  Planar lenses 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 S0=0.5 to balance wide-field imaging
(theoretically evaluated by the Strehl ratio) and subdiffraction-limit
focusing. To verify this, a NA=0.9 objective chip with a record-long focal
length of 1 mm is designed with S=0.535, which is the nearest to the
equilibrium point among all reported planar lenses. Consequently, our
fabricated chip can focus light with subdiffraction-limit size of 0.44{\lambda}
and image fine details with spatial frequencies up to 4000 lp/mm in experiment.
These unprecedented performances enable ultracompact reflective confocal
microscopy for superresolution imaging.
