Fig. 1. Schematic of the proposed super-resolution (SR) scheme through the high-dimensional (H-D) light-field information based on the GISC camera. (a) Principle illustration of single-shot SR imaging. When imaged through a lens system, the object consisting of two sources with H-D light-field information becomes diffraction-limited and cannot be resolved via direct 2D point-by-point imaging mode due to the diffuse spots. In contrast, the GISC camera can capture and reconstruct the H-D light-field information from a single-shot measurement. The spatial resolution can be improved by utilizing the discernibility in the H-D light-field space, resulting in an SR image through a synthesis process. (b) Schematic of the GISC camera for SR imaging. The GISC camera consists of the conventional imaging system including lens 1, iris, and lens 2 to project the object’s information on its focal plane, the spatial random phase modulator (SRPM) to modulate the H-D image information into a detectable 2D speckle pattern, and an array detector to record the pattern record in a single shot. The proposed SR scheme consists of three processes: calibration, detection, and SR. During the calibration process, the system response of the GISC camera will be measured by scanning a point calibration source in H-D light-field space, which is done after the system is setup. At the detection stage, the H-D information of the object is detected in single-shot detection. In the SR step, the H-D image information of the object is reconstructed with the input of single-shot measurement and the calibrated system response, and further the SR image is achieved by a synthesis process.

Fig. 2. Illustration of both statistical resolution (a) and algorithmic resolution (b) in the H-D space (spatial, spectral) under different conditions including sparsity level K=2, 3, 4, sampling number m=1600,6400, and DSNR  =  100 (20 dB), 1000 (30 dB). The parameters of the GISC camera are set as f1=50  mm, D=1.48  mm, n=1.53, ω=3.5  μm, η=12  μm, λ¯=540  nm, and the classical Rayleigh’s criterion for the lens system is 1.22λ¯f1/D≈22.2  μm.

Fig. 3. Simulation results for the resolution target under the noiseless case. (A) Resolution test target. The width of each slit is 2 μm, and the spatial distances between each slit are 6 μm, 5 μm, 4 μm, and 3 μm, respectively. The purple scale bar is 8 μm, corresponding to the FWHM of PSF of conventional imaging system in the GISC camera. (B) Diffraction-limited image recorded by the conventional imaging system. (C) Wavelength of each slit labeled 1, 2, 3 on the resolution test target (A) when the resolution test target has spectral difference. (D) Reconstructed result without spectral difference. (E) Reconstructed result with spectral difference. (F) Comparison of resolution enhancement. Intensity profiles extracted from the cross-section green lines in (B), (D), and (E).

Fig. 4. Simulation results in noisy environments. (A) Ground truth, diffraction-limited image, and spectral distribution of the object. (B), (C) Reconstructed images for the no-spectral difference object and spectral difference object under different detection DSNRs. (D) Recovery comparison for the no-spectral-difference object and spectral difference object through the PSNR and SSIM [36].

Fig. 5. Simulation for dots’ object with different orientations. (A) Ground truth with two emitting wavelengths labeled with red and green colors. The nearest distance of two emitters is 3 μm. (B) Wavelength of each emitter. (C) Diffraction-limited image of the conventional imaging system. (D) Reconstructed image. The yellow rectangles and the blue rectangles denote the reconstructed images without spectral difference and with spectral difference, respectively.

Fig. 6. Experimental setup of the GISC camera, Xe, xenon lamp; Mc, monochromator; OF, optical fiber; BS, beam splitter; SRPM, spatial random phase modulator. A multicolor object through a conventional imaging system, which consists of a lens 1 with f1=50  mm, an iris with aperture size D=1.48  mm, and a lens 2 with f2=300  mm, is modulated into a speckle image by the SRPM, where z1=5  mm and z2=40  mm. The speckle image is expanded by a relay lens to match the pixel size of detector 1. The diffraction-limited image through the conventional imaging system is recorded on detector 2 by another optical path via a BS.

Fig. 7. Experimental results for resolving two point-like sources. (a) Reconstruction images of critically resolved two point-like sources under three cases: ① spatial distance 5.1 μm, spectral difference 9 nm; ② spatial distance 4.6 μm, spectral difference 17 nm; ③ spatial distance 4.1 μm, spectral difference 23 nm. (b) Localization error estimation by fitting the intensity curves of pixels along the green lines in the corresponding images shown in (a). (c) The Fourier rolling correlation (FRC) method is applied to evaluate the achieved resolution; here, corresponding FRC curves with the 2−σ curve are shown. (d) Comparison of the experimental resolving distance and the evaluated resolution with an error bar with two theoretical resolution bounds. (e) The diffraction-limited image from the conventional imaging system with aperture size 1.48 mm, and the deconvolution image through the classic Richardson–Lucy method.

Fig. 8. Experimental results of three slits. (A) Ground truth. The spatial distance between each slit is 5 μm; the purple scale bar is 10 μm. (B) Diffraction-limited image of the conventional imaging system. (C) Deconvolution image through the classic Richardson–Lucy method. (D) Spectral distribution of each slit. The spectral gap between each slit is 15 nm. (E) Reconstructed super-resolution image based on the GISC camera.

Fig. 9. Schematic of the GISC camera.

Fig. 10. Comparison between the theoretical and simulation results on the statistical resolution under different spectral discrepancies.

Fig. 11. Parameter (ω,ζ,z1,z2) selection of the GISC camera. (A) Comparison of the correlation coefficient curves for different parameters ω at fixed parameters ζ=12  μm, z1=5  mm, z2=40  mm. (B) Comparison of the correlation coefficient curves for different parameters ζ at fixed parameters ω=3.5  μm, z1=5  mm, z2=40  mm. (C) Comparison of the correlation coefficient curves for different parameters z1 at fixed parameters ω=3.5  μm, ζ=12  μm, z2=40  mm. (D) Comparison of the correlation coefficient curves for different parameters z2 at fixed parameters ω=3.5  μm, ζ=12  μm, z1=5  mm.

Fig. 12. Influence of the size of the calibration point source on g(2).

Fig. 13. Experimental results for the relationship between the resolved spatial distance and discernibility in the (x,θ) space. The upper one in the figure is the diffraction-limited image of the conventional imaging system, and the bottom ones are reconstructed images.