Holographic displays are widely regarded as the "ultimate" display technology, promising immersive 3D visuals with natural depth cues, continuous parallax, and perceptual realism. Realizing this potential, however, has remained elusive due to persistent image quality limitations -- most notably speckle noise, a byproduct of the random interference inherent to coherent light. This is typically further exacerbated by the hologram's phase randomness required for maintaining uniform energy distribution across the eyebox. While speckle suppression techniques like temporal multiplexing or smooth-phase heuristics exist, they often necessitate high-speed hardware and introduce visual artifacts, hindering their practical adoption. We introduce Ellipsography, a single-shot holography technique that achieves near-limit speckle suppression, reaching the image fidelity equivalent to averaging a million conventional scalar holograms -- in a single frame in simulation. By jointly modulating the phase and polarization of light, we structure optical interference and suppress speckle at its source. We present a full pipeline including a vectorial wave model, an end-to-end hologram synthesis algorithm, and a functional prototype display. Our experiments demonstrate substantial improvements in visual clarity, depth continuity, and focus cues over current state-of-the-art methods, achieving high-quality reconstructions approaching 30dB PSNR on a real holographic display for the first time -- a 10dB improvement over the best existing techniques. By pushing holographic reconstruction closer to the perceptual quality expected of modern displays, Ellipsography sets a new benchmark for practical, high-fidelity, speckle-free holography.

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