True 3D reconstruction in digital holography, Journal of Physics: Photonics 2, 044004 (2020)

This work proves a somewhat surprising result that holographic replay process as understood and described traditionally in all the Optics textbooks does not actually provide a 3D image. The replay process (2D -> 3D) is in fact shown to be a Hermitian transpose of the holographic recording (3D -> 2D) process. Further using this property we design a sparse optimization algorithm that is able to obtain a true 3D image. To give a simple illustration, if a hologram of an object consisting of a few point sources is replayed, the resultant 3D image consists of multiple wavefronts that converge to the individual point sources and then diverge beyond. The proposed algorithm however provides a 3D image which is non-zero only at the location of original point objects. Such a reconstruction is not possible using a physical replay process. The proposed algorithm thus goes beyond what traditional holography can do.

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