Frequency-diverse structured light for optical gradient sensing using heterodyne interferometry

We introduce a free-space optical sensing architecture in which spatial refractive-index gradients are mapped directly into heterodyne modulation sidebands using a frequency-diverse beamlet array. Mutually coherent beamlets with distinct frequency offsets sample the medium at different transverse positions, producing a time-dependent interference signal on a single detector whose Fourier transform yields a comb of heterodyne beat frequencies. Spatially varying refractive index gradients induce differential phase shifts between beamlets, yielding symmetric sidebands around each beat frequency that encode the local gradient. This approach enables multiple parallel sensing channels on a single detector without a reference arm or embedded sensing elements, with spatial sampling and detection defined entirely by the optical field. An analytic framework describing beat formation and sideband scaling is developed and validated experimentally. Using an eight-beamlet array at 532 nm with 5 MHz spacing, the system achieves > 80 dB beat-to-sidelobe ratios and near-pascal acoustic sensitivity. Because the detection bandwidth is set by the optical beat frequencies, this approach supports extension to substantially higher acoustic bandwidths, establishing a compact, reconfigurable platform for remote, non-contact acoustic sensing. This approach establishes a general framework for non-contact sensing of refractive index gradients using structured light, with potential applications beyond acoustics including turbulence and thermal sensing.