Fig. 1. Schematic of experiment-driven methodology. (a) Conceptual overview of methodology represents illumination of the imaging object with a sequence of tilted beams of THz pulses, and corresponding time-resolved distorted images are captured using a limited aperture THz imaging system via TDS experimental approach. The spatiotemporal fields produced by the different illumination angles are formulated and processed through a convex optimization framework that could reconstruct high-resolution images of the sample, revealing complex details previously obscured due to the finite space-bandwidth product offered by the THz imaging system. (b) Aperture synthesis in the k-space due to different tilted beam illumination defined by wavevector k→a≡(kxa,kya) at frequencies 0.5, 1, and 1.5 THz (Visualization 1). (c) Acquired distorted field amplitudes associated with the aperture shifts shown in (b). The 10  mm×10  mm object illumination area is spatially sampled at 50 μm resolution, corresponding to 200×200 pixels.

Fig. 2. Time-resolved retrieval of phase image object. (a) Phase object under investigation. (b) Measured diffraction-limited, low-resolution field images at t=−0.45, 0, and 0.63 ps obtained using conventional imaging system. (c) Reconstructed phase images at t=−0.45, 0, and 0.63 ps. (d) Temporal evolution of reconstructed THz pulses for two different pixels [red and blue dots shown in (c)]. (e) Line-cut plot for phase imaging object (red dashed line) and reconstructed image (cyan solid line). The 10  mm×10  mm object illumination area is spatially sampled at 50 μm resolution, corresponding to 200×200 pixels. We considered a 1 nJ THz pulse of duration 250 fs at the input with 30 dB SNR per pixel.

Fig. 3. Time-resolved retrieval of random media. (a), (b) Slowly varying random phase surfaces with spatial correlation 150 μm and 600 μm, respectively. (c), (d) Retrieved spatial phase distribution of random media at t=0  ps. (e) Line cut in the x-direction for random phase screen [white dotted line in (a)] and reconstructed phase image [red solid line in (a)]. (f) Line cut in the x-direction for random phase screen [white dotted line in (b)] and reconstructed phase image [green solid line in (b)]. (g), (h) Spatial autocorrelation function for the ground truth (black dashed) and retrieved (red and green) random phase screens. The 10  mm×10  mm object illumination area is spatially sampled at 50 μm resolution, corresponding to 200×200 pixels.

Fig. 4. Retrieval of imaging object concealed by random media. (a) Schematic of an experiment-driven THz imaging system, where an imaging object is placed in the middle of the random phase screens separated by 25 mm. The wave interaction with random surfaces and hidden object leads to diffraction and scattering, which could be modelled as free-space wave propagation and wave scattering, respectively. The impinging wavefronts illuminate the same area of phase objects and provide redundant information in the resulting output waveform, further enabling the simultaneous reconstruction of the transmission properties of the random phase screen and the hidden objects. (b) Hidden object under examination with random phase surfaces containing a spatial correlation of 200 μm and 600 μm. (c) Hidden random phase screen with a spatial correlation of 300 μm. (d) Reconstructed phase profiles of the random surfaces and the hidden imaging object at t=0  ps. (e) Retrieved hidden random phase screen. (f) Histogram (probability density function) for the phase element of ground truth (yellow shaded area) and retrieved (blue) random phase screens. (g) Spatial autocorrelation function for the ground truth (yellow shaded area) and retrieved (blue) random phase screens. The 10  mm×10  mm object illumination area is spatially sampled at 50 μm resolution, corresponding to 200×200 pixels.

Fig. 5. Hyperspectral imaging for material characterization. (a) Schematic of the 100 μm thick imaging object composed of Teflon, Topas, and HDPE, showing the spatial distribution of the refractive index at 1 THz. (b) Distorted spatial variation in the refractive index profile at 0.5, 1, and 1.5 THz recorded using a diffraction-limited imaging system. (c) Reconstructed spatial refractive index profiles at 0.5, 1, and 1.5 THz illustrating the high-resolution material selectivity. (d) Variation in the refractive index of Teflon, Topos, and HDPE as a function of frequency representing comparison in the reconstructed refractive indices (solid lines) and material refractive indices (dashed lines). The 10  mm×10  mm object illumination area is spatially sampled at 50 μm resolution, corresponding to 200×200 pixles.