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Design of Axisymmetrical Tailored Concentrators for LED Light Source Applications

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Design of Axisymmetrical Tailored Concentrators for LED Light Source Applications Design of axisymmetrical tailored concentrators for LED light source applications Bart Van Giel*, Youri Meuret and Hugo Thienpont Applied physics and photonics department (TONA), Vrije Universiteit Brussel Pleinlaan 2, 1050 Brussel, Belgium ABSTRACT In our contribution we present a solution to an important question in the design of a LED-based illumination engine for projection systems: the collimation of the LED light. We tested the principle in the modification of a common device in non-imaging optics, the compound Parabolic Concentrator. This CPC-like achieves a collection of 72% (ideal reflective coating presumed). This CPC-like was tailored by numerically solving an differential equation. This approach has some serious drawbacks. For a compact collection device with high collimation, an other approach is required. A more elegant design strategy will rely fully on geometrical principles. The result of our work is a compound collection lens that achieves a collection efficiency of 87%, assuming an ideal reflective coating and neglecting Fresnel losses. We study the performance of this device in detail. Further enhancements are suggested. Keywords: light-emitting diode, projection display, edge ray theorem, etendue, collimation, illumination, optimization, optical design, tailored surfaces 1 INTRODUCTION The increase of the emitted light flux of light emitting diodes (LEDs) makes it interesting to use these devices as light sources for projector applications. LEDs are small light sources with a narrow spectral emission band and a low operating voltage, which makes them a ideal light source for compact, very light and inexpensive projector applications. [1] However, LEDs have also an important disadvantage. The optical power per unit of étendue is significantly lower than e.g. an UHP lamp (at least 20 times) [2]. This makes it difficult to achieve a high luminance on the screen. For this reason we need to design optics that collect the light of the LED source both with high optical efficiency and high collimation. The LED we use in our study is a Luxeon V High Power LED from Lumileds. This LED consists of a rectangular 2x2mm² die encapsulated in an epoxy dome. Our problem was to efficiently transfer light from the rectangular die of the Figure 1: Compact illumination engine for a LED-based projector encapsulated LED to a circular target with a certain acceptance angle. This acceptance angle has a square distribution in * [email protected] ; phone +32 26283658 direction cosine space, due to the symmetry of the system and the square form of the die. The etendue of the resulting light beam should be approximately the same as the etendue of the LED and the optical efficiency should be as high as possible. Collimation devices for this type of LEDs were proposed earlier. Munoz and all proposed a high efficiency LED collection lens, tailored with the edge-ray principle of non-imaging optics (RXI) [3]. Shatz and Bortz proposed a lens doublet that was designed by searching an optimal set of parameters (65 parameters) of an axisymmetrical configuration [4]. Kudaev optimized CPC-like and RXI-like devices [5] [6]. In this contribution we propose two solutions to the problem. The first solution is a single surface reflector. It's design is inspired by the compound parabolic concentrator, a classical solution in non-imaging optics. We will call them CPC-like reflectors. The surface of the reflector is tailored using non-imaging techniques. Our second solution is an extension and simplification of these principles. Its a compound collection lens that is compact, efficient and it reaches a high collimation of the light bundle with small angular distribution at the exit of the lens (10 degrees). Our lens will be characterized by a small set of parameters. To achieve this non-imaging techniques are used to tailor surfaces that transform the light distribution of the LED. We provide a simple method to tailor surfaces fully relying on basic principles. The purpose of our collecting device was to use it in a compact LED-based projector system. Directly after the collecting device we place a fly's eye integrator. A relay lens system projects the uniform beam onto the light valve. This results in a compact illumination engine for our projector. [7] (figure 1) In this paper we will use two quantities that describe the performance of collecting devices; collection efficiency and collimation. C = tar 1 LED (1) C = E 2 E,max The collection efficiency is the flux on the target in relation to the total flux of the LED. The collimation is the flux in a certain etendue in relation to the maximal possible flux in that etendue, given by etendue conservation law. The ray-tracing code we use in this contribution is the Advanced