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Photon Noise, Dark Noise, Read Noise…, Confused?

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#26 Jon Rista

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Posted 17 December 2014 - 02:20 AM

Dark current happens always, light or no light. Photons can be striking the pixels or not, dark current will accumulate regardless...but I think it is misleading to say that it occurs when no photons are present.

 

Fixed pattern noise usually refers to the hot and cold pixel pattern that is actually revealed by the accumulation of both dark current and photons over longer exposures (or highly amplified exposures at very high ISO.) It's fixed because it arises due to physical traits of the silicon itself, slightly differing response to dark current. 

 

Banding is a form of structured, but not necessarily patterned, noise. It has structure, often semi-random, in that the bands may occur in the same place across frames, but are not guaranteed to occur in the same place across frames (or occur at all for a given set of frames.) Banding can present in a variety of ways as well. For example, a 300-frame master bias from a 7D presents a very pronounced 8-column wide vertical banding structure, which corresponds with the 8 readout channels. Banding can also be much softer, spanning multiple columns, although which columns are affected can be random from frame to frame. So...structured, but not necessarily a *fixed* pattern.

 

Banding could be caused by external interference...possibly because the electronics of the camera itself are not properly shielded.

 

There are other forms of noise. Salt and pepper noise, for example (a problem that occurred on the 5D II), appears like hot and cold pixels, but it is effectively a random distribution of white and black pixels. The distribution may not be the same frame to frame, and it is not a thermal signal, so sigma clipping is the only real means of eliminating it.



#27 freestar8n

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Posted 17 December 2014 - 12:36 PM

I'd just say that fixed pattern noise is any variation in pixel behavior that is roughly constant from exposure to exposure. This can happen in the bias, the darks, and the flats. You can also have moving pattern noise such as bands that are moving along. Even though that isn't fixed, it is the same basic pattern and it can be estimated and subtracted in each frame to reduce the noise.

With a fixed pattern, you can accumulate many exposures to get a good measurement of the pattern so you can remove it from the lights. Any time you create a master frame it is for the purpose of measuring pattern noise - in the bias, dark, or flat. If the bias was just a uniform image with a single mean pixel value plus Gaussian noise, then you could replace the master bias with a constant image at that mean value. But instead the bias offset varies at each pixel - so you create a master bias to capture that pattern.

Flats are different because they involve vignetting and dust motes - which isn't really pattern noise in the sensor - but it does repeat across exposures. But flats also capture pixel response non-uniformity - PRNU - and that is definitely a form of pattern noise.

As for dark current noise - that is somewhat ambiguous because dark current produces fixed pattern noise due to the variation in dark current *signal* across the pixels - and dark current also results in shot noise in each pixel. So there is dark current pattern noise - removed by subtracting the master dark - while the dark current shot noise remains and cannot be subtracted. The only way that shot noise term is dealt with is by accumulating many exposures to increase SNR.

So I wouldn't say dark current noise is a form of shot noise - but dark current shot noise is a form of shot noise.

With sony ccd's the dark current is very uniform and small except for a few hot pixels. If the dark current is uniform and has little variation, then there is no benefit in creating a master dark and subtracting the dark current pattern - because there is none.

Frank

#28 Jon Rista

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Posted 17 December 2014 - 02:52 PM

@Frank: 

 

So I wouldn't say dark current noise is a form of shot noise - but dark current shot noise is a form of shot noise.

 

 

Do you mean: "So I wouldn't say dark current is a form of shot noise - but dark current noise is a form of shot noise."?

 

I see it as dark current (the accumulating signal due to leakage current through the photodiodes), dark current noise (the shot noise from the dark current signal), and hot pixels (the fixed pattern noise that results from accumulation of dark current in a pixel over a long period of time, the remnant of which is not subtracted by a bias offset or CDS.)

