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Optical performance of a versatile illumination system for high divergence LED sources
Optik 125 (2014) 1657–1662
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Optical performance of a versatile illumination system for high divergence LED sources E. Rodríguez-Vidal a,∗ , D. Otaduy a , D. Ortiz b , F. González b , F. Moreno b , J.M. Saiz b a b
IK4-TEKNIKER, Polo Tecnológico de Eibar, Calle I˜ naki Goenaga, 5, 20600 Eibar, Guipuzcoa, Spain Group of Optics, Applied Physics Department, University of Cantabria, Avda. de los Castros, Spain
a r t i c l e
i n f o
Article history: Received 24 April 2013 Accepted 5 September 2013
Keywords: LED source Collimating system Optical design
a b s t r a c t An efficient flat-top illuminating optical system optimized for an extended light source is presented. The source is a high-brightness high divergence light emitting diode (LED), sized 1 mm × 1 mm, producing monochromatic emission (525 ± 5 nm) with viewing angle of 130◦ . The design is based on a rotationally symmetrical catadioptric system, developed on a geometrical optics basis, and modelled with ZEMAX® software. The device consists of two optical systems: (i) a collimating system which, in turn, is formed by an aspheric lenses system (low numerical apertures, NA < 0.26) and two-mirror system (0.26 < NA < 0.86), and (ii) an external mirror (NA > 0.86) designed and optimized for each purpose. By itself, the collimating system works with a residual divergence of C = 1.46◦ . The external mirror can be adequately designed to produce some given conditions. For instance, a flat-top profile is obtained in the selected focusing plane, with a maximum transversal intensity variation of 2.5% over 18 mm. In addition, when the focusing mirror is allowed to move along the optical axis in a ±1 mm range, other interesting profiles can be reached for a given working distance, therefore increasing the versatility of the system. © 2013 Elsevier GmbH. All rights reserved.
1. Introduction The advantages of LEDs as light sources include power consumption, lifetime or colour management and have produced an increase of their use in optical devices and general illumination systems. Nowadays LED technology is extending its domain from applications where high photometric levels are not needed [1] to other more demanding ones, rapidly replacing traditional lighting. In many applications, the light flux must be angular or spatially redistributed in order to meet the illuminating requirements of the case, and therefore a very convenient step in the design of a LED illuminating device is to produce a collimated beam. There are several types of commercial collimator optical systems for LED sources, that can be sorted into two groups: optical systems that are made up by an engineered thermoplastic lens that uses the total internal reflection mechanism to collimate the light [2–6], and collimator devices that are constituted by parabolic reflecting mirrors that would produce optimal collimation for point sources [1,7]. Some interesting examples of these systems are worth citing: Shatz and Bortz proposed a non-imaging TIR doublet-lens illumination system designed using inverse engineering approach [8,9]; Kudaev optimized some Compound Parabolic Concentrators
∗ Corresponding author. E-mail address: [email protected] (E. Rodríguez-Vidal). 0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.09.064
(CPC-like) and other Complex Multi Reflectors (RXI-like) devices [3,9]; Chen and Lin proposed a freeform surface design based on total internal reflection (TIR) [10]; Munoz et al. presented a high efficiency LED collections lens, tailored with the edge-ray principle of non-imaging optics [11]; and Vázquez et al. described a parabolic elliptical-based collimator design by means of an analytical and numerical optimization method [2]. The efficiency of the system, defined as the fraction of the energy emitted by the LED source that is collected at the system output in the desired conditions, is proportional to the aperture of these systems [12]. The analysis of these solutions shows that, attending only to the capacity of collimating extended sources, non-imaging optics outperforms its imaging counterpart. However, in contrast to the well-known approaches of imaging optics, with all its broadly extended designing tools, design algorithms of non-imaging optics do not allow for an easy variation of its parameters when pursuing some specific change in its performance. The purpose of this work is to obtain an optical system able to efficiently transform the light emerging from a specific extended source into a beam with good optical properties, in terms of spatial profile and collimation. The proposed design comprises the followings devices: (i) an extended high-divergence LED source; (ii) a lens system to collimate the rays with low numerical apertures (NA); (iii) a two-mirror collimating system for moderate NA and (iv) an external mirror for achieving a homogenization of the beam profile at a specific working distance (WD) for high NA. As will be shown, the system can either collimate a beam with high efficiency
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Fig. 1. LED mount with its silicone hemispherical protective lens (RS = 2.7 mm). Right: lateral view.
