Densified pupil spectrograph as high-precision radial velocimetry: From
  direct measurement of the Universe's expansion history to characterization of
  nearby habitable planet candidates
  The direct measurement of the Universe's expansion history and the search for
terrestrial planets in habitable zones around solar-type stars require
extremely high-precision radial velocity measures over a decade. This study
proposes an approach for enabling high-precision radial velocity measurements
from space. The concept presents a combination of a high-dispersion densified
pupil spectrograph and a novel telescope line-of-sight monitor. The precision
of the radial velocity measurements is determined by combining the
spectrophotometric accuracy and the quality of the absorption lines in the
recorded spectrum. Therefore, a highly dispersive densified pupil spectrograph
proposed to perform stable spectroscopy can be utilized for high-precision
radial velocity measures. A concept involving the telescope line-of-sight
monitor is developed to minimize the change of the telescope line-of-sight over
a decade. This monitor allows the precise measurement of a long-term telescope
drift without any significant impact on the Airy disk when the densified pupil
spectra are recorded. We analytically derive the uncertainty of the radial
velocity measurements, which is caused by the residual offset of the
line-of-sights at two epochs. We find that the error could be reduced down to
approximately 1 $cm/s$, and the precision will be limited by another factor
(e.g., wavelength calibration uncertainty). A combination of the high precision
spectrophotometry and the high spectral resolving power could open a new path
toward the characterization of nearby non-transiting habitable planet
candidates orbiting late-type stars. We present two simple and compact
high-dispersed densified pupil spectrograph designs for the cosmology and
exoplanet sciences.