 

I would also be wary of calling all banding noise fixed pattern. I think there is structured pattern noise and fixed pattern noise. Fixed pattern noise is always the same in every frame and can therefor easily be removed. All forms of banding, however, are NOT necessarily easily removed with a master dark. There are some forms of fixed banding, but also some non-fixed banding. You might be able to mitigate non-fixed banding, but ultimately all you really do is generate a third form of banding when you subtract a master dark from each light. This was exactly the case with my 7D (and to a degree my 5D III)...I was trying to use darks to remove the vertical banding, and it never really did that...all it did was result in a different set of bands that were the outcome of the bands in the dark interfering with the bands in the lights. When the lights were integrated, a fourth final set of bands (the result of the interference of the bands that were left in each calibrated light) were effectively baked into the final image.

 

I have had to use Carboni's vertical banding removal script since I started imaging, as the structured (but not fixed) banding in my cameras was not effectively being managed by darks. Carboni's action, however, is phenomenal. It's the best banding removal I've ever seen, so I'm quite happy with it. But I think there are structured forms of noise, some fixed (hot and cold pixels, banding bias signal) and some not (semi-random or random banding, salt and pepper noise). Darks can fix the former, they care not guaranteed to fix the latter. 


Edited by Jon Rista, 17 December 2014 - 02:55 PM.

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#29 freestar8n

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Posted 17 December 2014 - 03:05 PM

I would not use the term "dark current noise" because it is ambiguous. It could refer to dark current pattern noise, or dark current shot noise. Both are noise terms associated with dark current - but they are very different.

If there is banded noise in an image I would call it pattern noise. If it doesn't move I would call it fixed pattern noise. If it moves I would still call it pattern noise, or moving pattern noise, or dynamic pattern noise. As long as there is structure in the noise that somehow repeats - even if it moves - I would call it pattern noise.

I'm not making these things up - it's how the term is used. If you have fixed banded noise and it doesn't subtract properly then something is either dynamic or nonlinear about how it behaves. But if you can somehow use information gleaned from multiple exposures to model it and subtract it - then that is something to do and it will reduce the noise.

Here is an HST example of moving herring bone pattern in HST images. It contributes moving pattern noise to the image, but it can be modeled *for each light* and subtracted from each light individually - without creating a master frame. It still involves modeling a pattern noise term and subtracting it: http://www.public.as...ster_Letter.pdf

I would distinguish different noise reduction tools by whether or not they actually model the noise term and subtract it - rather than doing some kind of arbitrary fit to the data to remove ugly stuff. In the hst work, they study many frames and deduce what the noise looks like. Then they fit the background in the light to the model of noise they have. Other tools may just be based on heuristics to clean up the image without an explicit model of the noise term - and I think that is different and more akin to smoothing.

Frank
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#30 Jon Rista

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Posted 17 December 2014 - 03:45 PM

I agree, it's all pattern. I was just disputing the universal use of the word "fixed" as applied to banding. Both you and Mike were using it more globally, when not all banding or bright pixel noise is necessarily fixed, meaning just accumulating frames and integrating them into a master dark or bias is not necessarily sufficient to remove those non-fixed patterned noise elements. I just think that fixed should only be used to refer to literally fixed patterns of noise, like hit pixels or bais bands. Structured or paterned or dynamic, all fine with me for any structured noise that is not fixed. :p

 

Any non-fixed patterns need additional means to be removed. Non-fixed banding needs some kind of banding removal process in post. Salt and pepper noise needs sigma clipping. It doesn't matter to me if you model the noise in each frame...my point is simply that mobile forms of noise cannot be simply removed with a master dark or master bias. Additional, possibly more complex, means of removing patterns that change is necessary. Fixed vs...whatever, structured/moving/dynamic. 

 

I understand what your saying as far as dark current noise goes. It was just that your statement about it (the one I quoted) as worded was confusing. I think clearer terms are better, so dark current shot noise and dark current pattern noise or dark current fixed pattern noise (for hot pixels) is all fine with me. To that end, I think the following statement is a little more clear:

 

"So I wouldn't say that dark current noise is itself a form of shot noise, dark current noise can include dark current shot noise (a form of shot noise), dark current fixed pattern noise (a form of fixed pattern noise), etc."


