S.3. Limitations to Null Depth

Finite star diameter: Null depth is limited by the relative spatial extent of the object. For star diameter = 1 mas and ₀/D = 24 mas, the null depth is = 0.002.

Optical path jitter: Deep nulls require a high degree of pathlength stability between the two arms of the interferometer. The amount of variation is a function of the atmospheric parameters and the bandwidth of the interferometer fringe tracker. For median seeing at Mauna Kea and a 1 kHz closed-loop bandwidth the null depth _O = 1.2 x 10^-5. Note that there will be adequate photon flux from a bright central star for at least a factor of 10 faster fringe tracking than this example, and aggressive tracker algorithms can provide deeper nulls for the same sampling rate.

Wavefront aberration: Corrugations in the stellar wavefront caused by imperfect optics reduce the interferometer fringe visibility and hence the null depth. Relative to the combined intensity of the two beams, the null depth _S = 1 - S, where S is the Strehl ratio of an individual telescope with its AO system. Without further compensation, this limits the null depth _S to 0.016. However, it is possible to do significantly better by using a single-mode spatial filter to remove wavefront aberrations.

Scintillation: Unequal intensities between the two beams of the interferometer produce imperfect fringe visibility. We can approximate the instantaneous scintillation as the instantaneous change in the Strehl ratio. For the example above with S = 0.984, the estimated scintillation standard deviation would be 0.008, which would set the null depth to 1.6 x 10^-5. This yields a total null depth random component of _L ~ 3 x 10^-5 when combined with the path jitter from the 1 kHz fringe tracker described above.

Table S3 repeats the calculation in Table S2 but with the nulling in place. The background is still assumed to be 7 x 10¹⁰ electrons s^-1. We assume systematic leakage = 2 x 10^-3 and a total random leakage _L = 3 x 10^-5. As a result, the components of starlight leakage will be S = 3 x 10^-5 and _LS = 5 x 10³ electrons s^-1, respectively. We now find that the exozodiacal excess is readily detectable compared to the star.

The exozodiacal signal is reduced in Table S3 relative to Table S2 by a factor of 2 to represent some of the near-star dust emission being nulled along with the star. Important problems remaining to be considered (section S.4) include calibrating the background and the amount of random leakage through the null.