We describe the use of spatially incoherent illumination to make quantitative phase imaging of a semi-transparent sample, even out of the paraxial approximation. The image volume electromagnetic field is collected by scanning the image planes with a quadriwave lateral shearing interferometer, while the sample is spatially incoherently illuminated. In comparison to coherent quantitative phase measurements, incoherent illumination enriches the 3D collected spatial frequencies leading to 3D resolution increase (up to a factor 2). The image contrast loss introduced by the incoherent illumination is simulated and used to compensate the measurements. This restores the quantitative value of phase and intensity. Experimental contrast loss compensation and 3D resolution increase is presented using polystyrene and TiO2 micro-beads. Our approach will be useful to make diffraction tomography reconstruction with a simplified setup