Three dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil

Localisation microscopy overcomes the diffraction limit by measuring the position of individual molecules to obtain optical images with a lateral resolution better than 30 nm. Single molecule localisation microscopy was originally demonstrated only in two dimensions but has recently been extended to three dimensions. Here we develop a new approach to three-dimensional (3D) localisation microscopy by engineering of the point-spread function (PSF) of a fluorescence microscope. By introducing a linear phase gradient between the two halves of the objective pupil plane the PSF is split into two lateral lobes whose relative position depends on defocus. Calculations suggested that the phase gradient resulting from the very small tolerances in parallelism of conventional slides made from float glass would be sufficient to generate a two-lobed PSF. We demonstrate that insertion of a suitably chosen microscope slide that occupies half the objective aperture combined with a novel fast fitting algorithm for 3D localisation estimation allows nanoscopic imaging with detail resolution well below 100 nm in all three dimensions (standard deviations of 20, 16, and 42 nm in x, y, and z directions, respectively). The utility of the approach is shown by imaging the complex 3D distribution of microtubules in cardiac muscle cells that were stained with conventional near infrared fluorochromes. The straightforward optical setup, minimal hardware requirements and large axial localisation range make this approach suitable for many nanoscopic imaging applications.