Single-pixel sensing of rotating objects in Laguerre-Gaussian spectral domain

Single-pixel sensing (SPS) has proven to be a powerful tool for image-free object analysis. However, challenges arise when applying this technique to identify rotating objects, such as biological molecules and astronomical stars, because rotation disrupts the inherent correlation among numerous projections. Here, we propose and experimentally demonstrate a Laguerre-Gaussian (LG) spectral domain SPS approach. Benefiting from the circular symmetry of LG mode, the LG amplitude spectrum of an object exhibits rotation invariance, which is utilized to reconstruct the signal correlations of various projections. We prepare amplitude-type projection modes through the superposition of conjugate LG modes, which provides robustness against the phase fluctuations of light. The convolutional neural network (CNN) is trained using the LG spectra of static objects. In experiment, our method demonstrates high accuracies of 90.80%, 88.64%, and 82.5% when recognizing static objects, static objects after a random rotation, and rotating objects at 4831 rpm, respectively. Our approach opens new possibilities for extending the function of SPS to identify fast-rotating objects, which has potential applications in fundamental research areas such as biology and astronomy, as well as in industrial fields.