Nanoparticles have a key role in today's biotechnological research owing to the rapid advancement of nanotechnology. While metallic, polymer, and semiconductor based artificial nanoparticles are widely used as labels or targeted drug delivery agents, labeled and label-free detection of natural nanoparticles promise new ways for viral diagnostics and therapeutic applications. The increasing impact of nanoparticles in bio- and nano-technology necessitates the development of advanced tools for their accurate detection and characterization.;Optical microscopy techniques have been an essential part of research for visualizing micron-scale particles. However, when it comes to the visualization of individual nano-scale particles, they have shown inadequate success due to the resolution and visibility limitations. Interferometric microscopy techniques have gained significant attention for providing means to overcome the nanoparticle visibility issue that is often the limiting factor in the imaging techniques based solely on the scattered light.;In this dissertation, we develop a rigorous physical model to simulate the single nanoparticle optical response in a common-path wide-field interferometric microscopy (WIM) system. While the fundamental elements of the model can be used to analyze nanoparticle response in any generic wide-field imaging systems, we focus on imaging with a layered substrate (common-path interferometer) where specular reflection of illumination provides the reference light for interferometry. A robust physical model is quintessential in realizing the full potential of an optical system, and throughout this dissertation, we make use of it to benchmark our experimental findings, investigate the utility of various optical configurations, reconstruct weakly scattering nanoparticle images, as well as to characterize and discriminate interferometric nanoparticle responses.;This study investigates the integration of advanced optical schemes in WIM with two main goals in mind: (i) increasing the visibility of low-index nanoscale particles via pupil function engineering, pushing the limit of sensitivity; (ii) improving the resolution of sub-diffraction-limited, low-index particle images in WIM via reconstruction strategies for shape and orientation information. We successfully demonstrate an overall ten-fold improvement in the visibility of the low-index sub-wavelength nanoparticles as well as up to two-fold extended spatial resolution of the interference-enhanced nanoparticle images.;We also systematically examine the key factors that determine the signal in WIM. These factors include the particle type, size, layered substrate design, defocus and nanoparticle polarizability. We use the physical model to demonstrate how these factors determine the signal levels, and demonstrate how the layered substrate can be designed to optimize the overall signal, while defocus scan can be used to maximize it, as well as its signature can be utilized for particle discrimination purposes for both dielectric particles and resonant metallic particles. We introduce a machine learning based particle characterization algorithm that relies on supervised learning from model. The particle characterization is limited to discrimination based on nanosphere size and type in the scope of this dissertation.
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