Implement assistance tone for ranging

This implements an assistance tone time-delay interferometry ranging (TDIR).

The tone is modeled by

A \sin(2 \pi f \hat\tau + \phi_0)

with

• A the tone amplitude (can be MOSA-dependent)
• f the tone frequency (can be MOSA-dependent)
• \phi_0 the tone frequency (can be MOSA-dependent)
• \hat\tau the onboard clock time (THE)

It can be accessed through Instrument.tdir_tones, and is written to HDF5 as tdir_tones.

The tone is simply added to the carrier and sideband frequency fluctuations, for lasers locked on cavities, adjacent or distant beams. Therefore, the operation is carried out in lock_on_cavity(), lock_on_adjacent(), and lock_on_distant().

Details on the model

Laser actuators work in frequency, and they are used to inject our assistance tone. This tone is generated according to the onboard clock (THE) \hat\tau, such that the tone, expressed in the THE reads A \sin(2 \pi f \hat\tau + \phi_0). Our signals are simulated in the spacecraft proper time (TPS); in this time frame, the assistance tone reads

A \sin(2 \pi f \hat\tau^\tau(\tau) + \phi_0)

where \hat\tau^\tau(\tau) is the THE associated to a given TPS, given by the timer deviations \hat\tau^\tau(\tau) = \tau + \delta \hat\tau(\tau). Therefore, we have

A \sin(2 \pi f [\tau + \delta \hat\tau(\tau)] + \phi_0)

New parameters

• tdir_tone, 3-tuple (amplitude [Hz], frequency [Hz], initial phase [rad]) for TDIR assistance tone, or None for no assistance tone

New data

• tdir_tones for the assistance tones