An entropy-controlled objective chip for reflective confocal microscopy with subdiffraction-limit resolution

Planar diffractive lenses (PDLs) with optimized but disordered structures can focus light beyond the diffraction limit. However, these disordered structures have inevitably destroyed wide-field imaging capability, limiting their applications in microscopy. Here, we introduce information entropy S to evaluate the disorder of an objective chip by using the probability of its structural deviation from standard Fresnel zone plates. Inspired by the theory of entropy change, we predict an equilibrium point $${S}_{0}=0.5$$ S 0 = 0.5 to balance wide-field imaging (theoretically evaluated by the Strehl ratio) and subdiffraction-limit focusing. To verify this, a $${NA}=0.9$$ N A = 0.9 objective chip with a record-long focal length of 1 mm is designed with $$S=0.535$$ S = 0.535 , which is the nearest to the equilibrium point among all reported PDLs. Consequently, our fabricated chip can focus light with subdiffraction-limit size of 0.44 λ and image fine details with spatial frequencies up to 4000 lp/mm experimentally. These unprecedented performances enable ultracompact reflective confocal microscopy for superresolution imaging.