Generation and Manipulation of Superoscillatory Hotspots Using Virtual Fourier Filtering and CTF Shaping

Abhijit Sanjeev,Arrad Attar,Nadav Shabairou,Zeev Zalevsky,Yuval Kapellner,Moshe Sinvani,Daniel Scherbaum

doi:10.1038/s41598-020-61674-z

Abstract

Superoscillation is a technique that is used to produce a spot of light (known as ‘hotspot’) which is smaller than the conventional diffraction limit of a lens and even smaller than the optical wavelength. Over the past few years, several techniques have been realized for the generation of the superoscillatory hotspot. In this article, for the first time to the best of our knowledge, we propose a novel and a more efficient technique for producing superoscillation in microscopic imaging by shaping the Coherent Transfer Function (CTF) of a lens via virtual Fourier filtering followed by a phase retrieval algorithm. We design and realize a phase mask which when placed at the pupil plane of a diffraction-limited lens produces a superoscillatory hotspot with sidelobes properly matched to the field of view (FOV) required in microscopic imaging applications, i.e. hotspot always coexists with huge intense rings known as ‘sidebands’ close to it and hence limiting the FOV. Our technique is also capable of extending the FOV with minimal loss in resolution of the hotspot generated and considerable ratio between the intensity of the hotspot to that of the side lobes while optimizing the obtainable FOV to the requirement of microscopy.

Highlights

Superoscillation is a technique that is used to produce a spot of light which is smaller than the conventional diffraction limit of a lens and even smaller than the optical wavelength
Ernst Abbe, in 1873, demonstrated that there is a limit to the resolution that a conventional lens can achieve and it is dependent on the wavelength of light, λ, and the numerical aperture (NA) of the objective lens to be: d = 0.61λ/NA1
In order to show the proof of concept experimentally, we programmed a lens phase function in a computergenerated hologram and displayed it on our Spatial Light Modulator (SLM, HoloEye, 1080 × 1920 pixels, 8 μm pixel size) such that it produces a diffraction-limited spot corresponding to a lens of 400 mm focal length at a distance of 400 mm from the SLM in +1 or −1 diffraction order

Summary

Introduction

Superoscillation is a technique that is used to produce a spot of light (known as ‘hotspot’) which is smaller than the conventional diffraction limit of a lens and even smaller than the optical wavelength. While imaging smaller objects, conventional lens (due to limited aperture size) cannot collect all these light waves diffracted at a higher angle. It is possible to use immersion media to have NA greater than 1 because of its higher refractive index[2,3] Perhaps this fundamental limit has encouraged many researchers to come up with several techniques over the years to greatly enhance the resolution of optical microscope between tens and hundreds of nanometers. In terms of optical superoscillations, a hotspot will always be accompanied by high-intensity side lobes which are higher in energy than the hotspot in the center

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Conclusion