or produce desired profiles at a particular distance as, for instance, a homogeneous flat-top profile. The optimization and performance of the system have been calculated with ZEMAX® , a well-known optical design software. The paper is organized as follows: Section 2 describes the main considerations about the simulation of the LED source. In Section 3 the modelling of the optical system is described, as well as the optimization process used in order to achieve the desired requirements. Section 4 illustrates the results obtained by the proposed system in terms of beam quality and WD. Finally, in Section 5 the main conclusions are drawn. 2. The LED as an extended light source The light source (depicted in Fig. 1) is a high brightness LED [13], that emits at = 525 nm with 15 nm of spectral bandwidth. The source dimensions were measured by an optical microscope and realistically simulated with ZEMAX (Fig. 2). These correspond to the image produced by the LED silicone cover acting as a lens (RS = 2.7 mm in Fig. 1). Although the real size of the source could be easily assessed by means of conventional geometrical optics, the image produced by the silicone cover acts as a real source for the rest of the system. Besides, the LED specifications in terms of intensity are given by the manufacturer taking into account this cover. The only requirement was to place the source in the right place and keep the thickness of the silicone cover as a geometrical condition for the position of any other element that might follow. The directionality of the LED source (luminous flux versus angle of emission) has been modelled according to the emission specifications of the LED source [13] (dotted and solid lines in Fig. 3, respectively). The angle distribution LED is the same in both directions (X–X and Y–Y) and the maximum divergence of the LED emission is approximately 130◦ (viewing angle). 3. Optical system design The system proposed in this work, and depicted in Fig. 4, consists of a collimating system and an external focusing (imaging) system. The light coming from the source will cross one or other depending on the NA of the emitted rays. Rays emerging from the source with NA lower than 0.86 will find one of the following collimating systems: for NA < 0.26, collimation is made by a three lens system; for 0.26 < NA < 0.86, light is collimated through a two-mirror system. These two collimation
Fig. 2. Dimensions of the LED source seen through the silicon lens: (a) real image; (b) modelled by ZEMAX® .
Fig. 3. LED emission profile in Cartesian coordinates, showing its forward directionality. Solid line: from LED data sheet. Dots: realistic directional model of the LED emission.
subsystems, being responsible of driving the light up to NA = 0.86, produce the basic profile of the output beam. Finally, rays with NA > 0.86 are focused by means of an external mirror that modifies the profile given by the collimating system. Depending on the desired profile at some given WD (i.e. distance from the last optical surface of the lens system to the detector plane along the optical axis of the system), the curvature parameters of this external mirror will be optimized. This degree of freedom introduces versatility on the system. The shape of the mirrors is a conic that is optimized for each function. For the collimating system, we obtain a hyperbolic – parabolic pair (interestingly, this combination corresponds to the stigmatic perfect surfaces of real object + virtual image and image sent to infinity, respectively). For the external mirror, an elliptical shape is obtained (again, corresponding to the stigmatic solution of the case real object + real image). 3.1. Optimization technique The optimization process of the various optical systems involved in our design is performed with ZEMAX® by using a nonlinear optimization algorithm (damped least square (DLS)) [14]. In order to define the Merit Function some parameters must be fixed at a desirable value (operands Ti ). These are, for instance, the output angles from the back surface of each lens. Another set of parameters (variables Vi ) will be fitted by the ZEMAX® optimization process for achieving the desired requirements (radius and conic constants of each optical surface, for instance).
Fig. 4. (a) Schematic description of the different systems, each working for a different NA interval. (b) Cross section of the system, as shown in ZEMAX® .
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In ZEMAX® , there are two forms of ray tracing, namely sequential and non-sequential ray tracing. Non-sequential ray tracing implies that there is no predefined sequence of surfaces that the traced rays must hit. In non-sequential ray tracing, rays may reach any part of the system, and may do it repeatedly, or not at all. This can be contrasted with sequential ray tracing, where all of the rays traced must propagate throughout the same set of surfaces in a predefined order. The low-NA lens system has been designed and optimized in the sequential ray-tracing mode, while the moderate to high NA systems, that include backward paths, have been designed in the non-sequential mode. 3.2. System constrains Each individual element of the proposed design has to meet some constrains in order for the overall system to behave consistently. Although these conditions make the subsystems mutually dependent, increasing the designing effort, they produce a feasible and robust design with versatile and efficient performance. The first surface of the lens system (low NA) and the first mirror are actually parts of the same hyperbolic surface (the front side of the first lens is partially metalized). This condition reduces the number of pieces in the instrument and greatly improves the alignment of the low- and moderate-NA systems. The lens system is held inside a thin Polymethylmethacrylate (PMMA) cylinder, that acts as a case that makes the system mechanically feasible. The parabolic mirror (0.26 < NA < 0.86) is located along the optical axis in a position such that the distance between its vertex and the virtual source (virtual image of the source given by the first mirror) is equal to its focal length (natural collimation condition). The inner aperture of the parabolic mirror is sized so as to produce collimated rays travelling just outside the PMMA case. 3.3. Geometrical design The locations (Z), diameters (˚) and main curvature radius (R) of the elements of the system follow an order given by the design conditions and options imposed on the system and depicted in Fig. 5. 3.3.1. Boundaries of the collimating system First lens is located immediately after the source capsule, ZL1 (see Fig. 5 to follow this description). For NA = 0.26 (limit imposed to the collimating lens system), ˚L1 (diameter of the non-mirrored part of the first lens) is determined. Applying condition (1), this is also the internal diameter of M1, ˚iM1 . The design of the collimating lenses, described in Section 3.4, allow us to obtain the overall diameter of the lens system, namely ˚L3 , in reference to the third lens. Conditions (2) and (3) produce an estimate of ˚eM1 and ˚iM2 , the external diameter of M1 and the internal diameter of M2, respectively. 3.3.2. Surfaces curvatures and imaging system Rays reflected on the mirrored part of the first surface (M1) will impact on the second mirror (M2). The reflected ray for NA = 0.26 must reach M2 at approximately ˚iM2 , therefore establishing the curvature of M1 (and L1, for condition (1)). For moderate apertures 0.26 < NA < 0.86, rays reflected on M1 and reaching M2 must meet condition (3). This gives us the location ZM2 (and its curvature). The impact of the limit ray, NA = 0.86, on M2 gives ˚eM2 (and ˚iM3 = ˚eM2 ). Finally, the mean curvature of M3 will be given by the imaging condition imposed on the system (light distribution at some WD)
Fig. 5. Flux diagram of the design process described in Section 3.3: (a) low NA; (b) moderate to high NA. L and M stands for lenses and mirrors respectively. S source; R main curvature radius; Z axial position; diameter; e cylindrical case thickness. Conditions (1)–(3) are described in Section 3.2.
