Robin Glover talk - questioning calculated length of sub-exposure?

CMOS Acquisition Deep Sky
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Christian Koll avatar
Christian Koll avatar
Hello!

There is this excellent talk of Dr. Robin Glover about the longest reasonable sub-exposure time, depending on your sky brightness and the read noise of your CMOS camera:
https://www.youtube.com/watch?v=3RH93UvP358&t

However, when I do the math with my setup (QHY600 at gain 56, high gain mode, 1.6 e/sec/pixel equalling Bortle 4) I'll end up with a recommended subexposure time of around 30 seconds.

What is not adressed in the talk is, if I'll stick to this short exposure time, I'll end up with a small amount of signal per frame plus a terribly large amount of data!

10 hours of total exposure time equal 1200 sub-frames of 119MB each, resulting in almost 143GB of data (not to mention the cumbersome process of stacking such a large number of frames).

So is there anything wrong in taking 5- or 10-minute subs, accepting that my S/N-ratio woun't be any better than a 30-second frame?
After all, everything that counts is total exposure time, (almost) no matter how long the subexposure time is. Right?

Am I missing something here or hitting a point?

Thanks for your thoughts!
Chris
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Björn Arnold avatar
Björn Arnold avatar
Hi Christian,

Glover's idea is to maximize dynamic range for each sub but minimizing the contribution of the read noise to the "background signal" (NB: one shouldn't only consider the sky's background signal but also thermal noise/dark current. Depending on one's camera, the latter can be comparable to the sky background, especially under dark skies and narrow band filters.). The issue of collecting a huge number of data isn't subject to the discussion at all.

The SNR of 5 to 10 minute subs is better than that of a 30 second frame for the cost of losing dynamic range for each frame, which you would compensate (to some extent) by the total integration time (burnt stars will remain burnt stars however).

The best SNR is achieved if you were able to do a single exposure, e.g. the 10 hours you mention. Everything else has a (bit) less SNR, with SNR decaying the shorter the subs are.


Björn
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Rick Veregin avatar
Rick Veregin avatar
Glover's idea is to find the minimum exposure needed to reach a point where the contribution of read noise is small compared to sky noise. In other words, at this minimum it ensures you are basically only limited by sky noise, how dark your site is. The S/N continues to improve similarly with longer total exposure, no matter what the sublength. If you sublength is shorter than his minimum you subexposure is limiting your S/N, no matter how much exposure you take, you would have gotten a better result for equal total exposure with a longer sub. Note total dark noise depends only on total exposure and temperature, so if both of these are the same, then sublength doesn't matter.

I like to think of it this way: if you are at least at the minimum exposure, you know that your subexposure length is not limiting you very much. Longer subs will only be slightly better for equal total exposure. So absolutely, S/N wise, no reason not to run longer.

His point was the longer you run, the more sensitive you are to vibrations, winds, seeing, tracking, clouds, satellite trails, guiding. So if your setup can handle it, go as long as you like. But bad frames will tend to increase with sublength. Certainly true a full frame small pixel sensor creates a lot of data–I personally run short exposures based on Glover's work and do get lots of data. Data storage is cheap and for me I am lucky to get 15 hours a month, with a small pixel APSC sensor the data storage is cheap compared to the cost of my kit. And my images are better with shorter exposures.

It is all a trade-off based on your personal setup.
Clear skies
Rick
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Frédéric Auchère avatar
Frédéric Auchère avatar
I watched that video with interest. As already said, the idea is to determine the minimum exposure time beyond which little is gained in SNR. It may be worth pointing out that he arbitrarily picks 5% added noise compared to a single long exposure as acceptable. You could equally pick 10% or 1%. For what I'm doing, 10% extra does not make a difference, but maybe 5% will be too much for some. In any case, SNR-wise, there is no drawback in running for longer. But other challenges will hit you with longer exposures, so as Rick said, Glover's point is a guideline, and you have to adapt based on your setup.

Also, it may be worth measuring your actual sky brightness, e.g. in frames taken near the Zenith, and away from the Milky Way. The sky brightness in your subs will depend on where you're located exactly, the presence of the Moon, your instrument, the passband of the filters, etc. This will yield a more accurate estimate of the minimum sub length.

