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Old 10-11-2018, 10:33 AM
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Stonius (Markus)
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How dim can you go photographically?

I'm ashamed to admit this is something I am having trouble conceptualising in my head.

I *think it's true to say that you can capture objects that are far fainter than the sky noise simply because the sky noise is random and the signal from the object is not. There is the randomness of shot-noise of course, but this is overcome by integrating many images (analogous to the fact that while raindrops fall randomly, two adjacent rain gauges will measure the same rainfall levels). In a nutshell; we remove the randomness with temporal averaging.

Please correct me if I'm wrong on the above - as I said, I'm still learning and trying to wrap my head around this.

Okay. So given that, how do we figure out the dimmest object that can be imaged with any particular setup? How buried in noise can a signal be before it is irretrievable?

I know it's a matter of how much time you have and diminishing returns. But if you wanted to figure out a practical dimmest object limit for your setup given ideal conditions (sort of like a photographic version of the naked eye limiting magnitude used in visual observing).

Apologies if this is a dumb question. :-)

Markus
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Old 10-11-2018, 01:41 PM
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Slawomir (Suavi)
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Hi Markus,

That's a very good question and I will read everyone's input with a great interest.

One of the faintest features that I imaged with my 105mm telescope and that I am aware of was registering on average 1 photon every four 15-minute subs; signal in the area of interest was approximately 1 ADU above the floor in the final stack, where gain was 0.26e per ADU. Camera's read noise was 4e = about 16 ADU. I would need to measure how much sky glow was in each sub though.

It took about 10 hours of exposure to be able to (fairly) clearly notice this faint signal in a stack. Reaching 50 hours of exposure made this faint signal more distinct, but I was noticing little improvements with added exposure and estimated that a visually significant improvement would require at least another 25 hours of exposure (on top of final 50 hours).

I would venture to suggest that the faintest noticeable (without straining your eyes) signal that can be captured with 10 hours of integration with 3nm filters at f4.5, good QE, 105mm aperture giving 1.60 arcseconds per pixel and with darkish skies (backyard in a small town) is about 1/15th of the read noise.

To illustrate, the above-mentioned signal was in the thin long bows at the top of this image: https://www.astrobin.com/full/364378/G/
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Old 10-11-2018, 03:01 PM
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codemonkey (Lee)
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Good question Markus! I can't answer you directly, but I was doing some related analysis this morning which I thought I'd contribute.

I've always favoured shorter exposures because I seem to get sharper images with them. My recent images for example are composed of 120s subs and captured with a very low read noise, high QE CMOS sensor. I figured I was trading SNR for sharpness and I can always get more data and I loathe blurry images so it was a pretty easy decision.

I had a thought this morning though... even if I get equivalent SNR through more shorter subs, if the target has dim sections that are closer to the noise floor, will I find it as easy to bring out?

I think the answer is no. Looking at a recent image I picked a few areas and gathered some stats from my L master (after calibration of course):

Background: 442 ADU, 3.68 ADU/s
Dim but easy enough to pull out: 489 ADU, 4.075 ADU/s
Dim but could only *just* see in my stretched image without exacerbating noise more than I wanted: 460 ADU, 3.83 ADU/s

So based off that, it seems like I need a signal to be about 50 ADU above the background to find it easy to bring out. I know there's people that are a lot better at that than I am, but I'm working with my own limits here. Doing some math that tells me that for this particular target I "should" have used subs about 334s long.

I mention this because all of the discussion I ever see about this is focused on SNR but I think there's another factor to consider and that's how capable are you of pulling that data out of the noise floor.
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Old 10-11-2018, 08:37 PM
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The dimmest that can be achieved from Earth telescopes is around magnitude 28, with as I recall the original Dragonfly team going 40 times fainter and being able to image magnitude 32 with a 48 lens array. This compared with a human eye visual limit of perhaps 6 or 7.

All the usual stuff required: Low noise, high signal to noise ratio, low optical aberrations, low scattering, long exposure, large aperture, dark sky, good tracking, good processing.....

Best
JA
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Old 11-11-2018, 12:09 PM
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Interesting question so I did a some back of envelope calcs which may or may not be right.
First assumption is that you expose each sub to 10x the square of read noise so you are shot noise limited.
So lets say you have a 2e- RN camera, you expose the sky background to 40e-.
That background will have its own shot noise of sqrt(40) or 3.6e-
Now lets treat the sky background as noise rather than signal and I'm not sure whether it adds to shot noise in quadrature or by addition. Some more learned forumers may enlighten us on that. I've guessed it is in quadrature so sqrt(40^2 + 3.6^2) = 40.5e-
Next it depends on how much you stack. Stacking reduces noise by sqrt(N) so a stack of 100 would reduce the noise by a factor of 10 to 4e-
This article https://www.dspguide.com/ch25/3.htm indicates that the minimum contrast needs to be at least equal to the noise so you'd need a target signal of 4e- in the example.
If we take that as a ratio of the sky background that's also a factor of about 10 or roughly 2.5 magnitudes. That is, an object 2.5 magnitudes dimmer than the sky background will be discernible after stacking 100 subs. If the noise doesn't add in quadrature the result is different. More stacked subs will enable dimmer targets and vice versa.
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Old 11-11-2018, 01:43 PM
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A very interesting discussion.