for rays with NA > 0.86, and the external dimension of the system, ˚eM3 is obtained for the ray with NA = 0.86 that does not reach M1. 3.4. System description 3.4.1. Lens system The refractive indexes of the lenses are commercial values from the Schott catalogue (BK7 and SF2). The set is contained in a cylindrical tube, 1 mm thick, which acts as housing for the lenses, which, in turn, must fit inside a joining component to which the LED and mirrors are also fixed. The housing produces a compact system and do not affect the rays emerging from the LED source and travelling through the lens system. The six surfaces of this system (depicted in Fig. 4) are given by [15]:
z=
1+
R · 2 1 − (k + 1)R2 2
+
N
˛i i
(1)
i=1
where R is the curvature radius, k is the conic constant, is the radial coordinate and ˛i terms are the aspheric coefficients. The optimized parameters are listed in Table 1.
Table 1 Design specifications for the low NA system of lenses together with the hyperboloid mirror. Surface
Curvature radius (mm)
Distance to previous surface (mm)
Media
Conic constant
1 2 3 4 5 6
10.00 −2.41 −12.00 −13.90 −35.15 −27.16
2.66 13.00 1.60 10.63 3.80 26.44
Air/BK7 BK7/Air Air/SF2 SF2/Air Air/BK7 BK7/Air
−11.96 −30.00 −16.39 −1.22 −1.57 −0.40
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Table 2 Design specifications for the collimating mirror system. Mirror
Curvature radius (mm)
Conic constant
Minimum radius (mm)/aperture
Maximum radius (mm)/aperture
Hyperbolic (M1) Parabolic (M2)
10.00 28
−11.96 −1.00
0.72/0.26 9/0.26
12/0.86 30/0.86
3.4.2. Collimating mirror system The hyperbolic and parabolic mirrors (M1 and M2 in Fig. 4) combine to produce and efficient collimating pair for 0.26 < NA < 0.86. Their optimized parameters (curvatures and apertures) are in Table 2. For our calculations, both the hyperbolic and the parabolic mirrors will be considered metalized by means of an aluminium coating. 3.4.3. Imaging mirror The external elliptical mirror (M3 in Fig. 4, also aluminium coated) collects some of the most marginal rays emitted by the LED source (NA > 0.86) and sends them to a given plane (WD). For a WD = 125 mm, the light distribution can be optimized in order to produce a homogeneous beam. The curvature and aperture parameters for this particular condition are listed in Table 3, though results for other WD will be shown in the next section. Finally, if this mirror is considered a movable piece, shifts as small as ±1 mm can create new beam profiles for a given WD. This possibility is explored also in Section 4. 4. Results: optical performance The quality of the beam that emerges from the optical system is analyzing by the following three parameters: the collection efficiency (εC ), the uniformity error (U) and, only for the collimating part, the residual divergence ( C ). They have been obtained for certain transversal planes located at the following WDs: 100, 125 and 150 mm after the last surface. These parameters have been also used by other authors to assess the quality of several commercial collimation systems [4–6,8]. The profile of the beam at the observation plane was measured by a virtual detector simulated by ZEMAX® (80 mm × 80 mm, 300 × 300 pixels). 4.1. Collection efficiency (εC ) The incoherent illuminance (E) produced by the optical system on each point of a given surface is proportional to the density of rays that impact the surface at that point. For a fixed size of surface (namely a detector), the total number of rays crossing it is the collected light flux, FC . The collection efficiency (εC ) is defined as the ratio between FC and the flux emitted by the LED, FS (Eq. (2)), and informs about the energy performance of the optical system [16]. εC =
FC FS
smoothly from the centre, for all the sections analyzed. It tends to complement to the second collimating part (parabolic mirror in discontinuous – dashed line), mainly because of the sequential interval of NA used in both systems. However, the intensity distribution produced by the external elliptical mirror changes more abruptly from one section to another, as corresponding to a noncollimating system. This can be used not only to increase the overall efficiency but also to provide a flatter profile for a WD = 125 mm. The non-collimating nature of the external elliptical mirror, together with the high collection efficiency provided by high NA rays, produce a non-homogeneous, though still rotationally symmetric, intensity profile. Such distribution is strongly dependent not only on the WD, but also on the longitudinal position of the imaging element. In other words, small changes in the actual position of the elliptical mirror may produce significant changes in the spatial distribution on a fixed image plane. By controlling this property, a versatile illumination system can be obtained. As an example, consider variations in the longitudinal position of the external mirror as small as = ±0.5 mm and = ±1 mm (with respect to the initial design). In Fig. 7 the curves represent the illuminating profiles obtained for WD = 125 mm and for several values of . A remarkable variety of profiles is observed, from arm-chair to Gaussian-like profiles. Relatively small mirror shifts may produce significant changes in the top-hat profile obtained with the original optimized design. 4.2. Uniformity error (U) A commonly chosen quality used to characterize the flat-top quality is the uniformity error (U) defined as [17,18]: U=
EC max − EC min EC max + EC min
(3)
where ECmax and ECmin are, respectively, the maximum and minimum values of the illuminance along the flat area. Fig. 8 shows, separately, the profiles corresponding to the collimating system and to the whole system over an 18 mm aperture at a WD = 125 mm. The corresponding percent values of U over this aperture are 15.4% and 2.5% for collimation and the whole flat-top system respectively. Thus, the use of the external elliptical mirror highly improves the uniformity of the beam profile over an 18 mm
(2)
For our virtual detector, ZEMAX® obtains a collection efficiency (εC ) of the overall optical system of approximately 85%. The fraction of this flux for each optical system is: (i) lens system: 5.8%; (ii) collimating mirrors: 68.0%; (iii) external elliptical mirror: 26.2%, each of them with individual efficiencies of (i) 98.3%, (ii) 88.4% and (iii) 73.7% respectively. Fig. 6 shows the spatial distribution of the illuminance (EC ) for the flat-top illumination system for three different values of the WD (the flat-top conditions is imposed on the WD = 125 mm plane). The individual contribution of each system is represented by its transversal section. The distribution has some remarkable properties. As expected, the illumination produced by the central collimating part (lens system in short – dashed line) decays
Fig. 6. Spatial distribution and cross section of the incoherent illuminance obtained for the flat-top condition at WD = 125 mm. Profiles for (a) WD = 100 mm; (b) WD = 125 mm; (c) WD = 150 mm.
