Fig. 1. Modulation process of the SFTM and demonstration of variable-scale holography. (a) Schematic diagram of the transformation process of the SFTM in phase space for m>1. A typical PSD with a spatial extent Lo and a bandwidth Bo is sheared in the f-direction through chirp modulation and then undergoes coordinate transposition through simple Fourier transform. The PSD performs an inverse Fourier transform after shearing again and then magnifies it with a magnifier. After the last chirp modulation, the PSD becomes the Fresnel form of its original state. (b) Demonstration of full-color holography without pre-processing using SFTM based CGHs.

Fig. 2. (a) Allowed m-z space of the SFTM for λ=0.532  μm, N0=N/2=1000, and δxo=8  μm. The solid dots represent the data set used for the monochromatic CGH experiment. Plots (b) and (c) show the comparisons of y=0 slices of the analytic and SFTM based numerical results at z=200  mm and z=800  mm, respectively.

Fig. 3. Experimental results of SFTM algorithms under various circumstances. Comparison of the SFTM to (a) ASM and (b) SFT illustrates that within a considerable diffraction distance, the SFTM has almost the same effect within the applicable range of ASM and SFT. (c) The scaling ability of the SFTM is presented under different m and z. All m–z values have been marked with orange solid dots in Fig. 2(a). (d) Implementation of the SFTM’s long-distance and extreme magnification capability by projecting a 20× shark towards a distance of 1800 mm.

Fig. 4. Comparison of SFT (Fraunhofer) and the SFTM in full-color holography. (a) Chromatic aberration comparison using the SFT (Fraunhofer) based algorithm and SFTM based algorithm under vertical illumination in diffractive optical elements. (b) and (c) present the numerical reconstruction results for the two methods, while (c) and (e) are the respective optical reconstruction results.

Fig. 5. Implementation of variable-scale tomography. (a) Schematic of the SFTM based tomographic. The pixel sizes on three different image planes at different depths can be manipulated by SFTM algorithms as the SBP is conserved. (b) Three tomography images of 3×, 6×, and 10× pentagrams at depths of z=200  mm, 400 mm, and 700 mm were projected, respectively. (c), (d) The results of the two-layer full-color tomography experiment. The 1.5× rainbow flower locates at z=150  mm, and the 2.0× cube locates at z=300  mm.

Fig. 6. Full-color SFTM based metasurface holography design. (a) Schematic of full-color metasurface holography. (b) A TiO2 meta-atom with three independent tunable structure parameters D1, D2,θ. Scanning electron microscopy (SEM) images of the TiO2 holographic metasurface in (c) oblique-view and (d) top-view are presented. (e) Simulation and (f) experiment results for letters “H,” “N,” and “U.”

Fig. 7. Schematic diagram of the PSD transformation process for the (a) ASM, (b) SFT, and (c) PSF convolution method in phase space.

Fig. 8. The constraint relationship between m and z in cases (a) λ=0.450  μm, (b) λ=0.532  μm, and (c) λ=0.633  μm, respectively.

Fig. 9. Flowchart of the three-stage IFTA.

Fig. 10. Algorithm flowchart of three-plane tomography.

Fig. 11. (a) Algorithm flowchart of full-color metasurface holography. The (b) phase shift and (c) transmittance of the green light obtained by sweep operations are shown.

Fig. 12. Experimental setup with SLM.

Fig. 13. Experimental setup for metasurface holography.