Microoptics for Efficient Redirection of Sunlight Stephan Klammt,1 Andreas Neyer,1,* and Helmut F.O. Müller2 1

Microstructure Technology Lab, Faculty of Electrical Engineering and Information Technology, TU Dortmund University, Friedrich-Wöhler-Weg 4, D-44227 Dortmund, Germany 2

Green Building R&D, Graf-Adolf-Sr. 49, D-40210 Düsseldorf, Germany *Corresponding author: [email protected]

The development of a cost effective, non-tracking microstructured daylighting system is described in this paper. Ray-tracing calculations are employed to identify basic design rules for the configuration of microstructured daylighting systems. The results show the advantage of combinations of lenslike geometries in comparison to conventional micro prism arrays regarding the overall light redirection efficiency as well as the producibility and cost efficiency. Measurements at silicone prototypes and large scale industrially produced acrylic panels confirmed the simulation results. Optimization leads to freeform geometries which can further be improved by selective roughening of specific micro surfaces. OCIS codes: 220.2740, 220.2945, 220.4000, 350.3950

1. Introduction Energy efficiency is one of the most important objectives in a variety of research areas including the field of modern lighting. Daylighting, with sunlight as a natural and the most energy efficient light source, is one concept to reduce the electricity consumption while maintaining a high quality illumination. Because of sunlight’s high intensity, even relatively small window areas may be used not only to create a standard illumination but also to reach higher illuminances which are desirable for biological convenience [1]. Daylighting should not be affected by solar thermal control systems like shading devices or reflective glass. Conventional louvers, e.g., reduce the daylight so strongly that additional artificial lighting is often needed to reach the required minimum illuminance [2]. The source book on daylighting systems and components [2] describes plenty of different daylighting solutions. Of greater interest for this work are non-tracked light directing glasses like LUMITOP® [3] which already proved good performance [4,5]. In LUMITOP®, stacked PMMA (Polymethyl methacrylate = acrylic glass) profiles are used as light conductors to redirect the light as shown in Fig. 1. The profiles are extruded and have dimensions of 3,5mm by 12mm. They redirect the direct sunlight of solar altitudes from 15 to 65°, which represent the conditions in Middle Europe, to the ceiling deep into the room. Most of the light will be redirected above eye level to establish a glare-free environment. The light is spread to avoid hard shadows and contrasts on the ceiling.

Fig. 1: a) Light-directing glasses are placed above eye level to establish a glare-free environment. b) Cross section of LUMITOP and the here presented microstructured system: the microstructured light-directing element is slimmer and less complex. Microstructured daylighting systems have been described by the Institute of Solar Energy in Freiburg [6] and by [7]. However, the described solutions suffer from not redirecting efficiently a broad range of solar altitudes or are too expensive, due to usage of hybrid polymers. In this work the challenge was to reach equal or better illumination conditions than LUMITOP® with a cost-efficient alternative by substituting the complex light conductors by a continuous and mechanically stable PMMA pane which is micro structured by hotembossing (see Fig. 1). In this way thickness and total weight of the optically active elements are reduced by two third and a conventional manufacturing process is employed which is suitable for mass production.

2. Simulation To identify high-efficient light redirecting configurations extensive ray-tracing simulations have been undertaken. ZEMAX, a tool for the general development of optical systems has been used. The analyzed systems were designed with a CAD program (Solid Works) and then imported by the raytracing software. The simulation environment was adapted to simulate solar altitudes between 0 and 75° taking into account the conditions in Middle Europe. Therefore, due to obstructions close to the horizon and to reduced radiation intensity, solar altitudes between 0° and 15° were of lower significance as well as sun altitudes above 65°. In order to avoid demoulding complications at hot embossing of the PMMA panels, first approaches lead to prismatic structures such as saw-tooth. Simulations show that, regardless of the exact angle of the prism tip, micro prism arrays which are placed on the outward surface of a pane are generally better suited to redirect light of lower solar altitudes, while micro structures placed on the inner surface are suitable for high solar altitudes. The diagram in Fig. 2 depicts the relation between solar altitude and the amount of light which is redirected in an upward direction for a micro prism array. The solid graph shows that inward prisms efficiently redirect light from solar altitudes starting from 35° up to more than 75°.

