Which is best: many quick exposures or fewer lengthy exposures? 120 x 1 minute exposures or 10 x 12 minute exposures? Questions much like this one get requested actually usually and so they most likely obtain every kind of various solutions. Folks discuss concerning the digicam, faintness of the sign, dithering, stacking, mild air pollution and so forth. and so forth. So many elements creep into the dialogue that ultimately it can look like a private selection, nearly like a matter of opinion. Is that this actually a matter of opinion and/or difficult? Or can we discover some definitive reply to the query if extra shorter exposures are higher than fewer longer exposures?
Truly, it seems that though there are formulation for excellent (theoretical!) publicity occasions, private preferences and opinion and practicality will come into play in actuality when figuring out the publicity you wish to be utilizing.
Realizing how the subexposure time will impression the SNR of your stacked picture will make it easier to to find out the publicity time you select to make use of. Please bear with me whereas we discover the best way to find out this optimum publicity time, which is able to embrace fairly a little bit of math. I discover that going over the maths and truly calculate the SNR for a couple of totally different situations helps significantly in my understanding of this matter. So I encourage you to comply with together with the maths. For individuals who are largely inquisitive about the important thing take aways I’ll begin with these in a brief abstract, earlier than diving into particulars and the maths additional on.
Key take aways
When you find yourself imaging below mild polluted skies, you shouldn’t fear about your publicity occasions. It would make little or no to no distinction in case you are utilizing subexposures of 30sec. or 3minutes. It’s the entire integration time that issues.
If you’re imaging below darkish skies, you’ll profit from longer exposures when it comes to SNR. Nonetheless, it’s not price it to go to extremes and remember the price of throwing out a subexposure attributable to poor monitoring for example. Solely enhance publicity time in case you can dependable monitor precisely for that lengthy.
Should you don’t use darks and/or wish to use dithered (bayer) drizzel integration, be sure you get a minimum of 10 to fifteen subexposures.
Now that we’ve discovered to not fear about subexposure time below mild polluted skies and provides subexposure time precedence below darkish skies, let’s see why that is the case and the way we arrive at these conclusions.
Learn noise and background sky flux
To find out the optimum publicity it principally comes down to those two elements; learn noise and the background sky flux.
The learn noise is the noise that happens throughout the electronics of the digicam after we convert the electrons coming from the sensor into digital models (ADU) and retailer them. The background sky flux is the sign coming from the sunshine air pollution, moon mild and/or air glow. The background is rarely utterly black and the worth of the background sign is the background sky flux.
If the learn noise is swamped by sky background noise it turns into irrelevant and it doesn’t matter how lengthy our subexposures are
If we wouldn’t have learn noise, it wouldn’t matter if we take one very lengthy publicity or many shorter exposures with the identical complete integration time. If we wouldn’t have background sky noise however do have learn noise, the longer publicity would all the time have higher SNR than many shorter exposures.
In actuality we all the time need to take care of some form of combination of those two situations. There’ll all the time be some background sky noise and skim noise is all the time an element to take note of. Particularly for us DLSR customers. So how ought to we take these two elements under consideration? Properly, it comes right down to figuring out the purpose the place the sky background noise will make the learn noise irrelevant. Every time that is the case, it doesn’t matter any extra if we take many shorter or fewer longer exposures.
So in case you are imaging below robust mild air pollution this most likely applies to you. Alternatively, in case you are utilizing narrowband imaging and/or in case you are below actually darkish skies, it is going to be virtually not possible to succeed in this level and so the longer exposures will all the time be higher.
Now let’s analysis why that is the case and have a look at some take a look at outcomes;
Including a number of exposures and SNR
Let’s have a look at what precisely occurs to the SNR after we add a number of exposures and after we expose longer. We’ll dive into some math right here and I’ll strive to do that step-by-step and as clear as attainable. I do know lot’s of articles will skip steps and rewrite formulation with out explaining how or why which I’ll attempt to keep away from.
The SNR is solely the Sign divided by the noise. Sounds easy, however with totally different noise sources we have to dive in a bit deeper and see how we add noise. However first let’s outline the time period Sign precisely: S = sign per second (s) * time of the publicity (t) * variety of exposures (N). So
To be clear; that is the entire quantity of sign recorded over a number of exposures.
Subsequent let’s take into account the noise sources we’re coping with right here: Object shot noise, sky (shot) noise, darkish present noise and skim noise. Every time we’re coping with detecting photons we take care of shot noise. This shot noise is the sq. root of the variety of photons. This noise can be increase over time similar to the sign. So when it comes to the item shot noise, it’s the noise related to the sign of the item(s) we’re imaging and is the sq. root of the sign.
