Stacking Frames for Photometry

[George Fleming]

Have been experimenting with the Astroimagej and the new spreadsheet from Richard Lee for processing photometry data. My setup is ZWO 1600MMCooled Camera and for brighter variables 1 second exposures allows nice unsaturated images. However if I just process this data I can “follow the seeing” very easily. My objective then becomes stacking to smooth out this. My questions as a newbie is

a) when I stack with aligned astroimagesj frames should I sum, average or median the stack?

b) when I have stacked – what is the exposure which now has to edited into the FITS header?

c) Am I right in using the central frame of the stack as the observation time?   

[Dr Paul Leyland]

a) I would recommend NOT using median stacking.  Averaging and summing are essentially the same operation, just that the first divides by the number of images stacked.  Median stacking is not a linear operation and (almost?) all photometry assumes a linear detector response.

b) The exposure of the stacked frames is the sum of the exposures of the individual frames.

c) I believe you should use the weighted mean of the mid-point times of the individual frames, where the weights are the exposure times of each frame.  If your stack consists of equally spaced exposures of equal exposure times, the mid-point of the central frame (assuming it exists, what if you have an even number of frames?) is the same thing.

Something to be aware of if you want the highest accuracy: all the above assumes that the focus and the sky background do not vary greatly throughout the stack.  If you are in doubt, perform the photometry on each frame to give a flux measurement (not the magnitude, which varies as the logarithm of the flux) and its corresponding variance.  Then add up all the fluxes weighted by their corresponding variance .  The stacked variance is  the root-mean-square of the individual values.

All the above assumes you are doing differential photometry — that you are measuring the relative brightness of a target and a supposedly constant comparison star.

[George Fleming]

Yes I am doing differential photometry and relying on the standard comparison stars. 

To summarise – avoid median – non linear operation for stacking and this leads to exposures which should be recorded as the sum of the exposures in the stack.  Because of the way I take the frames I will have the equally spaced exposures of equal exposure times the mid point of the central frame will be very close to the stacked observation time.

Thank you for your advice – newbies can get a bit lost on some of the details. Last year’s data was processed with Muniwin which did not require much in the way of decisions about stacking – however the down side was entering the locations of comparison stars, I felt this was very error prone. Richard Lee’s spreadsheet for processing AstroimageJ measurements file does this in a very slick way, hence my experiments with this approach. However stacking raised these issues which you have answered. Thanks again 

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