Also, as was mentioned by Björn, one also needs to factor in thermal noise. In his talk, Glover assumes that the sensor is cooled enough so that thermal noise is negligible compared to the sky brightness shot noise. For people like me who don't cool (e.g. DSLR imaging), this contributes to decreasing the minimum required exposure time.

CS,

Frédéric
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Björn Arnold avatar
Björn Arnold avatar
For the interested people, Robin Glover provides some more detail on his SharpCap website and forum:
There’s a tool to estimate the electron rate of the sky background by providing sky conditions, telescope, camera and filter parameters:
https://tools.sharpcap.co.uk

if one wants to read more about the theory which he applied in his talk, check out his forum entries here:
https://forums.sharpcap.co.uk/viewtopic.php?t=456

Björn
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Frédéric Auchère avatar
Frédéric Auchère avatar
Assuming that I'm in Bortle 3, that tool gives values quite comparable to what I'm measuring in my subs smile

Something I noticed is that, at least from my site, the sky background is always about two times darker in the blue than in the green or red. So my sky is kind of yellowish!

Frédéric
Christian Koll avatar
Christian Koll avatar
A very interesting discussion - thanks very much for your insights!

Another thing that puzzles me is how to deal with sky flux (your background or sky brightness) in these equasions.
Isn't that background signal also some kind of noise?

And if so, even in Bortle 2, its amount is way larger than the other two noise components (thermal noise and read noise).
According to the rule of adding noise, you can ignore the smaller component(s) if they are way smaller than the larger component.

Is it fair to assume that, if sky background is in the hundreds and thermal noise and read noise are single digit numbers we can ignore the latter two? If so, why would we bother about the two small noises at all?

So my question is, when calculationg total S/N in a stacked image - am I supposed to add the background signal to the total noise or not?

Or is the background signal just an offset that I do not add to the total noise and simply get rid of in post processing by a levels (black point) adjustment?

Thanks!
Chris
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Björn Arnold avatar
Björn Arnold avatar
Christian Koll:
Isn't that background signal also some kind of noise?

Sky background is signal and not noise as it is data from the sky and not an inherent source from the telescope itself. Maybe a note on the side: when we talk about noise, people use it with two different meanings:
a) noise in the sense of unwanted (contribution to a) signal
b) noise in the sense of variation of a signal (signal in a broad sense: read-out noise, sky signal, dark current)
Christian Koll:
And if so, even in Bortle 2, its amount is way larger than the other two noise components (thermal noise and read noise).
According to the rule of adding noise, you can ignore the smaller component(s) if they are way smaller than the larger component.

Is it fair to assume that, if sky background is in the hundreds and thermal noise and read noise are single digit numbers we can ignore the latter two? If so, why would we bother about the two small noises at all?

To the first part: it depends on what parameters you placed in the sky calculator. Take a Bortle 2 sky at f/7.0 with a 2.3um Pixel size, 80%QE, monochrome and narrowband filter. The sky electron rate will be shown as 0 e/px/s. Of course it's not zero but certainly in the order of magnitude of dark current for common TEC cooled cameras and much much lower than any current read noise. Hence not negligible.

To the second part: Absolutely true. That's what happens if you do daylight photography with a DSLR. No need to care about read noise and thermal noise.
Read noise is most often to be corrected through the bias frames as in most cases cannot be neglected. Dark current really depends.
If you're shooting broad band, you might try to go with bias only and no darks if dark current is negligible. Nota bene: one needs to verify that this holds by doing tests.
Christian Koll:
So my question is, when calculationg total S/N in a stacked image - am I supposed to add the background signal to the total noise or not?

The background signal is part of the noise calculation. So, the answer is yes.

Björn
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Frédéric Auchère avatar
Frédéric Auchère avatar
Björn Arnold:
Read noise is most often to be corrected through the bias frames as in most cases cannot be neglected.

To be precise, bias frames will correct for the average value, but the random fluctuations will remain. Stacking will average out random fluctuations.

Frédéric
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Christian Koll avatar
Christian Koll avatar
Hmmm....

So the sky background is at first a pedestal added to your (wanted) deep sky object signal.
On the other hand, the variations of sky background from sub to sub are regarded as noise (shot noise) and add to the total S/N-ratio.

Correct?


