Scale Factor of the Laser Ranging Interferometer in GRACE Follow-On

The Laser Ranging Interferometer onboard GRACE-FO is a novel instrument, that measures  the inter-spacecraft distance up to nanometer precision with high reliability. An important quantity for this precise measurement is the absolute laser frequency (or scale factor), which is used to convert the raw phase measurements into physical biased ranges with unit of meters. The current processing scheme of LRI1B data products employed by SDS estimates the LRI scale factor by means of daily cross-correlations of LRI range with respect to KBR range. However, in potential future missions, where the LRI becomes the primary and only ranging instrument, such a cross-calibration would not be available. We therefore present a method to estimate the LRI laser frequency from telemetry and evaluate the model accuracy.

The laser frequency is determined and known to some extend from the settings of the lasers. We derived a simple linear model to relate the LRI level 1A telemetry to the absolute laser frequency, which is purely based on pre-flight ground measurements. This telemetry-derived frequency matches to the in-flight LRI-KBR cross-calibration value to approx. 100 MHz, which has to be compared to the absolute frequency of 281.615 THz of the laser light. The fractional accuracy of 3*10^-7 translates to a range scale factor uncertainty of 1.5*10^-7 due to the conversion from round-trip to one-way range.  The remaining residuals, given by the difference of our model with respect to cross-calibration values, are described in our analysis as an additional empirical model, which is dominated by a linear drift of 1.5 Hz/s. Some recurring features, likely with yearly periodicity, and of the order of a few 10 MHz are present and will be addressed as well.

With our presented model, based on pre-flight characterizations and in-flight LRI-KBR comparisons from approximately two years in orbit, one can compute the LRI laser frequency or scale factor continuously to a few parts in 10⁸. By applying the continuous scale factor in the LRI1B data generation, one can avoid discontinuities in the LRI range at the day bounds currently present in LRI1B RL04 data. We conclude with implications of our analysis to future mission developments utilizing LRI-like instruments.