Three-dimensional structure determination of semi-transparent objects from holographic data

A solution is presented to an inverse scattering problem that arises in the application of holography to the determination of the three-dimensional structure of weakly scattering semi-transparent objects. This solution, together with a result obtained in another recent publication, relating to the determination of the complex amplitude distribution of scattered fields from measurements of the intensity transmission functions of holograms, makes it possible to calculate the distribution of the (generally complex) refractive index throughout the object. In general many holograms are needed. corresponding to different directions of illumination of the object.