Higher-Order Optical Differential Operations Based on Synergetic Integrated Geometric Phases

Optical differential operations are a core technology in image processing, playing a crucial role in optical information processing and precise measurements. Higher-order differential operations provide enhanced imaging resolution and greater modulation degrees of freedom but are typically limited to single geometric phases. Here, a higher-order differential method, achieved through the synergetic integration of the geometric Pancharatnam–Berry (PB) phase and Rytov–Vlasimirskii–Berry (RVB) phase, is proposed. This method demonstrates the generation of various spatial modes of Hermite–Gaussian (HG) beams through differential operations and can be applied to high-resolution edge detection of different targets, including those with varying amplitudes and phases. Furthermore, simple and accurate quantitative phase reconstruction can be realized based on higher-order differential operations. These results have the potential to improve measurement accuracy and provide new insights for all-optical image processing.