Modified time-delay interferometry with an optical frequency comb

Both the fluctuations of the onboard lasers and clocks in a space-based gravitational wave interferometer can significantly decrease the sensitivity of the detector to an unacceptable performance level. Implementing a self-referenced optical frequency comb (OFC) driven by the onboard laser can establish the relationship between these two phase fluctuations. This makes a modification of the time-delay interferometry (TDI) combinations, which is originally used to reduce the larger laser phase noise, to simultaneously reduce the phase noises of the onboard lasers and clocks. At present, only a few typically modified combinations with an OFC have been constructed. In this work, we develop a general method obtaining all of the modified TDI combinations, the core of which is a skillful substitution of the time-delay operator. More specifically, with a skillful substitution, one can directly derive the modified TDI combination from an arbitrary TDI combination. This method avoids studying how to reconstruct the modified TDI combination with an OFC.