I'm wondering if I'm still stuck in the dark ages with thinking that very short subs put a cap on the faintest signals that can be detected.

If for example, with a given setup, an extended object records say 1 photon per pixel per hour of exposure, then statistically, with 1-minute subs only one sub per 60 would contain this information. No matter how low the RN is, this signal would be most likely rejected during stacking by a rejection algortithm, in particular, if guiding is not precise or there is some focuser/camera flexing and the above mentioned signal slightly drifts between pixels from sub to sub.
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Old 11-11-2018, 02:12 PM
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A great question, and as JA mentioned earlier " Low noise, high signal to noise ratio, low optical aberrations, low scattering, long exposure, large aperture, dark sky, good tracking (e.g. AO) all help to minimise noise and maximise signal.

The amateur record seems to be around Mag 27 (CCD with 17" scope)...something to aim for perhaps?
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Old 12-11-2018, 03:02 PM
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Personally I used trial and error. As my processing workflow improves so does my practical magnitude limit which is around +13.0 to +13.3 for my dslr tripod AP. Basically after I do a good processing (rather than just quick and dirty) I can compare my shot to star charts and lookup the vmags of the dots I'm confident are signal in my shot rather than alignment of noise. Doesn't take long really to do and only need a handful to check. I can then be confident about deciding to chase a target or not as I just wont get anything beyond my range since my processing is at my limit for the data. I usually use 500 dslr subs so I'm about the limit for dinishing returns reach already, plus diminishing wakefullness and unblocked skyview. I dont know the theoretical limit of my gear and should look into that maybe, not that I can afford to replace anything. But this way I have a number to work against to make good use of my time chasing targets I know I can bring out in the shot. Damned annoying pluto its just hovering out of my reach, even still I've done sessions where its in view and I fully processed but couldn't find it in the signal at all, confirming my estimatation is practical.
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Old 12-11-2018, 03:41 PM
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Of course the bigger your light bucket the more of those scarce photons you can scoop up. So I agree that large aperture gives an advantage.

However, very low arrival rates, as mentioned below by Suavi, are likely to not make it through processing.
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Old 12-11-2018, 05:06 PM
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As an aside to the op.
Due to technical difficulties I have been forced to use the short exposure approach.
If seeing fluctuates or a plane crosses your view you lose only a short sub ..so many of mine at only thirty seconds...but it surprises me just what you can capture with many good short subs.
It will be some time before I think I will take on very dim objects.
Alex
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Old 12-11-2018, 05:07 PM
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The deepest I’ve managed yet is low SNR at Mag 22 with 8” and dark skies in about 4 hours if luminance. That was at 1.3”/pixel. If I was to image at 2.6”/pixel it wouldn’t make much difference for a star because I was already well sampled but it would help with non-point light sources.

Capturing the same amount of photons would take 1 hour with a 16” or just under 30 minutes with a 24” or about 10 minutes with a 1m telescope.

The depth that can be achieved on dusty regions and the like can in some ways be less aperture related and more a function of aperture area and resolution. This is what makes the FSQ106 and KAF-16803 such a powerful instrument combination as Mike can attest to. Large pixels and F/5 sucks up photons and makes capturing fainter dust a breeze.
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Old 12-11-2018, 05:35 PM
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Quote:
Originally Posted by xelasnave View Post
As an aside to the op.
Due to technical difficulties I have been forced to use the short exposure approach.
If seeing fluctuates or a plane crosses your view you lose only a short sub ..so many of mine at only thirty seconds...but it surprises me just what you can capture with many good short subs.
It will be some time before I think I will take on very dim objects.
Alex
Thanks.

As mentioned before, I'm still learning, so I've been keeping quiet and learning from the others. Lots of good info here that I will be referring back to. I don't have the luxury of too much sky time at the moment, so in terms of finding practical limits it will be a while before I have the time to test things myself, but my curiosity did get the better of me on this point.

I guess from a practical point of view, I wonder how people assess the magnitude of stars when the freely available catalogs I've seen don't go past mag 21 or so. Or is it a simple astrometric calculation based on a plate solve?

