Efficient Modal Decomposition of Vortex Beams via Holographically Reconstructed Phase

We use phase-shifting digital holography to measure the amplitude and phase of twisted light. In our experiment, a spatial light modulator generates the studied vortex beams in addition to a co-propagating reference beam with a controllable relative phase. We show complex field measurements for single and superposition Laguerre Gaussian (LG) modes, demonstrate full modal decompositions into LG and orbital angular momentum (OAM) power spectral bases, provide error analysis and demonstrate high insensitivity to detector misalignment to show the robustness of the technique. This enables rapid determination of OAM spectra with low uncertainty, allowing us to report the first vortex beams with 99.9% purity.