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Abstract
The development of LEDs is growing very fast, frequently producing highly efficient and powerful light sources. This encourages optical designers to frequently change the design of secondary optical systems to be suited for newly developed light sources. One of the most critical differences between the current developed LEDs is their luminous intensity distribution, which is used as an input light source model in design procedures of secondary optical systems. Therefore, using a functional concept for the light source independent beam-shaping of LEDs is the main objective of this work. This functional concept can be considered to design secondary optical systems to generate the required luminous intensity distribution independently from the input light source intensity distribution. This leads to more freedom using the developed LEDs without changing secondary optical systems. In this paper, state of the art functional concepts have been discussed. The optical functional evaluation is performed by simulating a secondary refractive lens-array. Simulation results show the degree of the independency relation between the light source intensity distribution and the created luminous intensity distributions.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Designing a secondary lens for light beam-shaping is performed to redistribute the light intensity to meet the requirements of each application. There are many optical functional concepts that can be used to design refractive lenses considering the light energy mapping between the light source intensity distribution and the required light energy distribution [1,2]. In this section, two functional concepts are discussed assuming the use of a point-source.
One-to-one mapping functional concept is widely used in beam-shaping. In this concept, refractive lenses or reflective surfaces are designed in order to redistribute the light energy considering the light energy mapping between the light source intensity distribution and the required target distribution [3–13]. In the one-to-one mapping each incident ray from the light source is mapped to a specific direction to the target distribution as shown in Fig. 1(a). This can be performed by solving a set of differential equations [4–7], or by the intersections of the incident light rays with the local tangent planes [8–12]. For each application, the source-target mapping solution is based on the method of determining the mapping relation. Due to the one-to-one mapping relation between the light source and the target plane, the created distributions are sensitive to the imperfections in the light source.
Fig. 1. (a) Beam-shaping using a refractive freeform lens considering the one-to-one mapping concept and (b) Beam-shaping using lens-array considering the many-to-one mapping concept.
Many-to-one functional concept is widely used to create the required illuminance distribution at the required distant target. This has been proved to be an efficient concept for achieving homogenized intensity distributions by dividing and superimposing the light energy over the illuminated objects [14–18]. The idea is to divide the secondary optical system such as reflectors into multiple sections called facets, each facet illuminates the whole target. Superimposing the light from all facets leads to the total required illuminance. It can also be performed using lens-array as shown in Fig. 1(b). The influence of the imperfections in the light source on the target distribution is compensated by superimposing the light energy.
In some applications, like designing the automotive headlamps (US Patent No 4,704,661), the functional concept is based on the partial superimposing of light energy. The beam-shaping is achieved using a faceted reflector. The target and the faceted reflector are divided into multiple zones. Each facet is designed individually to achieve the required mapping relation. Then, all facets are merged together by fitting the gaps. In this concept the reflector is able to create asymmetric complex illuminated patterns. Lens-arrays of non-identical lens-lets can also be used for creating asymmetric illuminated patterns. The idea of using a micro-lens-array of non-identical lens-lets is proposed for the far-field beam-shaping distributions as presented in [19]. This creates the required output luminous intensity distribution nearly independently from the spatial illuminance and the angular intensity distribution with certain limits. Non-identical lens-lets help in generating asymmetrical far-field distributions, but the power of superimposing the complete amount of energy identically over the required angular range is not fulfilled. It is not fulfilled due to the partial overlapping of the light energy [19].
Based on the working principle of the discussed functional concepts, it can be concluded that the advantage of using the one-to-one functional concept is the ability to design freeform surfaces$\backslash$lenses for achieving asymmetric targets. The drawback is the dependency relation between the light source and the created luminous intensity distribution. On the other hand, the many-to-one functional concept shows a degree of independency between the created intensity distribution and the input light source intensity distribution, but it is mostly limited to create homogeneous distributions at distant targets.
2. Problem and approach
The development of the LEDs is growing very fast, producing high efficient and powerful light sources frequently. This encourages the optical designers to frequently change the design of the secondary optical systems to be suited for the new developed light sources. One of the most critical differences between the current developed LEDs is their luminous intensity distribution, which is used as an input light source model in the design procedures of the secondary optical systems. Changing the light source model influences the created output target luminous intensity distributions in case we use the same one-to-one mapping secondary optical system. On the other hand, based on the state of the art it is required to create secondary optics to generate asymmetric light luminous intensity distributions.
Combining the advantages of both functional concepts (one-to-one and many-to-one) can be considered in creating asymmetrical distributions in the angular domain. This can be performed by designing freeform lens-lets fulfilling the principle of complete light energy superimposition. Lens-array is used to distribute the light over the angular domain, each lens-let of the lens-array is a freeform lens designed using the one-to-one functional concept. Each lens-let redistributes the light energy over the complete required angular domain. The power of superimposing the complete amount of the light energy identically over the complete required angular range is fulfilled as shown in Fig. 2 (many-to-one).
Fig. 2. (a) The idea of dividing the light source energy into parts then redistributing the luminous intensity using each lens-let of the lens-array over the angular domain and (b) Light superimposing over the angular domain for generating an asymmetric luminous intensity distribution.
