Fresnel-like prism structure generating algorithm on a curved surface with iterative and noniterative forms

A Fresnel-like structure is required for various kinds of applications, such as contact lenses in the biomedical field, solar concentrators in the energy industry, wave-front correctors for display technology, and beam shaping for illumination systems. In this report, the author provides a simple iterative algorithm that can generate prism structures on arbitrary curved surfaces in an analytical form. Using this algorithm, a spreadsheet program can easily generate the profile of prism structures for optical software simulation. Moreover, a noniterative formulation is derived in order to reduce the design procedures. Comparisons between iterative and noniterative formulations prove the feasibility and robustness of the present approach.