1. An apparatus for performing quantitative phase tomography on a specimen, comprising: an illumination source for providing an illuminating beam; a condenser lens having an optical axis direction arranged to transform the illuminating beam into a convergent illuminating beam; a microscope objective arranged to collect a beam that is back-scattered by the specimen, the illumination source arranged to illuminate the specimen from a same side as the beam collected by the microscope objective; and a wave front analyzer for analyzing a wave field amplitude and phase of the beam back-scattered by the specimen, the wave front analyzer including, an array sensor for measuring an intensity of the beam back-scattered by the specimen and collected by the microscope objective, and outputting a measurement signal, a displacement device to move the specimen in a plane normal to the optical axis direction, and a processing device configured to process the measurement signal output by the array sensor to deliver quantitative phase tomography images representing the specimen in three dimensions based on the beam back-scattered by the specimen, and to provide quantitative values of a refractive index distribution.