Improving axial resolution is of paramount importance for three-dimensional optical imaging systems. Here, we investigate the ultimate precision in axial localization using vortex beams. For Laguerre-Gauss beams, this limit can be achieved with just
an intensity scan. The same is not true for superpositions of Laguerre-Gauss beams, in particular for those with intensity profiles that rotate on defocusing. Microscopy methods based on rotating vortex beams may thus benefit from replacing traditional intensity sensors with advanced mode-sorting techniques.
The ability to completely characterize the state of a quantum system is an essential element for the emerging quantum technologies. Here, we present a compressed-sensing inspired method to ascertain any rank-deficient qudit state, which we experiment
ally encode in photonic orbital angular momentum. We efficiently reconstruct these qudit states from a few scans with an intensified CCD camera. Since it requires only a few intensity measurements, our technique would provide an easy and accurate way to identify quantum sources, channels, and systems.
