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The laser source uses a 450 nm laser diode. The light emitted from the laser diode is concentrated by the first lens, then incidents to the phosphor. The light emits after absorption, scattering and refraction of phosphor. Therefore, the laser lamp consists of two parts: laser-driven white source system and optical system. The phosphor is the bridge between these two parts. For the optical design and simulation, it is necessary to test the characteristics of the light source and build a test platform, which studies the light efficiency of laser source, the distribution of spot energy and so on.
Firstly, the power conversion efficiency of laser-driven white source is tested, and the test platform is shown in Fig.1. Using this detection method, the luminous flux and illumination after passing through the phosphors is measured by different detection probes.
The power conversion efficiency is the ratio of optical power to the electric power. Using optical power probe, the light power is measured with different excitation electric powers, and the power conversion efficiency of the source is 26%, as shown in Fig.2.
Because of the complexity of phosphor luminescence mechanism, it is difficult to accurately establish simulation model in optical simulation software. In this paper, the machine vision method is used to study the change of the shape and size of the light spot before and after the phosphors, which provides a theoretical basis for subsequent optical design. As shown in Fig.3, a CCD is placed behind the phosphor to obtain the laser spot. After testing, it can be found that the shape of the two spots remain unchanged before and after the phosphor, but the size of the spot emitted by the phosphor is slightly larger than that of the incident on the phosphor. Three kinds of spherical lenses are used to converge the laser light, which found that a large F-number, large refractive index lens has a smaller spot size incident on the phosphor and the shape is closer to a square, as shown in Fig.4. Therefore, the first lens is chosen as the converging lens. The edge length of the square spot incident on the phosphor is about 2.30 mm, and the edge length of the square spot emitted from the phosphor is 2.68 mm. After the above analysis, the optical system design can regard the source as Lambertian source with the size of 3 mm × 3 mm.
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Fresnel lenses are commonly used in concentrated photovoltaic (CPV) systems to collect solar light[13]. In this paper, Fresnel lens is used in laser lamp system, which is the reverse of the concentrator design.
The optical structure of the laser lamp is shown in Fig.5. The blue laser emitted by the four-core laser diode converges through the first lens, and is become white light by the phosphor. Then it passes through the second lens and the Fresnel lens successively. Both the lenses are aspherical lenses.
The design requirement is that the diameter of the spot is less than 3 m at a distance of 25 m from the light source, and the irradiance of the receiving is not less than 150 lx.
Two approximations are made to the computational model: the light source is a point source and the exit light is collimated.
The design of Fresnel lens is based on two dimension geometric construction method (2DGCM)[14]. The principle of the design method of Fresnel lens is shown in Fig.6. Cartesian coordinate system is established with point source as coordinate origin and lens optical axis as Z axis. The light from the point source converges through the first lens and then collimates through the Fresnel lens. Because the Fresnel lens is symmetrical about Z axis, it only needs to calculate the surface shape of Fresnel lens in the positive direction of Y axis. The focal length of Fresnel lens is f and the refractive index is n2. The incident plane of Fresnel lens is a plane, which is represented by discrete point Ai,j. The exit surface is an effective working surface, and there are n units in the exit surface. Each unit calculates m sampling points, which is represented by Bi,j. The variable of the prism units is j (1≤j≤n), and the variable of discrete points of each prism unit is i (1≤i≤m). In other words, the point cloud Bi,j on the prism working face is solved on prism unit with edges of Aj and Aj+1.
The whole calculation flow chart is shown in Fig.7. The coordinates of point source O, the maximum angle of light γmax, the refractive index of lens n1 and the focal length f of Fresnel lens are known.
The vector of the incident ray is
$${{r}} = {[\begin{array}{*{20}{c}} {\cos ({\gamma _{i,j}})}&{\sin ({\gamma _{i,j}})} \end{array}]^{\rm{T}}}$$ (1) If the left surface normal vector of the lens is N0, the exit light u can be obtained by Snell’ Law, as shown in Eq. (2).
$${{u}} = {{r}} + \sqrt {{n_1}^2 - 1 + {{({{r}} \cdot {{{N}}_0})}^2}} {{{N}}_0}$$ (2) Similarly, the vector v of the exit ray passing through the lens can be determined as shown in Eq. (3), where N1 is the normal vector of the right surface of the lens.
$${{v}} = {{u}} + \sqrt {1 - {n_1}^2 + {{({{u}} \cdot {{{N}}_1})}^2}} {{{N}}_1}$$ (3) According to the maximum incident angle γmax, the exit light vector v1,1 of the edge light can be obtained, and then according to f, the coordinates of the edge point A1,1 of the Fresnel lens can be obtained.
