR value.
Hi anonymous, be careful. You refer much more to the signal-to-noise ratio than to DR. I will have a post about SNR as well in a few days. BTW : putting the definition of DR in my blog does NOT mean that I am happy with this definition. But it is simply the definition that I find back in many data sheets.
Albert, I know the difference between SNR and DR :). We simplify DR as the maximum detectable signal over the minimum detectable signal. If minimum detectable signal is 4e- (electronic noise at dark) then we expect to be able to detect signals >=4e-, right? If the pixel delivers 4e- we will not detect those as the signal will add photon shot noise (2 extra electrons). Now the minimum detectable signal becomes ~5e- and DR becomes 4ke-/5e- which is the real DR of the sensor.
When you say "detect" how does your detector work? Do you measure a signal crossing some threshold to decide that the signal has been detected? Something like 4e- threshold in your example?
Vladimir, for me a signal is detectable if SNR>=0db. If noise floor at dark is 4e and signal is 4e, SNR is NOT 0dB. You have to add the photon shot noise to the expression. Seems like also Erik adds the photon shot noise in the DR definition.
Sorry, I do not understand your statement "a signal is detectable." It's very hard to discuss this matter without looking at how exactly the signal is detected.
Your dynamic range, as far as I have learned is called the "intra-scene dynamic range", which never is available in one pixel, it is always referring to the maximum contrast you could distinguish within an image. I know that this is the dynamic range given by image sensor or camera manufacturers. The dynamic range of a pixel is more the maximum SNR in a pixel, and this is always smaller, than the dynamic range within the image.
"The dynamic range of a pixel is more the maximum SNR in a pixel, and this is always smaller, than the dynamic range within the image."
I don't think so.
Maximum SNR depends on full well capacity. Read noise (or shot noise) determines the lower end. Both are needed to determine DR.
Also, I think image DR is limited by pixel DR. If you are thinking binning improves image DR, then you need to use a binned pixel DR as the basic building block.
Albert is correct in providing a historically-correct definition of DR.
With deep sub-electron read noise sensors, and non-linear response, I have adopted a different definition of DR since the old definition is not as useful.
DR is the ratio of the light level when the light-referred SNR is unity at the high end (due to saturation) to that of the light level when the light-referred SNR is unity at the low end. In this case photon shot noise is included in the total noise.
I would like to suggest that DR can be defined as the ratio between the saturation level and the level to get a certain useful SNR, say 20dB. In this way, the DR will give the light variation tolerance in real pratical use.
So, instead of say 0dB you want 20dB SNR at the low end? I am not sure I see a big advantage here. I agree the xdB is arbitrary and certainly we can perceive objects when the SNR < 0dB. But I think we might as well stick with the historical* 0dB. You can then always adjust +/- in your head depending on the application requirements.
Well, I don't see how you can define 0dB on the high light side of the response. That is why I changed a little bit in my suggestion. I agree with you that the SNR at low light side is arbitrary. -yang ni
Light-referred SNR is the key for the high end (and low end). At ideal saturation, for example, there is still noise. The amount of noise-equivalent illumination is very large, because you are in saturation. That means you need a lot of light to get a small increase in output equivalent to the noise. The light-referred SNR easily drops below 0 dB. If you don't use light-referred SNR, then SNR seems to grow in saturation (noise goes to a small value while signal remains at saturation). You know this is not informationally correct. Using light-referred SNR solves this artificial anomaly and is more in line with what really happens.
Albert & Eric's DR definitions look like focusing on pixel performance, in my thinking. Those are very useful when looking at pixel characterization. but, user cannot see that dynamic range level at the practical scene. So, in my case, I have used several DR definitions, but roughly 2 groups. one is intrascene DR, and the other is interscene DR. The reason I'm using several DR is why there is many factors which can interrupt the incident light toward pixel through shifted CFA/ML, even different F# lens. DR definitions when pixel characterization normally doesn't handle those factor but those make the light disturbance and randomly or aliased more noisy situation, so commercial image sensor chip is hardly showing the DR value from datasheet, I think.
The photography community has many discussions on photographic DR which is image-centric, not pixel-centric, and where the lens is also important. From a sensor technologists point of view (in the Image Sensors World) we have to consider only the pixel. The results of our measurements listed in a datasheet should be reproducible by others. Pixel DR is an upper limit for photographic DR, if they are defined similarly.
Anonymous, you make a big mistake here. The shot noise is part of the signal, if a signal having 4e in average, then its amplitude will be changing around this value according to Poisson's law. This means that you can detect or not detect it in this case. The photon shot noise will come into consideration when you want to detect a contrast in an image, in this case, you need to effectively add two noises together.
in EMVA1288, the DR is specified including shot noise but again differently.
It assumes that the upper limit is the light intensity required to make the photon-transfer-curve decrease, i.e. the number of pixels saturating due to the tail of the shot noise distribution becomes statistically significant.
Good to know Arnaud! The definition of Albert does not include shot noise at the dark limit and that becomes a major limitation of the definition as the dark noise reduces (e.g. < 1e). I know his definition is the commonly known one, but might be time to change that?
Albert, I think also the photon shot noise should be added in the DR calculation. If the noise at dark is 4e and the saturation signal is 4ke, one would define the DR=60dB. At 4 electrons signal level (same as noise level) there are 2e of photon shot noise which will further lower the real DR value.
ReplyDeleteHi anonymous, be careful. You refer much more to the signal-to-noise ratio than to DR. I will have a post about SNR as well in a few days.
