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Flat optics for image differentiation


Image processing has become a critical technology in a variety of science and engineering disciplines. Although most image processing is performed digitally, optical analog processing has the advantages of being low-power and high-speed, but it requires a large volume. Here, we demonstrate flat optics for direct image differentiation, allowing us to significantly shrink the required optical system size. We first demonstrate how the differentiator can be combined with traditional imaging systems such as a commercial optical microscope and camera sensor for edge detection with a numerical aperture up to 0.32. We next demonstrate how the entire processing system can be realized as a monolithic compound flat optic by integrating the differentiator with a metalens. The compound nanophotonic system manifests the advantage of thin form factor as well as the ability to implement complex transfer functions, and could open new opportunities in applications such as biological imaging and computer vision.

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Fig. 1: Two-dimensional image differentiation using nanophotonic materials.
Fig. 2: Fabrication and characterization of the nanophotonic spatial differentiator.
Fig. 3: Differentiator resolution characterization.
Fig. 4: Edge detection microscope at visible frequencies.
Fig. 5: Large-scale image differentiator using nanosphere lithography.
Fig. 6: Compound metaoptic.

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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We acknowledge support from the Office of Naval Research under award no. N00014-18-1-2563 and DARPA under the NLM programme, award no. HR001118C0015. Part of the fabrication process was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility. The remainder of the fabrication process took place in the Vanderbilt Institute of Nanoscale Science and Engineering (VINSE) and we thank the staff, particularly K. Heinrich, for their support.

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Authors and Affiliations



Y.Z. and J.V. developed the idea. Y.Z. conducted the modelling and theoretical analysis. Y.Z. and H.Z. fabricated the samples with small die size (less than 1 mm2) and H.Z. fabricated the samples based on self-assembled masks. I.I.K. provided the substrates and fabricated the larger die size samples not based on self-assembled masks. Y.Z. performed all of the experimental measurements and data analysis, with assistance from H.Z. Y.Z. and J.V. wrote the manuscript with input from all of the authors. The project was supervised by J.V.

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Correspondence to Jason Valentine.

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Y.Z., H.Z. and J.V. have submitted a patent application for this work, assigned to Vanderbilt University.

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Supplementary Discussion and Figs. 1–8.

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Zhou, Y., Zheng, H., Kravchenko, I.I. et al. Flat optics for image differentiation. Nat. Photonics 14, 316–323 (2020).

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