Secondary Lens Optimization for LED Lamps

D Journal of Mechanics Engineering and Automation 4 (2014) 46-51 DAVID PUBLISHING Secondary Lens Optimization for LED Lamps José Luiz Ferraz Barbo...
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Journal of Mechanics Engineering and Automation 4 (2014) 46-51



Secondary Lens Optimization for LED Lamps José Luiz Ferraz Barbosa1, 2, 3, Wesley Pacheco Calixto1, 2, 3, Leonardo da Cunha Brito1, Aylton José Alves2, Enes Gonçalves Marra1, A. Paulo Coimbra4, Elder Geraldo Domingues2, Rafael Silva Ferraz1, 2 and Daywes Pinheiro Neto2, 3 1. Electrical, Mechanical & Computer Engineering School, Federal University of Goias, Goiânia 74605-220, Brazil 2. Nucleus of Experimental and Technological Studies, Federal Institute of Goias, Goiânia 74055-110, Brazil 3. Electrical Engineering Department, University of Brasilia, Brasilia 70910-900, Brazil 4. Institute of Systems and Robotics, University of Coimbra, Coimbra 3004-531, Portugal

Received: September 25, 2013 / Accepted: October 22, 2013 / Published: January 25, 2014. Abstract: The purpose of this paper is to present a methodology for optimizing the geometry of the LED (light emitting diode) secondary lens. The research objective is to uniform the illumination distribution on a target plane for nonimaging application. In order to achieve this, a software that simulates ray tracing is used, in conjunction with a heuristic process for enhancing the optimized parameters that form the geometry of the LED secondary lens. Spherical lenses was opted for optimization due to its lower manufacture complexity. Key words: LED lamps, genetic algorithm, lens, optimization.

1. Introduction Currently, about 20-40% of total electricity consumption is spent on artificial lighting [1, 2]. Lighting is an important and costly liability of heads of cities. An inefficient lighting wastes financial resources and creates unsafe conditions. The technologies used in the pursuit of energy efficiency and design can reduce lighting costs and these energy savings can reduce the need for new power plants and encourage capital to alternative energy solutions for populations in remote areas [3]. A significant improvement in the lighting efficiency can cause significant impacts on global energy consumption. Unfortunately, none of the conventional light sources (incandescent, halogen and fluorescent) had significant improvement in the last 40 years [4]. The relatively recent developments of technologies Corresponding author: José Luiz Ferraz Barbosa, M.Sc., engineer, research fields: optimization, genetic algorithm, intelligent control and process automation. E-mail: [email protected]

based on LED lighting are showing improvements year after year, proving that they may have profound impacts in the area of lighting. It is estimated that by 2020, the simple replacement of LED by traditional light sources will provide a 50% decrease of the total spend on electricity for lighting, and a decrease of 11% of total electricity consumption [4]. LED-based lighting technologies, also known as solid state semiconductor technology, may produce the next generation of white light for illumination [1]. The luminous efficacy of white LED recently surpassed 100 lm/W [5], achieving efficacy of 170 lm/W for a prototype LED lamp of 7.3 W, which emits 1,250 lm and is developed by Cree Incorporation. Due to the growing advances in research, the use of so-called high-power LED solutions, previously occupied by other light sources, is expanding [6]. Several factors contribute to this change, including many advantages of LED light sources as compared to conventional light sources. Among these benefits, it is worth mentioning: long life, brightness, lower energy

Secondary Lens Optimization for LED Lamps

consumption, smaller size, faster response and reliability [1, 5, 7]. When LED is being used for direct lighting, the radiation patterns are of circular symmetry with deformed irradiance intensity distribution, requiring the use auxiliary optical elements in order to redistribute the LED light and generate uniform illumination over the target plane [7, 8]. Most studies focus on the design of integrated LED lenses, i.e., primaries lenses that are usually made of Epoxy and PMMA, implying in chip manufacturing changes [9, 10]. The integrated lenses project, with specifically designed formats (freeform lenses), has been widely used as they have shown the least loss of luminous efficacy [11, 12]. Some efforts have been detached to optimize the LED primary lens. However, there is a need to study the behavior of secondary LEDs lenses. In Ref. [8], the authors propose a new design method for LED lens with spherical inner surface and freeform outer surface for imaging applications.