For sky shot noise it’s the sq. root of the background sign coming from the sky over time.
For the darkish present noise it’s the sq. root of the thermal sign (darkish present) construct up.
The learn noise is totally different within the sense that this doesn’t construct up over time but it surely does happen as soon as for each publicity. That is vital to understand. The whole learn out noise (RonTot) is:
We are able to sum random, uncorrelated noise by including them quadratically so we get the next system for the entire quantity of noise:
Bear in mind the truth that the shot noise is the sq. root of the Sign supply. So if we add this quadratically we will rewrite the Noise when it comes to the sign like this:
For the reason that variety of exposures (N) is current in every time period we will rewrite this as:
or
So the system for the SNR is:
Discover we’ve N as a time period current in each elements of the division. Since we will rewrite the above system into:
Now we’ve written the system down for SNR on this helpful format, we will discover what the impression of the background sky flux and the learn noise is on the SNR.
State of affairs with no learn noise
Possibly you begin to see now what we mentioned earlier; if we wouldn’t have learn noise it wouldn’t matter how lengthy we expose so long as the entire publicity time is similar. Let’s simply take out the learn noise (RN) out of the above equation. With out learn noise the SNR will probably be:
Since we’ve t current now in each time period we will group it:
which is similar as
and as we’ve seen earlier than we will write this down as
Now we will see it doesn’t matter for the SNR how we fill in values for N and t so long as N*t = the identical worth. So solely complete publicity time issues (N*t) and never how we divide it in subexposures.
However wait, what about actually faint sign? Don’t you want very lengthy exposures for that? Properly, not on this case the place we don’t have learn noise. You simply want (very) lengthy complete publicity time. If we have a look at the above system that is clear, but when we consider stacking and take into account that we’re averaging there this might sound much less intuitive abruptly. As a result of, the typical of some electrons collected by many frames is smaller than the typical of some electrons in a single body proper? Properly, positive that’s right after all. Nonetheless, that is solely contemplating sign. And it isn’t helpful to speak about sign alone, we all the time want to speak about SNR. That alone determines if you’ll have detected sign that can stand out in a picture or not.
And if we take into account the truth that SNR = merely sign / noise you’ll realise it doesn’t matter in what number of frames we detected the sign, since we’ll solely find yourself dividing each phrases of the division which doesn’t change something ((a*b)/(a*c) = (a/a) * (b/c) = 1*(b/c) = (b/c))
So sure, it’s true that if learn noise wouldn’t exist it doesn’t matter what publicity time you employ and what number of exposures you’re taking, all that issues is the entire integration time. And even with learn noise included within the system, you may see that after the opposite values are a lot a lot greater than the learn noise, the identical will apply; the learn noise turns into (nearly) irrelevant and we’re left within the scenario the place it doesn’t matter what publicity time you employ.
as soon as the opposite noise values are a lot a lot greater than the learn noise, the learn noise turns into (nearly) irrelevant and we’re left within the scenario the place it doesn’t matter what publicity time you employ.
State of affairs with little to no sky noise
Alternatively, take into account the situation the place we’re below a really darkish sky with no mild air pollution, no moon mild and solely a bit sky glow; we’ve little or no background sky sign (Sky_s). Let’s take into account the SNR system once more:
Now let’s say the DarkCurrent_s = 0.15e-/sec (which I discovered reported for the Nikon D7000), Sky_s = 1e- / sec and skim noise = 3e- (Nikon D7000 @ ISO200). If we take a really faint sign that’s much like the sky flux we’ll see the next SNR values for various variety of publicity occasions however identical complete publicity time:
Let’s evaluate situations with a complete integration time of 120 minutes and evaluate 120x1min and 12x10min.
120x1min:
12x10min:
Okay, so SNR is increased certainly as anticipated. What if we take this to the intense and simply take 1 picture of 120min?
1x120min:
Hmmm, that’s a extremely small enchancment over the 12x10min publicity. Clearly it is a case of (rapidly) diminishing returns. I made a graph displaying the SNR positive aspects in comparison with a 30sec publicity SNR for exposures between 30sec and 120min to point out the advantage of exposing longer on this situation:
This graph paints fairly a transparent image I’d say. In case of a darkish sky, the positive aspects in SNR whereas exposing longer is sort of massive at first and reaches a ten% enchancment already at 3,5minutes exposures in comparison with 30sec exposures. The enhancements tail off rapidly as effectively although, reaching solely an additional 1% enchancment at 8 minutes in comparison with the 30sec exposures. To be clear; on this situation, the distinction between exposing 3.5minutes and eight minutes (with the identical complete integration time) is even barely lower than 1% enchancment.
