# On-Axis Optical Bench for Laser Ranging Instruments in Future Gravity Missions
###### Abstract  
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. GRACE; laser interferometry; inter-satellite ranging; heterodyne readout +
Footnote †: journal: Sensors  
0202222207022222022220 glaciers, the contribution of water influx to sea level rise, as well as monitoring changes in underground water reserves, and in the hydrological cycle [3; 4; 5]. The LRI in the GRACE-FO enabled the first laser interferometer link between distant satellites, and provided range measurements with a sensitivity of \(200\,\mathrm{p}\mathrm{m}\mathrm{/}\sqrt{\mathrm{Hz}}\) at \(1\,\mathrm{Hz}\), more than 3 orders of magnitude lower than the \(0.6\,\mathrm{\SIUnitSymbolMicro m}\mathrm{/}\sqrt{\mathrm{Hz}}\) noise of the primary microwave ranging instrument [6]. The GRACE-FO LRI also served as a technology demonstrator for the ESA-NASA Laser Interferometer Space Antenna (LISA) mission [7], as well as the Chinese space-borne gravitational wave observatories Taiji [8] and TianQin [9] missions. The GRACE-FO LRI, as a technology demonstrator and not the primary science instrument, had restrictions on its design, e.g., volume, mass, instrument accommodation, and relaxed requirements on reliability and lifetime. After the success of the GRACE-FO LRI, the next generation of gravity missions are expected to use laser interferometry as the primary measurement principle. The optical bench (OB) is a central part of the LRI. Its primary purpose is to receive light from the remote satellite and combine it with a locally generated reference beam (LO) in order to extract their relative phase. The most promising phase measurement principle continues to be optical heterodyne detection [10; 11; 12]. In addition, the OB emits laser light with a well-defined phase that is obtained by phase locking to the received light. A secondary purpose of the OB is to measure the angle of the incoming light w.r.t. an OB frame of reference. This allows inference of the misalignment of the receiver S/C relative to the inter-satellite line-of-sight. This information is used in the LRI to actuate on the pointing of the transmitted beam to the remote S/C, and can be used in future missions to actuate in the attitude of the local S/C, in order to enhance the optical link power, keep the link stable, and minimize secondary noise sources. In the GRACE-FO mission, the LRI OB followed an \"off-axis\" design [13], where the receiving (RX) light and the transmitting (TX) light propagate into and out of the OB through separate apertures, namely the RX and TX apertures, and follow different paths along the OB. This type of design can lead to instruments with fewer optical components compared to the \"on-axis\" topology, where the RX and TX beam paths coincide, and the OB features a single aperture (Figure 1). The on-axis topology requires using polarizing optics in order to optimally combine the RX and LO light at the photodetectors, potentially yielding a more complex optical setup. However, due to the shared optical path between the RX and TX beams, an on-axis design has the potential to use a single baffle and a single telescope for both RX light reception and TX light transmission.