Sensor Temp and Dark Current Exposure Limits (when not using darks)

[symmetal]

For something to do I thought of calculating the maximum exposure durations where the accumulated dark noise is not too high compared to the read noise for various sensor temperatures and so doesn't significantly affect the image.

It's often stated that sensors needn't be cooled to -10C or below as the dark noise will still be insignificant at higher temperatures. I cool my ASI6200 to -15C but thought this may not be necessary. I thought of discarding my darks and using the bias as darks instead as there is no amp glow on the later Zwo cameras, so the dark noise needs to be determined.

Here's the Zwo dark current graph for the ASI6200

These are difficult to interpolate as the dark current scale is exponential. I plotted the values on the right (taken from the graph) in Excel with linear axes here

The low temperature values are still hard to interpret so here is that part of the graph expanded.

I made some Excel calculations to work out the exposure duration where the accumulated dark noise is half the read noise of 1.5e- and so doesn't make too much of an impact. Here's the results and the calculations used.

This implies that for L exposures up to 2 mins 0C is fine, for RGB up to 6 mins -5C is fine, though for long narrowband exposures -15C is preferred.

It would be good for @vlaiv to verify my reasoning and that the calculations are correct, 😊 if he has the time. I've used read noise as a comparison as that's the figure used in sky background noise exposure calculations. If the dark noise adds little to the read noise it doesn't affect these calculations.

Alan

[symmetal]

I don't think @vlaiv got my notification last time as it wasn't highlighted. 🤔 At least I'm hoping that's the case and that he didn't ignore me. 😬

Here's a graph of the above table. However, I now think the results as shown are valid only for unity gain and that dark current would increase linearly with camera gain. The ASI6200 has no unity gain setting, with ASI gain 0 having a gain 0f 0.79 e-/ADU, and the usual ASI gain setting of 100 having a gain of 0.26 e-/ADU. Should the dark current figures used in the equations above be multiplied by 3.85 (ie. 1/0.26) which implies at higher gain settings the dark current is more significant than originally thought?

Alan

[vlaiv]

19 minutes ago, symmetal said:

I don't think @vlaiv got my notification last time as it wasn't highlighted. 🤔 At least I'm hoping that's the case and that he didn't ignore me. 😬

Nope, did not pop up. If mention is not properly marked (that gray "badge" surrounding nick) - then it won't notify.

Give me few minutes to read the original post and I'll respond.

[vlaiv]

I don't think you should reason like that.

Let me explain.

All noise sources except read noise grow with exposure time. They all grow in same way.

If we exclude read noise - for example, if we have perfect sensor that has 0 read noise, then it makes no difference if we use short subs that we stack or we make one long exposure.

Resulting SNR is the same.

For dark current noise - it does not matter if you use 2 minute exposures or 10 minute exposures - total noise will be the same in the end and will depend only on level of dark current (and will be square root of total accumulated dark current).

Fact that you get dark current noise to the level of read noise - does not impact result with respect to dark current noise - it impact result with respect to read noise.

Maybe I should put it like this:

- we can change level of read noise by selecting different gain

- we can change impact of read noise by selecting sub exposure length

- we can change level of dark current noise by selecting temperature.

Each of these choices is a tradeoff - and first two choices are not independent choice - but third is.

Gain / read noise choice goes like this:

- we increase gain and thus decrease read noise - but we also decrease saturation point of our sensor / full well capacity. So this is a tradeoff

- Once we have chosen our gain - then we can choose sub length such that - we can comfortably guide that long and we don't get trailing or out of shape stars - and impact of read noise is minimal.

Thing is - impact of read noise will depend on other noise sources (but not the other way around) - and once we reach certain threshold - we enter domain of diminishing returns.

For example - doubling exposure length from 30s to 60s can have much more significant effect on total noise than doubling from 4 minutes to 8 minutes. In both cases we double sub length - but SNR won't improve the same in both cases.

Third choice is independent. No matter what we choose for first two cases - total amount of dark current noise will be the same. It does not depend on either selected gain nor on read noise of camera.

Only parameter to change here is temperature. That is what determines level of dark current noise.

Here we also have tradeoff and area of diminishing returns. However - we don't have "gradual tradeoff" - but rather we have "hard limit" - so in that sense it is much easier to decide.

