Free-form lens simulation design for uniform illumination of LED desk lamps

1 Introduction

In recent years, due to excessive eye use and poor writing environment, China has become the second most common incidence of myopia in young people in the world, and the number of young people blinded by high myopia is as high as 300,000 [1]. Vision protection and eye fatigue relief are necessary. The survey pointed out that the use of non-strobe flashing lamps can reduce eye fatigue and other bad eye feelings, such as dry eyes, pain and vertigo, compared to ordinary AC lamps [2].

As a new generation of DC light source with no flash and high luminous efficiency, LED has great potential in writing lighting applications. However, the optical characteristics of the LED's narrow angles are concentrated, resulting in an unevenness in the middle of the spot, which is rapidly attenuated as the radius increases. This extremely uneven illumination will cause frequent pupil focus adjustment, which can easily lead to eye fatigue and discomfort. The use of free-form lens is an important way to effectively improve the light distribution. At present, this method mainly focuses on the research of outdoor lighting such as LED street lamps [3]. The LED is a light source with a certain light-emitting surface size, but the light path of the surface light source is extremely complicated, so it is often simplified to a point source model for lens design. This will inevitably affect the actual light distribution effect. Compared to outdoor lighting, LED table lamps used for indoor lighting require higher uniformity in the illumination area. Therefore, the free-form lens design applied to the LED table lamp light distribution must fully consider the influence of the size of the light-emitting surface and the size of the lens on the light distribution effect.

2 rotationally symmetric freeform lens design

2. 1 Design principle

The illuminated area of ​​the desk lamp is mainly a circular area [4]. Therefore, the free-form lens that achieves uniform illumination of the desk lamp is rotationally symmetrical, and its design can be simplified as follows: The busbar of the free-form surface of the lens on the plane is obtained according to the Snell's law and the light distribution characteristics of the two-dimensional planar space LED. The LED light source is a Lambertian light source with cosine distribution characteristics, that is, I( θ) = I0·cos θ (1) where I0 is the light intensity of the LED on the normal axis, and θ is the angle between the light and the normal axis, such as Figure 1 (a) shows. Using the idea of ​​the meshing method [5], the topological relationship between the light source and the illumination area is established. In order to achieve uniform distribution of illuminance in the illumination area, the spacing of the mapped points of the emitted light with the same micro-angle spacing dθ after the dispersion in the illumination region must satisfy the characteristic of the cosine distribution, ie l( θ) = l0·cos θ ( 2)

Figure 1 shows the topological relationship between the point source and the illumination area. As shown in Figure 1 (b), in the equation, l0 is the distance between the map point of the illumination area and the center point of the illumination area; l ( θ) is the emission The distance between the ray of the angle θ and the angle of the ray of the emission angle (θ - dθ) in the illumination area.

The free-form surface lens has two refractive surfaces on the inner and outer surfaces. Since the transmittance of light increases with the decrease of the incident angle [6], the first refractive surface adopts a hemispherical surface in which the spherical center and the point source are coincident to increase the transmittance of light, and theoretically does not affect the propagation of the light of the point source. As shown in Fig. 2, when dθ takes a small value, the free-form surface bus can be approximated by a series of dθ angular sections.

In Fig. 2, Pn and Qn are a pair of mapping points. The light is refracted through a point Pn on the free-form surface and projected onto the corresponding point Qn of the illumination area. The incident angle i of the ray and the refraction angle γ have the following relationship:

Where α is the angle between the line PnQn and the line OPn. When the positions of the two points Pn and Qn are determined, α is determined; n is the refractive index of the lens material. From the equation (3), the incident angle i and the refraction angle γ can be obtained as shown in the following equation:

Therefore, the normal Nn and the tangent Tn of the Pn point can be obtained from the Snell constant.

Defining the Pn +1 point on the busbar is the intersection of the tangent of the Pn point with the clockwise angle dθ ray, which ensures the continuity of the busbar. According to the starting point P0 and the mapping point sequence (Qn) of the illumination area, the sequence of discrete points (Pn) on the busbar can be iteratively determined to determine the lens busbar.

2. 2 Design cases and simulation results

Writing desk lamps need to ensure uniform illumination of the illumination area with a radius of 500mm perpendicular to the exit surface of 400mm. PMMA with a refractive index of 1.5 is used as the lens material, and the P0 coordinate of the free-surface bus starting point is (-5,0). The busbar of the free-form lens is calculated by MATLAB programming iteratively, as shown in Fig. 3(a).