Systems Analysis Program (ASAP) from Breault. [8] This is a very flexible and powerful non-sequentially ray-tracing software package. Its script-driven interface and batch mode permits collaboration with other software packages. In this contribution we tailor lens profiles in MATLAB. These profiles can be imported directly into a ASAP script. ASAP returns its results into Matlab using a textfile. Other ASAP features include targets and sources with practically any angular or spatial distribution and free-form surfaces. In section two we will explain the design of the classical CPC and the etendue concept. In section three we will develop our 'CPC-like' and in the fourth section we design a compound collection lens. 2 Etendue and the Compound Parabolic Concentrator 2.1 Etendue The etendue of a light bundle is its integral over angular and positional extent, E=∫ dLdMdxdy (2) , where L and M are the directional cosines with respect to the x- and y-axis [9]. The etendue conservation law states that in an optical system without losses etendue is preserved. In an optical system with maximum collimation, the etendue of the source and the target are the same and all the light of the source is transferred to the target. Figure 2: Calculating etendue with optical Path Length A more elegant geometrical definition of etendue is reported in the literature. We will use it further in this contribution. In two dimensions, the etendue of the light bundle in figure 3 is calculated, e=2∗[ S1T2]−[S1T1] (3) , where the square brackets denote optical path lengths. In three dimension this becomes, 2 E= [S1T2]−[S1T1]2 (4) 4 This equation yields also in more complex situations with refractive index variations or reflections in the optical path. 2.2 The compound parabolic concentrator Figure 3: (a) the Compound Parabolic Concentrator (b) using a differential equation to tailor the CPC (c) using the string method to tailor the CPC The compound parabolic concentrator is a well known device for etendue limited collimation of light. It's design is based on the edge ray theorem. This theorem give a sufficient condition to have etendue limited collimation between a source and a target with the same etendue. The phase space boundaries of the source (spatial and angular) should be displayed on the phase space boundaries of the target . In figure 4, the rays that intersect the entrance of the reflector at the extreme angle of the incoming telecentric bundle are projected on the edge of the target. The entrance diameter a' and the target a are connected through etendue conservation, a a'= (5 sin The CPC and CPC-like devices can be tailored by solving a differential equation, fig 3b, [10] dR ,R− =R⋅tan (6) d 2 , where ,R is a polar coordinate system and ,R is the direction of the ray in the point ,R . is the desired direction of the ray after reflection (with respect tot the vertical direction) For the classical CPC, there is an analytical solution and ,R= (7) It is easy to solve this equation numerically for simple reflectors such as the CPC-like of the next section. However for more complex situations with multiple reflective surfaces or with refractive media variations this becomes too difficult. For our compound collection lens we use an elegant alternative approach, the so-called string method of non-imaging optics, that will overcome the disadvantages of using the differential equation. [11] It is based on Fermat's principle. In general when a wavefront is connected to a point, absorber edge ∫ ndL=constant (8) incomming wavefront where n is the index of refraction of the media where the ray passes and dL is the corresponding path length increment. Figure 3c is an illustration of the string method for the CPC. [12] The points of the CPC reflector are determined by the condition that the optical path length from a plane perpendicular to the incoming extreme angle beam to the edge of the absorber is a constant. This constant can be calculated easily from the geometry of the CPC. The string method can be used in situations with multiple reflection or with refractions and refraction index variation. 3 The CPC-like tailored reflector As we mentioned in our introduction, we want to design a efficient collimator for a LED source that exists essentially of a die and a dome encapsulating it. To get some experience in such systems we designed a CPC-like reflector. In such an illumination system the terms 'target' and the 'source' have to be switched in the previous sections. The classical CPC is not a suitable collimator for this type of device: • The edges of the CPC can not touch the edges of the LED source. This implies that it should be possible to collimate all LED light into a certain angle, but that this device would not be etendue limited. • The edge of the LED is not projected to the desired extreme angle due to refraction at the LED dome In our CPC-like solution, we take the refraction of the edge rays at the dome of the LED into account.
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