Please word that these positive aspects are dependant on the sign coming from our goal object as effectively. So if we’d take a a lot fainter object with a flux of solely 0.2e- in comparison with the 1e- we simply noticed, we get the next graph:
Wow! we will see the identical robust curve with diminishing returns, however the SNR enhancements for a fainter sign are clearly a lot a lot increased! Let’s have a look at the identical minute marks as earlier than: utilizing 3.5 minutes exposures in comparison with 30sec exposures offers you an SNR enchancment of 26.3%. Going from 3.5 minutes to eight minutes offers you an additional enchancment of two.86%. So despite the fact that we nonetheless see robust diminishing returns, the enhancements stay vital up until longer exposures as earlier than.
On this situation, the development in SNR between 8 and quarter-hour nonetheless is 1%.
Please word that we’re speaking about sign coming from the sensor right here. So this contains situations with gradual optics in addition to utilizing quick optics on very faint sign.
The position of learn noise in SNR
To make it actually clear what the position is of the learn noise within the situation’s we simply ran by way of, let’s check out the position of learn noise particularly and the way it provides up after we add extra exposures.
Let’s have a look at the SNR once more for a similar scenario as described earlier than, 12x10min subs versus 120x1min subs and rewrite it a bit simply to see what is going on to the noise phrases:
For the item shot noise, sky noise and darkish present noise we get the next:
12x10min:
which is; =
and for the 120x1min this then is; =
So that you see that is precisely the identical, simply as we may count on and have seen earlier than within the situation with out learn noise.
Now, let’s see what is going on with the learn noise; which is solely
12x10min:
120x1min:
So the learn noise is rising with the sq. root of the variety of exposures in our integration, whereas all the opposite phrases merely develop by complete publicity time alone. So for a given fastened complete publicity time, the learn noise will probably be smallest with the least variety of exposures.
Learn noise is rising with the sq. root of the variety of exposures in our integration
To see it’s impression within the complete noise let’s run the precise numbers. Bear in mind, uncorrelated noise provides up quadratically, so the entire noise we get in these conditions is;
12x10min:
120x1min:
Now we will clearly see how massive the impression is of the learn noise on this situation.
Subsequent let’s see what these numbers and the impression of learn noise appears to be like like in case of a shiny sky. Let’s say sky background flux is 50e-.
For the time dependant noise sources we get: =
If we add the learn noise:
12x10min:
120x1min:
It is a completely totally different scenario and the learn noise may merely be thought-about irrelevant.
Actually, this appears to be like very very like the hypothetical scenario with none learn noise we noticed earlier.
So we will conclude that the publicity time solely is related when the learn noise is related. And the learn noise is just related if the sky is darkish sufficient.
The publicity time solely is related when the learn noise is related. And the learn noise is just related if the sky is darkish sufficient.
Figuring out optimum publicity time
Now we’ve seen the situations above you may marvel what can be relevant to your particular scenario. As we simply concluded this will probably be dependant totally on the brightness of the sky you might be imaging below.
There are formulation to find out the optimum publicity utilizing the learn noise and sky flux as enter. There’s additionally a script in PixInsight which you should utilize to offer you an ‘excellent publicity size’. (Scripts->Instrumentation->CalculateSkyLimitedExposure)
Nonetheless, as we’ve seen within the graphs earlier than the profit in SNR is considered one of diminishing returns. This implies it isn’t attainable to offer one absolute reply to the query what the optimum publicity time is. Assumptions should be made about how a lot contribution of learn noise to the entire noise you’ll tolerate. And the variations on this assumption is usually enormous (issue 2 variations). Moreover they don’t take practicalities under consideration. So I’d like to only present you a couple of extra situations and the SNR corresponding positive aspects for longer exposures in comparison with utilizing 30sec exposures in a scenario the place we use a complete publicity time of two hours. I’ve listed the ‘95% enchancment mark’ for publicity time for every sky brightness.
The obvious factor we will be taught from this chart is that there’s a enormous distinction how a lot you profit from longer exposures below a darkish sky versus brighter skies. Moreover, the 95% enchancment mark appears to be awfully shut for all situations. Nonetheless, I’m undecided how helpful this quantity is because the subsequent step up in publicity after this mark below a darkish sky will nonetheless offer you 0.05% enhance whereas this enchancment is just 0.0012% within the brightest situation. To make this much more clear; for the brightest situation the SNR for 30sec. publicity was 11.83, whereas all the best way on the finish with one publicity of 120 minutes the SNR was 11.86. So we may safely take into account this a situation the place subexposure size is totally irrelevant.