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Table 3 Design specifications for the imaging mirror. Mirror
Curvature radius (mm)
Conic constant
Minimum radius (mm)/aperture
Maximum radius (mm)/aperture
External elliptical (M3)
21.25
−0.905
30/0.86
40/0.92
Fig. 9. Performance of the collimation part (lens + collimation mirror systems): (a) ray tracing representation and (b) divergence histogram.
Fig. 7. Illuminance profiles corresponding to different longitudinal position of the external elliptical mirror ( shift) at a working distance of WD = 125 mm.
aperture. In addition to this, an increase in the illuminance over this flat-zone is clearly noticed when the imaging mirror is added (about 37% increase). 4.3. Residual divergence ( C ) The histogram of the divergence of the output rays shows, as expected for a collimated beam, a typical symmetric shape with a central maximum. The divergence value for which we have 1/e2 of the maximum is called the residual divergence C . This parameter is evaluated here only for the collimating part of the flat-top illumination system. The angular divergence of the output rays is represented in the histogram of Fig. 9, along with the 3D layout of the collimating part. The residual divergence of the collimating beam is C = 1.46◦ ,
consistent with the LED size and the focal distance of the collimating systems (we can think of our collimating system as an imaging system with O → ∞. Then the finite size of the source – and its viewing angle – limits the collimation capacity of any system proposed for the purpose). Thus, the lens system along with the internal hyperbolic + parabolic mirror system behave as a low-divergence collimating system producing a beam with a 20 mm diameter. Moreover, the actual performance of the system can be improved, in terms of collection efficiency and uniformity, once a WD is assumed and the irradiance coming from the highest-aperture rays is added. 5. Conclusions In this work a flat-top illumination system with high collection efficiency has been developed for a high energy green LED source. The efficiency is about 85% for whole system and close to 65% for the collimating part (96% considering only the NA < 0.86). The illumination system has been optimized for a WD of 125 mm where a flat-top illumination profile is obtained with uniformity error of U = 2.5% over an aperture of 18 mm. This is achieved thanks to the external mirror properly focusing the light at this WD. One of the major advantages of this optical system is its modular design. The two systems that collimate the light are concentric around a cylindrical case producing a robust instrument able to collimate light with a residual divergence is C = 1.46 (therefore producing good quality illumination at different WD). In addition, when the external mirror is allowed to move along the optical axis in a = ±1 mm, a remarkable variety of profiles, from arm-chair to Gaussian-like profiles, can be reached for a given WD, increasing the versatility of the design. Finally, we think that this design, for its simplicity and efficiency, could serve other purposes, like those related to focusing or other applied fields like white-LEDs handling in medical illumination. References
Fig. 8. Flat-top profile over a 18 mm aperture at a WD of 125 mm for the whole system (continuous line) and only for the collimating system (dashed line).
[1] A. García-Botella, D. Vázquez, E. Bernabeu, Geometric and Thermal Design for a New Concentrator Collimator Lighting System Based on LED Technology, Metrología Sevres, Springer-Verlag, Berlin, New York, 2000. [2] D. Vázquez-Moliní, M. González-Montes, A. Álvarez, E. Bernabéu, Highefficiency light-emitting diode collimator, Opt. Eng. 49 (2010) 123001. [3] S. Kudaev, P. Schreiber, Optimization of symmetrical free-shape non-imaging concentrators for LED light source applications, in nonimaging optics and efficient illumination systems II, Proc. SPIE (2005) 5942.
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˜ [4] P. Benitez, J.C. Minano, The futures of illumination design, Opt. Photon. News 18 (2007) 20–25. [5] http://www.carclo-optics.com/ [6] http://www.philipslumileds.com [7] http://www.ledil.fi/ [8] J. Bortz, N. Shatz, Optimal design of a nonimaging tir doublet lens illumination system using a LED source, in nonimaging optics and efficient illumination systems, Proc. SPIE (2004) 5529. [9] N. Shatz, J. Bortz, An inverse engineering perspective on nonimaging optical design, Proc. SPIE 2538 (1995) 136–156. [10] J.-J. Chen, C.-T. Lin, Freeform surface design for a light-emitting diode-based collimating lens, Opt. Eng. 49 (2010) 8, 093001-1. [11] F. Munoz, P. Benitez, O. Dross, J. Minano, B. Parkyn, Simultaneous multiple surface design of compact airgap collimators for light-emitting diodes, Opt. Eng. 43 (2004) 1522–1530.
