Previous method, with the transformation coefficients derived from the average (not weighted) and the standard deviation (not weighted) of several measurements.
Transformations for differential photometry (with weights)
|b-v = (1/Tbv)*(B-V)+cst||(1)|
|B-b = Tb*(B-V)+cst||(2)|
|B-V = Tbv*(b-v)+k1||(3)|
|B-b = Tb*Tbv*(b-v)+k2||(4)|
|B = b+Tb*Tbv*[(b-v)-(Bc-Vc)]|
|V = B-(Bc-Vc)-Tbv*[(b-v)-(Bc-Vc)]|
Instead of Tb one may use Tv:
0ne gets then the transformation equations:
|V = v+Tv*Tbv*[(b-v)-(Bc-Vc)]|
|B = V+(Bc-Vc)+Tbv*[(b-v)-(Bc-Vc)]|
Tb and Tv are connected:
1/Tbv = 1 + Tv -Tb
A field of several stars whose magnitudes are precisely known is observed. Usually this is a
Landolt's standard field. The intensities of these stars
are measured and fitted with Pogson's law:
The measured magnitudes of the stars are then derived.
The transformation coefficients Tbv and Tb can be derived by fitting
the measurements with linear functions:
Actual observations of the field L95 that give Tbv=1.008+/-0.029 and Tb=0.008+/-0.006.
To determine Tbv, one wants to minimize:
where Cbv is a constant. The denominator is a weight factor: the larger the error on a measurement, the less it contributes to the determination of Tbv. (The errors on B,V are negligeable). I use m=1.
with the error:
To determine Tb, one minimizes:
with Cb a constant. The result is:
with the error:
The wider the B-V range of the field, the better is the determination of the slopes and of the transformation coefficients.
Let be N measurements of a coefficient T and of its error, from different
nights and different Landolt's fields. I adopt the weighted average of
the measurents as the value of T:
and as the error the weighted standard deviation:
B. Gary's web page on CCD transformations equations for use with single image photometry.
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