To stack or not to stack: 30 x 1s = 1 x 30s?

[Martin Meredith]

Motivated by some discussion on another thread concerning the difference between stacking M subs of N seconds each versus a single sub of length M*N, I started my session yesterday with a not-very-scientific test on M57. The first image is a stack of 30 x 1s subs while the second is a single 30s sub (the caption for the former says 36x1s which may be the case but I'm stopped the tracking at 30, so perhaps it was the live stacking catching up -- as I said, not a very well controlled experiment). Usual kit: Quattro 8" f4 reflector, Lodestar X2 mono camera, LodestarLive v0.11, no filters, AZ-EQ6 mount in alt-az mode.

I've looked quite carefully and I don't see a lot of difference. Especially around the nebula itself any evidence for the fainter extensions is similar in both. They both show the spiral galaxy IC 1296 to about the same (limited) degree, near the triangle of stars to the SW of M57.

If we were just collecting photons then theoretically the two images should be identical (i.e., unavoidable photon noise varying with the square root of the signal should be the same). But there are several factors that might have been expected to cause differences in practice: read noise (30x more in the 1s subs case); thermal noise (more in the 30s shot);  tracking issues (more in the 30s case); stacking failures (more in the 1s case); etc…

In spite of theory, it is quite surprising to me that the two turned out so similar. I expected read noise to have more of an impact in the 1s subs case. It is of course possible that other factors are masking any benefits of the longer subs. These might include the presence of a 70% moon, the lack of complete astronomical darkness (SQM 17.7 at this point), poor tracking, scope collimation etc. And no darks were used. But some of these are factors that I face on many observing sessions without undue concern.

If it turns out to be the case that more short subs are equivalent to fewer but longer subs, at least for the style of observing on this forum, then this is probably good news on gusty nights, or for less than top-notch mounts; and in any case for delivering a 'nearer' real time feel. One second is too short though, as live stacking (at least on my 3-year old MacBook Air) can't quite keep up. But it isn't far behind and 2-5s is certainly feasible, and the live stacking in LodestarLive works like a dream even when thrashed like this  .

More tests are needed on fainter objects on darker nights… I'd be interested to hear of similar tests or of views on performing more controlled experiments.

cheers

Martin

[nytecam]

Martin - interesting experiment and the two images look very similar despite wholly different exposure techniques.  It's difficult to judge stellar penetration from positive images due to computer/laptop settings black level and these effects appear more obvious in negative mode [though most folk avoid this presentation].    Keep up the good work.

I'm still playing with the binning modes in SX s/w eg 2x2, 2x1 [=Fast], 1x1 progressive etc eg fast + lower res to hi-res slower speed from the Lodestar with Fast mode my favour option for a long time...and it works in colour too !

[aparker]

Martin,

Great experiment. It's always good to challenge one's assumptions with some empirical evidence. I have to admit your results are a bit coumterintuitive to me as well. I wonder if part of the reason you are not seeing a big difference is that you have only bright objects in your field (stars, M57)? What I've read about astrophotography (which I have no personal experience with) suggests that exposure times should be set to maximally utilize the sensor's dynamic range over the object to be imaged. With too short an exposure you have only a small difference between the brightest pixel and the background noise level, which limits how much you can "stretch" the resulting data to reveal subtle differences. With stacking you then even out the noise, but you can't ever increase the native dynamic range of the individual subs. I would suggest that an extended object with low surface brightness like M51, or perhaps an Ha shot of the North America nebula, might be a place to try a more acute test of your M*N hypothesis.

Alex

[Martin Meredith]

Thanks Maurice for the thought of examining the negative. I'll do that. Something I just noticed (not sure why it took so long as it is staring me in the face) is the diagonal banding on the 30 x 1s image. Someone with more knowledge of the way these sensors work might be able to explain what is happening here (or it might be a stacking artefact). But it is certainly a regularity. 

Alex, its a good idea to test a low SB object. Next time out… (actually, I should have done it last night as I was examining a very low SB ring which I'll post later). I get what you're saying about the dynamic range, and I've always wondered if quantisation noise plays a part too down at the low end (though strangely a bright sky level will push the sensor response out of the really low end anyway, so probably not a problem). 

Another possibility is that the benefits of longer exposures will be more obvious seen in better seeing. Last night was 3/5 according to one of the  Meteoblue astronomy seeing indices. 