DeleteBTW : putting the definition of DR in my blog does NOT mean that I am happy with this definition. But it is simply the definition that I find back in many data sheets.
Albert, I know the difference between SNR and DR :). We simplify DR as the maximum detectable signal over the minimum detectable signal. If minimum detectable signal is 4e- (electronic noise at dark) then we expect to be able to detect signals >=4e-, right? If the pixel delivers 4e- we will not detect those as the signal will add photon shot noise (2 extra electrons). Now the minimum detectable signal becomes ~5e- and DR becomes 4ke-/5e- which is the real DR of the sensor.
DeleteWhen you say "detect" how does your detector work? Do you measure a signal crossing some threshold to decide that the signal has been detected? Something like 4e- threshold in your example?
DeleteVladimir, for me a signal is detectable if SNR>=0db. If noise floor at dark is 4e and signal is 4e, SNR is NOT 0dB. You have to add the photon shot noise to the expression. Seems like also Erik adds the photon shot noise in the DR definition.
DeleteSorry, I do not understand your statement "a signal is detectable." It's very hard to discuss this matter without looking at how exactly the signal is detected.
DeleteYour dynamic range, as far as I have learned is called the "intra-scene dynamic range", which never is available in one pixel, it is always referring to the maximum contrast you could distinguish within an image. I know that this is the dynamic range given by image sensor or camera manufacturers.
DeleteThe dynamic range of a pixel is more the maximum SNR in a pixel, and this is always smaller, than the dynamic range within the image.
"The dynamic range of a pixel is more the maximum SNR in a pixel, and this is always smaller, than the dynamic range within the image."
DeleteI don't think so.
Maximum SNR depends on full well capacity. Read noise (or shot noise) determines the lower end. Both are needed to determine DR.
Also, I think image DR is limited by pixel DR. If you are thinking binning improves image DR, then you need to use a binned pixel DR as the basic building block.
Albert is correct in providing a historically-correct definition of DR.
ReplyDeleteWith deep sub-electron read noise sensors, and non-linear response, I have adopted a different definition of DR since the old definition is not as useful.
DR is the ratio of the light level when the light-referred SNR is unity at the high end (due to saturation) to that of the light level when the light-referred SNR is unity at the low end. In this case photon shot noise is included in the total noise.
I would like to suggest that DR can be defined as the ratio between the saturation level and the level to get a certain useful SNR, say 20dB. In this way, the DR will give the light variation tolerance in real pratical use.
Delete-yang ni
So, instead of say 0dB you want 20dB SNR at the low end? I am not sure I see a big advantage here. I agree the xdB is arbitrary and certainly we can perceive objects when the SNR < 0dB. But I think we might as well stick with the historical* 0dB. You can then always adjust +/- in your head depending on the application requirements.
Delete*0dB when the old read noise was ~ >10e- rms
Well, I don't see how you can define 0dB on the high light side of the response. That is why I changed a little bit in my suggestion. I agree with you that the SNR at low light side is arbitrary.
Delete-yang ni
Light-referred SNR is the key for the high end (and low end). At ideal saturation, for example, there is still noise. The amount of noise-equivalent illumination is very large, because you are in saturation. That means you need a lot of light to get a small increase in output equivalent to the noise. The light-referred SNR easily drops below 0 dB. If you don't use light-referred SNR, then SNR seems to grow in saturation (noise goes to a small value while signal remains at saturation). You know this is not informationally correct. Using light-referred SNR solves this artificial anomaly and is more in line with what really happens.
DeleteAlbert & Eric's DR definitions look like focusing on pixel performance, in my thinking. Those are very useful when looking at pixel characterization. but, user cannot see that dynamic range level at the practical scene. So, in my case, I have used several DR definitions, but roughly 2 groups. one is intrascene DR, and the other is interscene DR. The reason I'm using several DR is why there is many factors which can interrupt the incident light toward pixel through shifted CFA/ML, even different F# lens. DR definitions when pixel characterization normally doesn't handle those factor but those make the light disturbance and randomly or aliased more noisy situation, so commercial image sensor chip is hardly showing the DR value from datasheet, I think.
ReplyDeleteThe photography community has many discussions on photographic DR which is image-centric, not pixel-centric, and where the lens is also important. From a sensor technologists point of view (in the Image Sensors World) we have to consider only the pixel. The results of our measurements listed in a datasheet should be reproducible by others. Pixel DR is an upper limit for photographic DR, if they are defined similarly.
DeleteAnonymous, you make a big mistake here. The shot noise is part of the signal, if a signal having 4e in average, then its amplitude will be changing around this value according to Poisson's law. This means that you can detect or not detect it in this case. The photon shot noise will come into consideration when you want to detect a contrast in an image, in this case, you need to effectively add two noises together.
ReplyDelete-yang ni
Hi all,
ReplyDeletein EMVA1288, the DR is specified including shot noise but again differently.
It assumes that the upper limit is the light intensity required to make the photon-transfer-curve decrease, i.e. the number of pixels saturating due to the tail of the shot noise distribution becomes statistically significant.
Arnaud.
This is one way of defining the saturation level. But it has nothing to do with the denominator of the DR-definition that holds the noise level(s).
DeleteThe dark limit is an interpolation of the SNR curve until SNR=1. Therefore it includes shot noise.
DeleteGood to know Arnaud! The definition of Albert does not include shot noise at the dark limit and that becomes a major limitation of the definition as the dark noise reduces (e.g. < 1e). I know his definition is the commonly known one, but might be time to change that?
Delete