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.