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This paper reports on electrically controlled holographic optical elements (HOEs) in the form of parabolic mirrors that have the ability to collect light. These mirrors were written in a material known as holographic polymer dispersed liquid crystal, where the liquid crystal embedded within the device allows for electronic control of the optical properties of the mirrors. Essentially, we have replicated the function of a focusing mirror in a lightweight, thin film, electro-optic device. In this work, we have experimentally characterized the optical and electro-optical properties of the HOEs and provided a qualitative explanation of the operation of these structures. This and further investigations of the properties of electro-optic HOEs will open avenues in bulk HOEs and integrated photonic device applications.