Sparsity-assisted phase retrieval in the Fresnel zone

We report simulation results on phase retrieval from single-shot Fresnel zone irradiance data. It is shown that a simplistic Gerchberg–Saxton (GS) type iterative approach fails to produce accurate phase recovery for this case. An image sparsity enhancement step added to the GS iteration is however seen to show excellent phase recovery. Discussion of sampling considerations is presented as this is an important point for achieving numerically accurate phase reconstructions. The implications of the simulation results for building a compact lens-less phase microscopy system are also described.