[naskies (Dave)]

Originally Posted by Shiraz

first off, you questioned whether sub length is proportional to read noise squared. I think that it is - the read noise and signal both increase linearly with multiple subs, but the shot noise only goes up with the square root. If you double the read noise, you need to increase the signal by 4x to get a doubling in shot noise, ie you need to expose for 4x as long if you want the shot noise to cover a doubling of read noise.

Actually, with the light of day I think we're talking about slightly different things... my mistake, sorry

Yes, I agree that with all else equal, a camera with half the read noise will only need one quarter the sub length to reach a sky-limited exposure.

(I was thinking of the SNR of an individual sub, where sub length is indeed a linear inverse relationship with read noise, but that doesn't factor into sky-limited exposure duration calculations.)

The other main points come from the underlying assumptions of the Anstey article, which are:
- you need to look at the noise in the target when you set sub length
- short subs will be messed up by quantisation noise.

I disagree on both points:
1. In any imaging I have done, the bright bits of the target are never an issue - they take care of themselves. The big problem is the noise that blights the dim parts of the scene when the target is barely visible or not present at all. For broadband imaging the primary source of noise in this region is shot noise from the sky background and target signal/ noise is quite unimportant. Hence, I consider that the Smith/Starizona approach is valid and that subs should be chosen to keep read noise below shot noise from the sky background. Noise is noise and it doesn't matter where it came from - there is nothing special about the target noise.

You don't just need to look at the target noise, but also the signal in the dim areas as you mentioned... [continued below]

2. I think that the quantisation issue is a non-starter. To take your example, consider a target with an average of 1 photon every five minutes. Some of the 2.5 minute subs (on average slightly less than half of them) will have no target photons, some will have one and maybe the odd one will have two or more. Add the signals over 12 such subs and you will typically get around 6 target photons - the same as you would get from one long 60 minute exposure. This of course depends on the stacking method - it won't work if the stacking is done by simply averaging the camera signals at the same bit resolution as the original (where you might get either 1 or 0 for the target). However, any stacking system worth its salt will at least add up the total signal and then divide by the number of subs. Then, if the internal signal representation is floating point, you may get something like "averagesignal = 0.5" and if you want to know how many photons you collected then just multiply by the number of subs - nothing has been lost by having sub signals below 1 photon on average. The final average signal will need to be stretched a bit more than it would for the longer exposure, but the SNR will be exactly the same, since the noise will also have been divided by the number of subs the get an average. ie, there is no quantisation issue at all. Even if the stacking system produces a fixed point representation, all is not lost - see http://www.stark-labs.com/craig/reso...thStacking.pdf. Maybe I have it wrong on stacking, but with my current understanding, I do not accept any of the Anstey arguments based on quantisation error.

If you don't accept quantisation noise/errors, then may I ask what your explanation is for the limiting magnitude under a given set of conditions?

It clearly applies, otherwise we could all just take huge numbers of 1 min sky limited exposures in the heart of an urban centre, and get nicely detailed mag 30 galaxies...?

In both the Smith and Anstey models, object signals are modelled as Flux*t + ShotNoise*sqrt(t).

The issue that Smith ignores is that the ObjectFlux*t signal term needs to be an integer constant - you physically can't record fractions of a target object electron in one sub. If you're recording 0 electrons for a substantial proportion of subs, then with mean/median combine the signal term is actually 0 under a least-squares fit... those occasionally 1 electrons become the shot noise (and are indistinguishable from camera read noise).

With a sum combine as you suggest, then yes - those 1 electron subs will register a signal. However, with sum combine noise increases linearly with the number of subs (SNR ∝ n) therefore stacking doesn't increase SNR. For mean combine it's SNR ∝ sqrt(n)), hence noise is effectively reduced. For our current cameras where read noise >> 0 e-, sum combine isn't practical beyond a few frames at most.

Even with low read noise cameras, a decent sub length is still required if you want to chase the really, really faint stuff... and the limiting factor will still be the target signal dominating over sky shot noise.

A couple of other comments:
- cameras with 1 electron read noise are available - they just cost an arm and a leg.

Yep. The maths should still work out the same as with 5 or 10 e- read noise cameras. The absolute game changer would be zero (or very, very, very close to zero) read noise cameras - much like a short wire at room temperature is very low resistance, but still nowhere near having superconductive properties.

- your conclusion that shooting something like the Orion nebula is similar to NB is valid, but only for the bright bits. I find that, to bring out the fine detail around it, you need to take into account the sky noise - the Smith/Starizona approach is still valid. Maybe it isn't on something like the moon or a planet, but then the issue is not one of long exposures anyway.

Yes, these SNR calculations are only valid at the individual pixel level.

- the simplest way to resolve some of these questions is by experiment, will try to do so if I can ever again find a nice clear night with good transparency.

Anstey included empirical data in his article. I've also done a few experiments myself, though nothing rigorous enough to share publicly.

Cheers and regards Ray

Thanks Ray, always a pleasure