Conical diffraction as a versatile building block to implement new imaging modalities for superresolution in fluorescence microscopy Clément Fallet, Julien Caron, Bioaxial (France); Jean-Yves Tinevez, Institut Pasteur (France); Lionel Moisan, René Descartes Univ. (France); Gabriel Y. Sirat, Philippe O. Braitbart,Bioaxial (France); Spencer L. Shorte, Institut Pasteur (France)

We present a new technology for super-resolution fluorescence imaging, based on conical diffraction. Conical diffraction is a linear, singular phenomenon taking place when a polarized laser beam is diffracted through a biaxial crystal [1]. The illumination patterns generated by conical diffraction in a thin biaxial crystal are more compact than the classical Gaussian beam; we use them to generate a super-resolution imaging modality. Whereas most of the current technologies in superresolution use non-linear processes [2] and require high quality immersion objectives and dedicated sample preparation, Bioaxial SuperResolution (BSR) resolution enhancement can be achieved with any type of objective no matter the magnification, numerical aperture, working distance, or the absence or presence of immersion medium on any kind of sample preparation and standard fluorophores. The system generates datasets made of thousands of images, one for each beam shape and beam position, similarly to some other Image Scanning techniques [3]. Given the low light doses used in each image, the data formation derives from a linear model with limits predicted by Fourier analysis and recent superresolution theory developments [4, 5]. In the framework of Bayesian Inverse Methods, we developed two numerical solvers that exploit the data formation model and the noise distribution in modern low-light cameras. This technique has been successfully used for live-cell super-resolution imaging over a long period [6], and shows that the light dose required for super-resolution imaging is far below the threshold likely to impact phototoxicity. [1] Berry, M V, 2004 'Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike', J.Optics.A 6 289-300. [2] Cremer et al. 2013 'Resolution enhancement techniques in microscopy', April 2013, Volume 38, Issue 3, pp 281-344. [3] Müller et al. 2010, 'Image Scanning Microscopy', Physical review Letter, Volume 104 Issue 19. [4] Candès E. J. and Carlos-Fernandez G. 2013, Towards a Mathematical Theory of Super-Resolution, Comm. Pure Appl. Math.. doi: 10.1002/cpa.21455 [5] Duval V. and Peyré G. 2013, 'Exact Support Recovery for Sparse Spikes Deconvolution.' arXiv preprint arXiv:1306,6909. [6] Caron, J et al, 2014 ‘Conical diffraction illumination opens the way for low phototoxicity superresolution imaging’, Cell Adh. And Mig., submitted.