This is the first of a series of papers devoted to derive the metallicity of old open clusters in order to study the time evolution of the chemical abundance gradient in the Galactic disk .
We present detailed iron abundances from high resolution ( R \lower 2.58 pt \hbox { $ \sim$ } \kern - 7.75 pt \raise 2.795 pt \hbox { $ > $ } 40 , 000 ) spectra of several red clump and bright giant stars in the open clusters IC 4651 , NGC 2506 and NGC 6134 .
We observed 4 stars of NGC 2506 , 3 stars of NGC 6134 , and 5 stars of IC 4651 with the FEROS spectrograph at the ESO 1.5 m telescope ; moreover , 3 other stars of NGC 6134 were observed with the UVES spectrograph on Kueyen ( VLT UT2 ) .
After excluding the cool giants near the red giant branch tip ( one in IC 4651 and one in NGC 2506 ) , we found overall [ Fe/H ] values of -0.20 \pm 0.01 , rms = 0.02 dex ( 2 stars ) for NGC 2506 , +0.15 \pm 0.03 , rms = 0.07 dex ( 6 stars ) for NGC 6134 , and +0.11 \pm 0.01 , rms = 0.01 dex ( 4 stars ) for IC 4651 .
The metal abundances derived from line analysis for each star were extensively checked using spectrum synthesis of about 30 to 40 Fe I lines and 6 Fe II lines .
Our spectroscopic temperatures provide reddening values in good agreement with literature data for these clusters , strengthening the reliability of the adopted temperature and metallicity scale .
Also , gravities from the Fe equilibrium of ionization agree quite well with expectations based on cluster distance moduli and evolutionary masses .