Separation measurement of two freely rotating dipole emitters at near optimal precision

According to Rayleigh’s criterion, two incoherent emitters with a separation below the diffraction limit are not resolvable with a conventional fluorescence microscope. One method of Super-Resolution Microscopy (SRM) breaks the diffraction-limited resolution by precisely estimating the centroid position of spatiotemporally independent emitters. However, conventional detection methods of SRM techniques are not optimal for estimating the separation of two simultaneously excited emitters. Recently, a number of detection methods based on modal imaging were developed to achieve the quantum Cramér-Rao lower bound (QCRB) for estimating separations between two nearby emitters. The QCRB determines the minimum achievable precision across all possible detection methods. Current modal imaging techniques assume a scalar field generated from a point source, such as an optical fiber or a pinhole. However, for fluorescently labeled samples, point emitters are single fluorophores that can be modeled as dipole emitters, and in practice are often freely rotating. Dipole radiation must be expressed in vectorial theory and the assumption of a scalar field no longer holds. Here we propose a detection scheme based on one of the modal imaging techniques, super-localization by image inversion interferometry (SLIVER), for separation estimation of two freely rotating dipoles. We introduce a vortex wave plate before the SLIVER detection to separate the radial and azimuthal components of the dipole radiation. We demonstrated that our method achieves near constant precision independent of the separation between two dipole emitters. We also quantified the effect of numerical aperture, detection bandwidth, number of estimation parameters, background and misalignment on separation estimation. Our method provides a near optimal detection scheme for measuring the separation of two freely-rotating dipole emitters such as fluorescently tagged molecules.