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We investigate rotational diffusion of fluorescent molecules in angular potential wells, the excitation and subsequent emissions from these diffusing molecules, and the imaging of these emissions with high-NA aplanatic optical microscopes. Although dipole emissions only transmit six low-frequency angular components, we show that angular structured illumination can alias higher frequency angular components into the passband of the imaging system. We show that the number of measurable angular components is limited by the relationships between three time scales: the rotational diffusion time, the fluorescence decay time, and the acquisition time. We demonstrate our model by simulating a numerical phantom in the limits of fast angular diffusion, slow angular diffusion, and weak potentials., Comment: 22 pages, 5 figures

We investigate the properties of a single-view fluorescence microscope in a 4$f$ 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., Comment: 21 pages, 12 figures. Portions of this work previously appeared as arXiv:1812.07093, which was split during refereeing

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 in-focus 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 towards a complete theory., Comment: 14 pages, 4 figures

In the presence of a non-adsorbing polymer, monodisperse rod-like particles assemble into colloidal membranes, which are one rod-length thick liquid-like monolayers of aligned rods. Unlike 3D edgeless bilayer vesicles, colloidal monolayer membranes form open structures with an exposed edge, thus presenting an opportunity to study physics of thin elastic sheets. Membranes assembled from single-component chiral rods form flat disks with uniform edge twist. In comparison, membranes comprised of mixture of rods with opposite chiralities can have the edge twist of either handedness. In this limit disk-shaped membranes become unstable, instead forming structures with scalloped edges, where two adjacent lobes with opposite handedness are separated by a cusp-shaped point defect. Such membranes adopt a 3D configuration, with cusp defects alternatively located above and below the membrane plane. In the achiral regime the cusp defects have repulsive interactions, but away from this limit we measure effective long-ranged attractive binding. A phenomenological model shows that the increase in the edge energy of scalloped membranes is compensated by concomitant decrease in the deformation energy due to Gaussian curvature associated with scalloped edges, demonstrating that colloidal membranes have positive Gaussian modulus. A simple excluded volume argument predicts the sign and magnitude of the Gaussian curvature modulus that is in agreement with experimental measurements. Our results provide insight into how the interplay between membrane elasticity, geometrical frustration and achiral symmetry breaking can be used to fold colloidal membranes into 3D shapes., Comment: Main text: 25 pages, 6 figures. Supplementary information: 6 pages, 6 figures

Polarized light microscopy provides unique opportunities for analyzing the molecular order in man-made and natural materials, including biological structures inside living cells, tissues, and whole organisms. 20 years ago, the LC-PolScope was introduced as a modern version of the traditional polarizing microscope enhanced by liquid crystal devices for the control of polarization, and by electronic imaging and digital image processing for fast and comprehensive image acquisition and analysis. The LC- PolScope is commonly used for birefringence imaging, analyzing the spatial and temporal variations of the differential phase delay in ordered and transparent materials. Here we describe an alternative use of the LC-PolScope for imaging the polarization dependent transmittance of dichroic materials. We explain the minor changes needed to convert the instrument between the two imaging modes, discuss the relationship between the quantities measured with either instrument, and touch on the physical connection between refractive index, birefringence, transmittance, diattenuation, and dichroism., Comment: 21 pages, 5 figures, accepted for publication in Journal of Optics

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, including coherently illuminated and incoherent, self-luminous 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., Comment: current: 17 pages, 8 figures, expanded to include biological simulations; previous version: 7 pages, 2 figures; related website: https://code.google.com/p/microlith

We study the liquid crystalline phase behavior of a concentrated suspension of helical flagella isolated from {\it Salmonella typhimurium}. Flagella are prepared with different polymorphic states, some of which have a pronounced helical character while others assume a rod-like shape. We show that the static phase behavior and dynamics of chiral helices are very different when compared to simpler achiral hard rods. With increasing concentration, helical flagella undergo an entropy driven first order phase transition to a liquid crystalline state having a novel chiral symmetry., Comment: 5 pages, 5 figures. submitted to Physical Review Letters. to appear in Phys. Rev. Lett