We previously showed how the measurements of some eighteen time series ofrelative frequency or phase shifts could be combined (1) to cancel the phasenoise of the lasers, (2) to cancel the Doppler fluctuations due to non-inertialmotions of the six optical benches, and (3) to remove the phase noise of theonboard reference oscillators required to track the photodetector fringes, allthe while preserving signals from passinggravitational waves. Here we analyzethe effect of the additional noise due to the optical modulators used forremoving the phase fluctuations of the onboard reference oscillators. We use arecently measured noise spectrum of an individual modulator to quantify thecontribution of modulator noise to the first and second-generation Time-DelayInterferometric (TDI) combinations as a function of the modulation frequency.We show that modulator noise can be made smaller than the expected proof-massacceleration and optical-path noises if the modulation frequencies are largerthan $\approx 682$ MHz in the case of the unequal-arm Michelson TDI combination$X_1$, $\approx 1.08$ GHz for the Sagnac TDI combination $\alpha_1$, and$\approx 706$ MHz for the symmetrical Sagnac TDI combination $\zeta_1$. Thesemodulation frequencies are substantially smaller than previously estimated andmay lead to less stringent requirements on the LISA's oscillator noisecalibration subsystem.
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