Research On The Design Of Super-resolution Filter Based On Vectorial Beam Focusing Theory

For a long time, the resolution of the optical imaging system are limited to the abbe diffraction limit. With the development in the field of nanoscale processing, biological detection and so on, it becomes more and more necessary to design effective solutions to break the limitation of Abbe diffraction limit and the Rayleigh criterion, and to achieve the sharper focus and super-resolution optical needle in visible spectrum region and to realize super-resolution optical focusing and imaging.This article “Research on the Design of Super-resolution Filter Based on Vectorial Beam Focusing Theory” aims at giving a thorough research on the vector non-diffracting beam focusing, binary phase super-resolution pupil filter optimizing and large numerical aperture spherical reflection system focusing, and exploring the new methods and new theory to achieve far-field optical super-resolution focusing or subwavelength optical needle.This research includes the following three aspects:1. For the incident beam, we explore the focusing result of the linearly polarized, circularly polarized, radially polarized and azimuthally polarized one-dimensional and two-dimensional Airy beam in high numerical aperture lens system. Non-diffracting beam has many advantages in the super-resolution and long DOF. The FWHM along y-direction achieves 0.37λ for the azimuthally polarized Airy beam. Additionally, we designe the cosine complex amplitude filter through analyzing the amplitude and phase characteristic of Airy beam on the pupil plane, and achieve controllable multi-foci near the focus. A separated dual focusing field is achieved and the distance between the two spots is easily controlled from 1.15λ to 3.56λ with almost same FWHM by adjusting the parameters of the Airy beam. The number of multi-foci can be controlle by the parameter of the cosine complex amplitude filter.2. To design a binary phase filter, we proposed a fast, efficient and widely used optimizing algorithm. Using the power series expansion formula, Richards–Wolf integral formula was deduced to quasi-analytic expression polynomial. This work can simplify the calculation of optimization algorithm, and reduced the computation cost in the iterative. Based on the improvement of the standard particle swarm algorithm, a hybrid genetic particle swarm optimization(HGPSO) algorithm is proposed to design the binary phase filter. The HGPSO algorithm includes self-adaptive parameters, recombination and mutation operations that originated from the genetic algorithm. Based on the benchmark test, the HGPSO algorithm has achieved global optimization and fast convergence. A multi-zone binary phase filter is designed by using the HGPSO. The long depth of focus and high resolution are achieved simultaneously, where the depth of focus and focal spot transverse size are 6.05λ and 0.41λ, respectively. In an easy-to-perform optimizing procedure, the iteration number of HGPSO is decreased to about a quarter of the original particle swarm optimization process. Therefore, the proposed HGPSO can be applied to the optimization of filter with multiple parameters.3. We theoretical analyzed the spherical reflection focusing system, and analyzed the super-long depth of focus of the spherical reflecting system. Based on the comparation of the similarities and differences of the integral expression for spherical reflection focusing system and the lens focusing system, we proposed the spherical phase filter applied in the lens system to realize a super-resolution optical needle with 0.4λ FWHM and ~400λ DOF.The results in this research provide some reference for the realization of the far field super-resolution focus, super-long optical needle and multi-focus, it can be wide applied in biomedical, super-resolution imaging and laser direct writing and other fields.