The disclosed invention describes a new apparatus performing a new data acquisition for quantitative refractive index tomography. It is based on a linear scanning of the specimen, opposed to the classical approaches based on rotations of either the sample or the illumination beam, which are based on the illumination with plane waves, which orientation is successively modified in order to acquire angular information. On the contrary, the inventive apparatus and method rely on a specially shaped illumination, which provides straightforwardly an angular distribution in the illumination of the specimen. The specimen can thus be linearly scanned in the object plane in order to acquire the data set enabling tomographic reconstruction, where the different positions directly possess the information on various angles for the incoming wave vectors.