˜ [12] R. Winston, J.C. Minano, P.G. Benitez, Nonimaging Optics, Academic Press, San Diego, 2004. [13] http://www.dotlight.de (Seoul Z-LED P4-green). [14] ZEMAX®: Software for Optical System Design, ZEMAX Development Corporation, 2013. [15] W.J. Smith’s, Optical Computation, in Modern Optical Engineering, 3rd ed., SPIE Press, New York, McGraw-Hill, 2000. [16] B.V. Giel, Y. Meuret, H. Thienpont, Design of axisymmetrical tailored concentrators for LED light source applications, Proc. SPIE (2006), 619603-1 10. [17] M. Karlsson, F. Nikolajeff, Fabrication and evaluation of a diamond diffractive fan-out element for high power lasers, Opt. Express 11 (2003) 191–198. [18] L. Jinsong, M.J. Thomson, A. Waddie, M.R. Taghizadeh, Design of diffractive optical elements for high-power laser applications, Opt. Eng. 43 (2004) 2541-2548.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Optical performance of a versatile illumination system for high divergence LED sources E. Rodríguez-Vidal a,∗ , D. Otaduy a , D. Ortiz b , F. González b , F. Moreno b , J.M. Saiz b a b
IK4-TEKNIKER, Polo Tecnológico de Eibar, Calle I˜ naki Goenaga, 5, 20600 Eibar, Guipuzcoa, Spain Group of Optics, Applied Physics Department, University of Cantabria, Avda. de los Castros, Spain
a r t i c l e
i n f o
Article history: Received 24 April 2013 Accepted 5 September 2013
Keywords: LED source Collimating system Optical design
a b s t r a c t An efficient flat-top illuminating optical system optimized for an extended light source is presented. The source is a high-brightness high divergence light emitting diode (LED), sized 1 mm × 1 mm, producing monochromatic emission (525 ± 5 nm) with viewing angle of 130◦ . The design is based on a rotationally symmetrical catadioptric system, developed on a geometrical optics basis, and modelled with ZEMAX® software. The device consists of two optical systems: (i) a collimating system which, in turn, is formed by an aspheric lenses system (low numerical apertures, NA < 0.26) and two-mirror system (0.26 < NA < 0.86), and (ii) an external mirror (NA > 0.86) designed and optimized for each purpose. By itself, the collimating system works with a residual divergence of C = 1.46◦ . The external mirror can be adequately designed to produce some given conditions. For instance, a flat-top profile is obtained in the selected focusing plane, with a maximum transversal intensity variation of 2.5% over 18 mm. In addition, when the focusing mirror is allowed to move along the optical axis in a ±1 mm range, other interesting profiles can be reached for a given working distance, therefore increasing the versatility of the system. © 2013 Elsevier GmbH. All rights reserved.
1. Introduction The advantages of LEDs as light sources include power consumption, lifetime or colour management and have produced an increase of their use in optical devices and general illumination systems. Nowadays LED technology is extending its domain from applications where high photometric levels are not needed [1] to other more demanding ones, rapidly replacing traditional lighting. In many applications, the light flux must be angular or spatially redistributed in order to meet the illuminating requirements of the case, and therefore a very convenient step in the design of a LED illuminating device is to produce a collimated beam. There are several types of commercial collimator optical systems for LED sources, that can be sorted into two groups: optical systems that are made up by an engineered thermoplastic lens that uses the total internal reflection mechanism to collimate the light [2–6], and collimator devices that are constituted by parabolic reflecting mirrors that would produce optimal collimation for point sources [1,7]. Some interesting examples of these systems are worth citing: Shatz and Bortz proposed a non-imaging TIR doublet-lens illumination system designed using inverse engineering approach [8,9]; Kudaev optimized some Compound Parabolic Concentrators
∗ Corresponding author. E-mail address: [email protected] (E. Rodríguez-Vidal). 0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.09.064
(CPC-like) and other Complex Multi Reflectors (RXI-like) devices [3,9]; Chen and Lin proposed a freeform surface design based on total internal reflection (TIR) [10]; Munoz et al. presented a high efficiency LED collections lens, tailored with the edge-ray principle of non-imaging optics [11]; and Vázquez et al. described a parabolic elliptical-based collimator design by means of an analytical and numerical optimization method [2]. The efficiency of the system, defined as the fraction of the energy emitted by the LED source that is collected at the system output in the desired conditions, is proportional to the aperture of these systems [12]. The analysis of these solutions shows that, attending only to the capacity of collimating extended sources, non-imaging optics outperforms its imaging counterpart. However, in contrast to the well-known approaches of imaging optics, with all its broadly extended designing tools, design algorithms of non-imaging optics do not allow for an easy variation of its parameters when pursuing some specific change in its performance. The purpose of this work is to obtain an optical system able to efficiently transform the light emerging from a specific extended source into a beam with good optical properties, in terms of spatial profile and collimation. The proposed design comprises the followings devices: (i) an extended high-divergence LED source; (ii) a lens system to collimate the rays with low numerical apertures (NA); (iii) a two-mirror collimating system for moderate NA and (iv) an external mirror for achieving a homogenization of the beam profile at a specific working distance (WD) for high NA. As will be shown, the system can either collimate a beam with high efficiency
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Fig. 1. LED mount with its silicone hemispherical protective lens (RS = 2.7 mm). Right: lateral view.
