Breaking the Nyquist limit: superlinear range extension in FMCW lidar via co-prime phase resampling and the Chinese remainder theorem

Frequency-modulated continuous-wave (FMCW) lidar offers high precision and the capability for non-cooperative target sensing. However, its performance is critically limited by laser frequency modulation nonlinearity. Conventional resampling methods for nonlinearity correction necessitate an auxiliary interferometer path delay greater than four times the target distance, as dictated by the Nyquist theorem. This requirement results in bulky and instability-prone systems. The work proposed a novel resampling method based on the Chinese remainder theorem (CRT) to resolve the fundamental trade-off between precision and range. The proposed approach digitally subdivided the phase of a short auxiliary interferometer signal into multiple co-prime factors, constructing several equivalent undersampled sequences. The true distance was mapped into a set of unique, shorter residue distances, which were then uniquely reconstructed via the CRT. The method achieved an over 55-fold extension of the unambiguous range (from 0.91 to 50.16 m) using a short auxiliary path of 3.669 m. A measurement precision was maintained better than 15.0 µm in 8 m. A superlinear range extension was achieved without proportional hardware or data overhead, providing a robust and compact solution for high-precision, long-range FMCW metrology.