Is it much better to have more subs and why we do it

[swag72]

Here's a little experiment that I thought I'd share here as it is something that is often mentioned by imagers. Do those extra subs really make a difference?

I have taken 2 seperate stacked subs. The first (1) contains 10x1800s in Ha and the second (2) contains 19x1800s subs. I was interested myself to see if it made much of a difference to the noise and overall FWHM between the 2 different stacks. 

They have been stacked and calibrated in PI, each with the same calibration data.

I initially looked at them together after doing an automatic stretch on them in PI and could see no discernible difference in noise or in the overall stacks in general. I decided to let the computer programme do the work for me and so put them both into the 'sub frame selector' in PI to see what that would make of it.

For this exercise sub (1) is the 10x1800s and (2) is 19x1800s

Noise

As you can see here, it's made a difference in the overall noise level in the image - While the graph makes it look like a significant difference, I don't know that the scale or measurement is really a significant measurement. Perhaps someone can offer some ideas there?

FWHM

I had noticed before when I did this that the more subs I used seemed to decrease the overall FWHM. Something that is going to be beneficial for all imagers and I am certainly happy to take the gain..... however small.

Eccentricity

I take this to be overall roundness of the stars.

I was surprised that this made much of a difference at all as the data was taken on consecutive nights so there was little difference by way of where the target was located. A small gain, but well received nonetheless.

I am of the school that you can never have enough data and always say that more subs will reduce noise - Perhaps there's some additional benefits as well. The relationship between these isn't going to be linear I am sure, so that another 9 subs will not have such a marked difference, but all being well, as I have nothing else to do tonight and the moon is still about I'll try to add some more and look again. 

I hope this has been useful or at the very least, interesting and may get us thinking about sub numbers in general.

[Earl]

can you repeate with 30 and 40 subs, is there a point that "not really worth it" arrives?

now of course there is also the issu of total time vs sub lenght

How does 20 x 10 min vs 10 x 20 min work out?

[Earl]

er hang on.....to quote "They have been stacked and calibrated in PI, each with the same calibration data.".

Come again

[Altais]

As you probably know, the noise (ideally) decreases by a factor of the square root of the number of stacked frames, which is also what we see in the first graph. Since the second stack has about twice the number of subs as the first one, the noise magnitude of stack 2 should be about 1/sqrt(2) times the noise in stack 1, and 40/sqrt(2) = 28.3 which seems to be about right.

The effect of sub length on final stack SNR (for a given total exposure time, eg. 3 hours) depends on the imaging parameters and conditions, but here's a plot that gives an idea of how it might look:

Usually for broadband imaging when you reach 5 min+ there isn't much to gain by increasing sub length, but again it depends on conditions. For narrowband I'm sure you'll still benefit from much longer sub lengths, because of the low skyglow.

[Earl]

to sum up my thoughts, ignoring target specific issue, thee has to be a rough best sub length and best number of subs (id probably go with odd numbers too 21 subs at 21 mins too as that seem s to have an impact on statistical stuff (I read that some where odd been better))

[Altais]

The optimal sub exposure length, i.e. when the benefit of increased final stack SNR is outweighed by the practical disadvantages of long subs (mount limitations, saturation, field rotation etc), will be quite different for different sky conditions, imaging trains and camera parameters. So the way I see it is that there is no overall "works for all" sublength. But you can surely work out what would be best four your specific imaging system and sky conditions.

When it comes to number of subframes, more is always better! But the SNR increase from one extra sub will be smaller when you already have many subs. So it just becomes a question of how much time you want to spend before you decide that acquiring more subs isn't worth the bother.

Do you know where you read about odd numbers being better? I fail to see why an odd number of minutes is beneficial, as the minute is just an arbitrary way to measure time.

[swag72]

er hang on.....to quote "They have been stacked and calibrated in PI, each with the same calibration data.".

Come again

Each separate sub was calibrated in PI with the same calibration subs (bias, darks and flats).

Thanks for your replies Lars

[Martin Meredith]

I recent asked myself a related question in the context of much shorter overall durations (for near real-time viewing), on this thread (post 27 in particular). My interest was in an answer to the question "what is the shortest sub length I can get away with without serious loss in SNR", the idea being to match that sub length to sky conditions and use stacking to achieve the decrease in SNR while providing as rapid an image update (the "near real time" point) as possible. 

As Lars says, the optimal sub length depends on quite a few factors. The graphs I plot in that thread show how sky conditions, sub length and target magnitude interact. I know it is not quite the same issue that Sara raises, but the SNR analysis is essentially the same.

Martin

[Earl]

her.

Do you know where you read about odd numbers being better? I fail to see why an odd number of minutes is beneficial, as the minute is just an arbitrary way to measure time.

I cant recall atm, it was something to do with number crunching / statistics  and image calibration if i remember where  ill link it.

[Earl]

Each separate sub was calibrated in PI with the same calibration subs (bias, darks and flats).

Thanks for your replies Lars

Its the "PI" bit

[D4N]

In statistics if you have an even number of observations the median will land between two observations, if you have an odd number of observations it will land on an observation giving you a median to start with. Since many stacking parameters are based on medians this will make things much easier for the computer to work out.

Consider the numbers 1,2,3,4; the median is between 2 and 3 and will need to be a calculated value. Now consider 1,2,3,4,5; the median is 3 - much easier

Choosing the middle one is much easier if there is a middle one

This applies to the number of sub frames, the length is irrelevant for this purpose.

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[Altais]

Thanks D4N, that makes sense. I can see how this would be something to consider for more computationally expensive projects, but I doubt that it would make much of a difference for stacking a bunch of frames. 