Tradeoffs are:

- can you reach set temperature (there is deltaT that cooling can achieve and achieved temperature will depend on ambient - we can't cool lower than (Ambient - deltaT) )

- how much power you are willing to spend (this is not important in 99% of cases unless you have limited power supply and you want maximize imaging time versus power consumption - but I'd say - get a bigger battery).

so we really only have issue of reaching set point temperature and I would say: simply go for lowest temperature that you can manage - it costs you nothing (except electrical power).

On the other hand - if you can't reach -20C, find comfort that dark current also has "domain of diminishing returns":

If you can manage only -15C - it won't add much more noise to the image than -20C because dependence is exponential versus temperature and at low temperatures curve is not steep.

In any case - choosing temperature based on already selected exposure length and read noise - is flawed as dark current does not depend on those.

(we choose sub length based on LP as impact of read noise on final result depends on ratio of its magnitude to largest noise source magnitude, but dark current is the same regardless what read noise we have and how long our subs are - it simply does not depend on any of that - only on temperature).

Makes sense?

[symmetal]

Thanks @vlaiv for the quick and detailed reply. 😀

I agree that the dark current is dependent only on temperature, but the dark noise which is what affects our images is dependent on sub length. A short sub will have less dark noise than a long sub. At a low enough temperature the increase in dark noise for long subs is negligible which is why we can use bias as darks on some cameras. From here

dark noise = SQRT( dark current * exposure length)

I thought that thermal noise and dark noise were essentially the same thing, though dark noise does have a shot noise element to it so is dark noise = thermal noise + dark current electron shot noise, or are they separate entities? Getting a bit confused here. 🤔

Is camera Amp glow effectively due to varying dark noise and/or thermal noise over the sensor due to localised temperature variations which increases with sub length, so darks are a necessity?

My initial reason for the post is that as the dark noise increases with sub length there comes a sub duration when the dark noise becomes significant. At low enough temperatures this doesn't matter. On this lecture by the author of Sharpcap at 22:18 he compares thermal noise contribution compared to light pollution and why it's unnecessary to cool beyond a certain temperature if you have light polluted skies as the thermal noise is insignificant.

I just chose read noise as a figure to use for comparison to where the accumulated dark and/or thermal noise remains at an 'acceptable' level where the dark/thermal noise is not significant.

Hope this makes sense.

Alan

 

Edited May 19, 2022 by symmetal

[vlaiv]

1 hour ago, symmetal said:

I agree that the dark current is dependent only on temperature, but the dark noise which is what affects our images is dependent on sub length. A short sub will have less dark noise than a long sub. At a low enough temperature the increase in dark noise for long subs is negligible which is why we can use bias as darks on some cameras

Dark noise does not depend on sub length.

Let me show that to you.

First thing to note is that stacking by average and stacking by addition gives the same SNR improvement. That one is rather simple as average is defined as: sum of subs divided with number of subs - in another words - average is just sum of subs divided with some constant. Signal to noise ratio does not change when you divide or multiply with a constant as you multiply / divide both components - so their ratio does not change.

It is easier to work with sums - simpler to show my point (hence above - just in case you wonder why did I choose sum instead of average - but they are the same thing).

Say you have 1e/s/px dark current.

Let's say that we have two subs of 100 seconds each and one long exposure of 200 seconds.

In first case we are summing two subs, each of them will have 100s x 1e/s/px = 100e of dark current. Dark current noise is SQRT(dark_current) - so each of them will have 10e of dark current noise.

When we add two subs - dark current noises in them add like noise adds - square root of sum of squares: sqrt(10^2 + 10^2) = sqrt(100+100) = sqrt(200) = 10*sqrt(2)

What about one long sub? Well that is easy 200s x 1e/s/px = 200e of dark current and dark current noise is square root of that so SQRT(200) = 10*SQRT(2)

Same thing.

After stacking you end up with same amount of dark current and dark current noise - no matter how long your subs are (provided that you have same total imaging time).

For dark current and dark current noise - it does not matter if you do  100 x 50s or 10 x 500s - you will end up with same amount of dark current and dark current noise.

What will be different is per sub amount of noise - but you know what will also be different - per sub amount of signal (light signal - important one) - so SNR of final stack does not change.

Only thing that changes final SNR is amount of read noise. This is because all other noise sources are dependent on time and only read noise is dependent on number of subs (each sub gets one dose - in 100x50s vs 10x500s case - first one will get 100 doses of read noise while second will get only 10 doses of read noise).

