Re: Enter apparent magnitude of reference stars to calculate magnitude of target stars (requires AIJ v3.1.0+)

Posted by karenacollins on Jun 02, 2015; 9:12am
URL: http://astroimagej.170.s1.nabble.com/Enter-apparent-magnitude-of-reference-stars-to-calculate-magnitude-of-target-stars-requires-AIJ-v3-1-tp236p271.html

NOTE: the equations below may be difficult to follow written in text format. It may help to write them out on paper to decipher them.

Target star apparent magnitude (Source_AMag_T[ap]) is calculated as follows (where ap is the target star aperture number). First the total reference star ensemble net integrated counts and magnitude are calculated as:

tot_comp_cnts = (Summation over all c (Source-Sky_C[c])), where c indexes the apertures of comparison stars which have had an apparent magnitude entered by the user.


TotalAMag = -ln(Summation over all c (2.512^(-AMag[c])))/ln(2.512), where AMag[c] is the comparison star apparent magnitude entered by the user, and c indexes the apertures of comparison stars which have had an apparent magnitude entered by the user.

Then the target star apparent magnitudes are calculated as:

Source_AMag_T[ap] = TotalAMag - 2.5 * log(Source-Sky_T[ap]/tot_comp_cnts)




Target star apparent magnitude error (Source_Amag_Err_T[ap]) is calculated as follows (where ap is the target star aperture number).

SourceError[ap] is calculated as described here:
http://astroimagej.1065399.n5.nabble.com/How-is-photometric-error-calculated-in-AstroImageJ-td188.html

SourceVar[ap] = SourceError[ap]^2    (i.e. source variance)

tot_comp_variance = (Summation over all c (SourceVar[c])), where c indexes the apertures of comparison stars which have had an apparent magnitude entered by the user.

AErr_T[ap] = (Source-Sky_T[ap]/tot_comp_cnts) * SQRT(SourceVar[ap]/(Source-Sky_T[ap]*Source-Sky_T[ap] + tot_comp_variance/(tot_comp_cnts*tot_comp_cnts)))

Finally,
Source_Amag_Err_T[ap] = 2.5 * log(1 + AErr_T[ap]/(Source-Sky_T[ap]/tot_comp_cnts))