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Opt Express. 2014 Feb 24;22(4):4029-37. doi: 10.1364/OE.22.004029.

Axial super-localisation using rotating point spread functions shaped by polarisation-dependent phase modulation.


We present an approach for point spread function (PSF) engineering that allows one to shape the optical wavefront independently in both polarisation directions, with two adjacent phase masks displayed on a single liquid-crystal spatial light modulator (LC-SLM). The set-up employs a polarising beam splitter and a geometric image rotator to rectify and process both polarisation directions detected by the camera. We shape a single-lobe ("corkscrew") PSF that rotates upon defocus for each polarisation channel and combine the two polarisation channels with a relative 180° phase-shift on the computer, merging them into a single PSF that exhibits two lobes whose orientation contains information about the axial position. A major advantage lies in the possibility to measure and eliminate the aberrations in the two polarisation channels independently. We demonstrate axial super-localisation of isotropically emitting fluorescent nanoparticles. Our implementation of the single-lobe PSFs follows the method proposed by Prasad [Opt. Lett.38, 585 (2013)], and thus is to the best of our knowledge the first experimental realisation of this suggestion. For comparison we also study an approach with a rotating double-helix PSFs (in only one polarisation channel) and ascertain the trade-off between localisation precision and axial working range.

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