1. Introduction

As the fourth generation light source,light-emitting diodes (LED) have many advantages over the conventional light sources, such as monochromaticity, energy and space savings, good reliability and long service life [1–3]. At present, due to low flux of one single LED compared with conventional one single light source, we need to integrate more LED chips on a base plate in order to apply in various luminaires [4]. However, it’s a conundrum to control all the light rays emitted from extended source. In recent years, as the development of non imaging optics, some excellent optical design methods based on extended source have been suggested, such as simultaneous-multiple-surface (SMS) [5,6]. Yi Luo and Zexin Feng had even done some excellent work on uniformity luminance of road lighting. In their design, feedback algorithm had been adopted to construct a secondary optical lens based on single chip source [7].

In this research, we introduced a high-efficiency method of design of optical system with symmetrical freeform lens for LED chip array packaging (LCAP) module. This method can get optimized light energy distribution by adjusting mashing parameters based on parameterized mapping relationship between source and target. As an example, modularized LCAP luminaires are designed to illuminate bi-directional three-lane major road. By calculation of luminance equation [8], we can find out values of luminance coefficient on the C2 road surface and then reversely regulate mapping parameters to optimize mesh grids distribution. Using this method, luminaire’s luminance uniformity can be improved and its optical performance can fully comply with the CIE [8]. Due to small volume of the primary lens, it can be integrated with cooling and powering functions easily. Comparing to the discontinuous freeform lenses, smooth freeform surface can reduce the manufacturing defects [9]. Through the numerical simulation, the relative optical efficiency of primary lens is 19.6% higher than that of traditional secondary optical packaging road lamp in theory. Since several advantages of this design, I hope that it could provide a new concept for extended sources and LCAP optical design.

2. Light source modeling

As shown in Fig. 1(a) , 16 blue LED chips form the blue light source and they are covered by yellow phosphor to form the LCAP module. The LED chip array is placed on the bottom of a trapezium groove which is carved on the top surface of metal core printed circuit board (MCPCB). Side length of the trapezium groove is 9mm and parietal slant angle is 45 degrees to horizontal. Sizes of each LED chip are 1 × 1 × 0.1mm. The distance between adjacent edges of two chips is 1mm for the convenience of chip bonding and wire bonding processes. Therefore the size of source of blue light reaches as large as 8 × 8mm.

 

Fig. 1 Schematic diagrams of LED chip array module (a) and flip chip structure (b).

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In order to achieve realistic result, it is essential to build precise optical models. The vertical electrode LED chip is lifted-off from sapphire and bonded on Si. The top surface of Si is coated with Ag to reflect lights. The size of the simulated LED chip is 1 × 1 mm, whose micro-structure and parameters are shown in Fig. 1 (b) and Table 1 [10]. Blue light (465 nm) is isotropically emitted from the top and bottom surfaces of MQW with uniform distribution.

Table 1. Parameters of Each Layer in Simulated LED

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The intermixture of phosphor and silicone form a phosphor layer with side length of 9mm and depth of 0.2mm. When the blue light emitting from LED chip array, the phosphor layer will absorb, scatter and refract the blue light. Absorbed light will be transferred into yellow light and then re-emitted from phosphor layer. In that case, phosphor layer will form a yellow light source which occupies approximately an area of 80mm² on the LED chip array. In this study, we set the simulation phosphor concentration to be 0.45 g/cm³ whose corresponding refraction index is 1.535. Based on Mie scattering model, the scattering and absorption coefficients of phosphor are 6.873 mm⁻¹ and 4.093 mm⁻¹ for blue light and 9.569 mm⁻¹ and 0.065 mm⁻¹ for yellow light respectively [11]. In order to get white light, blue light (465 nm) and yellow light (555 nm) are separately calculated with the Monte Carlo ray tracing method. The phosphor layer absorbs blue light and then re-emits yellow light from top and bottom surfaces. Finally, white light intensity distribution can be obtained by overlaying blue light and yellow light intensity distributions, and this simplification has been verified to be effective for white LEDs analysis [12].

3. Design primary freeform lens of LCAP for road lighting

In this section, the design method of system can be described by a flow diagram as shown in Fig. 2 :

 

Fig. 2 Flow diagram of designing primary optical system of LCAP module for road lighting.

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It has four main parts: Firstly, dividing light energy of source into 300 × 360 equal parts. Secondly, establishing light energy mapping relationship by edge ray principle and Snell’s law [13]. Thirdly, optimizing optical performance by adjusting parameters based on simulation luminance distribution results. Finally, constructing lens by lofting method. For the design and manufacturing convenience, the inner surface of lens is designed as an inner concave spherical surface, which will not change the transmission directions of the incidence lights. Therefore, we will focus on the construction of the outside surface of the freeform lens in the following study.

3.1 Conditions of road lighting

For the sake of the energy conservation and the environmental protection, LED road lamps as substitutions of traditional road lamps have been supported by national and local governments.

