Atmospheric refraction corrections in ground-to-satellite optical time transfer

Free-space optical time and frequency transfer techniques can synchronize fixed ground stations at the femtosecond level, over distances of tens of kilometers. However, optical time transfer will be required to span intercontinental distances in order to truly unlock the performance of optical frequency standards and support an eventual redefinition of the SI second. Fiber dispersion and Sagnac uncertainty severely limit the performance of long-range optical time transfer over fiber networks, so satellite-based free-space time transfer is a promising solution. In pursuit of ground-to-space optical time transfer, previous work has considered a number of systematic shifts and concluded that all of them are manageable. One systematic effect that has not yet been substantially studied in the context of time transfer is the effect of excess optical path length due to atmospheric refraction. For space-borne objects, orbital motion causes atmospheric refraction to be imperfectly canceled even by two-way time and frequency transfer techniques, and so will require a temperature-, pressure-, and humidity-dependent correction. This systematic term may be as large as a few picoseconds at low elevations and remains significant at elevations up to ~35 ° . It also introduces biases into previously-studied distance- and velocity-dependent corrections.