Abstract
Interactions between biomolecules are characterized by both where they occur and how they are organized, e.g., the alignment of lipid molecules to form a membrane. However, spatial and angular information are mixed within the image of a fluorescent molecule-the microscope's dipole-spread function (DSF). We demonstrate the pixOL algorithm for simultaneously optimizing all pixels within a phase mask to produce an engineered Green's tensor-the dipole extension of point-spread function engineering. The pixOL DSF achieves optimal precision for measuring simultaneously the 3D orientation and 3D location of a single molecule, i.e., 4.1° orientation, 0.44 sr wobble angle, 23.2 nm lateral localization, and 19.5 nm axial localization precisions in simulations over a 700-nm depth range using 2500 detected photons. The pixOL microscope accurately and precisely resolves the 3D positions and 3D orientations of Nile red within a spherical supported lipid bilayer, resolving both membrane defects and differences in cholesterol concentration in 6 dimensions.