Investigation of the method of local optical tomography by differential projections

A local tomography by differential interface contrast (DIC) projections is proposed for optical studies of the internal structure of transparent objects. The advantage of local tomography is that it allows quickly calculating the desired distribution in the point or area of interest without a complete reconstruction of the entire cross section. To obtain quantitative DIC-projections, a tomographic microscope with a transverse shear interferometer is developed, in which the method of phase steps for phase recovery is implemented. A procedure is proposed for normalizing projection data on geometric moments from DIC-projections. It is theoretically shown and confirmed by computer simulation that the total image from the DIC-projections is proportional to the Hilbert transform from the original function describing the object, and the application of the inverse Hilbert transform to this image leads to the restoration of the tomogram of the object. The results of reconstructing a tomogram of a ball made of silicon dioxide by its experimental DIC-projections are presented. Comparison of the simulation results with the experimental results showed their close agreement.