Fig. 1. Schematic layout of the experimental setup. A Si lens was used to collimate the output THz beam. The wave scattered by the sample forms the object wave, and the unscattered part of the illumination forms the reference wave. The interference pattern recorded by the detector array is called the in-line hologram. The object wave in dark blue represents the low-frequency components, and the object wave in light blue denotes the high-frequency parts. By moving the detector, multiple sub-aperture holograms can be recorded and combined to be a synthetic aperture hologram for the resolution enhancement.

Fig. 2. Schematic diagram of the aperture synthesis. (a) Four potential overlapped regions within a sub-hologram. (b) Synthetic aperture hologram with 3×3 tiles numbered by 1–9.

Fig. 3. Iterative sparse reconstruction scheme. SA_HN is the normalized synthetic aperture hologram, which is composed of the normalized sub-holograms with intensity correction.

Fig. 4. Simulated three types of objects with a THz pattern. (a) Type A: complex amplitude object. (b) Type B: pure amplitude object. (c) Type C: pure phase object.

Fig. 5. Autofocusing curves (left column) and their zoomed-in local counterparts (right column) for (a) the complex amplitude object (type A), (b) the pure amplitude object (type B), and (c) the pure phase object (type C). The black dashed lines show the correct position.

Fig. 6. Autofocusing curves for the pure amplitude object (type B) with d=6  mm.

Fig. 7. Synthetic aperture hologram with intensity correction for a dragonfly forewing. (a) Nine normalized sub-holograms with intensity correction. (b) Synthetic aperture hologram composed of (a). (c) Synthetic aperture hologram without intensity correction. (d) Optical image of the dragonfly forewing sample. (e) Amplitude distribution reconstructed from (b) with 20 iterations. (f) Amplitude distribution reconstructed from (c) with 20 iterations. The effect of non-uniform intensity on reconstruction can be seen from the parts marked by the white and blue dotted circles.

Fig. 8. Sparsity-based autofocusing reconstruction for a dragonfly forewing with 20 iterations. (a) Autofocusing curves for three criteria. (b) Complex amplitude reconstruction at d=14.55  mm. (c) Complex amplitude reconstruction at d=14.85  mm. (d) Complex amplitude reconstruction at d=14.93  mm. The regions in (b) marked by the dotted circles show sharper and clearer details than their counterparts.

Fig. 9. Optical images of the three samples for the resolution quantification. (a) 100 μm resolution target with a measured width and separation of ∼99  μm. (b) 80 μm resolution target with a measured width and separation of ∼77  μm. (c) 70 μm resolution target with a measured width and separation of ∼69  μm.

Fig. 10. Reconstructions of the 100 μm resolution target with and without synthetic aperture. (a), (b) The amplitude and phase-contrast distributions reconstructed by the sparse phase retrieval algorithm with 20 iterations based on the synthetic aperture hologram. (c), (d) The amplitude and phase-contrast distributions reconstructed by the sparse phase retrieval algorithm with 20 iterations based on the center sub-hologram. On the right side of each reconstruction, the intensity distributions along the black lines are displayed.

Fig. 11. Reconstructions of the 80 μm resolution target: the amplitude and phase-contrast distributions reconstructed by the sparse phase retrieval algorithm with 20 iterations.

Fig. 12. Reconstructions of the 70 μm resolution target: the amplitude and phase-contrast distributions reconstructed by the sparse phase retrieval algorithm with 20 iterations.

Fig. 13. Reconstructions of three biological samples with the proposed methods. (a) Complex amplitude reconstructions of a beetle’s leg. (b) Complex amplitude reconstructions of a cicada’s wing. (c) Complex amplitude reconstructions of a spider.

Fig. 14. Reconstructed (a) amplitude and (b) phase distributions of a silicon wafer, where the internal non-uniformity can be observed.