Rapidly Tunable Synthetic Wavelength Ranging with an RFSoC

TL;DR

This paper tackles the challenge of achieving accurate absolute optical range measurements with reduced system complexity. It presents a continuous-wave synthetic-wavelength interferometry method powered by digitally tunable electro-optic frequency combs controlled by an RFSoC, enabling dynamic sweeping of the synthetic wavelength and direct absolute-range estimation. By combining heterodyne beatnotes into a synthetic phase $ ext{Φ}_{ ext{λ'}}$ that cancels laser and AOM noise, the approach delivers precise ranging over both short free-space baselines and long fiber links. Experimental results show a best residual of $60 nm$ ($0.2 fs$) on a 1 m delay line and $15 μm$ ($50 fs$) over a 40 km fiber, corresponding to a fractional error of about $2×10^{-10}$, with system simplicity arising from reliance on CW interference and digital control.

Abstract

Measurements of optical range and time-of-flight are crucial for a variety of high-precision technologies. Competitive optical measurement techniques have been developed that balance precision with accuracy and system complexity. Here, we present a continuous-wave synthetic wavelength interferometry technique that employs digitally tunable electro-optic frequency combs. With a software-defined radio, our approach can dynamically sweep the synthetic wavelength and measure absolute optical range. We demonstrate this digital approach over a free-space optical delay line of 1 m and over an 40 km fiber link. The best obtained precision over the delay line is better than 60 nm (0.2 fs). Through a 40 km fiber spool, this precision degrades to 15 um (50 fs), which is a fractional error on the order of 2e-10 m/m. Our design is simple to implement, and only relies on continuous-wave interference, decreasing system complexity.

Figures (8)

• Figure 1: Schematic diagram showing the optical and radio-frequency layout for digital multi-wavelength optical absolute ranging. EOM, electro-optic modulator; AOM, acousto-optic modulator; PD, photodetector; PLL, phase-locked loop; $\omega_s$, optical source frequency; $\omega^x_E$ and $\omega^y_E$, EOM drive frequencies; $\omega^x_A$ and $\omega^y_A$, AOM drive frequencies; $T_{L}$, optical link delay mechanically actuated with a motorized collimator (ZFS06 stepper motor).
• Figure 2: Simplified illustration of the beat process at either optical transceiver. The optical signal from transceiver x is shown in dashed red, and the optical signal from transceiver y is shown in blue. Each transceiver tracks three beatnotes.
• Figure 3: Data processing for digital multi-wavelength ranging. For the short link (top panel), the synthetic wavelength is repeatedly reset. For the 40 fiber link (bottom panel), the synthetic wavelength is repeatedly stepped. The synthetic phase of the wavelength steps, $\Phi_{\lambda_1}$ (blue) and $\Phi_{\lambda_2}$ (green), are repeatedly measured. Each measurement has an interval of $\tau_m$. The mean is taken from each time-series to form a link estimate. The mean and standard deviation are drawn as error bars next to each measurement interval. Equation \ref{['eqn:integerCyc']} is used to determine the integer cycle of each time series, relative to the a priori link length.
• Figure 4: Absolute range estimates for the short link. The left panel shows the synthetic range estimate (green), the carrier displacement measurement (orange) and their difference residual (red) for a stationary optical link distance of 18.6. The right panel shows the synthetic range estimate (green), the carrier displacement measurement (orange) and their difference residual (red) for the same optical link with a continuous 5000 displacement.
• Figure 5: Absolute range estimates for the 40 fiber link. The left panel shows the synthetic range estimate (green), the carrier displacement measurement (orange) and their difference residual (red) for a stationary free-space optical link distance of 59681. The right panel shows the synthetic range estimate (green), the carrier displacement measurement (orange) and their difference residual (red) for the same optical link with a continuous 5000 displacement.