Resolution Enhancement in Terahertz Digital In-line Holography by Sparsity-Based Extrapolation

We introduce a generalized extrapolation framework as a constrained optimization problem to enhance the resolution in terahertz digital in-line holography. The alternating minimization method is employed to iteratively extrapolate the hologram beyond the actually detecting area and to reconstruct the complex amplitude distribution of the object wavefront. Within this framework, we propose a sparsity-based extrapolation model based on L-1-norm, where the object mask is not required and the generalized positive absorption constraint can be utilized. This work can achieve super-resolution reconstruction completely by numerical postprocessing without any modification to the imaging system. Both the simulation and experiments on the terahertz band demonstrate the feasibility of the proposed algorithms, and the limit of resolution can be extended by a factor of 1.67.