Broadband and parallel multiple-order optical spatial differentiation enabled by Bessel vortex modulated metalens

Abstract

Optical analog image processing technology is expected to provide an effective solution for high-throughput and real-time data processing with low power consumption. In various operations, optical spatial differential operations are essential in edge extraction, data compression, and feature classification. Unfortunately, existing methods can only perform low-order or selectively perform a particular high-order differential operation. Here, we propose and experimentally demonstrate a Bessel vortex modulated metalens composed of a single complex amplitude metasurface, which can perform multiple-order radial differential operations over a wide band by presetting the order of the corresponding Bessel vortex. This architecture further enables angle multiplexing to create multiple information channels that synchronously perform multi-order spatial differential operations, indicating the superiority of the proposed devices in parallel processing. Our approach may find various applications in artificial intelligence, machine vision, autonomous driving, and advanced biomedical imaging.

Fig. 1. Working principle of the BVML for multiple-order radial differential operations.

a Schematic of the proposed BVML based on a dielectric metasurface. The metasurface device modulates the incident object light field and outputs a lth-order differential image at the imaging plane according to the order of the Bessel vortex encoded in its profile. b Amplitude and phase distributions of the BVML combining a Bessel vortex and a focusing lens. c–f Simulated CTF curves for the first-, second-, third-, and fourth-order BVMLs and the corresponding fitting curves using the form $∣t\left(k_r\right)∣=a{∣k_r∣}^l$. The abbreviation “Sim” has the full name of “Simulation”. g–j Simulated differential processing results of the first-, second-, third-, and fourth-order BVMLs. The input object is part of the 1951 USAF test chart. The enlarged insets highlight the number of edges. Scale bars: 50 μm.

Fig. 2. The BVML design and characterization.

a Schematic of the designed metasurface. Unit cell structure is composed of rectangular shaped α-Si nanopillars on a SiO₂ substrate, with the long axis L = 150 nm, the short axis W = 80 nm, the height H = 400 nm, and the period P = 250 nm. b Schematic top view of the super-pixel realizing complex amplitude modulation. c The complex amplitude value as the function of the rotation angles of the two groups of nanopillars in the super-pixel. The abbreviation “Amp.” has the full name of “Amplitude”. d The optical photographs of the fabricated metasurfaces corresponding to the first- to fourth-order BVMLs, respectively. Scale bars: 200 μm. e Top and tilted views of the SEM images of the α-Si nanopillar arrays. Scale bars: 500 nm. f–i Experimentally measured PSF of the first- to fourth-order BVMLs at the wavelength of 633 nm. Scale bars: 10 μm. j–m The experimental CTF curves for these BVMLs extracted from (f–i), respectively, and fitted by the corresponding order polynomial. The abbreviation “Exp” has the full name of “Experiment”.

Fig. 3. Resolution testing of the BVMLs.

a Schematic of the experimental setup used to perform different order radial differential processing. b The standard 1951 USAF resolution test chart as the input object. c, d Imaging results of the test target 6-2 marked by the red box in (b) through the first- and second-order BVMLs. e, f Imaging results of the test target 5-4 marked by the blue box in (b) through the third- and fourth-order BVMLs. Each lower panel of (c–f): the normalized intensity distribution along the corresponding vertical dashed line.

Fig. 4. Experimental broadband differential imaging results of amplitude objects.

a The first- to fourth-order differential imaging results of the U-shaped and circular objects at the wavelength of 633 nm. Scale bars: 20 μm. b The first- to fourth-order differential imaging results of the circular object at the wavelengths of 580, 532, and 490 nm, respectively. Scale bars: 20 μm.

Fig. 5. The integrated multichannel BVML for parallel processing.

a Schematic illustration of the multichannel BVMLs synchronously performing the zeroth- to fourth-order differential operations. b The design flow and complex amplitude distributions of the multichannel BVMLs. Only the central region of the complex amplitude is presented at the right side to highlight the details. Scale bars: 300 μm. c Experimentally measured PSF of the multichannel BVML at the wavelength of 633 nm. d Experimental imaging results for the unstained limewood stem cell as a phase object under the wavelength of 633 nm. e Experimental imaging results for the rough surface of transparent drop-casted ultraviolet adhesives under the wavelength of 633 nm. Scale bars of (c–e): 50 μm.