Analysis on energy distribution of infinitesimal mapping method

The infinitesimal mapping method is an emerging design method for LED illumination lens, which is based on energy mapping between the source and the target plane. Occasionally the energy mapping is too complicated to calculate a smooth surface. In this case, as a substitution, tangent-plane iteration is often used to estimate the surface points. However, the process of tangent-plane iteration leads to a variety of errors which will make a strong negative impact on the energy distribution on the target plane. This article analyzes both the problem of energy distribution disproportion caused by vector discontinuity, and the problem of energy loss caused by accumulating iteration errors. Furthermore, this article discusses the functional relation between iteration errors and energy distribution, which is related to the number of iterations, iteration step length and the initial size of lens. This functional relation can be used in compensating the iteration errors when the surface points need to be estimated by tangent-plane iteration, which will greatly improve the accuracy and efficiency of lens design.