Doppler Compensation for Optical Inter-Satellite and Satellite-to-Ground Frequency Transfer

Abstract

Future space missions equipped with optical clocks and terminals for optical inter-satellite links may require syntonization with an accuracy comparable to the stability of typical optical oscillators, 1E-14 or better. In order to transfer frequency between satellites, and between satellites and the Earth, it is necessary to handle the significant Doppler and Doppler rate effects at the level of several GHz and hundreds of MHz/s, respectively. This paper shows how to estimate the offset between two optical frequency references by taking advantage of the bidirectional capabilities of the optical link, which allows continuous comparison of beat notes (differences between the phase of a locally generated signal and that of a signal received from the other side). Using an approximate knowledge of the position and velocity of the satellites hosting the optical references, we can correct the measurements from the propagation-induced frequency shifts and directly compare the linked clocks, thus retrieving absolute frequency differences. We also show how to mitigate the effect of the measurement noise of the beat notes, which is amplified in the phase-to-frequency transformation. We then evaluate the impact (sensitivity analysis) of the a-synchronicity between the transmission times at the two ends combined with the inaccurate knowledge of position and velocity estimates on the accuracy of the frequency offset determination. Finally, we analyze the rate at which phase measurements must be taken to allow frequency transfer at 1E-14 accuracy.