  The imaging and spectroscopy of habitable worlds will require large-aperture
space-based telescopes, to increase the collecting area and the angular
resolution. These large telescopes will necessarily use segmented primaries to
fit in a rocket. However, these massively segmented mirrors make high-contrast
performance very difficult to achieve and stabilize, compared to more common
monolithic primaries. Despite space telescopes operating in a friendlier
environment than ground-based telescopes, remaining vibrations and resonant
modes on the segments can still deteriorate the performance. In this context,
we present the Pair-based Analytical model for Segmented Telescopes Imaging
from Space (PASTIS) that enables the establishment of a comprehensive error
budget, both in term of segment alignment and stability. Using this model, one
may evaluate the influence of the segment cophasing and surface quality
evolution on the final images and contrasts, and set up requirements for any
given mission. One can also identify the dominant modes of a given geometry for
a given coronagraphic instrument and design the feedback control systems
accordingly. In this paper, we first develop and validate this analytical model
by comparing its outputs to the images and contrasts predicted by an end-to-end
simulation. We show that the contrasts predicted using PASTIS are accurate
enough compared to the end-to-end propagation results, at the exo-Earth
detection level. Second, we develop a method for a fast and efficient error
budget in term of segment manufacturing and alignment that takes into account
the disparities of the segment effects on the final performance. This technique
is then applied on a specific aperture to provide static and quasi-static
requirements on each segment for local aberrations. Finally we discuss
potential application of this new technique to future missions.