In our study, as shown in Fig. 3 , the type of road which will be illuminated is a bi-directional three-lane major road with isolation belt in the middle of road. The widths of each lanes and isolation belt are 3.5m and 1m respectively. Luminaire mounting height and spacing are 10m and 30m respectively. The length of bracket is 1.5m and elevation of lamp is 15 degree (as shown in the top-left of Fig. 2).We adopted bilateral symmetry luminance, so that each LCAP only need to illuminate mapping yellow rectangle area in Fig. 3.

 

Fig. 3 Schematic of the distribution of LED modules’ light pattern on the major road.

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3.2 Dividing light source energy

In section 2, white light LED source module has been built by coating phosphor on chips in the array. In order to get more accurate light performance, we calculated a ten-order polynomial to fit the tested light intensity distribution curve (LIDC) according to the leastsquares curve fitting method [14].

Figure 4 shows the Simulation and fitting LIDCs of source. It seems that the polynominal fits the test LIDC very well and the normalized cross-correlation (NCC) reaches as high as 95.5% [15].

 

Fig. 4 Simulation and fitting LIDCs of LCAP module.

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3.3 Mapping relationship from source to target

The total luminous flux of the source can be expressed as follow:

 

Fig. 5 Schematic of light energy mapping relationship.

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Since light energy distribution of source is rotational symmetry for Y-axis, field angle $d\varphi$ can be easily divided into M equal angles. In this partitioning method, light source distribution can be divided into M × N parts equally and each unit solid angle $\text{d}\Omega$has the same luminous flux.

At 10m distance over the source we build a 40m long and 10m wide rectangular target plane which is also equally divided into M × N grids by M lines and N frames. Since the light source and target plane both are of axial symmetry, we only need to consider one-quarter of them in first quadrant. According to edge ray principle [13], we can ensure that four rays superposing with$\text{d}\Omega$’s boundary can be irradiated at the four corresponding end points of the sub-rectangle dS after being refracted by the lens. When this method has been used all over the grids, the light energy mapping relationship has been established. The larger the M is, the more accurate the mapping relationship will be, but the corresponding computation work will also increase. In this study, we set N and M to be 300 and 360 respectively.

3.4 Light performance optimization

The method mentioned above can achieve an approximate uniform illuminance distribution for the point source, but luminance and extend source effect have been ignored [13]. The standard observer’s position was defined by CIE [8], and the road surface luminance can be obtained as Eq. (3).

The variables of luminance calculation are illustrated in Fig. 3. β is the angle between the light incident plane and the observation plane, and γ is the angle between the light ray and the vertical axis of the luminous. The reduced luminance coefficient $r(\beta ,\gamma )$was provided by CIE in the 1984s. Concrete (C1) and asphaltum (C2) road surfaces as two classes classification system has been introduced by CIE [16]. Due to wide use of asphaltum road in major road and express way, we adopt C2 as the evaluative criterion. $E_k(c,\gamma )$is the illuminance produced by the $(k)-th$luminaire, k = 1,2,3,…K, wherein c is the angle between the light incident plane and the road axis. Since light energy only irradiate under the corresponding lamp, we can mainly consider K = 1 and ignore the effects of any other adjacent lamps.

The Fig. 6(a) and (b) shows the distributions of luminance coefficient $q(\beta ,\gamma )$on the parallel lines 1, 2 and 3(with the distance of 1.75m, 5.25m and 8.75m to the roadside respectively) and on the perpendicular lines 1, 2 and 3(with the distance of −25m, 0m and 25m to the lamp pole respectively) to the road axis. We can easily observe that q increased rapidly in the part near the observer and shows a low value range under the lamp. According to this distribution, illuminance on the area under lamps must higher than that on boundary area of adjacent lamps, so that we need a dense girds in the center of the target plane. Now we use several parameters to re-mesh the target plane non-uniformly. Meanwhile, DIALux software is adopted to calculate adjusting effects. If the light performance can meet all the requirements of regulation, adjusting will be discontinued.

 

Fig. 6 Distributions of luminance coefficient $q(\beta ,\gamma )$in the directions of parallel and perpendicular (Observer position: −60m, 1.75m, 1.5m).

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The method of meshing the target plane is shown in Fig. 7 . The one-quarter of the target plane is divided into four parts in longitude and three parts in latitude. By adjusting area coverage and density of grids of above seven parts, light energy distribution is able to be optimized on the target plane.

 

Fig. 7 Sketch diagrams of meshing the target plane.

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In this figure, La and Lb are the bottom lengths of sub-regions on the different boundaries of target plane. a1 and a2 are the distances of concentric rectangular frames. La is divided into N_la equal parts, and Lb, a1 and a2 are also divided into different parts equally, which is shown in Fig. 7. Therefore the intersection points for unequal subareas on the one-quarter plane can be redetermined by adjusting above parameters. While adjusting the optimazation coefficients on the one quarter of target plane, the coefficients on the other three target planes will be modified in the same scale. Based on illuminance distributions in Fig. 6, when the light intensity was enhanced on the center and was reduced near the boundary of the target, we found that not only the illuminance uniformity was increased and effects of glare were reduced, but the luminance uniformity was decreased as well. By several repeating of adjustment and observation of simulation results, we found a group of appropriate optimization coefficients (L_a1/L_a2 = 2; N_la1/N_la2 = 3; L_b1/L_b2 = 2; N_lb1/N_lb2 = 4; (N_la1 + N_la2)/(N_lb1/N_lb2) = 0.5; a₁:a₂:a₃ = 1:1.2:1.3; N_a1:N_a2:N_a3 = 1:1.2:1) and freeform lens can meet the requirements of CIE very well.

