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Holography has demonstrated potential to achieve a wide field of view, focus supporting, optical see-through augmented reality display in an eyeglasses form factor. Although phase modulating spatial light modulators are becoming available, the phase-only hologram generation algorithms are still imprecise resulting in severe artifacts in the reconstructed imagery. Since the holographic phase retrieval problem is non-linear and non-convex and computationally expensive with the solutions being non-unique, the existing methods make several assumptions to make the phase-only hologram computation tractable. In this work, we deviate from any such approximations and solve the holographic phase retrieval problem as a quadratic problem using complex Wirtinger gradients and standard first-order optimization methods. Our approach results in high-quality phase hologram generation with at least an order of magnitude improvement over existing state-of-the-art approaches.