(5) Development of apparatus to assist in validating the results found. 2.1 Ray Tracing For the simulation of the geometry of the lenses, a numerical technique based on Snell-Descartes Law was used, known as ray tracing method, which calculates individual propagation of light rays. The simulation routine uses the stochastic method to simulate light rays emitted by the LED all the way to the target plane (Fig. 1). From this simulation, the luminous flux distribution is extracted. 2.2 Lens Geometric Parameters Fig. 2 illustrates the modelling of a spherical lens and the confinement. R1 is the radius of the surface S1, and R2 is the radius of the surface S2, with eccentricity y as illustrated in Fig. 2. Z1 is the curvature of S1, and Z2 is the curvature of S2. y is half diameter of the confinement,

The paper is organized as follows: Section 2 presents a methodology for optimizing the LED secondary lens, i.e., the external lens of the LED know as LED secondary optic. The general proposal is to use a heuristic optimization method (genetic algorithm) to generate lens geometries, use a software to simulate the distribution of illuminance on a target plane, and develop an apparatus able to assist in validating the results found; Section 3 presents results and

Fig. 1

Ray tracing application in 2D problem.

discussions; Section 4 gives conclusions.

S1 S2

2. Methodology The methodology developed in this work is based on (1) Using the Snell-Descartes Law, ray tracing method; (2) Definition of lens geometric parameter; (3) Using software for simulation of light emission from LED on the target plane; (4) Using heuristic method to search optimized parameters;

Z2 R2


Z1 Fig. 2

Lens and confinement geometry.

Secondary Lens Optimization for LED Lamps


and L is the distance between the source (LED) and the confinement opening. Also in Fig. 2, t is the lens axial thickness and defined mathematically by the expression

t  Z 2  Z1  te


where, Z1 and Z2 is given by

Z  R  R2  y 2


In Eq. (1), te is the lens edge thickness. Note that the value of t and te grow uniformly if R1 and R2 are fixed and te > 0. 2.3 Simulation Software Many common commercial simulation programs such as CODE V, ZEMAX, LightTools, ASAP or OSLO can simulate LED and run ray tracing with millions of rays. The Zemax was chosen and used to simulate the light rays emitted by LED to reach the target plane. From this simulation, the illuminance is extracted on the illuminated plane. After setting the confinement parameters and the source model via LED manufacturer data sheet, the simulation starts generating randomly rays that represent the light emitted by the source as illustrated in Fig. 3. 2.4 Optimization Method For the optimization process, a heuristic (genetic algorithm) was adopted that aims to optimize the secondary lens geometry in order to generate a uniform

illuminance on the target plane. GA modifies the lens geometry and requests a new simulation from Zemax. Zemax performs the ray tracing and returns to GA a vector containing the illuminance distribution curve on the target plane. GA, via an evaluation function, compares the new results of the simulation [13]. This process occurs to achieve a optimized geometry of the LED lamp lens. A possible solution of the problem, i.e., a GA gene is defined as x = [R1 R2 L GT R1 R2] where, R1 is the internal surface radius, R2 is the external surface radius, L is the distance between the source (LED) and the confinement opening, and GT is the added value to the lens total thickness. For example, when GT = 0, the lens edge thickness is te. When GT > 0, the lens edge thickness takes the value te + GT. R1 and R2 refer to internal and external lens curvature that can be positive or negative, such that R1 = ±1 and R2 = ±1, i.e., if positive is convex curvature or if negative is concave curvature. Fig. 4 illustrates the distribution curve of the desired illuminance Di (red curve) and the distribution curve of the simulated illuminance DS (blue curve), where deviation between two curves is the evaluation function f(x). Thus, a metric can be developed to measure the fitness of each simulated individual (lens) of the GA, given by the expression:

f ( xi ) 

( Di  Ds )   Di  


where,  is a value that prevents the division by zero.

Fig. 3

Model project for simulation.

Fig. 4

Evaluation function.

