PHASE-SPACE PERSPECTIVE OF PARTIALLY COHERENT IMAGING: APPLICATIONS TO BIOLOGICAL PHASE MICROSCOPY

Abstract

Many specimens (particularly biological) are phase objects, i.e., they do not affect the intensity of light, but rather alter the phase of incident illumination. Imaging of phase specimens requires appropriate illumination and appropriate manipulation of scattered light to produce an image with phase contrast. The specimen may be illuminated from a single direction (e.g. using a laser, as in holography) or from a range of directions (e.g. using a halogen lamp with high-NA condenser, as in conventional microscopy). Methods that illuminate from a range of directions using an incoherent source (and hence give rise to partially coherent field at the specimen) provide high transverse and axial resolution, freedom from coherent speckle, and immunity against imperfections in the light-path. A popular example of the partially coherent method is differential interference contrast (DIC). While DIC has been used for qualitative microscopy since its inception, there is recent interest in using partially coherent phase methods (of which DIC is a special case) for high-resolution quantitative imaging of specimens. Since imaging is an inverse problem ¿ of estimating the specimen¿s properties from measured intensity ¿ the forward problem of partially coherent imaging must be formulated in an elegant, computationally efficient and physically intuitive manner. Unlike fluorescence and coherent microscopy, partially coherent imaging is an inherently nonlinear process, which has impeded development of accurate forward analysis and useful inversion approaches.

This thesis reports four important advances in the direction of quantitative specimen analysis using partially coherent optical phase microscopy: 1) We provide an accurate model of image formation in DIC microscope. Our results correct some incorrect assumptions held in DIC community for three decades and elucidate the effects of key parameters of the DIC microscope. 2) We discuss a novel wide-field imaging method, called Asymmetric Illumination-based Differential Phase Contrast (AIDPC), which overcomes key limitations of DIC (viz., corruption of DIC image due to specimen birefringence, low light-throughput, and non-linearity of information in DIC image). 3) We develop a phase-space (i.e., joint space-frequency) model, termed the phase-space imager (PSI). The PSI model provides an equivalent of the point-spread function model used in linear imaging. PSI elegantly captures non-linear image formation due to partial coherence, allows efficient computation of partially coherent images under a variety of methods and exploits an intuitive link with the Wigner representation used widely signal processing literature. 4) We demonstrate biological applications based on above developments. In collaboration with Dr. Rudolf Oldenbourg and Dr. Naoki Noda (from Cellular Dynamics Program, Marine Biological Laboratory, Woods Hole, MA, USA), we analyze the dynamics of a highly conserved molecular machine (called the axoneme) that powers flagella and cilia. We describe a new and robust registration algorithm required to reconstruct the specimen phase from images produced by DIC and AIDPC.