Transverse image translation using an optical freeform single lens

In this paper, we have proposed an approach that utilizes freeform optical surfaces to realize a novel optical function called transverse image translation, which acts as a basic geometrical transformation for images. Its purpose is to make the image of a given optical system move directionally with the designated distance by means of inserting and arranging some extra optical elements behind the given system. The structure of the given system, as well as its optical specifications, stays unchanged when performing the translation. As the translation is transverse, the image can only move transversely in the plane where the original image lies. A freeform single lens comprising two different freeform surfaces is designed for the given system as the only translation element. The image of the given system is expected to be successfully translated transversely as designed when the freeform lens is properly inserted. The design method and process of the freeform lens is presented briefly. Additionally, a design example is introduced to demonstrate the feasibility of our proposed approach for this new type of transverse image translation.