Spiral sampling algorithm for calculating the complex orbital angular momentum spectrum

The orbital angular momentum (OAM) spectrum is a critical parameter for OAM-based applications, as it reflects the OAM components of the measured light field. However, traditional definition-based algorithms for determining the OAM spectrum are time-consuming and dependent on extensive prior knowledge. To solve it, we propose what we believe to be a novel method for calculating the complex OAM spectrum. Our approach utilizes spiral sampling and Fourier transform, followed by appropriate filtering and inverse Fourier transform to retrieve the radial coefficients of arbitrary OAM components. Both simulation and experimental results validate the effectiveness of our method. This algorithm provides a powerful tool for future OAM-based applications.