MBCAA Observatory

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)M. Bonnardeau

bv = (1/Tbv)*(BV)+cst  (1) 
Bb = Tb*(BV)+cst  (2) 
BV = Tbv*(bv)+k1  (3) 
Bb = Tb*Tbv*(bv)+k2  (4) 
B = b+Tb*Tbv*[(bv)(BcVc)] 
V = B(BcVc)Tbv*[(bv)(BcVc)] 
A variant:
Instead of Tb one may use Tv:
0ne gets then the transformation equations:
V = v+Tv*Tbv*[(bv)(BcVc)] 
B = V+(BcVc)+Tbv*[(bv)(BcVc)] 
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.
This gives:
with the error:
To determine Tb, one minimizes:
with Cb a constant. The result is:
with the error:
The wider the BV 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:
The transformation coefficients for my setup:
B, V transformations
V, Rc transformations
V, Ic transformations
Rc, Ic transformations.
B. Gary's web page on CCD transformations equations for use with single image photometry.









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