Martin

[Macavity]

Fascinating result. And useful too... I had long wanted to perform this experiment,

but was time & clear sky limited! Anecdotally (theoretically) this is the difference

between "classical" imaging stackers, and what we video astronomers do.

I suppose my MAIN reason for being a video astronomer (besides the real-time stuff)

is that my HEQ5 can guarantee some sort of "steadiness" over a 10 sec integration.

Although the facility exists to do "infinite" exposures with a Watec 120N+ I never tried. 

Great food for thought though! After many years in the financial doldrums, I have

just receive a (modest!) pension compensation for un/wisely remaining single. lol

Not sure whether to upgrade to a Watec 910HX or go the Lodestar (live) route... 

I still get a minor "buzz" when local society "classical" imagers look at my (stacked)

images and say... "Gosh that actually rather good... really interesting..." etc. etc.

The boundaries between the various methodologies become (hopefully) ever less! 

[Dragon Man]

Martin, I am having trouble understanding your results.

They seem to be a bit backwards.

I'll try to explain:

Your first image is the stacked image of 30 x 1 second frames.

Your second image is a single 30 second frame.

The first one should, because of stacking multiple frames, have a smooth background and be almost noise free. But it isn't.

The second one, because it is a long single frame, should have lots of noise. But it doesn't.

Your second image should be the result of your first method because it has a far smoother background and very little noise.

You first image should be the result of your second method because it shows noise and artifacts.

 Interesting!

On my monitor, the first image is very noisy and has interference artifacts about 1cm apart running across the entire height of the frame.

BUT!!! I really like your second image! 

So, to me, the results appear reversed to what they should be for some strange reason.

[Martin Meredith]

Hi Ken

Theoretically, leaving aside read noise, thermal noise, tracking/stacking errors, the images should be identical. The improvement you get in SNR from stacking is the same as you get by increasing the exposure. We're used to thinking of stacking as a form of noise reduction, but increasing exposure does exactly the same job. Craig Stark has some good tutorials on this.

One way I like to think of it is this: instead of letting the photon stream build up for 30s, you have a device that chops it up into 1s chunks and stores them. Then these chunks are averaged. Now, averaging is the same as summing apart from a single factor (the number of subs). This analogy assumes negligible cost to chunking them (no read noise) and no stacking errors (straightforward averaging without registration), but I think it illustrates the fact that from a noise reduction perspective the two approaches are identical.

I'm wondering what has made the first image look so bad on your screen. On mine I can see the diagonal lines but they're not very obvious at all which is why I missed them at first. To me the images are almost identical...

Martin

[Martin Meredith]

Hi Chris

I hope you get a chance to experiment too. If this kind of approach holds up, it may be that the range of suitable cameras and mounts is widened, but let's see if other DSOs show similar results too. I'm sceptical. But if I manage to capture more it would be interesting to compile the short subs into a video (at last!) to show the image improving in close to real time.

One of my goals at some point is to put together a portable kit based on a small travel scope and something like the Star Adventurer mount, which I assume isn't going to be great at tracking. If we can get away with shortish subs this might just work.

Martin

[Dragon Man]

Hi Ken

Theoretically, leaving aside read noise, thermal noise, tracking/stacking errors, the images should be identical. The improvement you get in SNR from stacking is the same as you get by increasing the exposure. We're used to thinking of stacking as a form of noise reduction, but increasing exposure does exactly the same job. Craig Stark has some good tutorials on this.

One way I like to think of it is this: instead of letting the photon stream build up for 30s, you have a device that chops it up into 1s chunks and stores them. Then these chunks are averaged. Now, averaging is the same as summing apart from a single factor (the number of subs). This analogy assumes negligible cost to chunking them (no read noise) and no stacking errors (straightforward averaging without registration), but I think it illustrates the fact that from a noise reduction perspective the two approaches are identical.

I'm wondering what has made the first image look so bad on your screen. On mine I can see the diagonal lines but they're not very obvious at all which is why I missed them at first. To me the images are almost identical...

Martin

Ahhhh, OK.

I am not familiar with the stacking methods of a Lodestar or however you are doing it. It sounds totally different to all the stacking procedures I am familiar with. 

Yes, the lines across the first image are very obvious on my monitor (HP Pavilion laptop). 

