Tracking moving masses in several degrees of freedom with high precision and large dynamic range is a central aspect in many current and future gravitational physics experiments. Laser interferometers have been established as one of the tools of choice for such measurement schemes. Using sinusoidal phase modulation homodyne interferometry allows a drastic reduction of the complexity of the optical setup, a key limitation of multi-channel interferometry. By shifting the complexity of the setup to the signal processing stage, these methods enable devices with a size and weight not feasible using conventional techniques. In this paper we present the design of a novel sensor topology based on deep frequency modulation interferometry: the self-referenced single-element dual-interferometer (SEDI) inertial sensor, which takes simplification one step further by accommodating two interferometers in one optic. Using a combination of computer models and analytical methods we show that an inertial sensor with sub-picometer precision for frequencies above 10 mHz, in a package of a few cubic inches, seems feasible with our approach. Moreover we show that by combining two of these devices it is possible to reach sub-picometer precision down to 2 mHz. In combination with the given compactness, this makes the SEDI sensor a promising approach for applications in high precision inertial sensing for both next-generation space-based gravity missions employing drag-free control, and ground-based experiments employing inertial isolation systems with optical readout.

We developed a digital optical phase locking loop (OPLL) with three advantages, including high precision of phase locking, high control bandwidth up to 2.8 MHz, and automatic laser locking strategy. Spaceborne laser interferometers will be used to measure tiny displacements caused by gravitational waves in millions of kilometers range. A slave laser will be heterodyne phase locked to the incoming weak light at the end of an arm, emitting a higher power light back to the other satellite to measure pathlength variations at the picometer level. Such accuracy requires extremely precise OPLL. We report an experiment to demonstrate a digital OPLL that can automatically lock two independent free-running Nd:YAG lasers with residual phase error below 1 m r a d / H z above 0.01 Hz, which is the best performance recorded for digital servos, to our knowledge. Such performance tested under a normal laboratory environment will be highly improved in a vacuum environment with temperature and vibration well controlled. Both the digital OPLL and the automatic strategy were implemented on a field programmable gate array that could be potentially used for future gravitational-wave detection. Our experiment might change the thinking of scientists who study phasemeters of gravitational-wave detection because we are aware that the digital phase locking loop used for “optical phase tracking” is differently designed from “optical phase locking.”

The laser ranging interferometer onboard the Gravity Recovery and Climate Experiment Follow-On mission proved the feasibility of an interferometric sensor for inter-satellite length tracking with sub-nanometer precision, establishing an important milestone for space laser interferometry and the general expectation that future gravity missions will employ heterodyne laser interferometry for satellite-to-satellite ranging. In this paper, we present the design of an on-axis optical bench for next-generation laser ranging which enhances the received optical power and the transmit beam divergence, enabling longer interferometer arms and relaxing the optical power requirement of the laser assembly. All design functionalities and requirements are verified by means of computer simulations. A thermal analysis is carried out to investigate the robustness of the proposed optical bench to the temperature fluctuations found in orbit.

A new off-axis optical design alternative to that of the GRACE Follow-on mission for future NGGM missions is considered. In place of the triple-mirror assembly of the GRACE Follow-on mission, a laser retro-reflector is instead generated by means of lens systems. The receiving (RX) beam and transmitting (TX) beam are enforced to be anti-parallel by a control loop with differential wavefront sensing (DWS) signals as readout, and a fast-steering mirror is employed to actuate the pointing of the local beam. The tilt-to-length (TTL) coupling noise of the new off-axis optical bench layout is carefully studied in the present work. Local TTL originated from piston noise as well as assembly and alignment errors of optical components are studied. Effort is also made to have an in depth understanding of global TTL due to relative attitude jitter between spacecraft. The margin of TTL noise in the position noise budget for laser ranging is examined. With an open loop control of the offset between the reference point of the optical bench and the centre of mass of a satellite, the TTL noise of the new off-axis optical bench design may be suppressed efficiently.

The inter-satellite laser ranging heterodyne interferometer is vital for future gravity missions to achieve high ranging accuracy. This paper proposes a novel off-axis optical bench design which integrates merits of the off-axis optical bench design of GRACE Follow-On mission and other on-axis designs. This design makes use of lens systems subtly to restrict the tilt-to-length coupling noise and takes advantage of the DWS feedback loop to maintain the transmitting beam and receiving beam anti-parallel. The critical parameters of the optical components are determined and the carrier-to-noise ratio for a single channel of the photoreceiver is calculated to be more than 100 dB-Hz for the high case. The off-axis optical bench design is a potential candidate for China’s future gravity missions.

Future GRACE-like geodesy missions could benefit from adopting accelerometer technology akin to that of the LISA Pathfinder, which employed laser interferometric readout at the sub-picometer level in addition to the conventional capacitive sensing, which is at best at the level of 100 pm. Improving accelerometer performance holds great potential to enhance the scientific output of forthcoming missions, carrying invaluable implications for research in climate, water resource management, and disaster risk reduction. To reach sub-picometer displacement sensing precision in the millihertz range, laser interferometers rely on suppression of laser-frequency noise by several orders of magnitude. Many optical frequency stabilization methods are available with varying levels of complexity, size, and performance. In this paper, we describe the performance of a Mach–Zehnder interferometer based on a compact monolithic optic. The setup consists of a commercial fiber injector, a custom-designed pentaprism used to split and recombine the laser beam, and two photoreceivers placed at the complementary output ports of the interferometer. The structural stability of the prism is transferred to the laser frequency via amplification, integration, and feedback of the balanced-detection signal, achieving a fractional frequency instability better than 6 parts in ${10}^{13}$, corresponding to an interferometer pathlength stability better than $1\mathrm{pm}/\sqrt{\mathrm{Hz}}$. The prism was designed to host a second interferometer to interrogate the position of a test mass. This optical scheme has been dubbed “single-element dual-interferometer” or SEDI.