Multi-order optical differentiator integrated with an omnidirectionally selective subtracter

Optical computing offers high-speed, low-power data processing, while optical differentiation enables instant edge detection for applications like autonomous driving, object recognition, and bio-detection. Introducing an extra algorithm to optical differentiation will further extend its functionality. Here, we integrate an omnidirectional subtracter with a multi-order optical differentiator via combining distinct spiral lens phases with deflection phases. With this design, zeroth-, first-, and second-order differentiations are spatially separated, and the local linear polarization always orients toward the normal of optical edges for linearly polarized incidence. Thereby, selective edge subtractions can be carried out through simply rotating a polarizer. The design is verified in a photopatterned liquid crystal, whose electro-optical tunability enables a broadband operation across the entire visible spectrum. Rotating a polarizer confirms omnidirectional edge extraction in first- and second-order differentiations while preserving the zeroth-order bright field imaging. The direction-selective defect suppression enhances applications like rainy-day autonomous driving and object recognition in directional noise. This work advances optical differentiation, enabling high-performance edge-sensitive imaging.