[arkosg]

Hi Martin,

Thanks for posting this - interesting & thought provoking!  Look forward to seeing this explored with other targets...

I see what Ken sees as well - although, I must admit, I didn't notice the lines until I looked carefully after Ken mentioned them!  

Cheers,

- Greg A

[D4N]

I think you need to remember that you will see a greater difference when both sub lengths are stacked.

For example if you have 10 hours of data on a target in 10 minutes subs that is 60 subs, a nice healthy number of subs to stack.

If you have 10 hours of data in 1s subs that is 36000 subs. Apart from taking a ridiculously long time to stack and using a phenomenal amount of hard disk space this data set will have gone well past the point of diminishing returns.

Sent from my iPad using Tapatalk

[stash_old]

Inverting the picture and turning up the contract and turning down the brightness(in Gimp) shows the lines better well it did on my screen - hope that helps Martin 

https://drive.google.com/file/d/0B9aHac2P5RgVQTV1N3JJWkR2ZGs/view?usp=sharing

https://drive.google.com/file/d/0B9aHac2P5RgVNjRfSnBKQnZyNG8/view?usp=sharing

[orion25]

Interesting experiment, Martin! Thanks for sharing the results. I can see the lines in the first pic on my desktop at default brightness; it was the first thing I noticed. Other than that, the two pics look nearly identical, and pretty darn nice!

Cheers,

Reggie

[HiloDon]

Hi All,

I think the explanation to Martin's question lies in the issue of dynamic range as pointed out by Alex. That includes both the dynamic range of the object and of the recordable dynamic range of the sensor. Stacking does two things. It reduces random noise and it increases dynamic range to a limited degree. Here is an excellent paper written by Kieth Wiley that best explains it.

http://keithwiley.com/astroPhotography/imageStacking.shtml

My suspicion is that the recordable dynamic range of the LS is greater than M57. So, all the M57 data is recorded both at one second and at 30 seconds. Therefore you don't see much difference in Martin's images. A different object with a larger dynamic range may produce different images.

I am not an expert on this, but it appears to be what Kieth is saying in his article.

Don

[Martin Meredith]

Here's a little more data I collected last night. This time I went for a compromise of 5s stacking time since this allows LL to stack in real time with no hold ups. I did collect darks for the 5s exposures but not the rest, so you might see some hot pixel trails on the 30s versions.

Starting with M57 again, here are 500s worth expressed as 100 x 5s frames versus 17 x 30s frames. Here I've inverted in GIMP, blown up 4x, and scaled so the brightness is more or less equal. I realise that M57 is a bright object but it also has faint extensions.

Next, as requested, a fainter group of objects: Seyfert's Sextet (Hickson 79) in Serpens. Similar process to above but with overall times of 270s.

Finally, a quiz. The following panels show part of an Abell cluster in Hercules in the region of NGC 6050. All represent 300s total exposure, in stacks of 5s, 10s and 30s subs. Can you guess which is which?

I'll come back later to the dynamic range point raised by Alex and Don (which I tend to agree with) and also with more thoughts/data on the origin of the diagonal lines.

cheers

Martin

[Martin Meredith]

I've been reading (again) the excellent Keith Wiley article that Don recommended. Here's a quick summary. He covers three separate but related issues.

First, the question of whether mean and sum stacking are the same. I entirely agree with his argument that sum and mean stacking are the same thing if the internal representation of the data is in floating point. This last part is important and relevant to the current discussion, which is phrased in terms of summing but applies equally well to the mean stacking that I use in my images.

Second, he states that the "classical application of image stacking is to increase the signal-to-noise ratio". This is true, although what isn't mentioned is that stacking is not the only way to achieve this. It can also be done by increasing exposure. Stacking -- to my mind -- is not about increasing SNR, but about a way to increase SNR without making unrealistic assumptions about tracking, without over-exposing, and with the opportunity to reject transient artefacts (i.e. bad subs).

Third, he argues that stacking increases the dynamic range of the signal: too short an exposure risks not recording the faintest information, but pushing up the exposure time to deal with this risks saturation of brighter parts. The solution is to stack subs that are short enough to avoid saturation.

