Modelling Optical Invisibility in a Lenticular Microlens array with methods of Geometrical Optics and Weber's Contrast

Abstract

Though many advances have been made in exploring the ‘cloaking’ capabilities of metamaterials and optical systems in a wide range of the light spectrum, e.g. electromagnetic cloaking or paraxial ray optics, the phenomenon of unidirectional cloaking associated with ‘woodpile’ optical structures has not yet been widely discussed in the scope beyond experimental findings or digital integral cloaking; moreover, the relatively low cost of a lenticular array renders the investigation of its concealment properties in the visible regime of great interest for practical purposes. Thus, the following research paper provides an comprehensive theoretical model and analytical criterion for the phenomenon of unidirectional cloaking in the visible regime associated with a lenticular microlens array within the methods of computational ray optics (computing lens’s spherical aberration using governing ray optics equations) and Weber’s contrast (as perceived by the human eye) by considering the concealed object’s virtual image as seen through a lenticular lens. Having shown that the criterion for practical invisibility adheres to our experimental results in determining the boundary case of invisibility, we employed it to explore the effect system parameters have on the array’s cloaking capabilities. We established that the critical parameter for the array’s cloaking capability is the diverging angle of an array’s lenticular lens, the value of which positively correlates with the refraction index and the lens concave segment’s curvature. Therefore, a lenticular array with most prominent cloaking capabilities consists of lenses with the greatest admissible index of refraction and a arc measure for the lens’s concave segment.