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The GRACE Follow-On satellites carry the very first inter-spacecraft LaserRanging Interferometer (LRI). After more than four years in orbit, the LRIoutperforms the sensitivity of the conventional Microwave Instrument (MWI).However, in the current data processing scheme, the LRI product still needs theMWI data to determine the unknown absolute laser frequency, representing theruler for converting the raw phase measurements into a physical displacement inmeters. In this paper, we derive formulas for precisely performing thatconversion from the phase measurement into a range, accounting for a varyingcarrier frequency. Furthermore, the dominant errors due to knowledgeuncertainty of the carrier frequency as well as uncorrected time biases arederived. In the second part, we address the dependency of the LRI on the MWI inthe currently employed cross-calibration scheme and present three differentmodels for the LRI laser frequency, two of which are largely independent of theMWI. Furthermore, we analyze the contribution of thermal variations on thescale factor estimates and the LRI-MWI residuals. A linear model called ThermalCoupling (TC) is derived that significantly reduces the differences between LRIand MWI to a level where the MWI observations limit the comparison.

Scale Factor Determination for the GRACE-Follow On Laser Ranging Interferometer including Thermal Coupling