Optical microscopy, thanks to the noninvasive nature of its measurement, takes a crucial role across science and engineering, and is particularly important in biological and medical fields. To meet ever increasing needs on its capability for advanced scientific research, even more diverse microscopic imaging techniques and their upgraded versions have been intensively developed over the past two decades. However, advanced microscopy development faces major challenges including super-resolution (beating the diffraction limit), imaging penetration depth, imaging speed, and label-free imaging. This dissertation aims to study high numerical aperture (NA) imaging methods proposed to tackle these imaging challenges.
The dissertation first details advanced optical imaging theory needed to analyze the proposed high NA imaging methods. Starting from the classical scalar theory of optical diffraction and (partially coherent) image formation, the rigorous vectorial theory that handles the vector nature of light, i.e., polarization, is introduced. New sign conventions for polarization ray tracing based on a generalized Jones matrix formalism are established to facilitate the vectorial light propagation with physically consistent outcomes.
The first high NA microscopic imaging of interest is wide-field oblique plane microscopy (OPM) for high-speed deep imaging. It is a simple, real-time imaging technique recently developed to access any inclined cross-section of a thick sample. Despite its experimental demonstration implemented by tilted remote focusing, the optical resolution of the method has not been fully understood. The anisotropic resolving power in high NA OPM is rigorously investigated and interpreted by deriving the vectorial point spread function (PSF) and vectorial optical transfer function (OTF). Next, OPM is combined with stochastic optical reconstruction microscopy (STORM) to achieve super-resolution deep imaging. The proposed method, termed obliqueSTORM, together with oblique lightsheet illumination paves the way for deeper penetration readily available in localization-based super-resolution microscopy. The key performance metrics of obliqueSTORM, quantitative super-resolution andaxial depth of field, are studied. obliqueSTORM could achieve sub-50-nm resolution with a penetration depth of tens of microns for biological samples.
The last part of the thesis covers the development of nonparaxial imaging theory of high NA differential phase contrast (DPC) microscopy for high resolution quantitative phase imaging. The phase retrieval in conventional optical DPC microscopy relies on the paraxial transmission cross-coefficient (TCC) model. However, this paraxial model becomes invalid in high NA DPC imaging. Formulated here is a more advanced nonparaxial TCC model that considers the nonparaxial nature of light propagation, apodization in high NA imaging systems, and illumination source properties. The derived nonparaxial TCC is numerically compared with the paraxial TCC to demonstrate its added features. The practical forms of the TCC for high resolution phase reconstruction are discussed for two special types of objects, weak objects and slowly varying phase objects.
The theoretical studies conducted here can help to bring such high NA microscopy techniques into the real world to solve imaging challenges.
