Modulator noise suppression in the LISA time-delay interferometric combinations

Laser Interferometer Space Antenna (LISA) is a mission to detect and study low-frequency cosmic gravitational radiation through its influence on the phases of six modulated laser beams exchanged between three remote spacecraft. We previously showed how the measurements of some 18 time series of relative frequency or phase shifts could be combined (1) to cancel the phase noise of the lasers, (2) to cancel the Doppler fluctuations due to non-inertial motions of the six optical benches and (3) to remove the phase noise of the onboard reference oscillators required to track the photodetector fringes, all the while preserving signals from passing gravitational waves. Here we analyze the effect of the additional noise due to the optical modulators used for removing the phase fluctuations of the onboard reference oscillators. We use the recently measured noise spectrum of an individual modulator (Klipstein et al 2006 Proc. 6th Int. LISA Symp. (Greenbelt, MA) (AIP Conf. Proc. vol 873) ed S M Merkowitz and J C Livas pp 19–23) to quantify the contribution of modulator noise to the first and second-generation time-delay interferometric (TDI) combinations as a function of the modulation frequency. We show that modulator noise can be made smaller than the expected proof-mass acceleration and optical-path noises if the modulation frequencies are larger than ≈682 MHz in the case of the unequal-arm Michelson TDI combination X₁, ≈ 1.08 GHz for the Sagnac TDI combination α₁, and ≈706 MHz for the symmetrical Sagnac TDI combination ζ₁. These modulation frequencies are substantially smaller than previously estimated and may lead to less stringent requirements on the LISA's oscillator noise calibration subsystem. The measurements in Klipstein et al were performed in a laboratory experiment for a range of modulation frequencies, but we emphasize that, for the reference oscillator noise calibration algorithm to work, the modulation frequencies must be equal to the frequencies of the reference oscillators.