3.5 Construction of Primary Optical System

We will calculate the out surface of freeform lens according to the Snell’s law expressed as Eq. (4):

As shown in Fig. 8 , we fix a point P₀ which is not only as the start point of each construction curves, but also determine the height of primary lens. According to the Snell’s law, the other points on the curves can be determined by the intersection of incident rays and the tangent plane of the previous point. Based on these construction curves, we can construct freeform surface of lens by lofting method [12]. After optimizing meshing parameters, DIALux software simulation and lens’ construction, we can obtain the final design of primary lens for LED chip array source.

 

Fig. 8 Schematic of point generation method of freeform lens.

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As shown in Fig. 9(a) , primary optical system was designed according to precedingly described method. To provide enough space for LED packaging process (e. g. wire bonding), the radius of inner spherical cavity is set as 1.8 mm. As shown in the Fig. 9(b), the cavity is filled with silicone whose refractive index is 1.52. K9 glass which is available in China (refractive index is 1.5163) is adopted as material of freeform lens. Due to the limitation about volume and weight, we set the distance between LED chip array and the central point in the outside surface as 22mm. The largest value of length and width of the China K9 glass freeform lens is 51.4mm and 29.2mm. This kind of optical module could be more easily integrated with electrical power and sidewall heat dissipation structure.

 

Fig. 9 Primary optical system of LED chip array module.

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4. Simulation of Light Performance

4.8 million rays have been traced to simulate the optical performance of the primary optical system. Final LIDC and radiation pattern has been shown in Fig. 10(a) and (b) , radiation pattern was shaped into a sub-rectangular at the distance of 10 m. By adjusting coefficients, more light energy has been focused on central area of target plane.

 

Fig. 10 Simulation lighting performance of LIDC (a) and radiation pattern (b) of LCAP module.

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In order to demonstrate optimizing result, DIALux software is used to calculate lighting performance on the C2 road. As an example, we set a LED lamp consisting of 10 16W ASLP modules to illuminate two-way three-lane major road. According to the lighting category M2 recommended by CIE [16], overall and longitudinal luminance uniformity (U0 and Ul) of road illuminance must ≥0.4 and ≥0.7 respectively and average road surface illuminance (L_av) 1.5~2.0cd/m² and glare limitation threshold increment (TI) ≤10. From comparisons as shown in Table 2 , we can find that the LED road lamp based on the LCAP modules could meet requirements of CIE standards very well. In the practical road lighting projects, the number of LCAP modules can be arbitrarily increased to satisfy the different illuminance requirements.

Table 2. Comparison of Road Lighting Performance of LED Road Lamp in Simulation and National Standards

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Lens optical efficiency is another important issue for our design and traditional secondary optical packaging method (LCAP module and silicon was covered by a hemisphere lens and then secondary optical lens set on hemisphere lens) will be a reference. Relative light extraction efficiency of this primary optical system reaches as high as 96.9% of that of the traditional LED module only with hemisphere lens, whose light extraction efficiency is defined as 100%. However, because of Fresnel reflection loss and material absorption, secondary optical lens and cover lens will waste more light output efficiencies of traditional road lamps.

As shown in Table 3 , considering the light loss of safety cover (~10%) and traditional secondary optics (~10%), the light output efficiency (LOE) of traditional LED road lamp is always at a low level of about 81%. As shown in Fig. 11 , since neither secondary optics nor cover lens is needed to the LED road lamp based on the LCAP modules, the system optical efficiency of the new road lamp is 19.6% higher than that of the traditional LED road lamp. That means primary optical system of LED chip array module is a remarkable luminaire with good lighting performance, high energy-efficient and easy assembling.

Table 3. Comparison of System Optical Efficiencies Between Traditional LED Road Lamp and New LED Road Lamp Based on LCAP Modules

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Fig. 11 Simple LED road lamp consists of 9 LCAP modules.

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5. Conclusion

A practical freeform lens design method of extended sources for road lighting was introduced in detail. There are several meshing parameters to optimize the illuminance distribution on the target plane. By iteratively using this method, high optical efficiency primary optical system for LCAP can be obtained. By resetting adjustable-factors, luminance and illuminance uniformity can satisfy the CIE standards well. Through numerical simulation, enhancement of relative optical efficiency of primary lens is more than 19% in theory. Small volume of LCAP module can be easily integrated with cooling and powering. In future work, we hope to optimize all the parameters by computer automatically to shorten the design time. Micro-structure will be used on the surface of phosphor layer and inner surface of lens to achieve batter light performance. And also attempts on other forms of LED chip array will be made.