Z‐Engineered Equivalent Complex Amplitude Modulation for Trichromatic Differentiation Imaging

Optical spatial differentiation is a key requirement for edge detection and feature extraction in all‐optical computing, yet realizing an achromatic and compact device remains a challenge. We present a monolithic trichromatic differential lens based on a dual‐twist liquid crystal (DTLC) platform that integrates broadband circular polarization conversion with complex amplitude modulation. The z ‐engineered complex amplitude profile is encoded into a single phase‐only diagram through double‐phase encoding. The design eliminates longitudinal chromatic focal shifts and enables simultaneous, color‐corrected edge detection across red, green, and blue (RGB) wavelengths on a confocal plane. The trichromatic differential lens performs spatial differentiation under both monochromatic and RGB mixed white‐light illumination in high‐fidelity. The design further supports off‐axis color‐routed imaging and higher‐order differentiations. This work establishes a versatile and integrable platform for broadband differential optics, promising for applications in real‐time imaging, on‐chip bioimaging, and machine vision systems.