or produce desired profiles at a particular distance as, for instance, a homogeneous flat-top profile. The optimization and performance of the system have been calculated with ZEMAX® , a well-known optical design software. The paper is organized as follows: Section 2 describes the main considerations about the simulation of the LED source. In Section 3 the modelling of the optical system is described, as well as the optimization process used in order to achieve the desired requirements. Section 4 illustrates the results obtained by the proposed system in terms of beam quality and WD. Finally, in Section 5 the main conclusions are drawn. 2. The LED as an extended light source The light source (depicted in Fig. 1) is a high brightness LED [13], that emits at = 525 nm with 15 nm of spectral bandwidth. The source dimensions were measured by an optical microscope and realistically simulated with ZEMAX (Fig. 2). These correspond to the image produced by the LED silicone cover acting as a lens (RS = 2.7 mm in Fig. 1). Although the real size of the source could be easily assessed by means of conventional geometrical optics, the image produced by the silicone cover acts as a real source for the rest of the system. Besides, the LED specifications in terms of intensity are given by the manufacturer taking into account this cover. The only requirement was to place the source in the right place and keep the thickness of the silicone cover as a geometrical condition for the position of any other element that might follow. The directionality of the LED source (luminous flux versus angle of emission) has been modelled according to the emission specifications of the LED source [13] (dotted and solid lines in Fig. 3, respectively). The angle distribution LED is the same in both directions (X–X and Y–Y) and the maximum divergence of the LED emission is approximately 130◦ (viewing angle). 3. Optical system design The system proposed in this work, and depicted in Fig. 4, consists of a collimating system and an external focusing (imaging) system. The light coming from the source will cross one or other depending on the NA of the emitted rays. Rays emerging from the source with NA lower than 0.86 will find one of the following collimating systems: for NA < 0.26, collimation is made by a three lens system; for 0.26 < NA < 0.86, light is collimated through a two-mirror system. These two collimation
Fig. 2. Dimensions of the LED source seen through the silicon lens: (a) real image; (b) modelled by ZEMAX® .
Fig. 3. LED emission profile in Cartesian coordinates, showing its forward directionality. Solid line: from LED data sheet. Dots: realistic directional model of the LED emission.
subsystems, being responsible of driving the light up to NA = 0.86, produce the basic profile of the output beam. Finally, rays with NA > 0.86 are focused by means of an external mirror that modifies the profile given by the collimating system. Depending on the desired profile at some given WD (i.e. distance from the last optical surface of the lens system to the detector plane along the optical axis of the system), the curvature parameters of this external mirror will be optimized. This degree of freedom introduces versatility on the system. The shape of the mirrors is a conic that is optimized for each function. For the collimating system, we obtain a hyperbolic – parabolic pair (interestingly, this combination corresponds to the stigmatic perfect surfaces of real object + virtual image and image sent to infinity, respectively). For the external mirror, an elliptical shape is obtained (again, corresponding to the stigmatic solution of the case real object + real image). 3.1. Optimization technique The optimization process of the various optical systems involved in our design is performed with ZEMAX® by using a nonlinear optimization algorithm (damped least square (DLS)) [14]. In order to define the Merit Function some parameters must be fixed at a desirable value (operands Ti ). These are, for instance, the output angles from the back surface of each lens. Another set of parameters (variables Vi ) will be fitted by the ZEMAX® optimization process for achieving the desired requirements (radius and conic constants of each optical surface, for instance).
Fig. 4. (a) Schematic description of the different systems, each working for a different NA interval. (b) Cross section of the system, as shown in ZEMAX® .
