  This paper is concerned with the inverse medium problem of determining the
location and shape of penetrable scattering objects from measurements of the
scattered field. We study a sampling indicator function for recovering the
scattering object in a fast and robust way. A flexibility of this indicator
function is that it is applicable to data measured in near-field regime or
far-field regime. The implementation of the function is simple and does not
involve solving any ill-posed problems. The resolution analysis and stability
estimate of the indicator function are investigated using the factorization
analysis of the far-field operator along with the Funk-Hecke formula. The
performance of the method is verified on both simulated and experimental data.
