| The sensitivity of a stellar interferometer at low light levels is limited by the optical detection limits of its fringe tracker. The purpose of this research activity was to determine the optimal sampling parameters of the interferometer and group delay fringe tracker such that the signal-to-noise ratio (SNR) of the feedback, the group delay, is maximized or 90% of the SNR potential is realized. Computer simulations were carried out by modeling a stellar interferometer encountering atmospheric disturbances in low-light scenarios, typically defined where the average number of photons was less than one per sample. The coherent integration time, incoherent integration time, number of spectral channels, sweep resolution, fast Fourier transform (FFT) length and windowing techniques were all tested independently with the signal-to-noise ratio examined. The simulation results infer that the optimal sampling configuration of a stellar interferometer is the following: Coherent integration of 1.6 atmospheric coherence times (t0) was optimal in atmosphere limited scenarios, but longer integration times of at least 10 t0 were favorable in photon noise limited scenarios. Long incoherent integration times were favorable as a low pass filter to the response curve, but its performance was limited by fringe motion on large timescales and is probably best determined experimentally on a per instrument basis. An increased number of spectral channels was favored, more so in light deprived situations given that the FFT length is sufficiently large. Sweep resolution had negative returns to the signal-to-noise ratio when sampled less than 7.5 times the fringe frequency. FFT length caused the group delay algorithm to under perform substantially when its length was less than 2 times the number of spectral channels. Windowing provided a small (less than 5%) improvement to SNR when used during the calculation of the group delay power spectrum when using a Kaiser or Taylor window with a high photon flux. |
