Slava G. Turyshev

We have surveyed all conventional methods proposed or conceivable for obtaining resolved images of an Earth-like exoplanet. Generating a 10x10 pixel map of a 1 R_Earth world at 10 pc demands ~0.85 uas angular resolution and photon collection sufficient for SNR >= 5 per "micro-pixel". We derived diffraction-limit and photon-budget requirements for: (1) large single-aperture space telescopes with internal coronagraphs; (2) external starshades; (3) space-based interferometry (nulling and non-nulling); (4) ground-based extremely large telescopes with extreme adaptive optics; (5) pupil-densified "hypertelescopes"; (6) indirect reconstructions (rotational light-curve inversion, eclipse mapping, intensity interferometry); and (7) diffraction occultation by Solar System bodies. Even though these approaches serve their primary goals - exoplanet discovery and initial coarse characterization - each remains orders of magnitude away from delivering a spatially resolved image. In every case, technology readiness falls short, and fundamental barriers leave them 2-5 orders of magnitude below the astrometric resolution and photon-budget thresholds needed to map an Earth analog even on decadal timescales. Ultimately, an in situ platform delivered to <= 0.1 AU of the target could, in principle, overcome both diffraction and photon-starvation limits - but such a mission far exceeds current propulsion, autonomy, and communications capabilities. By contrast, the Solar Gravitational Lens - providing on-axis gain of ~1e10 and inherent uas-scale focusing once a spacecraft reaches >=550 AU - remains the only near-term, scientifically and technologically viable means to acquire true, resolved surface images and spatially resolved spectroscopy of Earth-like exoplanets in our stellar neighborhood.