Accurate Axial Localization By Conical Diffraction Beam Shaping Generating A Dark-Helix Psf

We present here a new PSF-shaping technique using biaxial crystals to generate a highly z-dependent distribution in single molecule localization microscopy (SMLM). This distribution features two zeros of intensity that rotate together with defocus. This PSF features similarities to the double-helix introduced by Moerner and Piestun and thus has been dubbed dark-helix since we track zeros of intensity. Preliminary numerical studies based on Cramer-Rao Lower Bound (CRLB) show that this PSF has the potential to obtain up to 20nm localization precision. This PSF can be easily generated by a very simple, monolithic add-on added in front of the detection camera. Additionally, the PSF remains of the approximate size of the Airy PSF, the x-y localization precision is not substantially affected and no trade-off is required. The xy compacity of the PSF also enables theoretically a higher density of emitters than the doube-helix which spreads on a larger scale. Limiting factors for SMLM such as loss of photons, complexity and robustness will be discussed and considerations about the practical implementation of such techniques will be given.