Producing superresolved point-spread functions using a phase modulation technique

Abstract

ABSTRACT In this paper we will be discussing different techniques fo r producing superresolved point- spread functions (PSFs) that are based on amplitude and phase pupil masks. We propose a novel method of producing elongated superresolved point-spread functions (PSFs) using a combination of a vortex phas e modulation technique and ellip tical amplitude masking at the pupil of an optical system. When comp ared to diffraction-limited PSFs produced by an optical system with the same pupil ellipticity, the proposed method produces a significant reduction in PSF width. The proposed technique can be applied to a variety of applications, including scanning microscopy and optical micromanipulation, as well as high-density optical data storage. Keywords: superresolution, point-spread function, pupil filte rs, amplitude filters, phase filters, vortex phase 1. INTRODUCTION Resolution enhancement techniques constitute of a subset of more general point spread function (PSF) engineering techniques that are being actively explor ed [1-4]. Resolution enhancements in the far field are commonly achieved using pupil filters [5-6]. Point spread functions that have improved resolution as compared to diffraction-limited PSFs of aberration-free optical systems obtained w ith uniform circular pupils, also known as Airy pattern s, are often termed as superresolving PSFs. Pupil filters producing superresolved PSFs are playing an increasingly im portant role in a variety of fields, such as optical data storage [7] and confocal scanning imaging systems [8]. Fundamentally, the PSF size in the optical system is proportional to the operating wavelength of light and the focal length, and is inversely proportional to the pupil size of the optical system. For example, optical systems in projection lithography operate at short wavelengths and employ high numerical aperture lenses with large pupil sizes. In certain applications, a reduction in the operating wavelength may not be an option due to the fundamental nature of the application phenomenon and system constraints such as the availability of an appropriate recording medium or emitting source. An increase in the lens numerical aperture is usually associated with a drastic increase in the lens fabrication costs, and may also be limited by the instrument’s geometrical constraints and residual aberrations. Reduction in PSF size using pupil filters presents an attractive alternative to adjustments in the operating wavelength and the numerical aperture of the optical system. The purpose of this paper is twofold. The first is to review various techniques that were previously used to achieve super resolution, including the use of pupil amplitude and phase masks comprised of a variety of phase steps [9-10]. These techniques will be discussed in the second through fourth sections of this paper. The second purpose is to evaluate a novel superresolution technique which we propose that is ba sed on a pupil filter composed of a combination of a vortex phase mask and an elliptical amplitude mask. We evaluate the resultant PSF for various levels of ellipticity of the pupil amplitude mask, and define the ellipticity range where the modified PSF based on our proposed technique produces a reduced width of the central peak as compared to a diffraction limited distribution produced with the same level of ellipticity at the pupil.