Single freeform surface imaging design with unconstrained object to image mapping

An imaging design approach which is free of third-order astigmatism for one freeform optical surface and the image is presented in this paper. A set of differential equations is derived from generalized ray tracing. The solution of the above derived equations provides the anastigmatic freeform optical surface, the image surface and the object to image mapping. The obtained design can be used as a good starting point for optimization. As an example, a reflective freeform surface is designed for a single reflective Head Mounted Display (HMD). This example has a 3 mm pupil, 15mm eye clearance, 24-degree diagonal full field of view, and the final design yields an average MTF of 62.6% across 17 field points.