But the issue I'm raising is at the other end of the scale, as Alex points out, and concerns the representation of faint objects.  Wiley also deals with this. I'd like to quote the article here: "you take a bunch of images that are carefully exposed so as not to saturate the brightest parts. This means you honestly risk losing the dimmest parts. However, when you perform the stack, the dimmest parts accumulate into higher values that escape the floor of the dynamic range, while simultaneously increasing the dynamic range as the brightest parts get brighter and brighter as more images are added to the stack".

He then goes on to say "Now, it should be immediately obvious that there is something slightly wrong here. If the raw frames were exposed with a short enough time period to not gather the dim parts at all, because the dim parts were floored to zero, then how were they accumulated in the stack? In truth, if the value in a particular raw falls to zero, it will contribute nothing to the stack. However, imagine that the true value of a dim pixel is somewhere between zero and one. The digitization of the A/D converter will turn that value into a zero, right? Not necessarily. Remember, there is noise to contend with. The noise is helpful here, in that the recorded value of such a pixel will sometimes be zero and sometimes be one, and occasionally even two or three. This is true of a truly black pixel with no real light of course, but in the case of a dim pixel, the average of the Gaussian will be between zero and one, not actually zero. When you stack a series of samples of this pixel, some signal will actually accumulate, and the value will bump up above the floor value of the stacked image, which is simply one of course."

(BTW This is why an internal representation in floating point is crucial)

My reading is that stacking can help us overcome an apparent loss of information at the faint end, which in the context of the current discussion presumably permits us to get away with shorter subs than we might have expected, leading to all sorts of advantages for near real-time observing (including the use of longer FLs on alt-az mounts without field rotation, not hanging around for ever collecting darks, seeing the image develop at a faster rate). I guess the question becomes: what is the shortest sub I can get away with for each type of object? 

Martin

[Martin Meredith]

This article from Craig Stark explains more rigorously how stacking increases bit depth.

Martin

[aparker]

Martin,

Thanks for the review of the Wiley article and the pointer to the Craig Stark article. I'm going to go read them both now.

I played a bit with the math today just to make sure I had the issue straight in my head, and I agree with the point you emphasize above: this only works if the stacking process maintains a floating point representation of the mean pixel value. We should confirm with Paul how LL does this, although given the quality of the results you show above I can't believe it doesn't do it this way.

The quote you show about faint objects rising above the noise floor with sufficient sampling is right on the money from a statistical standpont, although there is probably a floor imposed by stuff like read moise that accumulates in a non-time-dependent way.

[aparker]

Finally, a quiz. The following panels show part of an Abell cluster in Hercules in the region of NGC 6050. All represent 300s total exposure, in stacks of 5s, 10s and 30s subs. Can you guess which is which

Martin

I'm going to guess A=30sec, B=10sec, C=5sec.

[HiloDon]

Martin,

Thanks for the review of the Wiley article and the pointer to the Craig Stark article. I'm going to go read them both now.

I played a bit with the math today just to make sure I had the issue straight in my head, and I agree with the point you emphasize above: this only works if the stacking process maintains a floating point representation of the mean pixel value. We should confirm with Paul how LL does this, although given the quality of the results you show above I can't believe it doesn't do it this way.

The quote you show about faint objects rising above the noise floor with sufficient sampling is right on the money from a statistical standpont, although there is probably a floor imposed by stuff like read moise that accumulates in a non-time-dependent way.

Hi Alex,

I started a thread about this a while back and there is a response from Paul regarding the stacking process.  

http://stargazerslounge.com/topic/236544-sum-v-mean-stacking/

Don

[Martin Meredith]

I'm going to guess A=30sec, B=10sec, C=5sec.

Close. Actually, it is A=30, B=5, C=10. But that suggests you can detect the 30s subs, which is interesting….

Martin

[Martin Meredith]

On Saturday I did some further 'fast stack' experimentation in Ursa Major/Draco comparing 5s and 30s subs on various types of objects, some of which I'm posting here. As before, I collected darks for the 5s case (rapid!) but not for the 30s, so some hot pixel trailing can be seen on the latter. My approach was to first observe with the 5s subs stacking away and choose brightness/contrast/nonlinear mode to suit; then do the 30s subs up to a similar overall maximum exposure, using the same settings. 

Conditions: 92% illuminated moon, SQM 18.7, but very good seeing for a change.

Here's M101 with the same total exposure (240s) in 5s subs (left) and 30s subs (right). I've inverted and adjusted the brightness to make the comparison fairer. 

