Optical analog image processing technology holds great potential for numerous modern applications due to its advantages of high-throughput parallel processing and ultra-low power consumption. The optical spatial differentiator, as a fundamental component of optical analog image processing, finds extensive applications in edge extraction, biomedical imaging, and feature classification. Unfortunately, most current optical differentiators are restricted by a constant modulation transfer function (MTF) across the working wavelength range, which restricts the application of optical differentiators in the spectral domain. Here, we propose and experimentally demonstrate a hybrid operation differentiator that can perform hybrid operations of the 0th-order and 2nd-order radial differential operations within its operational bandwidth, and convert similar color information, which is indiscernible to the human eye, into intensity information that is easily distinguishable. As a proof of concept, we fabricated an electrically tunable liquid crystals (LCs)-based device, which enables continuous adjustment of the MTF at different wavelengths while preserving its broadband operational characteristics, by leveraging the dispersion and electrically tunable characteristics of LCs. The proposed method extends the application range of optical differentiators, expanding from the traditional edge information recognition function to wavelength information recognition. Our approach may have various applications in metamerism recognition, ore color sorting, and advancing biomedical imaging, among others.
Wang et al. (2026) studied this question.