Context : Optical interferometry allows a measurement of the intensity profile across a stellar disc , leading to a direct test and calibration of theoretical model atmospheres as well as to a precise determination of fundamental stellar parameters .

Aims : We present a comparison of the visual and near-infrared intensity profile of the M0 giant \gamma Sagittae to plane-parallel ATLAS 9 as well as to plane-parallel & spherical PHOENIX model atmospheres .

Methods : We use previously described visual interferometric data obtained with the Navy Prototype Optical Interferometer ( NPOI ) in July 2000 .
We apply the recently developed technique of coherent integration , and thereby obtain visibility data of more spectral channels ( 526-852 nm ) and with higher precision than before .
In addition , we employ new measurements of the near-infrared K -band ( \sim 2200 nm ) diameter of \gamma Sagittae obtained with the instrument VINCI at the ESO VLT Interferometer ( VLTI ) in 2002 .

Results : The spherical PHOENIX model leads to a precise definition of the Rosseland angular diameter and a consistent high-precision diameter value for our NPOI and VLTI/VINCI data sets of \Theta _ { \mathrm { Ross } } = 6.06 \pm 0.02 mas , with the Hipparcos parallax corresponding to R _ { \mathrm { Ross } } = 55 \pm 4 R _ { \odot } , and with the bolometric flux corresponding to an effective temperature T _ { \mathrm { eff } } = 3805 \pm 55 K. Our visual visibility data close to the first minimum and in the second lobe constrain the limb-darkening effect and are generally consistent with the model atmosphere predictions .
The visual closure phases exhibit a smooth transition between 0 and \pi .

Conclusions : The agreement between the NPOI and VINCI diameter values increases the confidence in the model atmosphere predictions from optical to near-infrared wavelengths as well as in the calibration and accuracy of both interferometric facilities .
The consistent night-by-night diameter values of VINCI give additional confidence in the given uncertainties .
The closure phases suggest a slight deviation from circular symmetry , which may be due to surface features , an asymmetric extended layer , or a faint unknown companion .