A method of tomographic imaging the real part of the refractive index of the internal structure of an image volume and a corresponding apparatus for performing the method. The method includes a two-step process of first retrieving phase projections of an image volume from projective intensity measurements through the image volume. The second step of the method includes iterative image reconstruction of an image of the image volume using phase projections taken at multiple projection angles. The first step of intensity measurements and subsequent phase retrieval can use one of many possible phase retrieval methods including the Bronnikov phase retrieval method. The second step of iterative image reconstruction can be performed using the total variation minimization method, the algebraic reconstruction technique method, or any other iterative image reconstruction method.
