# Comparing Link Budget Requirements for Future Space-Based Interferometers
## 1 Introduction  
Inter-satellite interferometers provide access to critical measurements that can not be made by ground-based sensors. The Gravity Recovery and Climate Experiment-Follow On (GRACE-FO) mission continuously tracks changes in the Earth's mass distribution to monitor global ice mass and ground water movement [1, 2]. GRACE-FO operates using both inter-satellite microwave links and interferometric laser links; tracking nanometer changes in spacecraft separation over hundreds of kilometers. Earth gravimetry missions are typically designed to operate for 5+ years, motivating multiple space collaborations to invest in follow-up missions to ensure measurement continuity. The European Space Agency (ESA) and the National Aeronautics Space Administration (NASA) are developing next-generation mission architectures in their respective missions: the Next-Generation Gravity Mission (NGGM) [3] and the GRACE-C mission (previously named the Mass change mission) [4]. New missions are opportunities to revise system designs and improve system architecture, measurement robustness, and cost. Figure 1 shows three possible optical configurations for future Earth geodesy missions. The transponder configurations, left in Figure 1, are the configurations currently used for the GRACE-FO laser ranging instrument (LRI) [5] with a frequency offset of \(\sim\)10 MHz. The dual-stabilized configuration, middle in Figure 1, uses two ultra-stable cavities to independently stabilize both optical sources. Using a second cavity on satellite B suppresses the laser frequency noise of that optical source, relaxing the tracked signal dynamics at that satellite but introducing the technical challenge of manufacturing two ultra-stable cavities with an exact frequency offset. The retro-reflector configuration, right in Figure 1, usesa single retro-reflecting element on satellite B to directly reflect the light from satellite A back. This configuration relaxes signal dynamics relative to the transponder configuration and decreases the number of optical components but does require the inclusion of an acousto-optic modulator to produce the desired frequency offset between the incoming and local light (typically around 10 MHz). In this configuration, the optical field also suffers the divergence loss twice due to the beam being double passed. The comparison between different mission configurations as viable candidates for the Next-Generation Gravity Mission architecture, in particular between the transponder and retro-reflector schemes [6; 7], concluded that the retro-reflector configuration could not meet the received carrier-to-noise density ratio requirement of 70 dB-Hz with spacecraft separation greater than 30 km without increased laser power. The minimum operable carrier-to-noise density signal, and hence the received optical power, is set by the phasemeter; this is a digital tool used in the mission to extract the phase information from a megahertz frequency carrier tone and down sample it to a lower data rate that can be transferred for analysis. In the presence of excessive noise, as in the case for tracking low-power signals, linear approximations within the phasemeter break down, causing non-linear errors such as cycle slips [8; 9] to occur. Cycle slips corrupt the scientific measurement being performed with the phasemeter, and as such, their onset defines the minimum operable optical power level. This has motivated significant study into phasemeter performance in optical phase tracking [10; 11; 12]. Recent experimental demonstration has confirmed that the minimum trackable optical power of a phasemeter is dependent on the frequency dynamics of the tracked signal [12], a factor that differs between the optical mission configurations presented in Figure 1. This difference means the minimum trackable optical power will vary between configurations and should be considered on a case by case basis. Figure 1: Configuration of comparison for interferometric satellite mission architectures.