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We introduce the basic elements of a spatio-angular theory of fluorescence microscopy, providing a unified framework for analyzing systems that image single fluorescent dipoles and ensembles of overlapping dipoles that label biological molecules. We model an aplanatic microscope imaging an ensemble of fluorescent dipoles as a linear Hilbert-space operator, and we show that the operator takes a particularly convenient form when expressed in a basis of complex exponentials and spherical harmonics-a form we call the dipole spatio-angular transfer function. We discuss the implications of our analysis for all quantitative fluorescence microscopy studies and lay out a path toward a complete theory.

We investigate the properties of a single-view fluorescence microscope in a 4f geometry when imaging fluorescent dipoles without using the monopole or scalar approximations. We show that this imaging system has a spatio-angular band limit, and we exploit the band limit to perform efficient simulations. Notably, we show that information about the out-of-plane orientation of ensembles of in-focus fluorophores is recorded by paraxial fluorescence microscopes. Additionally, we show that the monopole approximation may cause biased estimates of fluorophore concentrations, but these biases are small when the sample contains either many randomly oriented fluorophores in each resolvable volume or unconstrained rotating fluorophores.

We investigate the use of polarized illumination in multiview microscopes for determining the orientation of single-molecule fluorescence transition dipoles. First, we relate the orientation of single dipoles to measurable intensities in multiview microscopes and develop an information-theoretic metric-the solid-angle uncertainty-to compare the ability of multiview microscopes to estimate the orientation of single dipoles. Next, we compare a broad class of microscopes using this metric-single- and dual-view microscopes with varying illumination polarization, illumination numerical aperture (NA), detection NA, obliquity, asymmetry, and exposure. We find that multi-view microscopes can measure all dipole orientations, while the orientations measurable with single-view microscopes is halved because of symmetries in the detection process. We also find that choosing a small illumination NA and a large detection NA are good design choices, that multiview microscopes can benefit from oblique illumination and detection, and that asymmetric NA microscopes can benefit from exposure asymmetry.

A number of histopathology studies have utilized the label free microscopy method of Second Harmonic Generation (SHG) to investigate collagen organization in disease onset and progression. Here we explored an alternative label free imaging approach, LC-PolScope that is based on liquid crystal based polarized light imaging. We demonstrated that this more accessible technology has the ability to visualize all fibers of interest and has a good to excellent correlation between SHG and LC-PolScope measurements in fibrillar collagen orientation and alignment. This study supports that LC-PolScope is a viable alternative to SHG for label free collagen organization measurements in thin histology sections.

We have developed an imaging system for 3D time-lapse polarization microscopy of living biological samples. Polarization imaging reveals the position, alignment and orientation of submicroscopic features in label-free as well as fluorescently labeled specimens. Optical anisotropies are calculated from a series of images where the sample is illuminated by light of different polarization states. Due to the number of images necessary to collect both multiple polarization states and multiple focal planes, 3D polarization imaging is most often prohibitively slow. Our MF-PolScope system employs multifocus optics to form an instantaneous 3D image of up to 25 simultaneous focal-planes. We describe this optical system and show examples of 3D multi-focus polarization imaging of biological samples, including a protein assembly study in budding yeast cells.

Image simulation remains under-exploited for the most widely used biological phase microscopy methods, because of difficulties in simulating partially coherent illumination. We describe an open-source toolbox, microlith (https://code.google.com/p/microlith), which accurately predicts three-dimensional images of a thin specimen observed with any partially coherent imaging system, as well as images of coherently illuminated and self-luminous incoherent specimens. Its accuracy is demonstrated by comparing simulated and experimental bright-field and dark-field images of well-characterized amplitude and phase targets, respectively. The comparison provides new insights about the sensitivity of the dark-field microscope to mass distributions in isolated or periodic specimens at the length-scale of 10nm. Based on predictions using microlith, we propose a novel approach for detecting nanoscale structural changes in a beating axoneme using a dark-field microscope.

We propose image processing algorithms for measuring two-dimensional distributions of linear birefringence using a pair of variable retarders. Several algorithms that use between two and five recorded frames allow us to optimize measurements for speed, sensitivity, and accuracy. We show images of asters, which consist of radial arrays of microtubule polymers recorded with a polarized light microscope equipped with a universal compensator. Our experimental results confirm our theoretical expectations. The lowest noise level of 0.036 nm was obtained when we used the five-frame technique and four-frame algorithm without extinction setting. The two-frame technique allows us to increase the speed of measurement with acceptable image quality.