Bear in mind we noticed earlier that the SNR enhancements had been a lot bigger if we’re coping with faint indicators. So let’s have a look at the SNR enhancements for various sky brightness with the beforehand used faint 0.2e- sign
The impression of the sky brightness could be very clear once more on this chart. Though we do profit extra from longer exposures when coping with fainter sign additionally from brighter skies, the distinction is negligible for very shiny sky and is admittedly enormous for the actually darkish sky.
Primarily based on these graphs we will conclude that in case you are imaging below a light-weight polluted sky you shouldn’t fear a lot about your publicity size. Each sky brightness between 5e- and 50e- principally has a complete SNR enchancment between 0.2% and a couple of% for which you’ll attain 80% of most SNR enhance already at 3 minute exposures.
Different sensible issues to take note of
Subsequent to the learn noise and background sky flux, we have to take some sensible elements under consideration as effectively after we wish to decide the optimum publicity size. The flexibility to information precisely for longer exposures for example is after all actually vital, in addition to the price of lack of information if it’s essential throw out a subexposure. Do not forget that the entire built-in publicity time is most vital for SNR, so there’s a actual vital price when it’s essential throw out subexposures.
Moreover you may wish to use (bayer) drizzle integration, which is able to want a minimal quantity of (dithered) subexposures to offer correct outcomes.
These are all crucial issues to think about which could change issues utterly when it comes to the optimum publicity time for you personally.
Mild air pollution and slender band filters
I received requested rather a lot concerning the affect of filters. I haven’t examined this out myself, however the e book The Astrophotography Handbook covers a comparability between totally different mild air pollution filters and concluded that in his take a look at it didn’t impact the background sky flux all that a lot (which was shocking). As all the time, try it out to know for positive, however I believe the impact of sunshine air pollution filters is minimal on the learn noise contribution to the general noise.
Narrowband filters however will principally change even a light-weight polluted sky to a darkish(er) sky on the whole. So with narrowband filters you’ll profit rather a lot from longer subexposures.
After all there’ll all the time be exceptions to this, like OIII imaging with full moon, and actual particulars will depend upon the velocity of your scope and the quantum effectivity of your digicam for example. Nonetheless, the generalisations will maintain true in most conditions.
A comparability from a darkish web site
Let’s have a look at the next information that I shot whereas I used to be in Namibia. There’s virtually no mild air pollution there and this was shot with out the moon current. The one little bit of background sky flux was the sky glow and maybe a little bit of zodiacal mild.
The information was shot throughout 3 totally different nights so some variation is to be anticipated primarily based on circumstances for that specific night time. There have been no noteworthy variations between these nights so I’ve no cause to consider that is influencing the comparability a lot.
I had used totally different publicity lengths: 8, 12 and quarter-hour. For this comparability I made three integrations that every one had the entire integration time of 120minutes. So 15 frames of 8 minute exposures, 10 frames of 12 minute exposures and eight frames of 15 minute exposures. No processing is completed to those integrations. Only a STF utilized to make the info seen.
Primarily based on what we discovered earlier than we’d count on the less however longer exposures may have the higher SNR. Let’s see if this was the case:
Laborious to inform from this huge shot, so let’s zoom in a bit.
Right here we will already see some distinction within the quantity of noise. Let’s zoom in additional to have a greater look.
The variations in SNR are clearly seen now and we see certainly what we anticipated: the 8x15min. integration appears to be like (a lot!) higher than the 15x8min. integration.
That is even higher seen at nighttime area of Barnard 44A:
So visually we will already draw the conclusion that we had been proper: longer publicity has higher SNR on this scenario the place we’re clearly learn noise restricted. Now let’s test the numbers to verify.
First let’s have a look at the quantity of noise:
Noise is increased in longer exposures which is predicted. The query is; did the sign develop greater than the noise?
The SNRWeight measure (to be clear; it is a relative measure and never reflective of the particular SNR variations)
So sure, it clearly did.
Until you might be below darkish skies, the subexposure size received’t matter a lot as soon as you might be utilizing 2 to three minute exposures.
Conclusion and ultimate issues on sub publicity time and variety of exposures
With all that we discovered and the simulations we checked out and the true world darkish web site take a look at we’ve fairly some details about the optimum subexposure size. Nonetheless, I wager you continue to are questioning how this impacts your explicit scenario and what the optimum subexposure size is. That can stay tough to reply precisely, and far of the main points go proper out of the window if we have to take different elements like drizzle integration and guiding errors under consideration. Nonetheless, I really feel a very powerful conclusion most likely is the truth that the publicity size is just related when the learn noise is related. And the learn noise is just related when you’re imaging below a darkish sky.
With most reasonably to robust mild polluted skies, the subexposure size received’t matter a lot as soon as you might be utilizing 2 to three minute exposures.
Let me know within the feedback under in case you agree or disagree or nonetheless are left with questions at this level!
