Computer-based methods and associated computer systems are disclosed for designing free space reflective optical surfaces (13) for use in head-mounted displays (HMDs). The reflective optical surface (13) produces a virtual image of a display surface (11) for viewing by a user's eye (15). The method includes using one or more computers to: (i) represent the display surface (11) by display objects (25); (ii) represent the free space reflective optical surface (13) by surface elements (23); and (iii) iteratively calculate spatial locations, normals, and radii of curvature for the surface elements (23) which will cause a virtual image of each display object (25) to be displayed to a nominal user's eye (15) in a desired direction of gaze of the eye (15).