Total variation extrapolation algorithm for high-fidelity terahertz in-line digital holography

In-line digital holography offers the advantages of compact layout and full utilization of the spatial bandwidth product of the detector, making it widely used in the terahertz band. In this paper, we propose an extrapolated iterative algorithm that combines the object's absorption characteristics with the sparsity of the complex field, enabling high-fidelity retrieval of both amplitude and phase images from a single in-line hologram. At the same time, the size of the hologram is numerically expanded without increasing the system complexity or the data acquisition time. The effectiveness of this algorithm is demonstrated through high-quality imaging of a Siemens star, polypropylene sheet, and dragonfly hindwing. Compared with the phase retrieval algorithm which includes positive absorption constraint, extrapolation method and support domain constraint, our method achieves superior reconstruction quality and more effective twin-image suppression, enhancing the resolution from 310 μm (2.6λ) to 228 μm (1.9λ) and enabling high-fidelity reconstruction of a 30 μm dragonfly hindwing. This work will further enhance the application of continuous-wave terahertz in-line digital holography in biomedical imaging and non-destructive testing.