Fig. 2: Light redirection by micro prism arrays: The diagram depicts the amount of light which is redirected in an upward direction as a function of the solar altitude. Prisms on the inner surface redirect light from high solar altitudes (top left and solid graph) while sunfacing prisms are better suited for low solar altitudes (bottom left, dotted graph). Unfortunately this interval does not fit with the preconditions (15° to 65°) and simulations show that a single-sided panel will not meet the desired performance. To redirect sunlight also under lower solar altitudes both surfaces of the panel have to be structured. The discussion of double sided daylighting systems turns out to be quite difficult as there are numerous combinations of geometries. However, some basic drawbacks of prism – prism combinations have been determined: they display inefficient behavior under certain solar altitudes, are sensitive to manufacturing tolerances (e.g. shift between inner and outer profile) or simply show refractive color effects. Fig. 3 illustrates this problem: in pure prism systems all direct sunlight will penetrate the panel under the same angle due to the prisms’ simple geometry. So the majority of the light will cross the panel on only one or two clearly defined angular paths. Due to small manufacturing variations, e.g. variance in thickness, poor plan parallelism, misalignment between the inside and outside structures or just a critical solar altitude, a path may not be redirected with the consequence that the system will cause severe glare at certain times of the day.

Fig. 3: Systems with micro prism arrays on both surfaces may significantly change their performance due to small profile variances, e.g. by vertical shifts Δ. Extensive simulations show that a lens-like profile on the sun-facing panel side performs quite well. The angle of the daylight is widened considerably and will reach the saw-tooth prisms

under a steep angle which will be redirected (see Fig. 4). The spreading is a vital point since it is a solution to overcome the problem mentioned above. By using lenses the amount of misdirected light is reduced to a negligible quantity.

Fig. 4: a) Microlenses at the sunfacing panel side spread the incident light widely and reduce the amount of sudden critical glare significantly. b) Comparison between two daylighting configurations which only distinguish in panel thickness (2.8 mm and 4mm between the structures). Coming below a critical minimum thickness will result in an oscillating redirection performance. In Fig. 4a it is shown that the parallel incident rays are focused by the lens-like geometries and angularly distributed over the prismatic side. Care must be taken in the design of the panels that the focal length of the lenses is not longer than the panel thickness. If the foci are situated in the range of the prism side undesired effects may appear like a rapidly changing light direction at small changes of the incident light angle (see Fig. 4b), similar as in pureprism systems. These effects are avoided by limiting the minimum panel thickness to more than the double of the focal length. The large scale PMMA panels described in this work are using structures of 500µm (pitch and structure height) which limit the minimum panel thickness between the structures to about 4 mm. Thinner panels may be used together with smaller structures. The simulations show that the lens-like microstructures lead to reasonably homogeneous angular redirection efficiencies. Furthermore, due to lens induced angular scattering color effects are avoided which are inherently present in pure prismatic systems. Further analysis addresses the influence of the refractive index on the redirection performance. Fig. 5 shows the redirection performance of a Polydimethylsiloxane (PDMS = silicone) panel (dotted lines) with a refractive index nPDMS = 1.41 in comparison to an acrylic panel with nPMMA = 1.49 (solid lines). Both systems employ the same optical and mechanical geometries, but differ in their refractive indices. In principal, the redirection performances of both systems are well suited for efficient light directing systems. The basic influence of the refractive index is seen in the redirection efficiencies for angles between 40° and 65°: Due to stronger back reflections of the incident light caused by the higher refractive index of PMMA, the transmission is more reduced in this angular range than for PMDS. Based on this consideration, lower refractive indices would be desirable for more efficient and homogeneous light redirection.

Fig. 5: Influence of different refractive indices (PMMA n=1.49; PDMS n=1.41) on the redirection performances.

