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A complex wavefield imaging using single-pixel compressive sensing of an off-axis digital Fresnel hologram is proposed. A digital micromirror device (DMD) sampling prior to the single-pixel detection does the sparse representation of the hologram. The digital hologram is computationally recovered using a compressive sensing (CS) algorithm, and then the  complex object wavefield is reconstructed using a complex wave retrieval method. The impact of the use of two measurement operators namely random and Walsh–Hadamard measurement matrices on the reconstruction quality of the hologram and complex object wavefield is compared. The cases of CS algorithm using different sparsification criteria i.e. Haar wavelet, Fresnelet sparsification and without sparsification of the digital hologram are analysed.  The computer simulation results of the proposed CS method reveals that the Walsh–Hadamard sampling with Fresnelet sparsification achieves good quality reconstructions of both intensity and phase of the object wavefield.

Complex object wave retrieval using single-pixel compressive imaging of an off-axis Fresnel hologram