Secondary Lens Optimization for LED Lamps


2.5 Apparatus Development

3. Results and Discussion For initial studies, it is proposed an equation for measuring the illuminance value of a LED using only data-sheet, considering the confined LED.

E (i ) 

 m  I (i ) A I m

Fig. 5

Proposed apparatus.

Illuminance (lx)

In order to validate the geometry of the lenses found, an apparatus was developed to test the different lenses and collect voltage, current and illuminance values of the LED studied. The apparatus comprises a confinement with radius r = 35 mm attached to a heatsink which is fixed to a cooler as shown in Fig. 5. A digital thermometer is fixed on the top of confinement in direct contact with LED base through a hole. Temperature monitoring is a factor of extreme importance, since high temperatures can damage LED and directly change the illuminance values. During all experiments, the LED temperature remains constant at 28.6 °C.

(4) Voltage (V)

whereby, m is the maximum luminous flux, A is the surface area of the luxmeter semi-sphere to be

Fig. 6 Relationship between the voltage and the experimental and theoretical illuminance.

illuminated, A = 2r2, Im is the LED nominal current, i = 1, 2, ..., n, where, n is the number of points of the curve, r is the radius of the sphere which forms the luxmeter surface to be illuminated. Therefore, with the current values of I(i) and voltage V(i) Eq. (4) in hands it becomes possible to estimate the value of the illuminance E(i) on the surface of the luxmeter semi-sphere. In order to validate Eq. (4), the apparatus was used to collect current, voltage and illuminance values. Fig. 6 shows the relationship between the voltage and the illuminance by using the experimental apparatus and theoretical illuminance using Eq. (4). As for the proposed apparatus, the illuminance using any type of lens can be plotted experimentally. The idea of this study is to validate data obtained by simulation through the stochastic method routine.

Fig. 7 shows a lens fixed at confinement opening and the luxmeter on target plane. Thus, using a lens, data can be collected experimentally and compared with simulated values. Fig. 8 illustrates experimental and simulated illuminance curves for a given lens model. In the acquisition of the experimental curve, a target plane was used at a distance of 820 mm from the source, and a lens geometry with (1) flat inner surface (R1 = ); (2) external radius R2 = 24.17 mm. For the simulation, a 5W LED, YETDA W081F-5W model, Im = 700 mA,

m = 250 lm, Vm = 7 V, with Lambertian radiation pattern, was used. In Fig. 9, the luminous flux distributions related to the studied lens are shown. Illustrations have been obtained by stochastic simulation and through photographs of the target plane.

Secondary Lens Optimization for LED Lamps


Fig. 10

Fig. 7

f(x) for convex S1/concave S2 lens.

Experimental data collection.



Fig. 11 Simulation data with f(x) = 6.38: (a) Optimized lens geometry; (b) Distribution of the luminous flux.

Parameters optimized values found for this other

Fig. 8

Experimental and simulated illuminance curve.

case were: R1 = 35, R2 = 110, L = 20, GT = 6, R1 = -1, R2 = -1 and evaluation function of f(x) = 6.38. The material of the lens is quartz with refractive index of 1.5442.

4. Conclusions

Fig. 9 Experimental (photograph) (stochastic) illuminance curve.



By using a genetic algorithm, it is possible to find a lens geometry capable of improving the distribution of the illuminance on the target plane. Fig. 10 illustrates the result of the optimization process of the illuminance curve of a lens with optimized geometry. Fig. 11a is illustrated optimized lens. Fig. 11b shows the distribution of the luminous flux on the target plane. It is observed that there was an uniformization of the luminous flux on the target plane.

Practical tests using the proposed apparatus showed that a lens fixed at confinement opening can change luminous flux distribution on a target plane and this results was validated by simulation. The developed equation measures the value of illuminance, using only the values found in the data-sheet and the current applied to the LED. Finally, it was shown that the optimization process proposed is feasible for generating new secondary lenses geometries for LED lamps, bringing uniform distribution of the illuminance on the target plane.

References [1]

Y. Uchida, T. Taguchi, Lighting theory and luminous characteristics of white light-emitting diodes, Optical Engineering 44 (12) (2005) 124003.

Secondary Lens Optimization for LED Lamps [2] [3]






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