Edited by Jon Rista, 17 December 2014 - 03:59 PM.


#31 TimN

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Posted 17 December 2014 - 03:55 PM

Thanks Mike for starting this interesting discussion and to Frank and Jon for clarifying a lot for me.  :bow:


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#32 mmalik

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Posted 20 December 2014 - 01:43 AM

Thanks Frank/Jon/Tim; I have updated my sum up above... of major noise types in light of this discussion, hope it "approximates" most noise types?

 

 

Next I would like to get into measuring criteria and units of measurement for each of the major noise types we have discussed thus far. Here is my take/questions:

 

 

1. Shot Noise (?Criteria) = ?Unit

 

2. Dark Current/Pixel [@Temperature] = Electrons/second [and/or Electrons/Exposure Time, e.g., Electrons/300sec]

 

3. (Apparent) Read Noise/Pixel [@ISO] = Electrons/second

 

4. Fixed-pattern (Banding) Noise) [@ISO] = ?Unit [Is this visual inspection based?]

 

 

Regards


Edited by mmalik, 20 December 2014 - 01:45 AM.


#33 wfektar

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Posted 20 December 2014 - 09:34 PM

Here is the wrap up thus far on the major noise types:

 

 

1. Shot noise (also called Photon/Poisson/Dark noise) results from ‘random’ arrival of photons, and is more apparent at low signal levels (i.e., small number of arriving photons). Note: Shot noise can also be electronic noise due to electrical charge

 

Poisson noise at high signal levels (i.e., large number of arriving photons) can become Gaussian noise. Poor illumination/low signal can produce Gaussian noise which can be viewed as upper level of Poisson noise

"Poisson" in this context really refers to a distribution, just like "Gaussian", so "Poisson" noise really is just noise with that distribution. Shot noise at low count levels have it, but so do other sources of noise that follow counting statistics. At high count levels it does indeed converge to a Gaussian, but then so does everything else (Central Limit Theorem).  I don't see why Poisson noise is a "core noise type" any more than Gaussian is.

 

This type of noise is in "count space", whereas certain of your others, namely fixed-pattern noise, is in "position space" (in this context anyway). There's a bit of apples and oranges here. But maybe that's OK.


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#34 freestar8n

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Posted 22 December 2014 - 08:18 AM

I'm afraid I can't really endorse the re-statement of terms earlier in this thread - partly because it shouldn't even be using the terms in those ways.

I would not use the term "dark current noise" at all because it is confusing and ambiguous. There are two distinct types of noise from dark current - dark current pattern noise and dark current shot noise. They are totally different. You can say things like "pattern noise from the dark current" or "shot noise from the dark current" - but dark current noise is vague.

And Poisson noise doesn't "become" Gaussian at high signal. It simply acquires a distribution that can be approximated as a particular Gaussian - with the same mean and sigma. That's an important point. It is because it is Poisson that you can estimate the noise when you know the signal. With an arbitrary Gaussian you cannot do that.

If someone says the noise is the square root of the signal - it means two things: the signal has a Poisson distribution, and it is being measured in counting units (electrons) - not adu.

Frank
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#35 mmalik

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Posted 22 December 2014 - 03:16 PM

I would not use the term "dark current noise" at all because it is confusing and ambiguous. There are two distinct types of noise from dark current - dark current-pattern noise and dark current-shot noise.

 

Frank, how do you reconcile term thermal dark current with those two terms? Regards



#36 freestar8n

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Posted 22 December 2014 - 03:51 PM

I think dark current is normally considered thermal dark current - and it doubles with about every 6C of temperature change.

So every pixel has some mean dark current at a given temperature. In several exposures the pixel will have some mean electron count due to the dark current or thermal dark current - and there will be noise in that count due to shot noise since it is a counting thing. So the shot noise is then dark current shot noise.

Across the whole sensor, the mean current in each pixel will be different at a given temperature - and the spatial variation in dark current (mean dark current) at each pixel contributes pattern noise to the image.

