Double surface imaging designs with unconstrained object to image mapping under rotational symmetry
In this work, we present a novel imaging design formed by two optical surfaces with rotational symmetry. In these designs, both object and image shapes are given but mapping from object to image is obtained through the design process. In the examples considered, the image from a planar object surface is virtual and located at infinity and is seen from a known pupil, which can emulate a human eye. The differential equation method is used to provide single optical surface imaging designs by considering the local properties of the imaging surface and the wavefronts. In the first introductory part, both the rotational symmetrical and the freeform single surface imaging designs are presented using the differential equation method. In these designs, not only the mapping is obtained in the design process, but also the shape of the object is found. In the second part, the method is extended to two surface designs with rotational symmetry and the astigmatism of the image has been studied. By adding one more optical surface to the system, the shape of the rotational symmetrical object can be designed while controlling the tangential rays and sagittal rays simultaneously. As a result, designs without astigmatism (at the small pupil limit) on a planar object surface have been obtained.