Single-pixel identification of 2-dimensional objects by using complex Laguerre–Gaussian spectrum containing both azimuthal and radial modal indices

We simulate and experimentally demonstrate the optical single-pixel identification of two-dimensional (2D) objects by analyzing the corresponding complex-valued (i.e, amplitude and phase) Laguerre–Gaussian​ (LGl,p) spectra containing both the azimuthal (i.e., l) and radial (i.e., p) indices. A sequence of optical beams, each carrying a different superposition of one LG mode and one fundamental Gaussian mode, propagate through the objects. The amplitude and phase contributions of each LG modal component are then obtained by four sequential power measurements using a single-pixel detector. We reconstruct the 2D spatial structures of fan-shaped objects with different orientation angles and an “SC” logo using the measured complex LG spectra that contain 31 different azimuthal and 31 different radial index values. The simulation and experimental results show that (i) the minima positions of the amplitude-only LG sub-spectra (fixed l=0, varying p) are dependent on the object’s spatial information along its radial direction, (ii) the amplitude-only LG spectrum is likely to be insensitive to the object’s orientation angle, and (iii) the slopes of the phase-only LG sub-spectra (fixed p, varying l) are linearly proportional to the object’s orientation angle.