The calculation flow chart of discrete point Bi,j is shown in Fig.8.
Firstly, the first prism unit of Fresnel lens is calculated, and the edge points of the incident plane is A1,1. The incident ray v is traveling in a direction difined by unit vector v1,1. The ray v1,1 is refracted from the incident plane of the Fresnel lens and becomes ti,j. The exit ray passes through the working surface of Fresnel lens is wi,j.
The edge point of working face is B1,1, B1,1 = A1,1, t1,1 = v1,1, the normal to the surface is given by unit vector N. Accroding to Snell’ Law, the normal to the surface N1,1 on B1,1 is
$${{N}} = \frac{{{{{p}}_{{1}}} - {{{p}}_{{2}}}}}{{\left\| {{{{p}}_{{1}}} - {{{p}}_{{2}}}} \right\|}}$$ (4) Where, p1=n2t and p2=w are the optical momenta of the ray before and after refraction, and
$\left\| {{t}} \right\| = \left\| {{w}} \right\| = 1$ .Then, ray vector ti,j is solved according to Snell's law as shown in Eq. (5), and the second discrete point Bi,j (i=2, j=1) of the first unit is solved according to 2DGCM. The vector of line
$\overline {{B_{i,j}}{B_{i - 1,j}}} $ is perpendicular to the normal vector Ni,j, which satisfies Eq. (6).$${{t}} = {{v}} + \sqrt {{n_2}^2 - 1 + {{({{v}} \cdot {{{N}}_2})}^2}} {{{N}}_2}$$ (5) $$ {{{N}}_{{{i - 1,j}}}} \cdot \overline {{B_{i,j}}{B_{i - 1,j}}} = 0 $$ (6) Where, N2 is the normal vector of incident plane of Fresnel lens, N2=[−1 0]. Bi,j can be obtained by Eq. (6), and the normal vector Ni,j (j=1) at Bi,j can be obtained by Eq. (4).
According to the same calculation process, the discrete points Bi,j and the normal vector Ni,j of all the working face of Fresnel lens can be obtained. After fitting and rotating the points, the model of the Fresnel lens is obtained, as shown in Fig.9.
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The established model is imported into optical software for ray tracing under the point source, as shown in Fig.10. From the trace results, all light is collimated which agrees with the calculation. The point source is replaced by 3 mm × 3 mm surface source, and two receiving surfaces are established at the distance 40 mm (surface ①) and 25 m from the light source (surface ②) respectively. The illumination distribution on the two receiving surfaces is shown in Fig.11. From the simulation results, the size and uniformity of the spot at 25 m meets the design demand.
Design and fabrication of a Fresnel lens for laser lamps
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摘要:
激光车灯对比于LED车灯,具有能耗小、体积小、亮度高等优点,是汽车车灯发展的新方向。提出了一种激光车灯的完整的设计思路。光源采用激光二极管激发荧光片得到白光。通过搭建光学检测平台研究激光驱动白光光源的光学特性,通过机器视觉的方法研究荧光片前后光斑的形状和尺寸的变化,从而精确地建立光源的仿真模型,为后续的光学设计提供理论依据。通过非成像光学设计方法,设计了Fresnel透镜实现了对激光的整形,并利用超精密车削实现透镜的加工。完成了车灯的设计和组装,并通过光学仿真和光学实验验证了设计的正确性。
Abstract:Compared with LED lamp, laser lamp has the advantages of small energy consumption, small volume and high brightness. It will become a new trend of vehicle lamp. A design method of laser lamp is proposed. The light source is laser diode, which is converted into white light by phosphors film. The optical test platform is built to study the optical characteristics of the source, and the machine vision method is used to study the change of the shape and size of the light spot before and after the phosphors, which provides a theoretical basis for subsequent optical design. Fresnel lens is designed by non-imaging optical design method to achieve laser convergence and shaping. The Fresnel lens is machined using ultra-precision turning. The laser lamp prototype is assembled and tested, and the feasibility of the design method is verified by optical simulation and optical experiment.
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