Fractional-Fourier-Domain Broadband Noise Cancellation for Ultrafast High-Precision Ranging

Dual-chirp interferometric ranging enables continuous distance measurements over an extended unambiguous range by introducing a controlled chirp-rate mismatch between probe and reference optical pulses. Extending the continuous range requires a larger chirp-rate mismatch, which increases the detection and processing bandwidth requirements. However, the resulting bandwidth expansion admits more broadband noise, degrades zero-frequency-point (ZFP) localization, and limits ranging precision, creating a trade-off between measurement range and precision. Here, we present a chirp-matched fractional-domain representation framework for high-precision dual-chirp interferometric ranging over an extended range. By projecting the chirped interference waveform into adaptively optimized fractional Fourier domains, the chirped-signal energy is compressed into localized distributions while broadband noise remains dispersed. This separation enables robust ZFP localization and accurate phase retrieval without discarding the bandwidth-dependent ranging information needed for large-range measurements. Experiments demonstrate meter-scale continuous ranging at a megahertz-level measurement frame rate, with a representative signal-to-noise ratio enhancement of approximately 63 dB relative to direct demodulation of the corresponding unprocessed waveform and an Allan deviation of 38.58 nm at an averaging time of 210.8 μs. The framework thereby converts bandwidth expansion from a source of ranging degradation into a resource for signal recovery. By introducing a chirp-matched fractional-domain representation of asymmetric dual-chirp interference signals, this work substantially mitigates the conventional range-precision trade-off and offers a practical approach to large-dynamic-range, high-precision optical metrology.