  The precise determination of the position of point-like emitters and
scatterers using far-field optical imaging techniques is of utmost importance
for a wide range of applications in medicine, biology, astronomy, and physics.
Although the optical wavelength sets a fundamental limit to the image
resolution of unknown objects, the position of an individual emitter can in
principle be estimated from the image with arbitrary precision. This is used,
e.g., in stars' position determination and in optical super-resolution
microscopy. Furthermore, precise position determination is an experimental
prerequisite for the manipulation and measurement of individual quantum
systems, such as atoms, ions, and solid state-based quantum emitters. Here we
demonstrate that spin-orbit coupling of light in the emission of elliptically
polarized emitters can lead to systematic, wavelength-scale errors in the
estimate of the emitter's position. Imaging a single trapped atom as well as a
single sub-wavelength-diameter gold nanoparticle, we demonstrate a shift
between the emitters' measured and actual positions which is comparable to the
optical wavelength. Remarkably, for certain settings, the expected shift can
become arbitrarily large. Beyond their relevance for optical imaging
techniques, our findings apply to the localization of objects using any type of
wave that carries orbital angular momentum relative to the emitter's position
with a component orthogonal to the direction of observation.
