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Abstract

Time delay interferometry (TDI) is a post-processing technique used in the
Laser Interferometer Space Antenna (LISA) to reduce laser frequency noise by
building an equal-arm interferometer via combining time-shifted raw phase
measurements. Many so-called 2nd generation TDI variables have been found that
sufficiently suppress laser frequency noise considering realistic LISA orbital
dynamics. In this paper, we want to investigate the relationships between these
different TDI channels to understand the optimal approach for recovering all
information from the raw phase measurements. It is already well known from the
literature that the entire space of TDI solutions can be generated out of the 4
combinations $\alpha$, $\beta$, $\gamma$, and $\zeta$, at least under the
approximation of three different but constant constellation arms (1st
generation TDI). We apply this result to a core subset of the 2nd generation
combinations reported in the literature, for which we compute explicitly how
they can be approximated in terms of these 4 generators and show numerically
that these approximations are accurate enough to model the noises not
suppressed by TDI. Finally, we identify multiple possible 2nd generation
representatives of $\alpha$, $\beta$, $\gamma$, and $\zeta$, and discuss which
might be ideal to use for the LISA data analysis. In addition, we demonstrate
that newly found variants of the variable $\zeta$ significantly out-perform the
ones previously known from the literature.