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In ZEMAX® , there are two forms of ray tracing, namely sequential and non-sequential ray tracing. Non-sequential ray tracing implies that there is no predefined sequence of surfaces that the traced rays must hit. In non-sequential ray tracing, rays may reach any part of the system, and may do it repeatedly, or not at all. This can be contrasted with sequential ray tracing, where all of the rays traced must propagate throughout the same set of surfaces in a predefined order. The low-NA lens system has been designed and optimized in the sequential ray-tracing mode, while the moderate to high NA systems, that include backward paths, have been designed in the non-sequential mode. 3.2. System constrains Each individual element of the proposed design has to meet some constrains in order for the overall system to behave consistently. Although these conditions make the subsystems mutually dependent, increasing the designing effort, they produce a feasible and robust design with versatile and efficient performance. The first surface of the lens system (low NA) and the first mirror are actually parts of the same hyperbolic surface (the front side of the first lens is partially metalized). This condition reduces the number of pieces in the instrument and greatly improves the alignment of the low- and moderate-NA systems. The lens system is held inside a thin Polymethylmethacrylate (PMMA) cylinder, that acts as a case that makes the system mechanically feasible. The parabolic mirror (0.26 < NA < 0.86) is located along the optical axis in a position such that the distance between its vertex and the virtual source (virtual image of the source given by the first mirror) is equal to its focal length (natural collimation condition). The inner aperture of the parabolic mirror is sized so as to produce collimated rays travelling just outside the PMMA case. 3.3. Geometrical design The locations (Z), diameters (˚) and main curvature radius (R) of the elements of the system follow an order given by the design conditions and options imposed on the system and depicted in Fig. 5. 3.3.1. Boundaries of the collimating system First lens is located immediately after the source capsule, ZL1 (see Fig. 5 to follow this description). For NA = 0.26 (limit imposed to the collimating lens system), ˚L1 (diameter of the non-mirrored part of the first lens) is determined. Applying condition (1), this is also the internal diameter of M1, ˚iM1 . The design of the collimating lenses, described in Section 3.4, allow us to obtain the overall diameter of the lens system, namely ˚L3 , in reference to the third lens. Conditions (2) and (3) produce an estimate of ˚eM1 and ˚iM2 , the external diameter of M1 and the internal diameter of M2, respectively. 3.3.2. Surfaces curvatures and imaging system Rays reflected on the mirrored part of the first surface (M1) will impact on the second mirror (M2). The reflected ray for NA = 0.26 must reach M2 at approximately ˚iM2 , therefore establishing the curvature of M1 (and L1, for condition (1)). For moderate apertures 0.26 < NA < 0.86, rays reflected on M1 and reaching M2 must meet condition (3). This gives us the location ZM2 (and its curvature). The impact of the limit ray, NA = 0.86, on M2 gives ˚eM2 (and ˚iM3 = ˚eM2 ). Finally, the mean curvature of M3 will be given by the imaging condition imposed on the system (light distribution at some WD)
Fig. 5. Flux diagram of the design process described in Section 3.3: (a) low NA; (b) moderate to high NA. L and M stands for lenses and mirrors respectively. S source; R main curvature radius; Z axial position; diameter; e cylindrical case thickness. Conditions (1)–(3) are described in Section 3.2.
for rays with NA > 0.86, and the external dimension of the system, ˚eM3 is obtained for the ray with NA = 0.86 that does not reach M1. 3.4. System description 3.4.1. Lens system The refractive indexes of the lenses are commercial values from the Schott catalogue (BK7 and SF2). The set is contained in a cylindrical tube, 1 mm thick, which acts as housing for the lenses, which, in turn, must fit inside a joining component to which the LED and mirrors are also fixed. The housing produces a compact system and do not affect the rays emerging from the LED source and travelling through the lens system. The six surfaces of this system (depicted in Fig. 4) are given by [15]:
z=
1+
R · 2 1 − (k + 1)R2 2
+
N
˛i i
(1)
i=1
where R is the curvature radius, k is the conic constant, is the radial coordinate and ˛i terms are the aspheric coefficients. The optimized parameters are listed in Table 1.
Table 1 Design specifications for the low NA system of lenses together with the hyperboloid mirror. Surface
Curvature radius (mm)
Distance to previous surface (mm)
Media
Conic constant
1 2 3 4 5 6
10.00 −2.41 −12.00 −13.90 −35.15 −27.16
2.66 13.00 1.60 10.63 3.80 26.44
Air/BK7 BK7/Air Air/SF2 SF2/Air Air/BK7 BK7/Air
−11.96 −30.00 −16.39 −1.22 −1.57 −0.40
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Table 2 Design specifications for the collimating mirror system. Mirror
Curvature radius (mm)
Conic constant
Minimum radius (mm)/aperture
Maximum radius (mm)/aperture
Hyperbolic (M1) Parabolic (M2)
10.00 28
−11.96 −1.00
0.72/0.26 9/0.26
12/0.86 30/0.86
3.4.2. Collimating mirror system The hyperbolic and parabolic mirrors (M1 and M2 in Fig. 4) combine to produce and efficient collimating pair for 0.26 < NA < 0.86. Their optimized parameters (curvatures and apertures) are in Table 2. For our calculations, both the hyperbolic and the parabolic mirrors will be considered metalized by means of an aluminium coating. 3.4.3. Imaging mirror The external elliptical mirror (M3 in Fig. 4, also aluminium coated) collects some of the most marginal rays emitted by the LED source (NA > 0.86) and sends them to a given plane (WD). For a WD = 125 mm, the light distribution can be optimized in order to produce a homogeneous beam. The curvature and aperture parameters for this particular condition are listed in Table 3, though results for other WD will be shown in the next section. Finally, if this mirror is considered a movable piece, shifts as small as ±1 mm can create new beam profiles for a given WD. This possibility is explored also in Section 4. 4. Results: optical performance The quality of the beam that emerges from the optical system is analyzing by the following three parameters: the collection efficiency (εC ), the uniformity error (U) and, only for the collimating part, the residual divergence ( C ). They have been obtained for certain transversal planes located at the following WDs: 100, 125 and 150 mm after the last surface. These parameters have been also used by other authors to assess the quality of several commercial collimation systems [4–6,8]. The profile of the beam at the observation plane was measured by a virtual detector simulated by ZEMAX® (80 mm × 80 mm, 300 × 300 pixels). 4.1. Collection efficiency (εC ) The incoherent illuminance (E) produced by the optical system on each point of a given surface is proportional to the density of rays that impact the surface at that point. For a fixed size of surface (namely a detector), the total number of rays crossing it is the collected light flux, FC . The collection efficiency (εC ) is defined as the ratio between FC and the flux emitted by the LED, FS (Eq. (2)), and informs about the energy performance of the optical system [16]. εC =
