Multi-adaptive super-resolving pupil filter for sub-diffraction limited focusing and imaging

With the rapid advances of optical information technology, numerous optical systems in both scientific and industrial fields are pursuing a resolution that surpasses the classical diffraction limit. Super-resolving pupil filters, whose transmittance or phase can be spatially modulated, have attracted intense interest for squeezing the focal spot of optical systems through wavefront manipulation, and have also been implemented in the fields of optical microscopy, optical storage, telescopes, etc. However, all the previously reported super-resolving pupil filters are tailored exclusively to specific optical systems with fixed focal lengths, rendering them incompatible with zoom or variable-focus optical platforms. In this work, we introduce a multi-adaptive super-resolving pupil filter that retains sub-diffraction-limited performance across a range of variable focal lengths. Such a pupil filter is composed of concentric annular belts in a binary phase configuration, designed via a two-step optimization algorithm and fabricated by using the ultraviolet optical lithography technique. Both numerical simulation and experimental results demonstrate that the sub-diffraction-limited focal spot can be consistently yielded at the designed wavelength of 633 nm when the super-resolving pupil filter is paired with plano-convex lenses of 50 mm,75 mm,100 mm, and 150 mm focal lengths, respectively. As a proof-of-concept demonstration, we integrate the filter into an optical imaging system and experimentally verify its resolution enhancement performance over the full focal-length range. Owing to its planar geometric structure and negligible insertion loss, the proposed multi-adaptive super-resolving pupil filter offers a practical way for the development of super-resolution zoom microscopy and zoom telescopes.