Next, the fascinating Arp 214 plus Hickson 56 (below the highly warped NGC 3718). 

Here I think the 30s version has slightly better defined extensions in the main galaxy, and perhaps more contrast in the leftmost member of the 5-strong Hickson group.

Next, a tough challenge, Hickson 50, known as the most difficult group in that catalogue, along with M97. A 60s total exposure managed to capture the 4 'brightest' components (mags 18.6 to 19.5). The labelled inset is from the DSS image (from Reiner Vogel's excellent Hickson guide, available online).

The mag 20 'e' component was reliably seen in 90s for both sub lengths. The Owl is maybe a little better defined in the 30s subs, but this might just be the settings. In any case, for the faint galaxies there seems little to choose.

Now, another favourite Hickson of mine, HCG 55, a very compact chain of 5 galaxies in Draco with the faintest component (2nd from top) having mag 17.4. Here the total integration times are not quite the same, at 85s for the 5s subs and 90s for the 30s subs. I also did a 66 x 1s integration which is noticeably noisier (perhaps the extra read noise?).

Finally, not far from Hickson 56 is the exceedingly faint compact group, Shakhbazian 2, at nearly 2 billion LYs distance. Only 3 of the 9 members are catalogued in LEDA, with mags as indicated in the schematic. Only positional information is available for the remainder.

Some of the members are simply not visible at all without stacking, as the figures below show. By 75s (15 x 5s), 5 or 6 members are detectable, with component 5 appearing by 29x5. 

Unfortunately the stacking reset itself after 44 so I couldn't continue, but I also did the same for the 30s case, and this went deeper, with component 9 just about making an appearance in the 16x30s stack. 

Note that this isn't a one-for-one comparison: the total sub lengths need to be taken into account. I believe that in this case the 30s stacks are a little cleaner (comparing say the 4x30 with 23x5, but in terms of galaxy detection there isn't a lot of difference (compare 44x5 with 8x30). 

====

In summary, I'd say that the differences between the fast stack technique and the 'longest sub possible' approach are pretty marginal. Fast stacking can find very faint galaxies, even down to mag 20 with a 90% moon. It also pulls out faint diffuse detail in galaxies such as M101. At the same time I'm willing to accept that there may be objects where the advantage of the longer subs is more noticeable.

But I'm starting to prefer the fast stack approach since it is great to see additional details appearing almost in real time. It reminds me of eyepiece viewing, with the time required to tease out information. The best example of this for me was Shakhbazian 2. It is exciting to see nothing at first and then see the galaxies emerging one by one. For some reason, waiting 30s now seems too long…almost like imaging ;-) But seriously, 30s is long enough for a fairly noticeable discrete change in the image, whereas in 5s the process seems more continuous. What makes this possible at all is the excellent live stacking in LodestarLive. 

Martin

[Macavity]

Impressive stuff!

I think it would come as a welcome *relief* to some (many!) of us?

Simply, I haven't had sufficient time (skies) to explore the plethora of

"variables" involved in VIDEO astronomy! After beginning my (video)

Messier, Caldwell (and O'meara) marathons, I recently increased the

integration time for "faint" objects to 100 x 10.24s with Watec 102N+

(I get away with 100 x 2.56 sec for brighter objects: GC's, OC's etc.) 

But 20min real time approaches my limit of patience / practicality?

Again, I think I do need a *little* more sensitivity - Perhaps via the

Watec 910HX or Lodestar II (uses same, 4x more sensitive, chip?).

Just bought an Altair Astro 66mm / F6 (ahem, semi-APO!) - Wider

fields, but I now need to start winning back some "light"! Apologies

for veering off-topic, but THIS really helps my "upgrade strategy".

[aparker]

Close. Actually, it is A=30, B=5, C=10. But that suggests you can detect the 30s subs, which is interesting….

Martin

I was pretty sure about A=30; the B and C were a guess. Stars look larger in A suggesting the beginning of tracking imprecision creeping in.

[dph1nm]

But are you read noise limited? I did some quick calculations. Assuming a sky of 18 mag/sq.arc., a 0.2m aperture scope and 2" pixels, I get very roughly for mono (i.e. unfiltered visible) imaging around 100 photons per second per pixel from sky.  So if the read noise is less than 10e-, sky noise is the greater effect.

NigelM