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We propose a new approach for high-contrast imaging at the diffraction limitusing segmented telescopes in a modest observation bandwidth. This concept,named "spectroscopic fourth-order coronagraphy", is based on a fourth-ordercoronagraph with a focal-plane mask that modulates the complex amplitude of theAiry disk along one direction. While coronagraphs applying the complexamplitude mask can achieve the theoretical limit performance for any arbitrarypupils, the focal plane mask severely limits the bandwidth. Here, focusing onthe fact that the focal-plane mask modulates the complex amplitude along onedirection, we noticed that the mask can be optimized for each spectral elementgenerated by a spectrograph. We combine the fourth-order coronagraph with twospectrographs to produce a stellar spectrum on the focal plane and reconstructa white pupil on the Lyot stop. Based on the wavefront analysis of an opticaldesign applying an Offner-type imaging spectrograph, we found that theachievable contrast of this concept is 10^{-10} at 1.2 - 1.5 times thediffraction limit over the wavelength range of 650 - 750 nm for the entrancepupil of the LUVOIR telescope. Thus, this coronagraph concept could bring newhabitable planet candidates not only around G- and K-type stars beyond 20 - 30pc but also around very nearby M-type stars. This approach potentially promotesthe characterization of the atmospheres of nearby terrestrial planets withfuture on- and off-axis segmented large telescopes.

Spectroscopic fourth-order coronagraph for the characterization of terrestrial planets at small angular separations from host stars