Revisitation of time delay interferometry combinations that suppress laser noise in LISA

Understand

With the purpose of understanding how time delay interferometry (TDI) combinations can best be used for the characterisation of LISA instrumental noise, we revisit their laser frequency noise cancellation properties.

• We have developed an algorithm to search for all possible combinations that suppress noise at the same level as the X, Y and Z classical combination.
• The algorithm calculates delays using symbolic formulas that explicitly include velocities and accelerations of satellites up to the relevant order.
• In addition, once a combination has been identified, delays are verified by solving numerically the relevant equations using Keplerian orbits and Shapiro delay corrections.