  Transit spectroscopy of habitable planets orbiting late-type stars requires
high relative spectro-photometric accuracy between wavelengths during
transit/eclipse observation. The spectro-photometric signal is not affected
only by image movement and deformation due to wavefront error but also by
electrical variation in the detector system. These time-variation components,
coupled to the transit signal, distort the measurements of atmospheric
composition in transit spectroscopy. Here we propose a new concept for
improvement of spectro-photometric accuracy through the calibration of the
time-variation components in the detector system by developing densified pupil
spectroscopy that provides multiple spectra of the star-planet system. Owing to
a group of pixels exposed by the object light (i.e., science pixels),
pixel-to-pixel variations can be smoothed out through an averaging operation,
thus only common time-variation components over the science pixels remain. In
addition, considering that the detector plane is optically conjugated to the
pupil plane, a pupil mask can completely block astronomical light incoming into
residual pixels. The common time-variation components are reconstructed with
the residual pixels and reduced into a random term. Applying the densified
pupil spectrograph with a mid-infrared detector system to a large space
cryogenic telescope such as the Origins Space Telescope, we show that the
system nearly achieves photon-noise-limited performance and detects absorption
features through transmission spectroscopy and secondary eclipse of terrestrial
planets orbiting M-type stars at 10 pc with 60 transit observations. Thus, the
proposed method contributes to the measurement of planetary habitability and
biosignatures of the nearby transiting habitable candidates.
