1 Introduction
Since 1879, Thomas Edison invented the world's first incandescent lamp, and humans have entered another new era of lighting - the era of electrical lighting. Since 1962, light-emitting diode (LED) technology has experienced rapid development for more than 40 years. Semiconductor light sources have been applied to two major bottlenecks in the field of lighting: light efficiency and cost issues have also been rapidly improved. At present, the efficacy of high-power LEDs has exceeded Traditional indoor lighting sources (incandescent lamps, fluorescent lamps), so the lighting field has generally been considered as the fourth generation of new green solid-state cold light sources after the flare, incandescent, fluorescent, and gas lamps, because LEDs are safe and energy-saving. Long life, green, colorful, shock-resistant, miniaturized, fast response, etc., such as the ability to completely replace the traditional light source for illumination, it will become another leap after the incandescent lamp and fluorescent lamp in the history of human lighting. Its economic and social significance is huge. In the earliest lighting design, people generally use the empirical method based on experience, that is, first make an actual model based on experience, and then see if the model meets the design requirements. Although the actual measurement method is more accurate, it is only manufactured in the lighting system. It can only be carried out later. Once it is found that its optical properties cannot meet the requirements, it can only be redesigned and manufactured. This not only increases the consumption of manpower and material resources, but also prolongs the design and manufacturing cycle of the lamps.
With the development of applied optics, people have gradually mastered the design principles of spherical lenses, aspherical lenses, and various basic forms of reflectors, achieving design goals through devices and their combinations. During this period, the design method of imaging optics was mainly used. Designers often regard similar energy harvesting or distribution problems as an imaging optics problem with a large numerical aperture. Optical systems designed by this method usually do not achieve the desired energy harvesting rate. However, the goal of designing such optical collectors is to achieve or approach the maximum limit of theoretical values. So how can you get the ideal device?
In the mid-1960s, a series of new theories were developed on the basis of traditional imaging optical design methods, and were applied to the above methods of energy collection and distribution. This new theory of light collecting devices was named nonimaging concentrators. This newly developed optical system differs from conventional imaging optical systems in that it has the properties of some light pipes or imaging optical systems with large distortions. The design and theoretical research of these non-imaging systems has opened up many new ideas and theories for the development of geometric optics. Since non-imaging collectors focus on the distribution of energy rather than on clear imaging, this device is well suited for use in the field of illumination. In the field of illumination, the light emitted by the light source generally has a wide angle (for example, the light emitted by the LED is a Lambertian distribution, and the light emitted by a light source such as an incandescent lamp is spherically distributed), so that the non-imaging optics can be used for the light. Perform efficient alignment. Therefore, lighting devices that operate on the principle of non-imaging optical design can accomplish the design goals well.
At present, the system of non-imaging optical theory and the secondary optical design technology of LED are relatively loose. The domestic literature on design methods in this aspect lacks systematicness and integrity. The purpose of this paper is to systematically summarize, organize and expound some of the main basic theories of non-imaging optics. On this basis, the design methods of secondary optical light distribution devices for some LED lamps are introduced in a more complete and systematic way.
2 Basic concepts and theories of non-imaging optics
In general, the basic theoretical framework of non-imaging optics can be summarized into two concepts (energy collection rate and optical expansion), three principles (edge ​​ray theory, Fermat principle and Marius-Doberman's law), and geometry. The four basic laws of optics (the law of linear propagation of light, the law of independent propagation of light and the law of refraction of light, the law of reflection), it mainly studies two types of problems, the first type of problem is generally called "beam coupling problem" (bundle-coupling) The key to this problem is how to collect the light onto the target receiver while maximizing the collection rate. The second type of problem in non-imaging optics research is often referred to as the "specified radiance" or "prescribedirradiance" problem, which is mainly used in the field of lighting. In this article, the second type of problem is mainly considered. For example, in the field of automotive lighting or indoor lighting, the commonly used light source is a bulb or LED chip, and the target surface is away from the light source, and the target surface is required to achieve a specified light intensity distribution. In the field of non-lighting, there are some similar applications, such as wide-angle infrared receivers for indoor communication. When the sensitivity of the receiver is specified, the receiver's sensitivity is compensated for the different connection distances of multiple transmitters on the desktop. It is similar to the effect of light intensity distribution in lighting design.
2.1 The concept of energy collection rate (concentrationratio)
Since non-imaging optics focuses on the distribution of energy, when a model of a non-imaging device as shown in (1) is created, it can be seen that it has a plane with an incident aperture area of ​​A and an exit aperture area of ​​A'. The plane. Assuming that its exit aperture area A' allows all of the light to exit through it, the ratio C of the area of ​​the incident beam of the device to the area of ​​the exit beam of the device is typically defined as the energy collection rate.
Figure 1 Concept of energy harvesting rate
The maximum collection rate of this energy for a 2D system is C2D = 1/sin θ, while for a rotationally symmetric 3D system, the maximum energy collection rate is C3D = 1/sin2θ. The current concept of energy harvesting rate is commonly used in the evaluation of non-imaging optical systems.
2.2 The concept of optical expansion (ètendue)
The concept of optical expansion is due to the transmission of light energy in non-imaging optical systems. When light energy has no loss during transmission, the transmission of luminous flux can be expressed as φ = φ '. According to the formula of the light intensity Lθ, the intensity of the Lambert cosine distribution Iθ and the solid angle ω, an LED light source with a light intensity of Lambertian cosine distribution can define its luminous flux φ according to the following formula, and dS is an LED light source in the hypothesis a tiny object surface, the brightness of which is Lθ, so the luminous flux emitted by the tiny object surface is
(1)
By simplification of equation (1) and carrying the lossless luminous flux transfer formula φ=φ', we can obtain equation (2), where U is the aperture angle of the normal and the chief ray.
(2)
Considering the problem of the transmission of light in space, you can simplify (2) and get the formula (3).
(3)
This formula is a mathematical expression of the optical expansion amount, whereby the relationship between the luminous flux φ and the optical expansion amount (ètendue) can be easily obtained.
(4)
Étendue is from French, the original meaning is geomett-ricalextent, there is no unified Chinese translation. Therefore, the author translates the amount of optical expansion according to his meaning. It is an important indicator in optical systems. In non-imaging optics, the larger the value, the more light energy is transmitted. Using the concept of conservation of optical spread, the derivation of the design equation for free-form surface light distribution devices can be performed.