Problems of using the PMA adaptive mesh method in lens-array design for LED signal lighting

Several investigations have been performed in the field of designing a lens-array for LED signal lighting applications. Solving the parabolic Monge-Ampere (PMA) equation to design the required lens-array leads to problems in matching the boundaries of the lens-lets. Therefore, considerations should be taken into account while generating the mapping adaptive grids. In this paper, we focus on the mathematical investigations of the numerical solution of the PMA equation for the steady state solution, as it is one of the state of the art methods. The first objective is to use the solution of PMA equation for generating the adaptive grid. The second objective is to test the quality of the light-energy mapping by applying the Monte-Carlo simulation to the generated adaptive mesh grid. The last objective is to use the resulting mesh grids in designing a lens-array for signal lighting applications. The paper starts by presenting the difference between signal lighting and optical illumination. Then, an explanation of the advantages of using the beam-let transformation concept in the optical systems designs which is the motivation for us to investigate the solutions of the PMA equation. After that, procedures of generating the adaptive grid are discussed. Also, results of the Monte-Carlo simulation are presented to evaluate the quality of the generated grid. Finally, the problems of using the generated grid for designing a lens-array are discussed, including an approach to control the light-energy mapping to design the boundaries of the optical surfaces as a part of our future investigations.