Geometric plane shapes for computer-generated holographic engraving codes

We report a new theoretical and experimental study on hologravures, as holographic computer-generated laser-engravings. A geometric theory of images based on the general principles of light ray behaviour is shown. The models used are also applicable for similar engravings obtained by any non-laser method, and the solutions allow for the analysis of particular situations, not only in the case of light reflection mode, but also in transmission mode geometry. This approach is a novel perspective allowing the three-dimensional (3D) design of engraved images for specific ends. We prove theoretically that plane curves of very general geometric shapes can be used to encode image information onto a two-dimensional (2D) engraving, showing notable influence on the behaviour of reconstructed images that appears as an exciting investigation topic, extending its applications. Several cases of code using particular curvilinear shapes are experimentally studied. The computer-generated objects are coded by using the chosen curve type, and engraved by a laser on a plane surface of suitable material. All images are recovered optically by adequate illumination. The pseudoscopic or orthoscopic character of these images is considered, and an appropriate interpretation is presented.