  A mid-infrared nulling-space interferometer is a promising way to
characterize thermal light from habitable planet candidates around Sun-like
stars. However, one of the main challenges for achieving this ambitious goal is
a high-precision stability of the optical path difference (OPD) and amplitude
over a few days for planet detection and up to a few weeks for in-depth
characterization. Here we propose a new method called phase-space synthesis
decomposition (PSSD) to shorten the stability requirement to minutes,
significantly relaxing the technological challenges of the mission. Focusing on
what exactly modulates the planet signal in the presence of the stellar leak
and systematic error, PSSD prioritizes the modulation of the signals along the
wavelength domain rather than baseline rotation. Modulation along the
wavelength domain allows us to extract source positions in parallel to the
baseline vector for each exposure. The sum of the one-dimensional data converts
into two-dimensional information. Based on the reconstructed image, we
construct a continuous equation and extract the spectra through the singular
value decomposition (SVD) while efficiently separating them from a long-term
systematic stellar leak. We performed numerical simulations to investigate the
feasibility of PSSD for the LIFE mission concept. We confirm that multiple
terrestrial planets in the habitable zone around a Sun-like star at 10 pc can
be detected and characterized despite high levels and long durations of
systematic noise. We also find that PSSD is more robust against a sparse
sampling of the array rotation compared to purely rotation-based signal
extraction. Using PSSD as signal extraction method significantly relaxes the
technical requirements on signal stability and further increases the
feasibility of the LIFE mission.
