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Zhou, Y., Zheng, H., Kravchenko, I.I. et al. Flat optics for image differentiation. Nat. Photonics 14, 316–323 (2020). https://doi.org/10.1038/s41566-020-0591-3

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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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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.

Flatoptics with designer metasurfaces

In rigid body mechanics we presume that all objects are perfectly rigid. This means they change neither their form nor their volume when forces act on them. It simplifies the following mechanical analysis. Parts of human body are of course not perfectly rigid. Deformations would often make the analysis of motion too complicated. Fluid mechanics is concerned with mechanics of gases and liquids. Relativistic mechanics is related to the Einstein relativity theory and quantum mechanics describes behaviour of objects on atomic and subatomic level. In biomechanics we mostly make use of rigid body mechanics which is best applicable for describing the motion of human body and its parts. Since certain sport events take place in fluid environment, biomechanics also uses knowledge of fluid mechanics. Repeated little deformations of human body may cause injuries, therefore we will also partly inquire into mechanical deformation of human body and its parts.

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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.

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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