Adding an extra condition: a general method to design double freeform-surface lens for LED uniform illumination
© Hu and Luo; licensee Springer. 2014
Received: 7 October 2013
Accepted: 18 February 2014
Published: 23 April 2014
Uniform illumination is an essential optical requirement for light-emitting diode (LED) applications. In this paper, a general method was proposed to design double freeform-surface lenses for uniform illumination of LED packages. Detailed algorithms of the design method were presented, in which the inner and outer surfaces of the lenses could be designed simultaneously. This problem can’t be solved unless providing an extra condition. Two kinds of extra conditions were introduced to design the lens and validate the method. Besides uniform illumination, the present method can also realize extra functions with providing different extra conditions, like conformal phosphor coating and minimum Fresnel loss. The present method can be extended to design various freeform-surface lenses for LED uniform illumination provided that different conditions are added based on different application requirements.
KeywordsLens Light-emitting diode Non-imaging optics Illumination
Recently, light-emitting diodes (LEDs) have become a vast lighting market due to its extraordinary features [1–5]. The direct output of a bare LED chip, however, is usually a circle spot with non-uniform illuminance distribution; therefore it can’t be applied without packaging. Hence, appropriate primary or secondary optics are usually used to redistribute the spatial light distribution so that high quality LED illumination can be obtained by controlling the light pattern, illumination uniformity, etc. Among all the LED optics, a freeform lens has the advantages in abundant design degree of freedom (DoF), compact size and accurate light pattern control, thus it has become the dominant optics in LED illumination. There are many methods to design freeform lens, such as simultaneous multiple surface (SMS) method [6–8], partial differential equations method , tailored freeform surface method , discontinuous  or continuous [12–16] freeform lens method. These design methods except the SMS method, however, usually deal with the outer surface and the inner surface is considered as hemispherical shape for simplicity, which would cause light energy loss and abandon an important design freedom in the inner surface of freeform lenses. The SMS method is good at controlling the light direction precisely, but it is some difficult and lacks the ability to realize highly uniform illumination.
In this paper, we tried to develop a general method to design double freeform-surface lenses for LED uniform illumination. The algorithms of the design method were presented in detail. Two kinds of extra conditions were introduced to validate the method.
Surface function relationship control
As one kind of extra condition, we also can supply the relationship between the two surfaces. The relationship can be assigned based on appropriate assumptions. As the simplest cases, we can give the function of one surface and solve the other surface of the freeform-surface lens. For example, we can give the function of inner surface to calculate the function of the outer surface and vice versa.
Light deviation control
If the lens is designed as axis-symmetrical lens, then we can get the freeform lens by rotating the contour line around the symmetry axis. If not, we can use the similar method to calculate the other contour lines. After obtaining all the contour lines, the lofting method can be used to form smooth surfaces of the lens between the contour lines .
What should be emphasized is that this general design method has many design DoFs. The extra conditions could be varied according to the different requirements and the resulting double freeform-surface lenses have different applications. Even for the two aforementioned extra conditions, it also has many design DoFs. As long as the optical performance, volume and profile of the designed lens are acceptable, the inner surface could be given as spherical, cubic, cylinder or even spheroidic and parabolic, while the outer surface is freeform, and vice versa. The ratio of the two deviation angle is also can be changed according to different applications. With other extra conditions, the method could be extended to design different double freeform-surface lenses.
Results and discussions
where the RMSE is the standard error and is the mean value of the sample points of the target plane. The smaller the CV(RMSE) is, the higher the uniformity is.
Design example I
Inspired by the flat inner surface of such double freeform lens, we designed a novel lens to realize uniform illumination and conformal phosphor coating simultaneously. The flat inner surface can realize uniform thickness of phosphor layer, and then we designed the outer surface to achieve uniform illumination by controlling the direction of the emergent ray from the preset inner surface. The detailed design process and validation can be referred to our previous study .
Design example II
Design example III
In summary, a general method was developed to realize uniform illumination of LED packages by adding extra conditions. The algorithms of the design method were presented in detail. Two kinds of extra conditions were introduced to design the lens. It is found that the lens design by present method not only can realize uniform illumination, but also can realize another extra function as well, like phosphor conformal coating and minimum Fresnel loss. Different double freeform-surface lenses can be designed with different extra conditions. Since the extra conditions may be flexible according to the different requirements, the general design method may have plentiful design DoFs and extensive applications.
This work was supported partly by National Science Foundation of China (51376070) and partly by 973 Project of The Ministry of Science and Technology of China (2011CB013105).
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