Super-resolution orbital angular momentum holography

Abstract

Computer-generated holograms are crucial for a wide range of applications such as 3D displays, information encryption, data storage, and opto-electronic computing. Orbital angular momentum (OAM), as a new degree of freedom with infinite orthogonal states, has been employed to expand the hologram bandwidth. However, in order to reduce strong multiplexing crosstalk, OAM holography suffers from a fundamental sampling criterion that the image sampling distance should be no less than the diameter of largest addressable OAM mode, which severely hinders the increase in resolution and capacity. Here we establish a comprehensive model on multiplexing crosstalk in OAM holography, propose a pseudo incoherent approach that is almost crosstalk-free, and demonstrate an analogous coherent solution by temporal multiplexing, which dramatically eliminates the crosstalk and largely relaxes the constraint upon sampling condition of OAM holography, exhibiting a remarkable resolution enhancement by several times, far beyond the conventional resolution limit of OAM holography, as well as a large scaling of OAM multiplexing capacity at fixed resolution. Our method enables OAM-multiplexed holographic reconstruction with high quality, high resolution, and high capacity, offering an efficient and practical route towards the future high-performance holographic systems.

Fig. 1. Holographic video display beyond the resolution limit by temporal multiplexing binary OAM holography (TMBH).

a Schematic illustration of varied degrees of resolution degradation by sparse and dense discrete samplings in OAM holography. b Advantage of enlarging the sampling condition γ beyond unity in obtaining higher resolution (super-resolution) and higher capacity of OAM holography. c Schematic illustration of TMBH setup based on DMD. d Reconstructed super-resolution frames of the holographic video by the TMBH method, with sampling condition of γ = 4.7 and multiplexing channel number of K = 201. e Evolution of reconstructed image quality of TMBH and CAH methods based on the averaging results of initial 21 frames, evaluated by the metrics of SSIM and CV, versus the growing multiplexing channels. The empty box in the reconstructed frame marks the area where the CV is calculated for all frames. f Reconstructed frames by the CAH method at γ = 1 (corresponding to the conventional resolution limit at 201 multiplexing channels) and γ = 1.5.

Fig. 2. Schematic illustration of the OAM property transfer in the spatial frequency domain.

a–d Reconstructed images with two OAM channels are shown, where the enlarged areas (marked as i to p) are compared in the rightmost panel. a General coherent case. b General incoherent case. c Pseudo incoherent case. d Coherence suppression case with temporal multiplexing.

Fig. 3. Two types of interference in OAM reconstructed images.

a OAM beams with the helical mode index l = 1 is incident on the OAM-multiplexed hologram, and images carried by different OAM channels are displayed simultaneously (left). In the coherent case (top right), these coherently superposed images have the interference of different OAM modes at all pixels. In the pseudo incoherent case (bottom right), these images are superposed by the intensity and demonstrate no interference. b Three representative pixels from the reconstructed image in a, for the coherent (left) and pseudo incoherent (right) cases. Intensity distributions are presented in both 2D profiles and 1D cross-sectional views where the values indicate the normalized intensity integral within the region as denoted by vertical dotted lines. c Intensities of all pixels in the post-processed results of the reconstructed image in a.

Fig. 4. General interference model between adjacent pixels.

a OAM modes involved in the multiplexing. b Schematic of API effect on a signal location, with densely packed OAM modes (l = 0, 5, 10, 15) at nine adjacent locations (top) as well as cross-sectional views (bottom). c Fluctuations of intensity integral in b versus γ. The CV value indicating the intensity fluctuations is calculated from 100 trials. Specific intensity results of each trial are shown for the cases of γ = 0.96 and γ = 2.90 (bottom). d Schematic of API effect on a non-signal location, with densely packed OAM modes (l = 5, 10, 15) at nine adjacent locations (top) as well as cross-sectional views (bottom). e Average intensity integral in d versus γ.

Fig. 5. Design principles of binary OAM-selective holograms and OAM-multiplexed holograms for temporal multiplexing.

a Design approach for a binary OAM-selective hologram. b Flowchart of generating binary OAM-multiplexed holograms.

Fig. 6. Numerical reconstruction results of binary images by three classes of OAM holography.

a Reconstructed results (partially shown) with 7 OAM channels. b Reconstructed results (partially shown) with 11 OAM channels. c Quantitative comparison of reconstruction quality. d Evolution of intensity fluctuation of reconstructed images versus the number of OAM-multiplexing channels, where the multiplexing channel numbers for γ = 1 and γ = 2 are marked.

Fig. 7. Super-resolution reconstruction of binary images by TMBH method.

a Intensity fluctuations of reconstructed images versus increasing OAM-multiplexing channel number. b Comparison between TMBH and CAH methods in terms of reconstruction quality at the same resolution, operating far beyond the sampling criterion limit. c Reconstruction results of the CAH method at the resolution limit of high capacity (γ = 1, K = 81).

Fig. 8. Numerical reconstruction results of densely sampled grayscale images by three classes of OAM holography.

a Ground truth for densely sampled grayscale images. b Reconstructed results of the TMBH method. c Reconstructed results of the CAH method. d Reconstructed results of the PH method.

Fig. 9. Experimental demonstration of densely sampled grayscale reconstructed images of PH and TMBH methods.

a Ground truth for densely sampled grayscale images. b Reconstructed results of the TMBH method. c Reconstructed results of the PH method.