All dark current is thermal in nature - and after accumulating that current for a while you will have some count of electrons. That count will have shot noise - as it always does when accumulating discrete objects that are arriving randomly but at a steady overall rate.

If you raise the temperature 6C the current will roughly double - and the count of electrons in a given pixel for a given exposure time will also double. The noise in that count will increase by sqrt(2) - because the accumulation of electrons is a Poisson process.

So the dark current pattern noise across the image will double with 6C temperature change.

If you average many, many dark images of that pattern noise, you can get a good image of the "signal" corresponding to the dark current. You can then take a single light exposure of an object and subtract away that dark current "signal" - and remove the ugly pattern noise that it represents. But it will still leave behind the shot noise from the dark current - and it will have the same overall pattern. If you then accumulate many such "dark corrected light" exposures - the residual shot noise will also be dominated by the growing signal you accumulate.

If you had not subtracted that dark current "signal" (the pattern noise) then it would accumulate in the images just like the signal from the object (linearly) and you would just get a clearer and clearer image of that pattern noise along with the object. If you don't have pattern noise - like in some sony sensors - that's ok. But if you do have pattern noise - you want to remove it. Dithering helps a lot - but it is even better to subtract and remove the pattern noise - and then dither.

Frank

#37 mmalik

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Posted 04 May 2016 - 01:50 PM

More on the nature of dark current, and the pattern...
 

Patterns in the dark current are the reason to do a dark subtract. Hot and cold pixels are effectively dead and carry no information and need to be dithered away. But if you use in camera noise reduction on a terrestrial scene with a 1 minute exposure - the image will be much cleaner and less "noisy" due to the removal of variations of dark current across the sensor. Those variations will roughly repeat in the same pattern on multiple exposures. They are randomish spatially - but fixed temporally. Those spatial variations in dark current signal amount to noise in the image - and it is called fixed pattern noise - and it can be subtracted if you "take a good image of it." ICNR just uses one dark image for the subtraction and it can work very well and represent a net gain - if the pattern noise is greater than the net change in dark current shot noise.

So when I talk about patterns in the dark current - I am referring to fixed pattern noise - and the presence of FPN in the dark current is the entire reason for doing a dark subtract - and it's the reason ICNR with a single dark image can be very effective. If you don't have such undulations you would not dark subtract at all. At worst you would just have a fixed amount of added dark current across the image and you could subtract that constant number from each pixel.

Frank



#38 spokeshave

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Posted 04 May 2016 - 05:07 PM

mmalik, on 12 Dec 2014 - 5:45 PM, said:

Before getting to the first one, let get to one commonly used yet NOT well understood term, Poisson Distribution. It as a fancy term for a sequence of known averages, that's all. 'Average' is the genius, not the distribution!

I think this is at best incomplete, if not incorrect.

 

There are three things that define a Poisson distribution - the events that comprise the distribution are independent, discrete and random.

 

If you are going to engage in a discussion about the different types of "noise" it is best to settle on a definition of "noise". As is common in threads like this, lively discussion will likely emerge about whether thing like fixed-pattern "noise" are actually noise. There seem to be two schools of thought. The first one contends that anything other than target signal is considered "noise". That would include things like target shot noise, light pollution, dark current noise, PRNU and bias signal. However, I don't like that definition because it clearly includes things that are signal, and also excludes things (like vignetting and dust donuts) that fit the definition nonetheless.

 

To me, the less ambiguous definition is to classify those things that are truly Poisson in nature as "noise" and everything else as "signal". Noise, therefore, would be limited to photon shot noise and true dark current noise since those are the only ones that are independent, discrete and random. Whereas "signal" might be best defined as a reproducible response to a stimulus. Pretty much everything else would then fit well into this category.

