Experimental Demonstration of an On-Axis Laser Ranging Interferometer for Future Gravity Missions

TL;DR

The paper demonstrates a laboratory-scale on-axis Laser Ranging Interferometer (LRI) that uses a transponder-based, mono-axis link with two independent, high-bandwidth beam-steering loops to suppress tilt-to-length coupling. By mounting the reference bench on a hexapod to emulate spacecraft attitude jitter and employing differential wavefront sensing (DWS) and differential power sensing (DPS) for real-time alignment, the system achieves pointing stability below $10~\mu\mathrm{rad}/\sqrt{\mathrm{Hz}}$ in the GRACE-FO relevant band ($2~\mathrm{mHz}$ to $0.5~\mathrm{Hz}$) and only a $0.14\%$ reduction in carrier-to-noise-density ratio over 15 hours due to polarization fluctuations. Tilt-to-length coupling was characterized under controlled rotations, yielding TTL values below a few hundred micrometers per radian, with residual inaccuracies primarily due to hexapod positioning and spectral leakage during FFT filtering. Collectively, these results validate the feasibility of an on-axis LRI for future gravity missions and highlight the path toward higher precision implementations, including vacuum testing and improved hexapod hardware to eliminate longitudinal coupling.

Abstract

We experimentally demonstrate a novel interferometric architecture for next-generation gravity missions, featuring a laser ranging interferometer (LRI) that enables monoaxial transmission and reception of laser beams between two optical benches with a heterodyne frequency of 7.3 MHz. Active beam steering loops, utilizing differential wavefront sensing (DWS) signals, ensure co-alignment between the receiving (RX) beam and the transmitting (TX) beam. With spacecraft attitude jitter simulated by hexapod-driven rotations, the interferometric link achieves a pointing stability below 10 urad/$\mathrm{\sqrt{Hz}}$ in the frequency range between 2 mHz and 0.5 Hz, and the fluctuation of the TX beam's polarization state results in a reduction of 0.14\% in the carrier-to-noise-density ratio over a 15-hour continuous measurement. Additionally, tilt-to-length (TTL) coupling is experimentally investigated using the periodic scanning of the hexapod. Experimental results show that the on-axis LRI enables the inter-spacecraft ranging measurements with nanometer accuracy, making it a potential candidate for future GRACE-like missions.

Figures (14)

• Figure 1: Concept sketch of the inter-spacecraft laser interferometry in on-axis configuration. S/C, spacecraft; FIOS, fiber-injector optical subassembly; Pol, polarizer; FSM, fast steering mirror; M, mirror; QWP, quarter-wave plate; HWP, half-wave plate; QPR, quadrant photoreceiver; PBS, polarizing beamsplitter; CoM, center of mass.
• Figure 2: Schematic of reference point arrangements in an on-axis system using folding mirrors. The CoM is the virtual image of the AP, positioned via geometric unfolding of the optical path to serve as the center of the accelerator (ACC). The points of incidence on mirrors M1 and M2 are labeled A and B, respectively. The center of AP is designated as point O. The primed components M1$^{\prime}$, M2$^{\prime}$, AP$^{\prime}$, A$^{\prime}$, B$^{\prime}$ and O$^{\prime}$ denote the rotated configurations of M1, M2, AP, A, B and O, respectively, following a rotation of angle $\alpha$ about the CoM. The red and green traces illustrate the beam trajectories before and after rotation about the CoM. The total length $\text{OA+AB}$ equals the combined length $\text{O}^{\prime}\text{A}^{\prime} + \text{A}^{\prime}\text{B}^{\prime} + \text{B}^{\prime}\text{B}$, ensuring no piston effect during the rotation. M, mirror; AP, aperture; CoM, center of mass; ACC, Center of the Accelerator.
• Figure 3: Schematic of the experimental setup. The red, blue, green, and black dashed lines denote the laser beam from the free-running laser, the laser beam from the frequency offset locked laser, the optical fiber, and the electronic connections, respectively. The coordinate system in the center of mass (CoM) is used to define yaw, pitch, and roll rotations. The definitions of the RX beam and the TX beam are referenced with the reference bench. L, lens; M, mirror; FC, fiber collimator; FSM, fast steering mirror; QWP, quarter-wave plate; HWP, half-wave plate; SEPR, single-element photoreceiver; QPR, quadrant photoreceiver; BS, beamsplitter; PBS, polarizing beamsplitter; BD, beam dump; PZT, piezo-electric transducer.
• Figure 4: Beam configurations in the beam steering loop: (a) ideal alignment with zero DWS signal, (b) misalignment with non-zero DWS signal, and (c) realignment with zero DWS signal. The polarization states of the red and blue beams are denoted by red and blue text, respectively. The beam tilts illustrated in (b) and (c) are exaggerated for visualization, whereas in actual scenarios, the angular jitter would result in much smaller beam tilts. FSM, fast steering mirror; QWP, quarter-wave plate; HWP, half-wave plate; QPR, quadrant photoreceiver; PBS, polarizing beamsplitter; RHC, right-handed circularly polarized; LHC, left-handed circularly polarized; P, parallel-polarized; S, perpendicular-polarized.
• Figure 5: Measured open-loop transfer function of the laser frequency lock loop, including (a) the Bode magnitude plot and (b) the Bode phase plot. The laser frequency lock loop comprises a high-speed piezoelectric transducer (PZT) feedback loop and a low-speed temperature feedback loop. During the transfer function measurement, perturbations were injected into the PZT loop to characterize its frequency response. UGF, unity gain frequency; PM, phase margin.