Object identification using correlated radial momentum states and beyond

The joint orbital angular momentum (OAM) spectrum has been widely utilized for characterizing the azimuthal structure of objects, particularly those with rotational symmetry. However, its inherent insensitivity to radial features limits its applicability in more complex object recognition tasks. To overcome this limitation, we introduce an object recognition approach based on the joint radial momentum spectrum (RMS). Through lunar-like phase object identification experiments, we demonstrate that the joint RMS effectively captures an object's radial structural features. Furthermore, we show that the RMS successfully differentiates Laguerre-Gaussian modes with identical azimuthal properties but distinct radial distributions-an ability unattainable using the joint OAM spectrum. These results underscore the complementary role of the joint RMS in enhancing the joint OAM spectrum, highlighting the necessity of their combined use for comprehensive spatial structure recognition. This work provides new insights into RMS-based remote sensing and optical information processing, paving the way for more versatile object recognition methodologies.