Abstract: A serpentine integrated grating spectrometer includes a serpentine delay line and a plurality of grating couplers. The serpentine delay line includes a plurality of parallel waveguide segments that are coplanar in a delay-line plane. The serpentine delay line serially connects each of the plurality of grating couplers. Each of the plurality of grating couplers (i) is located at a respective one of the plurality of parallel waveguide segments, and (ii) direct light propagating in the serpentine delay line out of the delay-line plane. The plurality of waveguide segments is M in number and impart a total group delay time ry on light propagating therethrough. Each of the plurality of grating couplers impart a grating coupler delay tx on light propagating therethrough that exceeds (ty/M), the time delay for a single segment of the M parallel segments.

Abstract: A range-resolved imaging method includes sampling a plurality of 3D Fourier components of a target with a plurality of frequency-shifted beams that pair-wise interfere at the target. Each of the plurality of frequency-shifted beams has been emitted by a respective transmitter of a sparse transmitter-array. The method also includes extracting amplitudes and phases of temporal oscillations of a detected signal back-scattered by the target in response to the pair-wise interference of the plurality of frequency-shifted beams. The amplitudes and phases correspond to selected 3D Fourier components of a plurality of temporal Fourier components of the detected signal. The method also includes assembling the amplitudes and the phases in a 3D spatial-frequency representation; and producing a range-resolved image of the target via Fourier synthesis of the 3D Fourier representation.