Re: Software to perform inhomogeneous ensemble photometry

[Stupendous Man <richmond@stupendous.cis.rit.edu>]

  Michael K. wrote:

> I am very interested in uncertainties. Does your software compute an 
> uncertainty for each data point? As I recall, when I've looked at your 
> photometry, you do not report uncertainties per data point.

  Let me answer carefully.  When I analyze images taken at the
RIT Observatory, I extract magnitudes from images with aperture
photometry.  The software I use for that task does provide an 
estimate of the uncertainty in each measurement, based on the 
number of counts from the star, and from the sky, and from the
readout noise of the chip.  Those magnitudes, each with an 
associated uncertainty, go into a set of data files.  One file
per image, with lots of stars in each file.

  These values then serve as the input to the "ensemble" analysis
code.  The ensemble code assigns a weight to each measurement in 
the group: bright measurements get a large weight, faint measurements
a smaller weight.

> The software I use, Mira Pro, gives a 1/SNR type uncertainty for each 
> point. It also writes the zeropoint error into the FITS header for each 
> image. I can also (of course) calculate the sigma of the comp star 
> magnitudes. 

  It sounds to me as if Mira Pro is doing the same thing my code does
(or most photometry programs do) in calculating an uncertainty
based on the SNR for each measurement.  I do not understand how it
determines a zeropoint value and error therein for the entire
frame, but perhaps you are giving it some extra information,
such as the catalog magnitudes for stars in the frame.

 ....
> When you are done the standard deviation of any given comp star is the 
> same as for all the other comp stars. It is basically doing some sort 
> of least squares.

  Hmmm.  Are you sure that you meant to write "the standard deviation
of any given comp stars is the same as for all the other comp stars?"
If I have two comp stars, a bright one and a faint one, I would
expect that the standard deviation from the mean magnitude would be
smaller for the bright star.  

  Apart from that, it sounds as if Mira Pro is doing something very
much like what I am doing.  It's not surprising -- the idea has been
around for quite a while.  It does indeed boil down to a big
least squares solution.

> As I recall, when I've looked at your 
> photometry, you do not report uncertainties per data point.

  That's right.  The estimated uncertainties from SNR calculations
often turn out to be underestimates, due to variations in 
sensitivity across the field, changes in transparency during
a night, and so forth.  I prefer to run the big ensemble solution,
make a plot of standard-deviation-from-mean versus mean-magnitude,
like the one shown halfway through this report:

      http://spiff.rit.edu/richmond/ritobs/sep18_2004/sep18_2004.html

and then use the standard-deviation-from-mean value for a 
constant star to estimate the uncertainty in my measurements
of a variable star.  Based on the graph in the URL above,
I see that the variable star is at about differential magnitude 0.6
in my ensemble solution.  Other stars of similar magnitude have
a standard deviation from the mean of about 0.004 mag.
I would therefore tell someone who asked, "the typical uncertainty
in my measurements of ASAS 002511 for this night was 0.004 mag."

  I suppose I could make a column for "uncertainty in magnitude"
in my reports, with the same value 0.004 for each measurement.

  Yes, it would be even better to figure out some sort of 
uncertainty for each individual measurement, based on a combination
of the SNR for that measurement and the overall nightly scatter,
but I don't know how to do that properly.

                                                   Michael Richmond