Is the total exposure always the same?

[Bugdozer]

Having read up a lot on exposures for deep sky photography, I had a thought which at first seemed logical but then I wasn't sure.

It's commonly accepted that a stack of 120 exposures of 30 seconds each is equivalent to 30 exposures of 2 minutes each, both resulting in a total exposure time of one hour. But is this true? Or is it that an exposure of a very short duration can never capture objects below a certain magnitude because they will always get lost in the noise? Is one long exposure better than several short exposures?

To summarise, (with an obviously silly extreme example) could you theoretically get an exposure of one hour out of stacking 3600 one second images? Leaving aside the problems you'd get with visible stars for alignment etc.

[FunkyKoval35]

Well, total explosure time will be the same in both cases, but you are absolutely right about noise. Stack of shorter single explosures will be much noiser - faint regions, if they will be visible at all, they will be much noinser.

Example:

[symmetal]

The only difference is the read noise added to each exposure. If there was no read noise in the camera then the above exposures would be identical as far as noise is concerned, including 3600 x 1 sec exposures and 1 x 1 hour exposure. 🙂

In the images above, 1 300sec exposure has 1 contribution of read noise added, while 10 x 30sec exposures have 10 contributions of read noise,  so the latter is noisier.

However, once you expose long enough such that the noise contribution from the sky background itself is more than about 5 times the read noise contribution,  therefore making the read noise contribution insignificant, then your initial assumption is true. 

In my bortle 3 skies with a fast RASA 11 and luminance filter I would achieve this read noise swamping figure in about 12 secs, so 20 x15 sec exposures will look just like 1 x 5 min exposure as far as the noise is concerned. The 1 x 5 min will show very bloated stars though so will look worse. Having hundreds of short exposures can take a long time to process as well as taking up storage space so a compromise is needed. With a OSC camera I take 3 min exposures, although the read noise is still swamped at under 2 mins.

Alan

Edited October 12, 2023 by symmetal

[ollypenrice]

1 hour ago, Bugdozer said:

 

It's commonly accepted that a stack of 120 exposures of 30 seconds each is equivalent to 30 exposures of 2 minutes each, both resulting in a total exposure time of one hour.

Quite simply, this isn't commonly accepted and has been the subject of endless debate.

The relationship between 'more and shorter' and 'fewer and longer' depends on the camera technology in question. What are now 'old technology' CCD cameras had significant read noise so you got one dose of this noise per exposure. This made 'fewer and longer' advantageous because you got fewer doses that way.  Modern CMOS cameras have remarkably low read noise so the penalty of read noise per exposure is reduced to very little. 

In any event, signal must overwhelm noise and the 'zero noise' camera does not exist, so that gives us a bottom line.

We must also remember that modern cameras have high pixel counts and that a serious image might need twelve hours. Now Alan, above, images with an F2 RASA - as do I. We can go deep in three hours. Turn that into twelve hours and ask yourself how many subs your computer can calibrate and stack.

Olly

[Bugdozer]

2 hours ago, ollypenrice said:

Quite simply, this isn't commonly accepted and has been the subject of endless debate.

The relationship between 'more and shorter' and 'fewer and longer' depends on the camera technology in question. What are now 'old technology' CCD cameras had significant read noise so you got one dose of this noise per exposure. This made 'fewer and longer' advantageous because you got fewer doses that way.  Modern CMOS cameras have remarkably low read noise so the penalty of read noise per exposure is reduced to very little. 

In any event, signal must overwhelm noise and the 'zero noise' camera does not exist, so that gives us a bottom line.

We must also remember that modern cameras have high pixel counts and that a serious image might need twelve hours. Now Alan, above, images with an F2 RASA - as do I. We can go deep in three hours. Turn that into twelve hours and ask yourself how many subs your computer can calibrate and stack.

Olly

OK, I only described it as commonly accepted because every internet article and YouTube video I have watched on deep sky imaging has presented it as a fact and I have never seen it debated, discussed or challenged. 

I am using a DSLR camera so not sure if that's CCD or CMOS. 

The length of computer processing time isn't relevant in the thought experiment scenario I suggested, although obviously in real life it would be if you were stacking 3600 images. 

[vlaiv]

3 hours ago, ollypenrice said:

In any event, signal must overwhelm noise and the 'zero noise' camera does not exist, so that gives us a bottom line.

Common misconception is that signal must overwhelm noise, and that is true for final image - but it is really not important in single exposure.

You can have single exposure with signal well below noise levels and still end up with final SNR that will be acceptable and show the target.

Another misconception is that "no photons" can be captured in single exposure and thus result will always be zero. I'd be happy to image something that has say 0.1 electron of signal per exposure - even if noise in that region is say 3e.

In that case roughly 9 out of 10 exposures will indeed fail to capture even single photon from target and all exposures will have signal much weaker than noise - yet, stack enough of them (in this particular example SNR is ~0.0333 and you would need to stack  (5 / 0.03333)^2 = 22500 exposures to reach SNR of 5, but it will happen.

