Efficient optimization of super-oscillatory lens and transfer function analysis in confocal scanning microscopy

Super-oscillatory lens (SOL) provides a promising way to achieve subwavelength focusing in the regime of far-field optics and realize super-resolution imaging in confocal scanning microscopy (CSM). Both binary amplitude and phase SOLs are designed with an efficient optimization method using genetic algorithm and fast Hankel transform algorithm either in oil immersion medium or in air. A much brighter hotspot is readily focused by a phase SOL compared with the amplitude counterpart, e.g., 5.8 times as bright as the latter. To fundamentally interpret the super-resolution imaging mechanism by SOL in CSM, transfer function analysis is conducted compared with basic confocal imaging. The coherent transfer function (CTF) is derived and numerically calculated. The extension of the cutoff frequency and the remarkable enhancement of the magnitude of CTF in the high frequency passband account for super-resolution imaging by SOL in CSM; however, the limited extension of the frequency domain also implies that the attainable resolution is physically limited.