The stacking of a substantial number of short exposures is what makes short exposures altazimuth astrophotography possible at all.
Surely, more and more sensitive and less noisy cameras also make things easier, by improving the Signal to Noise Ratio (SNR) of an image for a given time of exposure.
We are not yet able, however, to obtain a really pleasant image of a DSO with a single 15-60s exposure, so we have to “stack”, that is to “sum”, multiple short exposure pics in a single final image having the “quality” of a single long exposure.
How does this happen?
Essentially the signal (S), that is the information brought to us by the photons arriving from outer space, and in which we are interested, increases linearly with time. Hence a 60s exposure of a given subject collects twice the signal of 30s exposure of the same subject taken in the same context (i.e. under the same sky, with the same equipment).
The noise (N) instead, that is “all the unwanted (and, in general, unknown) modifications that a signal may suffer during capture, storage, transmission, processing, or conversion” (Wikipedia) increases as the square root of the exposure time (assuming it follows a Poissonian distribution). So a 60s exposure will have just twice and not four times the noise of a 15s exposure.
If we now take, as it is usually done in quantitative treatments, Signal to Noise Ratio (SNR) as the measure of the quality of an image, we can quickly work out that it increases as the square root of total exposure time.
Where t is, of course, the total time of the exposure, expressed in seconds.
Stacking is a complex, pixel by pixel, operation performed on a group of pics and it involves many mathematical operations on each pixel of each pic, so it has to be performed by a specialized software.
To this end I have used or use a good number of those available on the market: DSS, Regim and Sequator among the free ones and (in full or trial edition) Maxim DL, Astroart and Astro Pixel Processor among the commercial ones.
I did not use Regim or Sequator very much, but they both worked, Sequator being the simpler as far as options are concerned and Regim being probably the slowest (possibly because it relies on a Java Virtual Machine to run).
Deep Sky Stacker is clearly a classic and probably to many THE free stacking astrophotography software of choice. I used it also back in 2007 and surely it does its job, even if I never really came to like its interface and experienced a few crashes, particularly when using the kappa-sigma clipping algorithm.
Maxim DL and Astroart are rather similar in their processing flow and in their user interface, with Astroart being slightly faster and Maxim DL having perhaps more options.
Recently I have settled with Astro Pixel Processor (APP), a newcomer to the market, significantly slower than Maxim or Astroart (it too is based on Java), but so far the one which gives me the best results.
I particularly appreciate the possibility of stacking only a crop selection of the whole picture and the easiness with which APP is able to merge light frames of the same subject taken on different nights and with different scopes and/or cameras in one single final picture.
Details about each of this programs can be find on the respective Internet sites, but the basic logic is common to them all.
A reference picture is established and the others are aligned to it, so that even if the subject moves relatively to the frame, at least a common area is summed up (or “integrated” through all the pics. Then, after having established some quality criterion (usually based on the shape of stars or their FWHM) useful to decide which pics to integrate and which not, integration may start.
Integration consists essentially in taking (for all the pixels in the pic) the value of a given pixel and “add” it to the value of the same pixel in all of the other pics you are going to integrate, through the use of some mathematical formula.
There are usually three formulas common to most stacking programs: average, median and (kappa-) sigma clipping. Names can slightly vary, as well as flavors of the formulas themselves, but the root concepts are the same in all the programs.
The average is … a mean: the sum of the values divided by the number of the values summed.
The median is is the value separating the higher half of the pixel values from the lower half.
Sigma clipping is a more complex algorithm and the best one to reject plane or satellite trails (but also buildings or passing clouds) from the final image.
From its explanation on the DSS site :
Two parameters are used: the number of iterations and the standard deviation multiplier used (Kappa).
For each iteration, the mean and standard deviation (Sigma) of the pixels in the stack are computed.
Each pixel which value is farthest from the mean than more than Kappa * Sigma is rejected.
The mean of the remaining pixels in the stack is computed for each pixel.
After a few experiments with average and median at the start of my astrophotographic journey, I have settled on the sigma clipping method (or one of its variations) as the algorithm of choice for all of my integrations.
One must always be aware that stacking, especially when big files with many pixels are involved (RAW files from an APS-C DSLR are in the 20-30MB range each), is a very CPU and disk intensive task.
So, while a fair addition of gigabytes of RAM is always helpful, an SSD is the most useful upgrade to the PC which is going to do the job, with a powerful CPU coming second.
Of course the need for disk space must also be taken into account: consider approximately 0.4 to 0.8 GB per pic when stacking APS-C RAWs.
Likewise obvious (to the chagrin of your poor PC) is that RAW files and not JPEG ones must be used in stacking: with JPEGs you lose information from the start.