113 km absolute ranging with nanometer precision

Abstract: Accurate long-distance ranging is crucial for diverse applications, including satellite formation flying, very-long-baseline interferometry, gravitational-wave observatory, geographical research, etc. The integration of the time-of-flight mesurement with phase interference in dual-comb method enables high-precision ranging with a rapid update rate and an extended ambiguity range. Pioneering experiments have demonstrated unprecedented precision in ranging, achieving 5 nm @ 60 ms for 1.1 m and 200 nm @ 0.5 s for 25 m. However, long-distance ranging remains technically challenging due to high transmission loss and noise. In this letter, we propose a two-way dual-comb ranging (TWDCR) approach that enables successful ranging over a distance of 113 kilometers. We employ air dispersion analysis and synthetic repetition rate technique to extend the ambiguity range of the inherently noisy channel beyond 100 km. The achieved ranging precision is 11.5 $\mu$m @ 1.3 ms, 681 nm @ 1 s, and 82 nm @ 21 s, as confirmed through a comparative analysis of two independent systems. The advanced long-distance ranging technology is expected to have immediate implications for space research initiatives, such as the space telescope array and the satellite gravimetry.

• The paper presents a novel two-way dual-comb ranging (TWDCR) method designed to measure long distances with exceptionally high precision, overcoming transmission loss and atmospheric noise.
• The TWDCR method achieved remarkable ranging precision of 82 nm at 21 seconds over a 113 km path, validating its effectiveness for long-distance measurement.
• This technology has significant implications for space-based measurements, enabling improved satellite positioning, enhanced space telescope resolution, and better gravitational field measurements.

113 km Absolute Ranging with Nanometer Precision

The paper "113 km Absolute Ranging with Nanometer Precision" presents a novel two-way dual-comb ranging (TWDCR) approach designed to measure long distances with exceptionally high precision. This work addresses the technical challenges inherent in long-distance optical ranging, such as high transmission loss and atmospheric noise, which have previously limited the range and precision of existing techniques.

Background and Motivation

Precise long-distance ranging is critical for applications like satellite formation flying, very-long-baseline interferometry (VLBI), and space-based gravitational-wave observatories. Traditional optical ranging techniques, such as continuous-wave laser interferometry, provide high precision but are severely limited in ambiguity range. Conversely, techniques based on time-of-flight measurements offer greater ambiguity ranges but lack the required precision for nanoscale applications.

Optical frequency combs (OFCs), with their ability to bridge radio and optical frequencies, offer a promising solution to achieve both a wide ambiguity range and high precision. Prior to this work, dual-comb ranging techniques demonstrated sub-millimeter precision over relatively short distances and lacked validation over long outdoor paths.

Methodology

The TWDCR method proposed in this paper represents an innovative technique that mitigates noise and loss in signal transmission over long distances. It involves using two independent OFCs, each phase-locked to stable clocks at two separate terminals. This method allows the combs to produce interference signals that accurately extract distance information, benefiting from the phase comparison between the respective OFCs. The synthetic repetition rate and atmospheric dispersion analysis extend the ambiguity range, accommodating real-time atmospheric changes.

The experimental setup includes high-power OFCs and telescopes with large apertures, enabling transmission over a 113 km path with remarkably low power loss. A combination of low-noise photodetectors and sophisticated data acquisition systems enhances the sensitivity of this method, achieving detection even at high losses.

Experimental Results and Implications

The TWDCR method achieved ranging precision of 11.5 µm at 1.3 ms, 681 nm at 1 s, and 82 nm at 21 s over a 113 km path. These results emphasize the system's robustness and efficacy in precise distance measurement compared to microwave or laser pulse modulation methods.

The implications of this technology are significant, particularly for space-based measurements. Its ability to provide absolute distance measurements with sub-millimeter precision over hundreds of kilometers could revolutionize satellite positioning systems and enhance imaging resolution for space telescopes. The angular resolution for missions like the Micro-Arcsecond X-ray Imaging Mission (MAXIM) could be substantially improved, extending the baseline beyond current plans and offering clearer celestial observations.

Future Prospects

The accurate inter-satellite absolute ranging capabilities demonstrated here promise to improve gravitational field measurements of Earth and help prevent cycle slips in satellite gravimetry. Future developments could further enhance the system by addressing atmospheric refractive index uncertainties using dual-comb spectroscopy or the two-color method for atmospheric condition assessments.

In conclusion, the advancement of the TWDCR method represents a crucial step in the domain of high-precision optical ranging, with profound potential applications in scientific and extraterrestrial explorations.