TPF-I SWG Report - Exoplanet Exploration Program - NASA

C HAPTER 4
therefore increasing the dark field of view seen from the combiner spacecraft. Strategies for minimizing
stray light have been detailed by Noecker et al. (2004, 2005).
4.8 Instability Noise and Mitigation
In an ideal nulling interferometer, the electric fields of the light from the collecting telescopes are
combined with a prescribed set of amplitudes and phases that produce a perfect null response at the star
(Figure 4-17a). In this case the integration times needed for planet detection and spectroscopy depend on
the planet signal strength and the level of photon shot noise (from local and exozodiacal emission, stellar
leakage around the null, and instrument thermal emission).
a) Ideal stellar E-fields b) Amplitude and phase errors
c) Dynamic errors
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Figure 4-17. a) Summation of electric fields in the spatial filter for an ideal Dual Chopped
Bracewell nulling configuration. b) Amplitude and phase errors in the contributions from the
different collectors lead to a residual leakage of photons. c) As the amplitude and phase errors vary
with time, the residual photon leakage rate fluctuates and can mimic the presence of a planet.
4.8.1 Origin of Instability Noise
In practice, it will not be possible to maintain the exact set of amplitudes and phases – vibrations and
thermal drifts result in small path-length errors and time-variable aberrations. The null “floor” is
degraded, and there is a time-variable leakage of stellar photons that can mimic a planet signal (Fig. 4-17b
and c). This is known as ‘instability noise’ (previously “systematic error” or “variability noise”), and it
increases the integration time required. The analysis of instability noise is somewhat complex (Lay 2004).
Some components are removed by phase-chopping. Others, such as the “amplitude-phase cross terms”
and the “co-phasing error,” are not removed and result in leakage photon rates proportional to δA i δφ j and
δφ j , respectively, where δA i represents an amplitude error from the i th collector and δφ j is a phase error
from the j th collector. The analysis shows that a null depth of ~10 -5 is generally sufficient to control the
level of photon noise from the stellar leakage, but that a null depth of ~10 -6 is needed to prevent instability
noise from becoming the dominant source of noise. A 10 -6 null requires rms path control to within ~1.5
nm, and rms amplitude control of ~0.1%. It is therefore instability noise, not photon noise that drives the
performance of the instrument.
Table 4-1 lists the mechanisms responsible for amplitude and phase errors, along with their spectral
dependence and temporal nature. For example, vibrations in the optical path difference (OPD) result in a
phase error that scales as the inverse of wavelength and are inherently time varying. Beam shear also
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