TPF-I SWG Report - Exoplanet Exploration Program - NASA

C HAPTER 4
15
10
Response
5
0
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-5
-10
θ x / μrad
0 ± π/2 ± π ± 3π/2
0.40
1 2 3 4
Beamtrain
optics
Planet photon rate / s -1
0.30
0.20
0.10
0.00
0 1 2 3 4 5 6
-0.10
-0.20
Single-mode
spatial filter
-0.30
-0.40
Array rotation angle / radians
Figure 4-3. Chopped dual Bracewell configuration. Lower left – schematic of interferometer;
upper left – section through response on the sky; upper right – response on sky showing star at
central null and planet offset. The planet follows the red locus as the array is rotated about the
line of sight to the star; the corresponding photon rate vs. rotation angle is shown at lower right.
The lower right panel of Figure 4-3 shows the variation of the chopped planet photon rate with the
rotation angle of the array. This characteristic signature depends on the location of the planet relative to
the star. As we change the ‘azimuthal’ offset of the planet, the signature pattern is shifted left or right with
respect to the array rotation angle. Increasing the radial offset of the planet from the star means that the
circular locus in the upper right panel of Figure 4-3 expands and passes through more peaks and valleys
of the response, resulting in a signature pattern with higher ‘frequency’. In general, the data must be
inverted to obtain the fluxes and locations of any planets that are present.
The approach that has been used most commonly to do this is correlation mapping, first suggested by
Angel and Woolf (1997). The principle is described in Figure 4-4. The process is closely analogous to the
Fourier transform used for standard interferometric image synthesis. The cross-correlation process
generates a “dirty map” (a term borrowed from radio synthesis imaging), which must be deconvolved to
extract the point-like planets. The example in Figure 4-4 shows the noise-free dirty map for a single point
source, and therefore represents the point-spread function (PSF) for the array. Because we are dealing
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