3. Fabrication Because of its technical simplicity and high performance, casting of PDMS has been selected to fabricate first samples. Two brass moulds have been machined with the complementary lens-like and prismatic geometries with structure dimensions (pitch and structure height) in the range of 250µm on an area of 100 x 100 mm². PDMS has been chosen as casting material because of its high transparency and moulding precision. The liquid two-component material is applied with a thickness of 1-2 mm onto the casting mould and thermally cured. After curing, the structured sides are demoulded and the backsides of the replica are bonded together. The dimensions of the realized devices are therefore 100 mm x 100mm x 4 mm (see Fig. 6).

Fig. 6: Cross sections of PDMS prototypes with structure dimensions of 250µm. After experimentally proving the expected good light redirection efficiency of PDMS prototypes (see Fig. 8) the technology has been transferred to large scale industrial production by hot embossing (Jungbecker Technology, Olpe, Germany) with transparent PMMA of standard quality as material. Although PDMS shows the higher light redirection efficiency, the approved production process and the higher mechanical stability of PMMA were reasons to change the material. Fig. 7 shows a fabricated panel. The size of 1500mm x 400mm x 4mm is a size well suited for implementation in standard windows or skylights. Due to reasons of fabrication (e.g. the fabrication of the moulds is less complex as the number of structures is reduced by half), the structure dimensions were scaled to 500µm. With a thickness of 4mm, the microstructured PMMA panel weights a third of the light

conductor unit of the Lumitop system (thickness of 12mm) which leads to a saving of about 8kg per m².

Fig. 7: Large-scale prototype with dimensions of 1500 mm x 400 mm x 4 mm for implementation in windows / skylights

4. Experimental Tests After fabrication, the accuracy of the produced sample geometry and surface roughness has been controlled by photographic and white-light interferometric measurements. With a surface roughness in the range of 10 – 20 nm for the casted and about 100 nm for the hotembossed panels the daylighting systems meet optical quality. The geometry evaluation shows that the replication processes transfers the computer generated design values to the experimental sample with tolerances in the range of 1 to 2 %. The overall appearance of the panes is rather homogenous. The transmittance τ has been measured for perpendicular incident light and for 45° with the CIE standard illuminant D65 (which represents daylight). The light-directing element (PMMA) of the microstructured system has a transmittance of τ (D65, 0°) = 79% and τ (D65, 45°) = 78%, while the LUMITOP® system (with outer glasses) displays a transmittance of τ (D65, 0°) = 43% and τ (D65, 45°) = 47%. The redirection performance was measured with a goniometrical setup as outlined in Fig. 8a. As a light source a HE-Ne-laser with a wavelength of 633nm has been used. The “solar altitudes” between 0 and 75° have been measured in steps of 5°. For each resulting light distribution the light within a quadrant was detected by an optical power meter and summed up to gain two clear values: one for the percentage of the light leaving the system in an upward direction (green quadrant and green graph in the diagram) and one for the downward direction (red quadrant / graph).

Fig. 8: a) Principal of goniometrical measurements. b) Diagram of redirection performance: Comparison between microstructured PDMS prototypes and a LUMITOP sample. The obtained results (see Fig. 8b) prove the expected high efficiency in redirecting the daylight without causing glare and confirmed the estimated results of the simulation. The microstructured samples achieve a redirecting overall efficiency of about 68% (mean value) for solar altitudes between 15° and 65° which surpasses the value of the commercial system LUMITOP (mean value: 43%). In Fig. 9 the redirection performance is visualized with a torch.

Fig. 9: Demonstration of light redirection performance: light distribution without (a) and with inserted daylighting system (b)

5. Modifications Concerning the total amount of the redirected light, the demonstrated daylighting system proved the expected high efficiency. However, under specific solar altitudes a stripe structure of the redirected light could be observed (see Fig. 9b) and for solar altitudes of about 40° to 65° an efficiency decrease has been observed. In order to improve the homogeneity of the light distribution and to optimize the overall impression of the system, some modifications have been performed. Analysis revealed that the efficiency decrease comes from internal redirection of the light. Instead of entering the interior of the room the light is deflected back to the outside as depicted in Fig. 10. By applying a defined roughness on the outcoupling surface of the prisms the amount of deflected light is reduced significantly.

