This document provides supplementary information to "Single Molecule Light Field Microscopy."
3D POINT SOURCE LOCALIZATION IN SINGLE MOLECULE LIGHT FIELD MICROSCOPYIdeally, a microscope objective transforms a spherical wave emitted by a point source located at the origin x p , y p , z p into a plane wave at the pupil. Spherical waves emitted by a point emitter displaced from the origin, located at (x i , y i , z i ), generate more complex wavefronts in the pupil since in this case the optical path length to the principal sphere varies as a function of propagation direction. The majority of microscope objectives are designed according to the sine condition, according to which, ray height is preserved during mapping between principal planes ({x p , y p } → {u, v}) [11]. As a result, the phase difference in the pupil between wavefronts emanating from points located at x p , y p , z p and (x i , y i , z i ) depends on the optical path difference (OPD) between two rays that intersect at the principal sphere: