Measuring the complex spectrum of orbital angular momentum and radial index with a single-pixel detector

Typical methods to decode a complex orbital-angular-momentum (OAM) spectrum suffer from issues such as a narrow OAM range, unstable interferometer, and long measuring time. In this Letter, we use a single-beam interferometer to measure the complex OAM spectrum with a single-pixel detector. The complex OAM spectrum ranging from -10 to 10 can be measured in 11 ms with the fidelity approach of 97.0%, experimentally. Our approach allows one to characterize an unknown coherent field with any complex basis, e.g., the Laguerre-Gaussian (LG) basis is used for radial index spectrum measurement. Furthermore, single-pixel complex amplitude imaging based on the LG spectrum acquisition is presented, and the advantages in resolution and flexibility are demonstrated.