Using fluorescent beads to emulate single fluorophores.

We study the conditions under which fluorescent beads can be used to emulate single fluorescent molecules in the calibration of optical microscopes. Although beads are widely used due to their brightness and easy manipulation, there can be notable differences between the point spread functions (PSFs) they produce and those for single-molecule fluorophores, caused by their different emission patterns and sizes. We study theoretically these differences for various scenarios, e.g., with or without polarization channel splitting, to determine the conditions under which the use of beads as a model for single molecules is valid. We also propose methods to model the blurring due to the size difference and compensate for it to produce PSFs that are more similar to those for single molecules.

Birefringent Fourier filtering for single molecule coordinate and height super-resolution imaging with dithering and orientation.

Super-resolution imaging based on single molecule localization allows accessing nanometric-scale information in biological samples with high precision. However, complete measurements including molecule orientation are still challenging. Orientation is intrinsically coupled to position in microscopy imaging, and molecular wobbling during the image integration time can bias orientation measurements. Providing 3D molecular orientation and orientational fluctuations would offer new ways to assess the degree of alignment of protein structures, which cannot be monitored by pure localization. Here we demonstrate that by adding polarization control to phase control in the Fourier plane of the imaging path, all parameters can be determined unambiguously from single molecules: 3D spatial position, 3D orientation and wobbling or dithering angle. The method, applied to fluorescent labels attached to single actin filaments, provides precisions within tens of nanometers in position and few degrees in orientation.

Study of reflectors for illumination via conformal maps.

We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map that transforms the reflector's shape into a curve that describes light's direction after reflection. Both segmented reflectors and continuous reflectors are discussed, illustrating how certain reflector characteristics become apparent under this transformation. This method can also be used to study extended sources via translations.

Reflection formulae for ray tracing in uniaxial anisotropic media using Huygens's principle.

Ray tracing in uniaxial anisotropic materials is important because they are widely used for instrumentation, liquid-crystal displays, laser cavities, and quantum experiments. There are previous works regarding ray tracing refraction and reflection formulae using the common electromagnetic theory approach, but only the refraction formulae have been deduced using Huygens's principle. In this paper we obtain the reflection expressions using this unconventional approach with a specific coordinate system in which both refraction and reflection formulae are simplified as well as their deduction. We compute some numerical examples to compare them with the common expressions obtained using electromagnetic theory.

Deviation from orthogonal polarization for ordinary and extraordinary rays in uniaxial crystals.

We have derived a closed-form expression for the angle between polarizations of ordinary and extraordinary rays in uniaxial crystals for, first, any two rays propagating in the material, and, second, for rays coming from refraction. We show the cases in which orthogonality holds and that, in general, the deviation from orthogonality is rather small, for it depends on the difference of the optical indices. Specific examples for calcite and quartz are given.