1 hour ago, symmetal said:

I thought that thermal noise and dark noise were essentially the same thing, though dark noise does have a shot noise element to it so is dark noise = thermal noise + dark current electron shot noise, or are they separate entities? Getting a bit confused here. 

No - there is only one thing - thermal or dark current and associated noise. It is called shot noise because it behaves as shot noise - it is same thing in its nature. Both electrons themselves and photons are particles and act the same with regards to this - they never come in exact numbers but have randomness associated with how much of them has arrived / is detected. This process is called Poisson process and is described by Poisson distribution.

1 hour ago, symmetal said:

Is camera Amp glow effectively due to varying dark noise and/or thermal noise over the sensor due to localised temperature variations which increases with sub length, so darks are a necessity?

That really depends. Some of it is due to electronics around sensor (with CCDs) that either raises temperature or in other ways "infuses" electrons in that part of sensor. Or it can be simply some sort of electron leak from circuitry on sensor (CMOS) that acts like dark current (builds up with exposure time).

Note that dark current and amp glow are not noise - they are signal that is removed. Because of nature of that signal - there is always some "uncertainty" in how much of it has built up over time and that is what noise is.

We never calibrate out noise - we calibrate out signal. That is purpose of calibration to remove unwanted signal.

1 hour ago, symmetal said:

My initial reason for the post is that as the dark noise increases with sub length there comes a sub duration when the dark noise becomes significant. At low enough temperatures this doesn't matter. On this lecture by the author of Sharpcap at 22:18 he compares thermal noise contribution compared to light pollution and why it's unnecessary to cool beyond a certain temperature if you have light polluted skies as the thermal noise is insignificant.

Dark noise increases with sub length - but so does signal strength.

Signal increases linearly (all signals - our target signal, LP signal, dark current signal) while associated noise increases like square root of that

If signal goes

1, 2, 3, 4, 5, 6 ....

noise goes like

1, 1.41, 1.72, 2, ....

It rises slower.

That is why we get higher SNR with longer exposure.

(blue is square root and green is linear - green is getting larger than blue as time goes on - moving to the right)

With lowering temperature we get into domain of diminishing returns. That is true. If there is noise source that is larger than dark current noise, then yes, impact of dark current noise will be minimal - but it will not depend on sub duration.

Why? Because LP signal grows the same as Dark current signal - hence LP noise grows the same as Dark current noise - their ratio will be the same in 20s exposure, 60s exposure, 120s exposure.

There is no "swamping" of one with the other in certain sub length - they remain of the same ratio regardless of sub length.

I agree that in strong LP - it makes very little difference if you cool down to -20C vs say -10C - but benefit is "infinite"

If we define benefit like improvement / cost and if improvement is positive and cost is 0  we get positive/0 = + infinite

When we double sub length - it costs us something, there is greater chance that 10 minute sub will go to waste than say 5 minute sub - so for read noise there is point where we want to stop increasing our sub length as cost gets bigger than improvement - it is not worth to increase sub length any more.

This does not happen for cooling. Is it harder to cool to -20C than it is to -10C? It is just entering a number in app - set this particular temperature on sensor. As long as you can reach it due to deltaT - it makes no difference if you cool to -20C, -15C or -10C in terms of cost - so what ever improvement is - it is worth it.

[symmetal]

Thanks again for the detailed reply @vlaiv I think I've got it. 😊

I was initially confused by the first line of your reply,

47 minutes ago, vlaiv said:

Dark noise does not depend on sub length.

which seems to contradict the equation from the linked web page, dark noise = SQRT( dark current * exposure length). 

Further down you said

52 minutes ago, vlaiv said:

Dark noise increases with sub length - but so does signal strength.

which again seems to contradict your first line.  However, what you mean is that the noise component of the dark current signal increases more slowly than the target signal for increased sub length. The dark noise level you end up with is dependent only on the dark current signal which is dependent only on temperature.

I was doing my initial calculations only on dark subs so there was no target signal to consider. For a single sub the read noise is fixed and I was comparing the increasing dark noise with sub length as something to be concerned about. But in reality the increasing target signal with sub length always outpaces the dark noise increase anyway.

I found answers on the web saying thermal noise is white noise independent of frequency, and dark noise is shot noise which caused confusion. However from this lecture

which agrees with what you said, they are the same thing.

I'll discard all the excel files I've made as they don't mean much when actual target signal is taken into consideration. 😁

Thanks again vlaiv for taking the trouble in pointing out the error of my ways. ☺️

Alan