According to the size of the busbar, the radius of the first refractive sphere is 4mm and is modeled by pro/e, as shown in Fig. 3(b). Use Tracepro to simulate the illumination distribution of a 75lm LED Lambertian source over an illumination area with a vertical distance of 400mm. As shown in Fig. 4, in the case of the second optical design, the illuminance of the geometrical center of the illumination area is the largest, and the uniformity (minimum/maximum) of the illumination area of ​​the radius of 300 mm and 500 mm is about 0.45, 0.15, respectively. The light utilization on the 500mm circular illumination area is approximately 65%.

As shown in Fig. 5, the free-form lens can effectively improve the utilization efficiency of the LED Lambertian source light and the uniformity of the illumination area. The simulation result of the 0. 001mm radius circular field as the LED point source in Tracepro is shown in Figure 5 (a). The uniformity of the illumination area within the radius of 400mm is 95%, and the light utilization rate on the 500mm circular illumination area is about 92%.

However, in reality the LED light source is not a point source. At present, the size of high-power white LED chips on the market is mainly in the range of 40 mil to 60 mil, and a light-emitting surface with a radius of about 1 to 2 mm is formed in the structure. For example, Guoxing Optoelectronics FP-6070XW-AFT-EEM model high-power LED device has a light-emitting surface radius of about 2mm. The simulation results in Tracepro with a radius of 2 mm as the LED source are shown in Figure 5 (b). Obviously, the size of the LED's light-emitting surface will have an effect on the actual light distribution.

3 Light distribution effect analysis and lens optimization

The design of the light distribution using the free-form lens is achieved by changing the direction of light propagation by the principle of refraction. However, there is not only refraction on each of the refractive surfaces. Moreover, the properties of each point on the free-form surface are determined according to the relationship between the center point source and the target illumination area. The deviation between the non-center point emission ray and the center point emission ray causes an error between the actual ray propagation path and the design path.

3. 1 Effect of light reflection on the inner and outer surfaces of the lens

As can be seen from Fig. 2, the lens concentrates the light at the edge toward the center and disperses the light at the center. In particular, the path angle of the edge ray varies very much, so the transmittance of the edge ray through the lens is relatively small [6]. As shown in Fig. 6, the lens designed with a radius of 500mm illumination area shows that the illuminance profile curve of the illumination area is not rectangular but trapezoidal, and there is a dark area at the edge of the illumination area. The actual uniform illumination area radius Rlux is defined to be half of the two peak illumination distances d. Obviously, the uniform illumination area is smaller than the design illumination area.

3. 2 The effect of lens size on light distribution

The actual LED light source is approximately a circular surface light source with a radius r, and the light path is complicated. It is extremely difficult to quantitatively analyze the relationship between the lens size and the size of the light emitting surface by using a mathematical model. According to the theory of relativity, the point source is relative, and the adjustment of the lens size enables the surface light source to have a light distribution effect close to that of the point source.

The light distribution effect of the lens designed according to different lens size parameters on the LED with a radius of 2 mm on the light emitting surface is shown in Fig. 7. It can be seen from Fig. 7(a) that when the free curved surface is constant, increasing the hemispherical radius R has little effect on the uniform illumination region radius Rlux, and the illumination uniformity is significantly improved. It can be seen from Fig. 7(b) that when the radius R of the hemispherical surface is constant, increasing the size of the free-form surface can effectively enlarge the uniform illumination area to approximate the designed illumination area (radius 500 mm), and can improve the illumination uniformity to some extent.

3. 3 lens simulation optimization

The above analysis shows that in order to ensure the uniformity of the illumination area with a radius of 500mm, the design illumination area should be appropriately increased, and the light distribution effect increases with the increase of the free-form surface and the hemispherical size, and finally stabilizes.

The desk lamp is not only a means of home lighting, but also an ornament. Therefore, the size of the lens should be as small as possible to allow for more space for shape design and heat dissipation. According to the above analysis, the theoretical design of the illumination area radius of 600mm, the radius of the illumination surface of 2mm, the lens material refractive index of 1.5 and other preset parameters, optimize the free-form surface bus starting point P0 coordinates (- 8,0), hemispherical radius 7mm free-form lens. The results of the Tracepro simulation are shown in Fig. 8. The light utilization efficiency is 88%, and the illumination area uniformity of the radius of 500mm is 0.96.

4 Conclusion

According to the cosine topology relationship between the LED light source and the illumination target area and the free-form lens designed by the Snell rate, this paper can not only effectively improve the uniformity of the LED table lamp illumination area, but also effectively improve the LED utilization efficiency. The simulation results show that the larger the size of the free-form lens, the smaller the size of the LED light source, and the easier it is to improve the uniformity of the illumination area. Moreover, the optimal lens size of a certain size LED light source significantly improves the performance of the LED light source.

Edit: Nizi