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Astronomy Department

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Optical Photometry


The photometric uncertainties due to the flat fielding are expected to be less than 1% (0.01mag), while those arising from bias removal and linearity correction are likely to be negligible.

 

Calibration

Following Moles et al.(1985), we assume that, even though the atmospheric extinction varies night by night, the observing set remains stable during each observing run. This implies that the out-of-atmosphere instrumental magnitude of each standard star measured on a given chip of the mosaic, is constant throughout the run, being different on different chips. Calib1Thus, for each observing run and for each filter, this procedure provides us with an extinction coefficient for each night and with a set of zero points and color coefficients (one pair for each CCD of the mosaic) holding for the entire run.

First, we looked for the extinction coefficients (see table at the left), solving the following system of N generalized Bouger's equations:

PhotoCalib1

where k is the extinction coefficient, Χ is the airmass and N is the number of determinations (m) obtained for the out-of-atmosphere instrumental magnitude (m0) of a given star (s) during a given night (n) on a given chip of the mosaic (c). Then, for each observing run and for each filter, we computed the photometric

 

zero points Zc and the color coefficients Cc of the different mosaic CCDs(c) (see next Table) by solving a system of equations like this:

 

Photo Calib 2

 

Calib2

 

 

Final Magnitudes

After sky subtraction and exposure time normalization, each CCD of each image has been corrected, for atmospheric extinction and gain differences among the different CCDs, multiplying each pixel by the factor:

PhotoCalibEq3

where again n and c are the night and the CCD, while

and kn represent the CCD-averaged zero point and the extinction coefficient of the night, respectively. Then, the final magnitudes have been obtained by the formula: PhotoCalibEq4

where mSEx comes from SExtractor running with zero point:

PhotoCalibEq5

Cc represents the color coefficient of the particular CCD and the true color (B-V) can be easily evaluated by the equation:

PhotCalibEq6

whith:

PhotCalibEq7

The headers of the co-added mosaic frames of each cluster have been updated with keywords giving the proper photometric coefficients, including ZSEx (keyword: K_0) and δCc (keyword: DELTAC) and the subtracted background value (keyword: SKY).

 

Consistency checks

The typical r.m.s of the residuals we achieved with our calibration is of the order of 0.025mag (see Figure below). PhotResid