 

Tim



#39 freestar8n

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Posted 04 May 2016 - 05:54 PM

You can define things any way you want - but the convention I use is standard in textbooks and journal articles in broad areas of science and engineering - and that is to refer to signal as the thing you are trying to measure - and noise as anything that obfuscates it. Pattern noise comes in many forms in imaging - and the literature refers to it as a noise term. I am perfectly happy with that and am not confused at all by the fact that it is a noise term - yet refers to undulations of a dark current signal - that itself is Poisson in each individual pixel.

When noise and signal are discussed in the context of this convention - everything is perfectly clear to me and I can follow the literature with a good understanding. But if someone insists on noise being completely random, unknown, and unpredictable - then I can understand this convention would be hard to follow. But I would simply abandon the need to have noise be random and then things should make sense.

A dslr image may look noisy - and after applying in camera noise reduction the result is less noisy. That is because one of the noise terms - fixed pattern noise - has been reduced by a dark subtract. Another noise term, dark current shot noise - has increased. But the two terms add in quadrature - as shown in textbooks and journal articles on pattern noise in sensors - so the net result could be lower after the subtraction. That reduction in noise is why dark subtraction is done in the first place.

Frank

#40 spokeshave

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Posted 04 May 2016 - 06:33 PM

freestar8n, on 04 May 2016 - 6:54 PM, said:freestar8n, on 04 May 2016 - 6:54 PM, said:

You can define things any way you want - but the convention I use is standard in textbooks and journal articles in broad areas of science and engineering ...

As someone who has fairly extensive experience in science and engineering as well (I have worked at a multi-program national lab for many years), I'll just agree to disagree. Noise and signal are typically defined differently depending on the context, in my experience.

 

Additionally, I have no difficulty following your chosen convention, I just find it to be ambiguous. You are including things that are clearly signal into your definition of noise, and are also rather arbitrarily excluding things like vignetting and dust, and for that matter plane and satellite trails even though they fit your definition of things that obfuscate what you're trying to measure.

 

At any rate, I was just offering a convention that would remove ambiguity, but I don't really have a dog in the hunt. Feel free to define the terms as you choose.

 

Tim


Edited by spokeshave, 04 May 2016 - 06:34 PM.


#41 freestar8n

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Posted 04 May 2016 - 07:05 PM

I don't rely on credentials ever in discussions like this - it is ultimately meaningless and normally not done in professional technical circles to make a point. All you have to do is point to the literature and show me a good journal article or textbook on ccd noise terms that departs from my use of the term noise in this manner. Most sources don't bother to define noise at all - because it is clear from the context. Some will say it isn't a real "noise" term in the normal sense - but they go ahead and refer to it as a noise term anyway - because the context is clear.

I don't know any textbook on ccd noise that goes out of its way to say that noise must be random or the term should not be used. In fact - I see the opposite, including common usage of the phrase "random noise" - to distinguish it from noise that is not random.

The terms "pattern noise" (which may be moving in some predictable way, as in hubble bias frames that were noise-corrected) or "fixed pattern noise" are direct violations of the convention you support - yet they are solidly in the literature of imaging technology. The term "in camera noise reduction" is also a violation - because truly random noise cannot be predicted.

Sadly - there are a number of amateur astronomical imaging books - and countless web pages - that insist noise must be random. I think that is ultimately confusing because it makes it hard to explain why you do dark subtract in the first place if the "noise" can only increase. And again it is contrary to professional usage of the term in the literature. There is a lot of bad stuff in amateur astronomy that exists only in amateur writings.

My favorite summary of what is noise and what isn't is from Probability, Statistical Optics, and Data Testing by Frieden. Frieden was an early proponent of Bayesian methods and is recognized as such - along with early work on maximum entropy image restoration. I have quoted this before and I will do it again:
 

The concept of noise is always defined in a specific context. As a consequence, what is considered noise in one case may be considered "signal" in another. One man's weed is another man's wildflower... Hence any systematic or correlated tendency in the test object would there be unwanted, and rightfully regarded as "noise." This is of course contrary to our usual notion of "noise."

Whatever its application, the concept of noise always refers to the departure of an observed or otherwise used signal from its ideal or "true" value.


