Fig. 1. Schematic diagram of the DC-HSDH system based on spatial heterodyne interferometry. (a) Experimental setup. CLK, clock; RF, radio frequency; DD-MZM, dual-drive Mach–Zehnder modulator; COL, collimator; M, mirror; BS, beam splitter; OBJ, object. (b) The interferogram hypercube (IHC) is obtained by arranging the captured interferograms in temporal order, where x and y are the spatial coordinates and t is the temporal coordinate. DAQ, data acquisition card. (c) The Fourier hypercube (FHC) is obtained by applying a three-dimensional fast Fourier transform (FFT) to the IHC. (d) The FHC is spatially filtered and unrolled on the time-frequency (f_t) axis where the uniformly spaced comb lines can be resolved. (e) Temporal filters are used to extract each comb, and then the inverse fast Fourier transform (IFFT) is applied to obtain the phase map and the amplitude map on the camera plane. (f) For lens-less systems, free-space propagation (FSP) algorithms are used to obtain the phase map and the amplitude map on the object plane. (g) Cross-section of the FHC at f_t = 0. SSBI, single-signal-beating interference. (h) Cross-section of the FHC at f_t = 2m (Hz), where m is an integer that ≠0.

Fig. 2. Spectra of the two EOFCs. An optical spectrum analyzer with a spectral resolution of 0.02 nm was used to perform the measurement.

Fig. 3. Hyperspectral holographic imaging results on the object plane. (a) The phase map measured at a single comb line. (b) The depth map obtained by multi-wavelength hierarchical phase unwrapping (HPU). (c) The depth map obtained by local phase unwrapping (LPU). (d) Cross-sections of the depth maps in (b) and (c) at the dashed lines. (e)–(g) The amplitude maps measured at three different wavelengths. (h) The transmission spectrum of HCN gas obtained according to the intensity values of the pixels in the amplitude maps. The gray dashed line corresponds to the P10 absorption line. The true data is obtained by high-resolution spectral scans using a tunable laser.

Fig. 4. Hyperspectral holographic imaging results when the accumulation time was 1 s. (a) Temporal frequency spectrum. (b) Depth map. (c) Depth error map; the RMSE of depth was calculated as 152 μm. (d) The measured transmission spectrum of HCN gas.

Fig. 5. Verification experimental results of the maximum unambiguous depth range. (a) Real photograph of the stepped reflector used as the imaging object, and the distance between the two surfaces was 35 mm. (b) The amplitude map when focusing on the front surface. (d) The depth map obtained by HPU. (e) The cross-section of the depth map at X = 3.6 mm.