Intensity-only correlation-energy tomography in orbital angular momentum light

We present an intensity-only framework for extracting finite OAM correlation-energy observables under calibrated angular resolution. The recovered observable is a reduced-order OAM autocorrelation-energy profile, which captures finite intermodal correlation strength without requiring full modal-state reconstruction. Using the Fourier analysis of angular intensity, we show that intensity Fourier coefficients encode these finite autocorrelations, while calibrated Gaussian blur produces a tunable weighting on correlation index. This yields a blur-indexed scalar measurement family whose dependence on resolution defines a reduced-order inverse problem for retained correlation energies. Numerical results confirm the exact forward relations, illustrate regularized recovery of retained low-order observables under controlled noise, and quantify the dependence on retained bandwidth, blur range, and regularization. The approach is complementary to OAM spectrum measurement and full modal tomography: it sacrifices full state information in exchange for an intensity-only, phase-free correlation-energy diagnostic based on sampled angular intensity and calibrated point-spread response.