Frank
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#42 spokeshave

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Posted 04 May 2016 - 07:18 PM

Like I said, I don't have a dog in the hunt. You clearly want this conversation to yourself, given your rather thinly veiled insult regarding what is "normally done in professional technical circles" and your lecture about citing credentials. Ironically, this was done as you touted your "credentials" regarding behavior in professional technical circles.

 

I'll bow out of this conversation and endeavor to resist the temptation to offer constructive suggestions in the future.

 

Cheers.

 

Tim



#43 mmalik

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Posted 04 May 2016 - 08:41 PM

Frank/Tim, it is all good information regardless, thanks; let's not worry about the subtleties. Regards



#44 freestar8n

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Posted 05 May 2016 - 03:52 AM

Frank/Tim, it is all good information regardless, thanks; let's not worry about the subtleties. Regards


Thanks - I'm just citing the literature and encouraging nomenclature consistent with non-amateur descriptions of this stuff. The topic of noise often comes up and people insist it must be random - but when I ask for a professional text or journal article in ccd imaging as a source - I never get one.

In contrast I can and have provided references emphasizing the importance of context rather than randomness. The nomenclature is full of contradictions to this randomness criterion: fixed pattern noise, random noise - etc.

I don't view this point as subtle - I view it as important in understanding and communicating how this stuff works - and how dark subtract improves the image.

Frank

#45 Jon Rista

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Posted 05 May 2016 - 08:13 AM

I agree that "noise" can take on non-random forms. Noise is an unwanted deviation from the expected norm, and need not always and only be a random change. 

 

I do also agree that calling some things signals rather than noise is...well, perhaps more accurate, and as such for those who understand the source of those signals, less confusing. The dark current offset, for example, is a signal in a real sense. It can introduce many kinds of noise to the image, but the dark current itself is a counted accumulation of electrons from leakage current, and as such, is another source of shot noise that follows a Poisson distribution...as well as other forms of noise, including fixed and non-fixed patterns, arbitrary offsets in signal level (glows), etc. 



#46 nikao

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Posted 06 May 2016 - 03:35 AM

Good discussion! 

I find that it get's very complicated and confusing quickly, mostly because of different definitions. Therefor discussions tend to focus to much on the definition itself instead of useful discussion on the types of noise.  

Tried to do a write up on types of noise to take into account that is simple enough for everyone to understand;

http://dslr-astropho...trophotography/

 

Here I simply defined noise as 'all the undesired signal', as that seems the most practical as we are constantly combatting these electrons :)



#47 freestar8n

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Posted 06 May 2016 - 05:56 PM

I think the write up is ok but it avoids the term fixed pattern noise. It says some pixels are dead because they are hot or cold - but it doesn't say that each pixel will have slightly different behavior from the others - and that variation in behavior is a form of noise in the image that must be removed in the calibration process. If all pixels had dark current and read noise - but they behaved the same - you would not do dark subtract because it would only make things worse.

Any signal can be a noise term if it inhibits the ability to measure some other signal. And any noise term can be a signal if you are trying to measure it. The concept of both noise and signal depend entirely on the context and what you are trying to measure - and what is making that hard to do.

As an aside - read noise is not Poisson and it doesn't come from a Poisson process. It is more a form of thermal noise - and it's usually described just in terms of its standard deviation in electrons. That standard deviation is considered constant across the pixels - but the mean offset for each pixel is assumed to vary - hence the need for master bias frames.

Frank
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#48 mmalik

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Posted 25 October 2016 - 10:41 PM

Some relevant info...
 

There are two main types of noise: noise that is uniform across the sensor but random in time, and noise that is random or quasi-random across the sensor and constant in time.

In a given frame the total noise is due to the fixed pattern component and the random component that rides on top of it. The random (in time) component is mainly due to the roughly Gaussian read noise, plus the Poisson noise in the dark current.

When you subtract one frame from another, the FPN is constant and identical in each frame, so it subtracts completely. At the same time the noise that is random in time will go up by sqrt(2).




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