TPF-I SWG Report - Exoplanet Exploration Program - NASA

C HAPTER 4
Figure 4-5 shows a simplified version of the TPF-I error budget. The values shown result in an SNR of 10
for an ozone spectral channel spanning 9.5 to 10.0 μm, which currently represents the driving requirement
on the integration time. The Earth-like planet orbits a G2 Sun-like star with an angular separation of 50
mas at 15 pc distance. The ecliptic latitude is 30 degrees (this determines the contribution from local
zodiacal dust). The array has a linear Dual Chopped Bracewell configuration, comprising four 4-m
diameter collectors spaced at 30-m intervals with phases of 0, π, π/2, and 3π/2, for a total array size of
90 m.
The overall SNR is built up from 53 rotations of the array, each with a period of 50,000 s. The total
observing time is 31 days (which does not currently include any overhead for calibration). The SNR for a
single rotation is broken out into the root-mean-square (rms) of the planet signal variations and the
contributions from random and systematic noise. The rms planet signal in this spectral band is less than
0.1 photons/s, corresponding to a fraction 2.3 x 10 -8 of the stellar signal in the same channel. In this
example, the random noise has approximately equal contributions from the stellar size leakage and from
local zodiacal dust. Other contributions (including exozodiacal dust emission, instrument thermal
emission and stray light) have been omitted for clarity. The conversion from leakage photon rate to
leakage photon noise is based on shot noise for a rotation of 50,000 s. The null floor leak term represents
the photon noise arising from mismatches in the instrument beamtrains. The null floor makes a much
lower contribution to the random noise budget than the local zodiacal emission and stellar leakage since it
is driven by need to minimize the systematic error.
The instability noise contribution to the error budget is indicated by the blue boxes, and it is chosen to be
similar in magnitude to the random error. The contribution of 0.051 photon/s corresponds to a null
fluctuation of order 10 -8 at frequencies similar to the planet signal. These null fluctuations result primarily
from nonlinear combinations of amplitude (ΔA) and phase (Δφ) errors of the electric fields from the
collectors. Analysis shows that the electric fields delivered by each collector must be matched in
amplitude to within an rms error of less than 0.13% (equivalent to 0.26% intensity error), and matched in
phase to within 1 milliradian at λ = 10 μm (equivalent to 1.5 nm of path). These conditions must be met
simultaneously for all wavelengths in the science band, for both polarization states, and over all
timescales (including direct current [DC] offsets and vibrations in the kilohertz frequency range). The null
depth resulting from this level of control is 7.5 x 10 -7 . Meeting these amplitude and phase requirements is
the primary technical challenge for the TPF-I system, and these requirements drive almost all aspects of
the instrument design. Instability noise and its mitigation are described in more detail later in this
document.
In Figure 4-5 the amplitude and phase errors have been further categorized into static and dynamic terms.
Static errors arise from mismatches in the coatings, the reflective and transmissive optics, and the static
alignment of the system, including both dispersive and birefringent effects. Introducing an achromatic π
phase shift in the nulling beam combiner has been a focus of research, but matching the transmission of
the different beamtrains – each of which contains on the order of 30 optical elements – across the full
range of wavelengths and polarization is also a formidable challenge. The dynamic terms include all timevariable
effects. The formation-flying system is continually in motion, and a series of control systems
must be used to stabilize the optical path at the 1-nm level and to manage the tilt and shear of the
wavefront that couples into the single-mode spatial filter. It is clearly important to validate the static terms
over an optical bandwidth that is representative of the flight system. Conversely, if the instrument can be
66