Holographic optical elements (HOEs) have been used as important tools for implementing augmented reality (AR) and see-through displays because they are transparent and thin. Moreover, as HOEs usually come in the shape of a thin film, they can be bent, used for coating, or attached to curved surfaces. While they can be used to implement curved AR displays, however, the applications of the curved HOE have not been sufficiently studied. In this paper, an analysis method for curved/bent HOEs using the coupled-wave theory and the numerical ray tracing method is introduced. Using this method, the influence of the surface curvature on the optical characteristics of HOEs, including the aberration and diffraction efficiency, was analyzed. Also presented herein is a method of designing the optimal curvature that can reduce the aberration. Curved HOEs can be applied to see-through displays such as head-mounted displays (HMDs), head-up displays (HUDs), or transparent screens. They can be used to expand the field of view (FOV) and to reduce the form factor. The proposed analysis method provides a useful guideline for designing practical curved see-through displays.
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