 

[ollypenrice]

10 hours ago, Bugdozer said:

OK, I only described it as commonly accepted because every internet article and YouTube video I have watched on deep sky imaging has presented it as a fact and I have never seen it debated, discussed or challenged. 

I am using a DSLR camera so not sure if that's CCD or CMOS. 

The length of computer processing time isn't relevant in the thought experiment scenario I suggested, although obviously in real life it would be if you were stacking 3600 images. 

The discussion has become rather academic since the cooled CMOS chip arrived but that's quite recent. Regarding CCD, though, I was a firm advocate of the long sub. I routinely shot 30 minute subs in Ha and, occasionally, in luminance. In practical comparisons I was entirely satisfied that, when looking for faint signal, the long subs were the winners. When looking for the outer glow around M31 I found it only when I switched to 30 minute luminance subs. I know several very experienced imagers who agree with this and some who don't.

With an uncooled DSLR the build-up of thermal noise over long subs is a variable affecting the decision.  

In any event, I would urge you to experiment since, had I not tried it for myself, I might have believed that 10X15 in CCD equaled 5x30. I found that it didn't. The first gave a smoother result, the second a deeper.

Using CMOS in very fast optics we just use 3 minute subs across the board.

Edited October 13, 2023 by ollypenrice
False click

[vlaiv]

Well, I thought that this is well known thing.

Here is full explanation of how things behave.

Only difference in stack of many shorter subs vs stack of few longer subs (or one very long sub) all totaling to same exposure length is in read noise.

If we had cameras with zero read noise - it would be the completely the same (as far as SNR goes) whether you use many or few subs.

Since we don't have such cameras and every camera has some level of read noise - this creates a difference since read noise is only noise source that does not grow with time - it is exclusively per exposure type of noise. Everything else grows with time, both signal and associated noise and it does not matter if you sum them physically by using long integration time or you sum them mathematically which is in fact what stacking is (as far as data goes, it makes no difference if we sum or average pixel value - average is sum multiplied or rather divided with constant and image multiplied with constant remains the same - it just does the linear stretch which we alter again in processing anyway).

Thus, stack of many shorter subs will always be of worse quality (have lower SNR) than stack of few longer subs with same total imaging time. However - difference in SNR between the two can range between significant down to imperceptible and it solely depends on how big read noise is compared to some other noise source.

This is because of how noises add. They don't add "normally" like numbers, but rather "in a special way" - like vectors, or to be more precise - linearly independent vectors (ones that are at 90 degrees to each other).

Above image explains what happens. If we have two noise sources, a and b, here a is some noise source like thermal noise or LP noise and b is read noise, then in first example if a is equal or comparable in size to b - resulting total noise c will be obviously larger than a or in fact from either of them (a or b). Diagonal of square is longer then either of the sides.

In example two, we have that read noise b is significantly smaller than this other noise source a. This results in total noise c being about the same size as greater component a. Impact of read noise becomes insignificant.

All of this explains why people get different results when stacking different exposure lengths and it also gives way to calculate what is good sub exposure length which will not impact stack in visible way.

CCD cameras have high read noise and when they were popular fewer people were into astrophotography and most of them tried to do it in dark skies. Cooled camera in low light pollution (or when using narrowband filters) - does not have significant noise source to overpower read noise (thermal noise is low and LP noise is low) and long exposure is needed for either of the two to build up enough to swamp read noise.

With CMOS cameras that are very low read noise and increase in popularity of astrophotography which lead to many more people trying to image from cities where LP is high (and also steady increase in LP over years) brought totally different situation. Today many people use 1 minute or even 30s subs without problem rather than 20 or 30 minutes, simply because there is noise source (namely LP) that will quickly swamp low read noise of CMOS sensor.

In the end - good value by which LP noise should swamp read noise is in range of x3-x5. I personally advocate x5 because it produces only 2% difference in total noise per sub and that can't be distinguished by human eye.

Calculating optimum sub length in above sense is thus easy - one should measure sky signal in their sub and make sure it is at least (5*read_noise)^2 (average background signal in sub in electrons needs to be square of 5 times read noise since signal level and its noise are related by equation signal = noise^2 or noise = sqrt(signal)).

 

 

[ollypenrice]

10 minutes ago, vlaiv said:

CCD cameras have high read noise and when they were popular fewer people were into astrophotography and most of them tried to do it in dark skies. Cooled camera in low light pollution (or when using narrowband filters) - does not have significant noise source to overpower read noise (thermal noise is low and LP noise is low) and long exposure is needed for either of the two to build up enough to swamp read noise.With CMOS cameras that are very low read noise and increase in popularity of astrophotography which lead to many more people trying to image from cities where LP is high

An interesting thought. It hadn't occurred to me that the CMOS camera might have altered the demographics of astrophotography but I think you might well be right.

Olly

[iapa]

Roger Glover did a presentation, Deepsky CMOS imaging, which does (in my view) a good explanation.

Note that this is NOT “gospel” and some may disagree.