Single-molecule localization techniques are restricted by long acquisition and computational times, or the need of special fluorophores or biologically toxic photochemical environments. Here we propose a statistical super-resolution technique of wide-field fluorescence microscopy we call the multiple signal classification algorithm which has several advantages. It provides resolution down to at least 50 nm, requires fewer frames and lower excitation power and works even at high fluorophore concentrations. Further, it works with any fluorophore that exhibits blinking on the timescale of the recording. The multiple signal classification algorithm shows comparable or better performance in comparison with single-molecule localization techniques and four contemporary statistical super-resolution methods for experiments of in vitro actin filaments and other independently acquired experimental data sets. We also demonstrate super-resolution at timescales of 245 ms (using 49 frames acquired at 200 frames per second) in samples of live-cell microtubules and live-cell actin filaments imaged without imaging buffers.

Imaging of object structures using cylindrical vector beams in an aplanatic solid immersion lens (SIL) microscope is investigated. Based on a complete optical model of an aplanatic SIL microscope, images of some object structures using radial polarization, azimuthal polarization, and azimuthal vortex beams are simulated. Some interesting imaging effects of these object structures are observed. For example, counterintuitively, it is found that, compared to linear and circular polarizations, radial polarization requires a larger pinhole to acquire a good image and resolution. Similarly, it is shown that an azimuthal vortex beam provides good images for a variety of object structures and pinhole sizes. Theories and explanations are provided to justify the observed effects. The presented results play an important role in high-numerical-aperture optical imaging.

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The behavior of the multiple signal classification (MUSIC) algorithm is investigated when used to locate small dielectric cylinders of specific characteristics in noise-free and noisy scenarios using the TE incidence. We have made three observations regarding the performance of MUSIC in the two-dimensional TE scenario, which reveal the significance of the choice of signal subspace while employing MUSIC and the shortcoming of traditional MUSIC when used to detect degenerate cylinders (which might be so due to the material or geometry of the cylinders). The detailed analysis of the sources induced on a cylinder and their linear dependency on each other gives a distinct insight into the use of MUSIC algorithm to locate it. A non-iterative retrieval algorithm is provided that is based on the least squares method, which retrieves the electric and magnetic polarization tensors of the small cylinders. The algorithm proposed here is mathematically a simple and direct representation of the physical principles and is applicable to degenerate cylinders as well.

Linear sampling method (LSM) is a qualitative method used to reconstruct the support of scatterers. This paper presents a modification of the LSM approach. The proposed method analyses the multipole expansion of the scattered field. Only monopole and dipole terms are used for the reconstruction of the scatterer support and all other higher order multipoles are truncated. It is shown that such modification performs better than the mathematical regularization typically used in LSM. The justification for truncation of higher order multipoles is presented. Various examples are presented to demonstrate the performance of the proposed method for dielectric as well as perfectly conducting scatterers in presence of significant amount of additive Gaussian noise.

Segmenting subcellular structures in living cells from fluorescence microscope images is a ground truth (GT)-deficient problem. The microscopes’ three-dimensional blurring function, finite optical resolution due to light diffraction, finite pixel resolution and the complex morphological manifestations of the structures all contribute to GT-hardness. Unsupervised segmentation approaches are quite inaccurate. Therefore, manual segmentation relying on heuristics and experience remains the preferred approach. However, this process is tedious, given the countless structures present inside a single cell, and generating analytics across a large population of cells or performing advanced artificial intelligence tasks such as tracking are greatly limited. Here we bring modelling and deep learning to a nexus for solving this GT-hard problem, improving both the accuracy and speed of subcellular segmentation. We introduce a simulation-supervision approach empowered by physics-based GT, which presents two advantages. First, the physics-based GT resolves the GT-hardness. Second, computational modelling of all the relevant physical aspects assists the deep learning models in learning to compensate, to a great extent, for the limitations of physics and the instrument. We show extensive results on the segmentation of small vesicles and mitochondria in diverse and independent living- and fixed-cell datasets. We demonstrate the adaptability of the approach across diverse microscopes through transfer learning, and illustrate biologically relevant applications of automated analytics and motion analysis.

We present the derivation of the dyadic Green's function for the aplanatic solid immersion lens based microscopy system. The presented dyadic Green's function is general and is applicable at non-aplanatic points as well in the object plane. Thus, the electromagnetic wave formulation is used to describe the optical system without paraxial assumptions. Various important and useful properties of SIL based microscopy system are also presented. The effect of the numerical aperture of the objective on the peak intensities, resolutions and the depth of field are also reported. Some interesting longitudinal effects are also reported.

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