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Display power consumption is an emerging concern for untethered devices. This goes double for augmented and virtual extended reality (XR) displays, which target high refresh rates and high resolutions while conforming to an ergonomically light form factor. A number of image mapping techniques have been proposed to extend battery usage. However, there is currently no comprehensive quantitative understanding of how the power savings provided by these methods compare to their impact on visual quality. We set out to answer this question. To this end, we present a perceptual evaluation of algorithms (PEA) for power optimization in XR displays (PODs). Consolidating a portfolio of six power-saving display mapping approaches, we begin by performing a large-scale perceptual study to understand the impact of each method on perceived quality in the wild. This results in a unified quality score for each technique, scaled in just-objectionable-difference (JOD) units. In parallel, each technique is analyzed using hardware-accurate power models. The resulting JOD-to-Milliwatt transfer function provides a first-of-its-kind look into tradeoffs offered by display mapping techniques, and can be directly employed to make architectural decisions for power budgets on XR displays. Finally, we leverage our study data and power models to address important display power applications like the choice of display primary, power implications of eye tracking, and more¹.