  Phase singularities appear ubiquitously in wavefields, regardless of the wave
equation. Such topological defects can lead to wavefront dislocations, as
observed in a humongous number of classical wave experiments. Phase
singularities of wave functions are also at the heart of the topological
classification of the gapped phases of matter. Despite identical singular
features, topological insulators and topological defects in waves remain two
distinct fields. Realising 1D microwave insulators, we experimentally observe a
wavefront dislocation - a 2D phase singularity - in the local density of states
when the systems undergo a topological phase transition. We show theoretically
that the change in the number of interference fringes at the transition reveals
the topological index that characterises the band topology in the insulator.

Mesoscale and Nanoscale Physics