Fourier-basis active structured illumination sensing lidar imaging using crossed acousto-optic devices

We detail the experimental demonstration and mathematical formulation of a computational lidar remote-imaging scheme-Fourier-basis active structured illumination sensing (<i>F</i>-BASIS)-that utilizes structured-light traveling-fringe projection from a nearly non-redundant array of frequency-shifted beams emitted simultaneously from a single aperture. Pairwise interference between elements within a <i>K</i>×<i>K</i> nearly non-redundant array of doubly-diffracted, Doppler-shifted beams-produced by a pair of cascaded orthogonal crossed acousto-optic deflectors (XAO) driven by appropriately scaled non-redundant sets of radio-frequency (RF) tones-produces, to our knowledge, <i>O</i>{<i>K</i>⁴} unique traveling-wave sinusoidal interference fringes. Each traveling fringe probes a matched spatial Fourier component, whose amplitude and phase are encoded in the corresponding RF temporal beat note. Detection of the backscattered return, followed by a temporal Fourier transform, enables the complex demodulation of the temporal beat notes. The resulting amplitudes and phases provide the corresponding Fourier coefficients in the 2D spatial Fourier domain, from which a 2D lidar image is reconstructed via spatial Fourier synthesis.