Improved approximation of spatial light distribution

Abstract

The rapid worldwide evolution of LEDs as light sources has brought new challenges, which means that new methods are needed and new algorithms have to be developed. Since the majority of LED luminaries are of the multi-source type, established methods for the design of light engines cannot be used in the design of LED light engines. This is because in the latter case what is involved is not just the design of a good reflector or projector lens, but the design of several lenses which have to work together in order to achieve satisfactory results. Since lenses can also be bought off the shelf from several manufacturers, it should be possible to combine together different off the shelf lenses in order to design a good light engine. However, with so many different lenses to choose from, it is almost impossible to find an optimal combination by hand, which means that some optimization algorithms need to be applied. In order for them to work properly, it is first necessary to describe the input data (i.e. spatial light distribution) in a functional form using as few as possible parameters. In this paper the focus is on the approximation of the input data, and the implementation of the well-known mathematical procedure for the separation of linear and nonlinear parameters, which can provide a substantial increase in performance.

Improving approximation by switching between two error functions

“…Later, the results were improved by postprocessing using Newton's method [10]. Based on the remark of the reviewer from a previous report [8], we have considered the problem to be a nonlinear least squares problem in which variables can be separated [11], and have achieved a dramatic improvement in convergence speed that enables consideration of arbitrary distributions which are not necessarily symmetric. Originally, the model was applied to symmetric distributions which is equivalent to an approximation task on a single C-plane (See Fig.…”