1 Introduction
Since the LED light source has the physical characteristics of high efficiency, energy saving, environmental protection, and the advantages of long life and small volume, it is widely used in the field of general illumination. However, the brightness of a single LED is often difficult to meet the requirements of general lighting. To solve this problem, multiple LEDs are usually installed with optics. Therefore, the design of optical devices, that is, secondary optical design has become a hot spot in the research of LED light source applications.
At present, the secondary optical design of the LED light source usually uses a reflector or a lens to control the outgoing light to achieve the desired light distribution [2-10]. In the design process, according to the illuminating characteristics of the LED light source and the illuminance of the illuminated surface, different design principles and methods are used to establish the free-surface model of the reflector or lens, and the numerical method is used to solve the contour curve of the free-form surface, and then The optical simulation software corrects and evaluates the curved surface formed by the contour curve. The principles and methods commonly used in the design process are as follows: (1) based on the conservation of energy, refraction and reflection law to obtain free-form surfaces [2, 4, 5, 6, 10]; 2 based on optical expansion theory [3]; 3 based on multi-surface simultaneous design Method (SMS) [8,9]; 4 Free-form surface busbar solution method based on energy compensation and coordinate iteration [7]. However, the above design method is difficult and the manufacturing cost is high, so it is often used in the illumination of special requirements requiring relatively high illumination.
In general illumination, optical elements often employ a basic parabolic reflector. However, a single LED light source is often difficult to meet the illumination requirements of general lighting applications, so multiple LED stacking methods are often used. In this paper, based on the circular arrangement of multiple LED light sources, the influence of the characteristic parameters of the parabolic reflector on the illuminance of the illuminated surface is discussed. At the same time, the influence of the frosted glass plate at the exit of the reflector on the uniformity of the illumination of the illuminated surface is discussed.
2 Simulation experiment
2.1 Simulation experiment model and parameters
The cross-sectional view of the reflector is shown in Fig. 1. In Fig. 1, f denotes the focal length, d denotes the aperture, and l denotes the length, that is, the distance from the center of the light source (0, 0) to the aperture surface of the reflector. The relationship between the aperture d and the focal length f and the length l can be expressed by the following formula:
The LED light source of the simulation experiment is arranged in a circular arrangement (Fig. 2) with a radius of 2 mm, the area of ​​the light source model is 1 mm × 1 mm, and the center position of the light source is placed at the focus (0, 0) of the reflector (Fig. 1 The remaining outer ring light source is placed on a plane that is perpendicular to the axis of the reflector and overfocal. The radius of the illuminated surface is set to 200 mm and the distance to the center of the light source is 200 mm.
2.2 Reflector model characteristic parameters affect the illumination of the illuminated surface
In the simulation experiment, the characteristic parameters of the reflector, namely the length l of the reflector, the focal length f and the diameter d directly affect the illumination and illumination range of the illuminated surface, and there is a certain correlation between these three parameters. It can be seen from the formula (1) that when the length l is constant, the change in the focal length f causes a change in the diameter d.
Figure 3 is a illuminance distribution diagram of the illuminated surface. The reflector has a focal length of 5 mm and a diameter of 9 mm. It can be seen from Fig. 3 that when 9 LEDs are arranged in a ring, a clear halo appears, dark spots appear in the center area, and the illuminance of other areas is also significantly lower than that of the halo, which indicates the set illumination area. The internal illumination distribution is very uneven. Therefore, it is necessary to discuss the influence of the characteristic parameters of the reflector on the illumination of the illuminated surface.
2.2.1 The length of the reflector l is constant, and the influence of the focal length f on the illumination of the illuminated surface
Fig. 4 is a graph showing the trend of the illuminance of the illuminated surface as a function of the focal length f. It can be seen from Fig. 4(a) that when the focal length f is 3 mm, the illuminance of the illuminated surface in the radius of 40 mm is larger overall, and as the focal length f increases, the illuminance of the illuminated surface gradually decreases, especially The illumination in the central area drops rapidly. When the focal length f is 12 mm, the illumination in the central region drops to 2763.55 lux, and the radius of the recessed region between the two peaks also increases to 20 mm. However, as the focal length f of the reflector increases, the illuminance gradually increases in the region where the radius of the illuminated surface is larger than 40 mm. The decrease of illuminance in the central region tends to be faster and slower as the focal length f increases. That is, the illuminance drops sharply in the process of increasing the focal length f to 5 mm, and when f is greater than 5 mm, the illuminance decreases. Very gentle (Figure 4(b)).
2.2.2 The diameter d of the reflector is constant, and the influence of the focal length f on the illumination of the illuminated surface
When the diameter d of the reflector is constant, it can be known from the formula (1) that the length l will decrease as the focal length f increases, and the illuminance on the illuminated surface will change significantly, as shown in FIG.
As can be seen from Fig. 5, when the focal length f is 3 mm, the illuminance of the illuminated surface in the range of 40 mm is greater than that of the other focal lengths. As the focal length f increases, the illumination of the illuminated surface gradually decreases, especially in the central region. When the focal length f is 12 mm, the illumination in the central region drops to 2763.44 lux, and the radius of the concave region between the two peaks increases to 20.3. Mm. Fig. 5(b) is a graph showing the change trend of the central region illuminance with the focal length f. As can be seen from Fig. 5(b), as the focal length f increases, the illuminance of the central region decreases first and then tends to a certain value. In combination with Figures 4 and 5, the focal length of the reflector directly determines the distribution and uniformity of the illumination of the illuminated surface.
2.2.3 The focal length f of the reflector is constant, and the influence of the aperture d on the illumination of the illuminated surface
Fig. 6 is a graph showing a change in the focal length f of the reflector and the illuminance of the illuminated surface with the aperture d. It can be seen from Fig. 6 that with the increase of the aperture d, the illuminance tends to increase gradually in the illumination range of 40 mm, but the illumination range of the illuminated surface is smaller as the aperture d decreases. Increase.
It can also be seen from Fig. 6 that the change in illuminance in the central region of 20 mm is small except for the aperture of 30 mm. Therefore, when the focal length f of the reflector is constant, the diameter d is larger, and the light energy utilization rate is higher in a region having a radius of 40 mm from the center point. However, it should be pointed out that the larger the aperture, the larger the length of the reflector. In practical applications, the length of the reflector is as small as possible; in order to find the optimum value of the aperture d and the length l, we obtain the relationship between the illumination ratio and the aperture d, as shown in Fig. 6. The illuminance ratio is defined as the ratio of the maximum illuminance of the illuminated surface to the minimum illuminance of the recessed area on the distribution curve. It can be seen from Fig. 6(b) that the change trend is to decrease sharply first, and the change is slow when the diameter is larger than 50 mm. Therefore, 50 mm is the optimum value of the aperture. At this time, the length of the reflector calculated by the equation (1) is the smallest, and the illuminance distribution of the illuminated surface is very different from the illuminance distribution when the aperture is 90 mm in Fig. 6(a). small.
In practical applications, due to the length limitation requirements of the reflector, after selecting the appropriate parabolic equation of the reflector, the analysis method of Fig. 6 is applied, and the proportional relationship between the maximum illuminance of the illuminated surface and the minimum illuminance of the concave region on the distribution curve is obtained by calculation. Accordingly, a suitable caliber can be selected so that the illumination variation of the illuminated surface is less affected and the reflector length limit is met.