The flux difference between a terrestrial exoplanet and a much brighter nearby star creates an enormous optical design challenge for space-based imaging systems. Coronagraphs are designed to block the star's flux and obtain a high-dynamic-range image of the exoplanet. The contrast of an optical system is calculated using the point spread function (PSF). Contrast quantifies starlight suppression of an imaging system at a given separation of the two objects. Contrast requirements can be as small as 10~(110) for earth-like planets. This work reports an analysis of the September 2017 Habitable Exoplanet Imaging Mission (HabEx) end-to-end optical system prescription for geometric and polarization aberrations across the 450 to 550 nm channel. The Lyot coronagraph was modeled with a vector vortex charge 6 mask but without adaptive optics (AO) to correct the phase of the Jones pupil. The detector plane irradiance was calculated for three states of the telescope/coronagraph system: (1) free of geometric and polarization aberrations; (2) isotropic mirror coatings throughout the end-to-end system; and (3) isotropic mirrors with form birefringence on the primary mirror. For each of these three states the system response both with and without a coronagraph mask was calculated. Two merit functions were denned to quantify the system's ability to attenuate starlight: (1) normalized polychromatic irradiance (NPI), and (2) starlight suppression factor (SSF). Both of these are dimensionless and their values are functions of position across the focal plane. The NPI is defined as the irradiance point-by-point across the detector plane with a coronagraph mask divided by the value of the on-axis irradiance without a coronagraph mask. The SSF is the irradiance point-by-point across the detector plane with a coronagraph mask divided by the point-by-point value of the irradiance across the detector plane without a coronagraph mask. Both the NPI and the SSF provide insights into coronagraph performance. Deviations from the aberration-free case are calculated and summarized in table 2. The conclusions are: (1) the HabEx optical system is well-balanced for both geometric and polarization aberrations: (2) the spatially dependent polarization reflectivity for the HabEx primary mirror should be specified to ensure the coating is isotropic; (3) AO to correct the two orthogonal polarization-dependent wavefront errors is essential.
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