This concept is based on dividing the input light source energy into separate beams as shown in Fig. 2(a). Then, redistributing them over the angular domain identically at each lens-let of the lens-array. As shown in Fig. 2(b), superimposing the light energy shows the identical performance of all the freeform lens-lets. This leads to the final required luminous intensity distribution. The errors due to the change of the input light intensity distribution at the lens-lets cancelled each other over the angular domain. The error compensation is performed due the principle of light energy superimposing. The quality of the independency relation between the light source and the required distributions can be improved by changing the number of lens-lets of the lens-array.
3. Concept verification
In this chapter, the verification of the proposed functional concept is performed by simulating two refractive secondary lenses. Both lenses are designed to generated the same luminous intensity distribution using the same light source. The first lens is a single refractive freeform lens using one-to-one mapping. The second lens is a lens-array (10×10 freeform lens-lets) considering the proposed functional concept. The optical function of both lenses has been investigated using the same simulation setup, the same light source and light detector.
Design procedures of designing both lenses are explained in detail in [20]. The one-to-one mapping data are determined using the steady state solution proposed by Sulman et al. [21]. Mapping data are used to determine the surface gradients [22]. Surface gradients are corrected using an iteration process to fulfil the integrability condition of the required surface [4]. Finally, surface sag values are determined by integrating the surface gradients numerically.
The required optical function is to redistribute the collimated LED radiation into a luminous intensity distribution representing the symbol of the Town Musicians of City Bremen shown in Fig. 3 over the angular domain (±30○).
Fig. 3. Required target luminous intensity distribution, image of the Town Musicians of City Bremen (normalized dimensions).
3.1 Simulation results
Both lenses are modelled and the optical transformation by lenses is simulated using OpticStudio [23]. Simulation is performed by tracing 5 million rays using the non-sequential mode of the OpticStudio. The freeform lens and the freeform lens-lets are modeled by importing the grid sag lens (501×501 grid points) into OpticStudio. Lens material is PMMA. The light source wave length is 0.550 μm. Figure 4 shows the simulation results generating the required patterns of luminous intensity distributions.
Fig. 4. Simulation setup including the collimated rays and a detector used for the slope analysis to determine the luminous intensity distribution, (a) One-to-one mapping freeform lens used for redistributing the collimated rays over the angular domain representing the symbol of the Town Musicians of City Bremen and (b) Lens-array consists of 10×10 freeform lens-lets used for redistributing the collimated rays over the angular domain representing the same symbol.
3.2 Light source changing
In this section, the dependency relation between the light source intensity distribution and the generated luminous intensity distribution is presented. This has been performed by changing the light source cross section as shown in Fig. 5(a), then measuring the generated luminous intensity distribution. Simulation results show the strong dependency relation while considering the one-to-one mapping concept in the lens design as shown in Fig. 5(b). On the other hand, results show that the proposed functional concept can be used to design light source independent secondary lenses for creating asymmetric luminous intensity distributions as shown in Fig. 5(c). The luminous intensity distributions shown in the first raw of Fig. 5 are considered as a reference ($L{I_{ref}}$) to evaluate the change in the luminous intensity in case we change the light source. The absolute difference ($x$) between the first raw results and the created luminous intensity ($LI$) using different light sources is determined using
The standard deviation of the absolute difference is determined usingFig. 5. Dependency relation between the output luminous intensity distribution and the intensity distribution of the light source (Simulation results), (a) Light source intensity distribution (Perfectly collimated light beams based on a point source), (b) The influence of changing the light source intensity distribution on the created luminous intensity distribution using one-to-one mapping and (c) The independency relation in case we use a lens array of freeform lens-lets.
Fig. 6. Dependency relation between the output luminous intensity distribution and the intensity distribution of the light source (Simulation results), (a) Light source intensity distribution (Based on an extended light source), (b) The influence of changing the light source intensity distribution on the created luminous intensity distribution using one-to-one mapping and (c) The independency relation in case we use a lens array of freeform lens-lets.
4. Conclusion
In this paper, a functional concept for light source independent beam-shaping of LEDs is discussed. The light source energy is divided into separate beams using a lens-array of freeform lens-lets. Each beam is redistributed over the angular domain to match the required luminous intensity distribution. Superimposing the light energy identically and completely over the angular domain is the main principle of compensating the input light source imperfections. The dependency relation between the light source intensity distribution and the created luminous intensity distribution is presented. This has been performed by changing the cross section of the light source collimated rays, then measuring the created luminous intensity distribution. Simulation results show the source-target dependency relation while considering the one-to-one mapping in the lens design. On the other hand, results show the source-target independency relation using a lens-array of freeform lens-lets (creating asymmetric luminous intensity distributions over the angular domain). This leads to more freedom of using the developed LEDs without changing the secondary optical systems to generate the same required luminous intensity distribution. The quality of the independency relation between the light source and the required distributions can be improved by changing the number of lens-lets of the lens-array.
Funding
Bremen University of Applied Sciences; Bundesministerium für Bildung und Forschung (BMBF) (03FH023lX5).
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