[D4N]

Remember it is the median taken of every pixel, if you have 100 bias frames at with 8 million pixels each then that is 800 million calculations the poor computer has to do that it wouldn't have to if you had 101 bias frames.

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[StuartJPP]

Remember it is the median taken of every pixel, if you have 100 bias frames at with 8 million pixels each then that is 800 million calculations the poor computer has to do that it wouldn't have to if you had 101 bias frames.

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Doesn't the poor computer still have to arrange either 8 million pixels x 100 (or 101) bias frames in order to find the median? To find the median of an even number of samples you add the 2 "middle" values and divide the result by 2? That is 8 million extra "instructions", not 800 million. (though strictly speaking the "instructions" are two instructions...an add and a divide.

Or am I missing something?

[Altais]

Agreed Stuart. But my point D4N is that the simple operation of taking the mean of a lot of pixels is extremely fast. I tried loading up 21 and 20 4290x2856 CR2 frames in MATLAB and perform a pixelwise median on each set of frames. The median operation took just about the same time, 2.6 seconds, on both sets. So there is a slight increase in speed per frame for the 21-frame stack, but adding the extra frame certainly didn't reduce the processing time. The most used stacking algorithms are more sophisticated than taking a simple median, and I would think it's things like pixel rejection that takes most of the time.

[swag72]

Here's 3 further graphs showing the same but now (3) is 28x1800s of data. Those plots just keep on dropping

Noise

FWHM

Eccentricity

[swag72]

Here's a page I've added to my website if anyone is interested - If there's anything that you think is wrong etc then do let me know and I can amend it.

I hope that people find it of interest - There's a visual difference in there too. 

http://swagastro.weebly.com/the-benefits-of-extra-subs-in-graphics.html

[Big Jim Slade]

The docs for Image Integration in PI also have this graph on the subject:

So, theoretically you get the best bang-for-buck up to about 30 subs, and then you are in the zone of diminishing returns.

[Earl]

Thank you Sara for putting thime in on this target and sharing the results.

You have pusghed me to make sure I can do 30 min subs which i confirmed last night.

I just need to get the subs now.

Im not one to dedicate time to one frame atm, so i m working in two hour chunkc per frame, and besides the tareget ait going anywhere soon in my lifetime LOL

Im working on a Cygnus mosiac so need to cover some serious area my 2 hour results al bee it on 600s subs previosly are my best i feel and this will give me plenty of rom to improve.

Next trick will be merging panes smeelessly.

O and i sorted out the mosiac tool joby in sgp and hae made extensions on my sup with it

[swag72]

Cheers Ian and Earl.

Interestingly then about 30 subs seems to be the cut off point - So if I am looking at RGB data (which I don't often do!) I may as well not bother collecting more than 30 subs regardless of sub length? I tend to collect quite short RGB subs and have been known to get into 100 - Was I wasting my time? With RGB data will the colour improve as I get more subs?

[Martin Meredith]

I think the 30 subs 'rule' has to be treated carefully. What matters is the final SNR, not the incremental improvement. If I take 30 x 1s subs my final SNR (ignoring read noise and thermal noise) is theoretically the same as a single 1 x 30s sub, yet in the latter case I've only taken 1 sub. The same number of photons are involved in both cases. In spite of diminishing returns after 30 subs, there are still returns to be had, and they are absolutely necessary in order to achieve a good final SNR in the case of these hypothetical 1s subs because the initial (single sub) SNR is so poor. More signal is always better.

Having said that, there surely has to be a point of diminishing returns, but I think we need to take account of the capacity of later processing stages to make use of the improved SNR, including constraints imposed by display devices/media and ultimately the human eye. What is the SNR required to create a perceptual just-noticeable-differences between N and N+1 subs? This is a complex issue but surely worth studying.

cheers

Martin

[Altais]

I see no reason to limit yourself to 30 frames. According to the sqrt(x) - sqrt(x-1) plot, even at 100 frames there is still a 5% increase in SNR when adding another frame! I think it's misleading to talk about diminishing returns like it's a limitation for a sqrt(N) plot. For an exponential function yes, for a sqrt no.

[Altais]

It's supposed to be 0.5% rather than 5% above, but my point is that the increase is not insignificant. Go from 100 to 120 frames and you still have a 10% increase in SNR.

[Earl]

I see no reason to limit yourself to 30 frames. According to the sqrt(x) - sqrt(x-1) plot, even at 100 frames there is still a 5% increase in SNR when adding another frame! I think it's misleading to talk about diminishing returns like it's a limitation for a sqrt(N) plot. For an exponential function yes, for a sqrt no.

100 30 min frames would probably take a UK based imager a whole year to do? unless the weatehr is on your side. x that by LRGB for instance and your talking 120 frames for 60 Hours, that is one serious undertaking. let alone 400 subs if tou use a 1:1 for them  of course this is not awlays the way but still you get my point.

[Altais]

100 30 min frames would probably take a UK based imager a whole year to do? unless the weatehr is on your side. x that by LRGB for instance and your talking 120 frames for 60 Hours, that is one serious undertaking. let alone 400 subs if tou use a 1:1 for them  of course this is not awlays the way but still you get my point.

I agree, most people will not take 100+ frames. I just used it as an example to illustrate that even with a large number of frames, you can still get significant gains in SNR by adding some more.

But to put it more realistically, adding another 10 frames to a 30 frame stack increases the SNR by 15%. Compare this to the 22% increase when going from 20 to 30 frames. Whether or not it's worth it comes down to personal opinion, but I don't think people should just stop at 30 because they think their images won't improve by going beyond.