  We motivate metrology schemes based on topological singularities as a way to
build robustness against deformations of the system. In particular, we relate
reference settings of metrological systems to topological singularities in the
measurement outputs. As examples we discuss optical nano-position sensing (i)
using a balanced photodetector and a quadrant photodetector, and (ii) a more
general image based scheme. In both cases the reference setting is a scatterer
position that corresponds to a topological singularity in an output space
constructed from the scattered field intensity distributions.
