Context. Terrestrial-type exoplanets in or near stellar habitable zones appear to be ubiquitous. It is, however, unknown which of these planets have temperate, Earth-like climates or for example, extreme Venus-like climates. Aims. Technical tools to distinguish different kinds of terrestrial-type planets are crucial for determining whether a planet could be habitable or incompatible with life as we know it. We aim to investigate the potential of spectropolarimetry for distinguishing exo-Earths from exo-Venuses. Methods. We present numerically computed fluxes and degrees of linear polarization of starlight that is reflected by exoplanets with atmospheres in evolutionary states ranging from similar to the current Earth to similar to the current Venus, with cloud compositions ranging from pure water to 75% sulfuric acid solution, for wavelengths between 0.3 and 2.5 μm. We also present flux and polarization signals of such planets in stable but spatially unresolved orbits around the star Alpha Centauri A. Results. The degree of polarization of the reflected starlight shows larger variations with the planetary phase angle and wavelength than the total flux. Across the visible, the largest degree of polarization is reached for an Earth-like atmosphere with water clouds due to Rayleigh scattering above the clouds and the rainbow feature at phase angles near 40. At near-infrared wavelengths, the planet with a Venus-like CO2 atmosphere and thin water cloud shows the most prominent polarization features due to Rayleigh-like scattering by the small cloud droplets. A planet in a stable orbit around Alpha Centauri A would leave temporal variations on the order of 10-13 W m s-1 in the total reflected flux and 10-11 in the total degree of polarization as the planet orbits the star and assuming a spatially unresolved star-planet system. Star-planet contrasts are on the order of 10-10 and vary proportionally with planetary flux. Conclusions. Current polarimeters appear to be incapable to distinguish between the possible evolutionary phases of spatially unresolved terrestrial exoplanets, as a sensitivity close to 10-10 would be required to discern the planetary signal given the background of unpolarized starlight. A telescope or instrument capable of achieving planet-star contrasts lower than 10-9 should be able to observe the large variation of the planets resolved degree of polarization as a function of its phase angle and thus be able to discern an exo-Earth from an exo-Venus based on their clouds unique polarization signatures.

One of the most exciting scientific challenges is to detect Earth-like planets in the habitable zones of other stars in the galaxy and search for evidence of life. During the past 20 years the detection of exoplanets, orbiting stars beyond our own, has moved from science fiction to science fact. From the first handful of gas giants, found through radial velocity studies, detection techniques have increased in sensitivity, finding smaller planets and diverse multi-planet systems. Through enhanced ground-based spectroscopic observations, transit detection techniques and the enormous productivity of the Kepler space mission, the number of confirmed planets has increased to more than 2000. Several space missions, including TESS (NASA), now operational, and PLATO (ESA), will extend the parameter space for exoplanet discovery towards the regime of rocky Earth-like planets and take the census of such bodies in the neighbourhood of the Solar System. The ability to observe and characterise dozens of potentially rocky Earth-like planets now lies within the realm of possibility due to rapid advances in key space and imaging technologies and active studies of potential missions have been underway for a number of years. The latest of these is the Large UV Optical IR space telescope (LUVOIR), one of four flagship mission studies commissioned by NASA in support of the 2020 US Decadal Survey. LUVOIR, if selected, will be of interest to a wide scientific community and will be the only telescope capable of searching for and characterizing a sufficient number of exo-Earths to provide a meaningful answer to the question “Are we alone?”. This contribution is a White Paper that has been submitted in response to the ESA Voyage 2050 Call.

The polarization state of starlight reflected by a planetary atmosphere uniquely reveals coverage, particle size, and composition of aerosols as well as changing cloud patterns. It is not possible to obtain a comparable level of detail from flux-only observations. It is therefore a powerful tool to better understand the crucial role played by clouds and aerosols in the chemistry, dynamics, and radiative balance of a planet. Furthermore, polarization observations can probe the atmosphere of planets independently of the orbital geometry (hence it applies to both transiting and non-transiting exoplanets). A high-resolution spectropolarimeter with a broad wavelength coverage, particularly if attached to a large space telescope, would enable simultaneous study of the polarimetric planetary properties of the continuum and to look for and characterize the polarimetric signal due to scattering from single molecules, providing detailed information about the composition and vertical structure of the atmosphere.

Segmentation can degrade a high-quality dose distribution obtained by fluence map optimisation (FMO). A novel algorithm is proposed for generation of MLC segments to deliver an FMO plan with step-and-shoot IMRT while minimising quality loss. All beams are considered simultaneously while generating MLC segments for reproducing the 3D FMO dose distribution. Segment generation is only steered by the 3D FMO dose distribution, i.e. underlying FMO fluence profiles are not considered. The algorithm features prioritised generation of segments, focusing on accurate reproduction of clinical objectives with the highest priorities. The performance of the segmentation algorithm was evaluated for 20 prostate patients, 15 head-and-neck patients, and 12 liver patients. FMO dose distributions were generated by automated multi-criteria treatment planning (Pareto-optimal plans) and subsequently segmented using the proposed method. Various segmentation strategies were investigated regarding prioritisation of objectives and limitation of the number of segments. Segmented plans were dosimetrically similar to FMO plans and for all patients a clinically acceptable segmented plan could be generated. Substantial differences between FMO and segmented fluence profiles were observed. Avoidance of the usual reconstruction of 2D FMO fluence profiles for segment generation, and instead simultaneously generating segments for all beams to directly reproduce the 3D FMO dose distribution is a likely explanation for the obtained results. For the strategies of limiting the number of segments large reductions in number of segments were observed with minimal impact on plan quality.