Fig. 10: a) For solar altitudes of about 45° the redirection efficiency is decreased due to internal deflections. b) By roughening the marked surface the inner deflection is reduced due to light scattering. To identify suitable roughness characteristics for the prism surfaces experimental tests have been undertaken. Unstructured PMMA panes have been roughened by sandblasting. The roughness characteristics were varied by adjusting the pressure and the working angle while sandblasting. In this way the surface was modified with a roughness Ra in the range of 400nm – 2500nm. The transmission properties of the roughened PMMA panes have been measured as depicted in Fig. 11. Then the measured light distributions were included into the simulation by approximation with the Harvey-Shack scattering model. As a result, a light distribution which features a distinct peak (see Fig. 11) promises best improvement of this application. The corresponding surface roughness Ra is in the range of about 900 to 1000nm.

Fig. 11: a) Measurement of light distribution after scattering at the roughened surface. b) Light distribution for a surface roughness of about 900 – 1000nm. Finally, the geometry of the prisms has been slightly adjusted to a more curved, almost freeform layout to further reduce the stripe structure and to optimize the light transmission deep into the room. In Fig. 12 the gained improvements due to the enhanced form and the applied roughness are illustrated. The diagram shows the increase in efficiency for solar altitudes of 40° to 65°. As a

side effect the basic illuminance is also increased for lower solar altitudes. Fig. 12 further shows the significant reduction of the stripe structure of the redirected light. Two light distributions for an incident angle of 30° are compared. The basic system with plane prism walls has a peaked graph (black lines) which leads to the stripe structure. In comparison the modified system shows a clubbed graph which corresponds with a more homogeneous transmission.

Fig. 12: a) Redirection efficiency of the basic system and the modified system. The modification leads to an increase in redirected light for solar altitudes of 40° to 65°. b) Light distribution for light with a solar altitude of 30° (simulation results): The peaked graph is based on a system with straight bottom flats. The shaded graph corresponds to a modified system which uses curved geometries and a specifically applied roughness.

6. Conclusion The development of a micro structured daylighting system which reaches an illumination comfort similar to established daylighting systems while reducing the complexity and costs significantly was successfully demonstrated. Inconveniences caused by pure prismatic systems could be avoided by using lens-like geometries at the sun-facing side. The quality of the light distribution and the guidance deep into the room has further been enhanced by using freeform geometries. The homogeneity and redirection efficiency could be increased by introducing specific roughness. The presented microstructured daylighting system is industrially manufacturable by conventional hot embossing technology and will result in affordable high quality products – a precondition for a wider market penetration of energy saving daylight illumination systems.

References: 1. W.J. M. van Bommel, G.J. van den Beld, “Lighting for work: a review of visual and biological effects,” Lighting Res. Technol. 36,4, pp. 255–269 (2004) 2. IEA International Energy Agency, “Daylight in Buildings, A Source Book on Daylighting and Systems and Components,” A Report of IEA SHC Task 21 (2000) 3. Saint-Gobain Glass, Product Information SGG LUMITOP, http://uk.saint-gobainglass.com/upload/files/sgg_lumitop_.pdf

4. H. F.O. Mueller, “Daylighting and Solar Control,” presented at LAEL Symposium at the Kyung Hee University, South Korea, 18 May 2006 5. H. F.O. Mueller, A. Emembolu, M. Oetzel, H. Schuster and I. Soylu, “Sonnenschutz und Tageslicht in Büroräumen,“ in Bauphysik-Kalender 2005, E. Cziesielski, Ernst & Sohn, Berlin. 6. G. Walze, P. Nitz, J. Ell, A. Georg, A. Gombert, B. Bläsi and W. Hoßfeld, “Combination of Microstructures and Optically Functional Coatings for Solar Control Glazing,” Solar Energy Materials and Solar Cells, Vol. 89, 2-3, pp. 233-248 (2005) 7. H. Hocheng, T. Huang, T. Chou and W. Yang, “Microstructural fabrication and design of sunlight guide panels of inorganic-organic hybrid material,” Energy and Buildings. Vol. 43, 4, pp.1011-1019 (2011)