FC FS
smoothly from the centre, for all the sections analyzed. It tends to complement to the second collimating part (parabolic mirror in discontinuous – dashed line), mainly because of the sequential interval of NA used in both systems. However, the intensity distribution produced by the external elliptical mirror changes more abruptly from one section to another, as corresponding to a noncollimating system. This can be used not only to increase the overall efficiency but also to provide a flatter profile for a WD = 125 mm. The non-collimating nature of the external elliptical mirror, together with the high collection efficiency provided by high NA rays, produce a non-homogeneous, though still rotationally symmetric, intensity profile. Such distribution is strongly dependent not only on the WD, but also on the longitudinal position of the imaging element. In other words, small changes in the actual position of the elliptical mirror may produce significant changes in the spatial distribution on a fixed image plane. By controlling this property, a versatile illumination system can be obtained. As an example, consider variations in the longitudinal position of the external mirror as small as = ±0.5 mm and = ±1 mm (with respect to the initial design). In Fig. 7 the curves represent the illuminating profiles obtained for WD = 125 mm and for several values of . A remarkable variety of profiles is observed, from arm-chair to Gaussian-like profiles. Relatively small mirror shifts may produce significant changes in the top-hat profile obtained with the original optimized design. 4.2. Uniformity error (U) A commonly chosen quality used to characterize the flat-top quality is the uniformity error (U) defined as [17,18]: U=
EC max − EC min EC max + EC min
(3)
where ECmax and ECmin are, respectively, the maximum and minimum values of the illuminance along the flat area. Fig. 8 shows, separately, the profiles corresponding to the collimating system and to the whole system over an 18 mm aperture at a WD = 125 mm. The corresponding percent values of U over this aperture are 15.4% and 2.5% for collimation and the whole flat-top system respectively. Thus, the use of the external elliptical mirror highly improves the uniformity of the beam profile over an 18 mm
(2)
For our virtual detector, ZEMAX® obtains a collection efficiency (εC ) of the overall optical system of approximately 85%. The fraction of this flux for each optical system is: (i) lens system: 5.8%; (ii) collimating mirrors: 68.0%; (iii) external elliptical mirror: 26.2%, each of them with individual efficiencies of (i) 98.3%, (ii) 88.4% and (iii) 73.7% respectively. Fig. 6 shows the spatial distribution of the illuminance (EC ) for the flat-top illumination system for three different values of the WD (the flat-top conditions is imposed on the WD = 125 mm plane). The individual contribution of each system is represented by its transversal section. The distribution has some remarkable properties. As expected, the illumination produced by the central collimating part (lens system in short – dashed line) decays
Fig. 6. Spatial distribution and cross section of the incoherent illuminance obtained for the flat-top condition at WD = 125 mm. Profiles for (a) WD = 100 mm; (b) WD = 125 mm; (c) WD = 150 mm.
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Table 3 Design specifications for the imaging mirror. Mirror
Curvature radius (mm)
Conic constant
Minimum radius (mm)/aperture
Maximum radius (mm)/aperture
External elliptical (M3)
21.25
−0.905
30/0.86
40/0.92
Fig. 9. Performance of the collimation part (lens + collimation mirror systems): (a) ray tracing representation and (b) divergence histogram.
Fig. 7. Illuminance profiles corresponding to different longitudinal position of the external elliptical mirror ( shift) at a working distance of WD = 125 mm.
aperture. In addition to this, an increase in the illuminance over this flat-zone is clearly noticed when the imaging mirror is added (about 37% increase). 4.3. Residual divergence ( C ) The histogram of the divergence of the output rays shows, as expected for a collimated beam, a typical symmetric shape with a central maximum. The divergence value for which we have 1/e2 of the maximum is called the residual divergence C . This parameter is evaluated here only for the collimating part of the flat-top illumination system. The angular divergence of the output rays is represented in the histogram of Fig. 9, along with the 3D layout of the collimating part. The residual divergence of the collimating beam is C = 1.46◦ ,
consistent with the LED size and the focal distance of the collimating systems (we can think of our collimating system as an imaging system with O → ∞. Then the finite size of the source – and its viewing angle – limits the collimation capacity of any system proposed for the purpose). Thus, the lens system along with the internal hyperbolic + parabolic mirror system behave as a low-divergence collimating system producing a beam with a 20 mm diameter. Moreover, the actual performance of the system can be improved, in terms of collection efficiency and uniformity, once a WD is assumed and the irradiance coming from the highest-aperture rays is added. 5. Conclusions In this work a flat-top illumination system with high collection efficiency has been developed for a high energy green LED source. The efficiency is about 85% for whole system and close to 65% for the collimating part (96% considering only the NA < 0.86). The illumination system has been optimized for a WD of 125 mm where a flat-top illumination profile is obtained with uniformity error of U = 2.5% over an aperture of 18 mm. This is achieved thanks to the external mirror properly focusing the light at this WD. One of the major advantages of this optical system is its modular design. The two systems that collimate the light are concentric around a cylindrical case producing a robust instrument able to collimate light with a residual divergence is C = 1.46 (therefore producing good quality illumination at different WD). In addition, when the external mirror is allowed to move along the optical axis in a = ±1 mm, a remarkable variety of profiles, from arm-chair to Gaussian-like profiles, can be reached for a given WD, increasing the versatility of the design. Finally, we think that this design, for its simplicity and efficiency, could serve other purposes, like those related to focusing or other applied fields like white-LEDs handling in medical illumination. References
Fig. 8. Flat-top profile over a 18 mm aperture at a WD of 125 mm for the whole system (continuous line) and only for the collimating system (dashed line).
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