Context :

Aims : We present an analysis of OGLE~2004–BLG–254 , a high-magnification ( A _ { \circ } \simeq 60 ) and relatively short duration ( t _ { \mathrm { E } } \simeq 13.2 days ) microlensing event in which the source star , a Bulge K-giant , has been spatially resolved by a point-like lens .
We seek to determine the lens and source distance , and provide a measurement of the linear limb-darkening coefficients of the source star in the I and R bands .
We discuss the derived values of the latter and compare them to the classical theoretical laws , and furthermore examine the cases of already published microlensed GK-giants limb-darkening measurements .

Methods : We have obtained dense photometric coverage of the event light curve with OGLE and PLANET telescopes , as well as a high signal-to-noise ratio spectrum taken while the source was still magnified by A \sim 20 , using the UVES/VLT spectrograph .
We have performed a modelling of the light curve , including finite source and parallax effects , and have combined spectroscopic and photometric analysis to infer the source distance .
A Galactic model for the mass and velocity distribution of the stars has been used to estimate the lens distance .

Results : From the spectrum analysis and calibrated color-magnitude of the event target , we found that the source was a K3Â III Bulge giant , situated at the far end of the Bulge .
From modelling the light curve , we have derived an angular size of the Einstein ring \theta _ { \mathrm { E } } \simeq 114 \mu as , and a relative lens-source proper motion \mu = \theta _ { \mathrm { E } } / t _ { \mathrm { E } } \simeq 3.1 mas/yr .
We could also measure the angular size of the source , \theta _ { \mathrm { * } } \simeq 4.5 \mu as , whereas given the short duration of the event , no significant constraint could be obtained from parallax effects .
A Galactic model based on the modelling of the light curve then provides us with an estimate of the lens distance , mass and velocity as D _ { \mathrm { L } } \simeq 9.6 Â kpc , M \simeq 0.11 M _ { \odot } and v \simeq 145 ~ { } \mbox { km } \mbox { s } ^ { -1 } ( at the lens distance ) respectively .
Our dense coverage of this event allows us to measure limb darkening of the source star in the I and R bands .
We also compare previous measurements of linear limb-darkening coefficients involving GK-giant stars with predictions from ATLAS atmosphere models .
We discuss the case of K-giants and find a disagreement between limb-darkening measurements and model predictions , which may be caused by the inadequacy of the linear limb-darkening law .

Conclusions :