My data is as follows:
QHY600 Mono 3.76px at Gain 56 in High Gain mode, read noise 1.683e, Gain factor 0.33, thermal noise (-5°C) 0.0068e/px/s
Refractor Telescope f/5.5, Bortle 3 observing site resulting in a sky flux of approx. 1e/px/s (according to Sharpcap online calculator tool)

So I'll end up with with a recommended exposure time (L-filter) of only 28 seconds, but I choose to go for 180 second subexposure time.
After these 180 seconds my sky flux totals 545 ADU's, my thermal noise is 3.7 ADU's and my read noise is 5.1 ADU's.
According to measurements on my sub frames a typical emission nebula sends in approximatels 4.6 e/px/s resulting in a signal after 180 seconds of 2520 ADU's.

So what is my S/N-ratio now?
If I regard the sky flux of 545 ADU's as a pedestal I only add thermal noise and read noise to a total of 6.3 ADU's (Pythagoras) and reach a S/N-ratio of 400.
If the entire 545 ADU's sky flux (background) are regarded as noise and I add thermal noise and read noise (these actually becoming irrelevant) I end up with a S/N-ratio of 4.6.

Which calculation is correct?

If 4.6 is the correct answer I am wondering why I bother about thermal and read noise at all and switch instead to a different gain setting (Gain 0) with higher read noise (3.6e) but more than double the Full Well Capacity of my previous Gain 56 setting?

Chris
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Björn Arnold avatar
Björn Arnold avatar
Christian Koll:
Which calculation is correct?

I think there's a misunderstanding here which goes like this: the object is the signal and the noise is somewhere in the background. That's not how it is working.
Let me just take your numbers as an example which we can hold on to:
To summarize: the pixel that collects part of the nebula "catches" in average 2520 ADU from the nebula while 545 of these 2520 are sky background (the nebula will "only" be 1975 ADU).
The SNR per single sub is 2520 / Square root( 5.1 + 3.7 + 2520 ) = 50.11
For the pixel that catches only the sky background you will get SNR=545 / sqrt(5.1 + 3.7 + 545) = 23.15 (also for the single sub only)
Just a note here: I assumed that the sky and nebula "ADU" are only the true average signal and you have had subtracted bias and dark.

The sky background is not just a pedestal. Of course, it's an additive signal but it's not a mathematical constant and for each sub frame subject to random variation.
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Frédéric Auchère avatar
Frédéric Auchère avatar
Note that SNR calculations have to be done in electrons: these are the units that you're "counting". Unfortunately, you can't increase SNR by increasing the number of ADU/electron.

In 180s, your signal (the nebula) is 180*4.6=828 e-.

The noise is the root sum square of all noise contributions =sqrt(read noise^2 + thermal shot noise^2 + sky shot noise^2 + nebula shot noise^2).

The shot noises are the square roots of the corresponding number of electrons. Note that for thermal noise this is a bit confusing since what is generally listed is the *average* number of thermal electrons/pixel/s, the random fluctuations are the square root of that, so thermal noise^2=tabulated values.

In the end, you get:

SNR = 180*4.6/sqrt(1.683^2 + 180*1 + 180*0.0068 + 180*4.6)=26

The dominant terms in the square root are the shot noises from the nebula (which dominates) and from the sky. The others are negligible.

Frédéric
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Christian Koll avatar
Christian Koll avatar
Frédéric Auchère:
1.683^2 + 180*1 + 180*0.0068/0.3


Frédéric, thanks very much for your detailed explanations - I very much appreciate that!

One thing I don't get is, why do you divide the thermal noise by 0.3?
Isn't the thermal noise just the noise rate given by the manufacturer multiplied by the exposure time?

Thanks!
Chris
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Frédéric Auchère avatar
Frédéric Auchère avatar
Oops, indeed my bad. Good catch that was a leftover from checking your numbers in ADUs. I fixed the original post
Gert Eriksen avatar
Gert Eriksen avatar
Sorry, I late to the party!

As I understand Glover, he calculates the minimum sub-exposure length in order not to compromise the S/N-ratio to much, assuming (and that is key) that you have a finite time for the captures. Longer exposure time increase the S/N, but at a cost of losing the sub due to satellite and airplane trails or other mishaps.

Say that you have 1 hour, do you take 12 5 minutes  subs, 60 1 minutes subs or 120  30 seconds subs? If there is two satellite passes in that hour, you will lose 17% signal in the first option but only 1,7% signal in the later. If you have infinite time, go for as long exposure time your guiding system allows.

At least, it is how I understand Glover.

Gert
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