We present a proof of principle demonstration of a reversible in-plane actuator activated by focused sunlight, and describe a concept for its use as a self-tracking mechanism in a planar solar concentrator. By actuating at the location of focused sunlight and splitting the solar spectrum for actuation energy, this phase change device aims to provide the adaptive mechanism necessary to efficiently couple concentrated solar light from a lens into a planar lightguide in a manner that is insensitive to incidence angle. As a preliminary demonstration we present a planar actuator array capable of in-plane deflections of >50μm when illuminated with focused light from a solar simulator and demonstrate solar light activated frustrated total internal reflection (FTIR) with the actuator array. We further propose how this solar induced FTIR effect can be modified using a dichroic facet array to self-adaptively couple and concentrate solar light into a planar lightguide.
©2012 Optical Society of America
Concentrated photovoltaic (CPV) systems aim to reduce costs by using less expensive optical materials for concentration of sunlight onto smaller area photovoltaic (PV) cells. Due to the fundamental principle of étendue, solar concentrators cannot simultaneously achieve large concentration and a large angular acceptance. In practical terms, this means that concentrator systems usually require mechanical tracking to keep the optics aligned for maximized efficiency. For moderate to high concentration (100-1000x) systems, complex and relatively expensive 2-axis trackers are required for alignment . Low (<10x) and non-concentrating systems are capable of fixed installation, but the cosine-theta obliquity factor of their orientation limits their effectiveness over the course of a day [2,3]. This inefficiency can be significantly improved with the use of coarse single-axis trackers, which can be made cost effective due to their simplicity and relaxed pointing tolerance. For the most part commercial trackers are active electronic systems that reduce the power produced by the PV cell. A different approach, demonstrated for simple single-axis tracking, is a self-adaptive mechanical (passive) mechanism, which uses thermal heating to orientate a panel toward the sun [4,5]. Although inexpensive and efficient, passive trackers have not found wide-spread acceptance, possibly due to drawbacks such as the need to be reset daily and sensitivity to environmental conditions.
The concepts of micro-tracking and integrated-tracking have recently been suggested as useful alternatives to traditional panel alignment [6–8]. With these approaches, small localized changes to the optical arrangement are used to align the concentrating system to the sun’s position. With fixed panels these approaches are limited in field of view (FOV) by the cosine-theta obliquity and not suitable for full diurnal tracking. However, they generally have the advantage of only requiring small movements for alignment. When combined with inexpensive coarse single-axis tracking, these approaches suggest new possibilities for low cost concentrating systems. Examples of micro-tracking have been based on moving an array of micro-scale solar cells at the focus of a lens array , or lateral translation of a waveguide coupling feature below a microoptic solar concentrator . The integrated-tracking approach is distinguished by lateral shifting lenses, which serve to steer the concentrated light to the solar cell .
Reactive self-tracking is a recent concept based on a combination of micro-tracking and a self-adaptive mechanism which directly uses energy from the sun to align the optics . This approach is based on micro or nano-scale changes to the coupling features of a planar microoptic solar concentrator [10,11], and bears some resemblance to luminescent concentrators which convert and guide light within waveguide using luminescence . In their paper, Baker et. al. proposed a reactive self-tracking concept where energy from the sun’s focal position is used to activate a nonlinear material response which increases the local index of refraction and creates a waveguide coupling region. Although preliminary results suggest the potential for creating a large index of refraction change in an electrically enhanced liquid colloidal suspension, a change large enough for efficient self-tracking operation has not yet been demonstrated. Other self-adaptive systems have also been proposed, such as a hydrogel filled lightguide which becomes scattering under solar heating for skylight light harvesting ; and movement of fluids within a cladding layer by thermocapillary forces for lightguide coupling .
In this paper we describe an alternative mechanism to the reactive self-tracking approach based on thermal phase-change actuation. Like the other reactive self-tracking approaches that have been suggested, our approach is based on a reactive coupling feature in a planar lightguide concentrator . In a planar lightguide concentrator light from an array of lenses is coupled into a slab waveguide which acts to homologize and transport the light to its edges. In contrast to other approaches for reactive self-tracking, our approach is primarily mechanical, using a phase-change actuator for in-plane displacement of a transparent elastomer and reflective facet array for lightguide coupling. Phase-change-materials (PCM) such as paraffin wax undergo large volume expansions when phase changing from solid to liquid making them useful as actuator materials. With their potential for high force and large stroke actuation, many groups have developed PCM-based devices for MEMS and microfluidic valves [15,16]. Microfabricated heaters are most often used to melt paraffin wax (or similar PCM) in an enclosed chamber with a deformable membrane. When melted, the liquid paraffin expands the membrane with in-plane deflections of tens to hundreds of microns depending on the geometry.
Our device concept shown in Fig. 1 uses a PCM to actuate an in-plane deflection of a transparent elastomer and reflective facet array to form a lightguide coupling feature at the location of the sun’s focus. When the transparent elastomer is deflected and pressed against the lightguide, light can be efficiently coupled into the lightguide at that location. A dichroic mirror on the facet array allows focused infrared (longpass) light from the sun to activate the PCM actuator while reflecting shorter wavelength light, which is coupled into the lightguide and delivered to the lightguide’s edges. In this way, wavelengths of light that are not useful for the desired application (for example: Silicon PV, daylighting, etc.) can be spectrally separated and used to power the self-tracking mechanism.
In this paper, we present preliminary analysis and experimental demonstration of a PCM actuator toward realization of the concept concentrator concept of Fig. 1. In Section 2 we discuss some basic optical design considerations related to the concentrator’s function over a useful tracking range. In Section 3 we describe the fabrication and characterization of two simple paraffin wax in-plane actuator candidates for light activated in-plane deflection. