Abstract
For the great variety of light-emitting diodes (LEDs), there exists a wide range of LED radiation patterns. An approach for constructing patterns of higher accuracy is here considered. The latter is required when the design of optoelectronic systems or their optimization is carried out analytically. A weighting function is introduced that allows increasing the gradient of the diagram of different widths. It has been selected through mathematical analysis of the emission diagrams of different LEDs used in optoelectronic systems. Based on the least squares method an algorithm is created, and programs are developed in MATLAB environment to estimate the parameters of the approximation function. Its accuracy is evaluated by comparison with the approximation with Lambert source of order n. The results show higher accuracy of the proposed approximation function compared to those obtained by conventional methods. Recommendations on the application of the proposed approach are given.
Highlights
Nowadays, light-emitting diodes (LEDs) are everywhere, in different forms, and cover a wide range of applications from solid-state lighting to indicator lights
There exists a wide range of LED radiation patterns
The third test aimed at the approximation of real LEDs radiation patterns and comparison of the root mean square error (RMSE) of the approximating Functions (4) and (8)
Summary
Light-emitting diodes (LEDs) are everywhere, in different forms, and cover a wide range of applications from solid-state lighting to indicator lights. The maximum intensity in the diagram is directed along with the optical axis, and the radiation pattern itself is a function only of the angle , i.e., This special case is here considered because it is of great importance for the practice. The radiation pattern is given mostly in tabular or graphic form in catalogs This is related to the where I(φ, θ) denotes the intensity of light emitted in a direction determined by the angles φ and θ By means of optical axis, and the radiation pattern itself is a function only of the angle θ, i.e., mathematical transformations, we obtain: P2( φ, θ ) = P(θ ), This special case is here considered it is of great importance for the practice. If the parameters of the additional optics used are known, the cumulative radiation pattern (diagram) will be more precisely determined, and the photometric calculations will be more accurate as well
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