TPF-I SWG Report - Exoplanet Exploration Program - NASA

C HAPTER 4
Negative antistar
image
Main peak
Sidelobes
Satellite
peaks
Figure 4-23. Example of the broad-band point-spread function for the X-array 2:1, obtained by coadding
the monochromatic PSFs from five wavelengths spanning 7 to 17 μm.
imaging properties of different array configurations. The following sections describe the distinction
between the nulling and imaging baselines, the angular resolution needed to separate multiple planets, the
properties of the point-spread function, the requirement on array size, and some of the approaches that
have been proposed for image deconvolution.
4.9.1 Separating Multiple Planets
In this section we derive a criterion for the angular resolution that is desirable to resolve multiple planets.
In the absence of measured planet data, we adopt the inner Solar System (Venus–Earth–Mars) as the
benchmark case. Figure 4-22 shows the statistics for the relative angular separation of these three planets
as viewed from a distance of 15 pc, averaged overall viewing angles. Figure 4-22b shows the cumulative
statistics for the separations between the planets themselves. If we also include the negative anti-Sun
image of each planet (a consequence of phase chopping – see next section), the average separations are
reduced, as illustrated in Fig. 4-22c.
With an angular resolution of 20 mas, Fig. 4-22c indicates that an Earth at 15 pc will be confused with
Venus or Mars approximately 25% of the time. We adopt this as the basis for a requirement on angular
resolution. Since the mid-Habitable Zone subtends 67 mas at this distance, we require that the full-widthto-half-maximum
(FWHM) of the PSF is less than or equal to 0.3 times the angle subtended by the mid-
HZ:
θres
≤ 0.3θ
MHZ
(2)
This is the requirement that drives the size of the array needed in most cases (Section 4.9.4).
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