[Aavso-photometry] Averaging images for optimal photometry

[Brad Walter]

 There is another way to average photometric results, which is to do your
photometry on individual images, group the measurements with either a
constant number of images per group if you don't have gaps in your sequence
that will affect our results, or group them into bins of equal time
duration. Then average the measurements of the images in each group. That is
often a lot easier and faster than actually stacking images. If you are
determining your error using a check star, which is normally a better
estimate of error than using SNR, your error becomes the sigma of the
averaged measurements NOT 1/SQRT(N) times the sigma of the individual check
star measurements, where N is the number of measurements that have been
averaged. It is interesting to compare the sigma of the averaged
measurements to 1/SQRT(N) times the sigma of individual measurements because
it gives you an idea of some kinds of systematic error in your measurement
("red noise" and extinction effects, for example). The 1/SQRT(N)
relationship breaks down when there are significant systematics (correlated
noise between images) present. 

After all when you align and combine images, hopefully you are averaging
them and not median combining, and then you are just averaging the numbers
anyway, if you aren't altering the images in the alignment process. Since
you want your stars to be on the same, or nearly the same pixels, in each
image of a series, you can generally auto-track your measuring tool through
the whole series anyway so you don't need the alignment step. 


Message: 1
Date: Sun, 6 Jan 2008 11:58:58 -0700
From: "Michael Newberry" <mnewberry at mirametrics.com>
Subject: Re: [Aavso-photometry] Averaging images for optimal
	photometry
To: <gianlucaros at gmail.com>, <aavso-photometry at mira.aavso.org>
Message-ID: <013401c85096$35611350$0a00a8c0 at CAYENNE>
Content-Type: text/plain; format=flowed; charset="iso-8859-1";
	reply-type=original

Generally, stacking (or "combining") is a good thing becasue it increases
the SNR and beats down the artifacts and imperfect flat field corrections. 
Rotating and deforming is OK as part of combining. However, if you are going
to do photometry on the combined image, image registration ("alignment") is
best done with no resampling (in other words, the pixels are shifted by
whole-pixel amounts rather than partial pixel amounts).

If you want the prettiest picture or the finest detail, then resampling is
OK but, if you want the most accurate representation of the noise structure
in the image (used for calculating the internal errors of the magnitude
estimate) then you want whole pixel shifts. Using whole pixel shifts for
combining many images inflates the FWHM by about 0.3 pixels---which is
acceptable for most photometric work.

Another thing to consider for combined images is that the time you reference
is the mid-time of the exposure, not the DATE-OBS keyword which gives the
beginning time of some image used in the stack.

Generally, speaking, the SNR of a combined image will grow by as much as the
square root of the number of images that are combined. This is the best
case, in which the difference in pixel values from one image to the next are
*purely* random. Since that is not exactly the case, the SNR will grow a
little less quickly than sqrt(n) would suggest.

Michael Newberry