We propose a theoretical description of a near-field observation of a
magneto-optical grating. We consider a scanning tunnelling optical mic
roscopy (STOM) experiment where the sample is a thin isotropic magneti
c material. We choose a transverse geometry: the magnetization is perp
endicular to the plane of incidence and parallel to the grating groove
s. For calculating the detected signal we use a perturbative diffracti
on theory of a multilayer anisotropic structure. The formalism has bee
n tested by modelling a far-field diffraction experiment. Then we calc
ulate STOM near-field signal above the grating and compare optical ima
ges and magneto-optical images.