Measurement of multipole phases in optics and electron microscopy by means of conformal transformations

Conformal mappings have been recently rediscovered as a practical
solution to measure physical quantities in an efficient manner by implementing
a unitary transformation on structured wavefields. For instance, one of the most
known is the log-pol mapping, enabling the measurement of orbital angular momentum
of optical and electron vortices. We report our latest research on a new
family of conformal mappings, the circular-sector transformations, applied to wavefunctions
endowed with multipole phases, showing disruptive applications in optics
and matter-waves physics, in particular electron microscopy. The results suggest an
innovative and promising method to measure astigmatisms and electric/magnetic
dipoles in a fast and direct way.