Best

Markus
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Old 12-11-2018, 07:08 PM
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I am learning also☺
My targets are selected if they are available...when I have covered the usual targets I may look for dim challenges but thise times are a long way off ...
ALEX
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Old 13-11-2018, 08:46 PM
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Quote:
Originally Posted by Atmos View Post
The depth that can be achieved on dusty regions and the like can in some ways be less aperture related and more a function of aperture area and resolution. This is what makes the FSQ106 and KAF-16803 such a powerful instrument combination as Mike can attest to. Large pixels and F/5 sucks up photons and makes capturing fainter dust a breeze.
Indeed, Colin! The "aperture rules" maxim is simplistic twaddle. What determines SNR is how many photons you can pack into each pixel. A small scope with a fast f/ratio in combination with a camera with large pixels works very well if what you care about is image depth (as opposed to resolution.)

My depth record currently stands at 27.6 mag/arcsec^2:

http://www.iceinspace.com.au/forum/s...d.php?t=114782

Cheers,
Rick.
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Old 13-11-2018, 09:36 PM
kens (Ken)
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Quote:
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Interesting question so I did a some back of envelope calcs which may or may not be right.
First assumption is that you expose each sub to 10x the square of read noise so you are shot noise limited.
So lets say you have a 2e- RN camera, you expose the sky background to 40e-.
That background will have its own shot noise of sqrt(40) or 3.6e-
Now lets treat the sky background as noise rather than signal and I'm not sure whether it adds to shot noise in quadrature or by addition. Some more learned forumers may enlighten us on that. I've guessed it is in quadrature so sqrt(40^2 + 3.6^2) = 40.5e-
Next it depends on how much you stack. Stacking reduces noise by sqrt(N) so a stack of 100 would reduce the noise by a factor of 10 to 4e-
This article https://www.dspguide.com/ch25/3.htm indicates that the minimum contrast needs to be at least equal to the noise so you'd need a target signal of 4e- in the example.
If we take that as a ratio of the sky background that's also a factor of about 10 or roughly 2.5 magnitudes. That is, an object 2.5 magnitudes dimmer than the sky background will be discernible after stacking 100 subs. If the noise doesn't add in quadrature the result is different. More stacked subs will enable dimmer targets and vice versa.
Made an error above in treating the sky background as noise. Only the shot noise from the sky background needs to be counted as noise. To verify I grabbed a couple of raw subs, measured the background mean and standard deviation. After converting to electrons the measured std deviation was close to the root of the mean i.e shot noise
In the above example shot noise was 3.6e-and stacking 100 subs should reduce that to about 0.4e-. However, looking at some of my own subs indicates that a SNR of 3 is more realistic for clearly discerning a star. So the star would need to be 1.2e- which is 3.8 magnitudes fainter than the sky background.
I'll do some experiments to see how that compares with real life.
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Old 13-11-2018, 09:59 PM
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Indeed, Colin! The "aperture rules" maxim is simplistic twaddle.
Cheers,
Rick.
Sorry, are you saying professional Astronomers constructing 50-100 meter aperture optical telescopes are deluded?

You can run the marathon, or drive it in a car. The car gets there sooo much faster.....
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Old 14-11-2018, 07:34 AM
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Sorry, are you saying professional Astronomers constructing 50-100 meter aperture optical telescopes are deluded?
And there are astronomers doing science with a tiny Dragonfly array that can't be done on 50-100 meter scopes. I'm saying it's not as simple as big aperture good, small aperture bad. Try to keep up, Peter

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You can run the marathon, or drive it in a car. The car gets there sooo much faster.....
Small scope + big pixels = motorbike?
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Old 14-11-2018, 08:28 AM
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Where's the Oracle of Ray when you need him...? to put everyone straight ...sorry Rick, you are a sane unbiased Oracle too buuuut Ray is well?...Ray ...

Mike
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Old 14-11-2018, 08:31 AM
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And there are astronomers doing science with a tiny Dragonfly array that can't be done on 50-100 meter scopes. I'm saying it's not as simple as big aperture good, small aperture bad. Try to keep up, Peter



Small scope + big pixels = motorbike?
Iím well aware of the Dragonfly array (they use SBIG cameras after all ) but the systemís magnitude limit has been slowly increased by effectively *increasing its aperture* (by adding additional lenses to the array) while keeping its f-ratio constant.

Also, while it is great at detecting very dim very extended flux sources, it also has very ordinary resolution. Sadly, no free lunch.
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Old 14-11-2018, 08:49 AM
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Quote:
Iím well aware of the Dragonfly array (they use SBIG cameras after all ) but the systemís magnitude limit has been slowly increased by effectively *increasing its aperture* (by adding additional lenses to the array) while keeping its f-ratio constant.

I think this is not quite the case - by addiing lenses, they are essentially adding the frames to the stack.

The only thing saved here is time (but not money, considering the price of Canon 400mm f/2.8 lens)
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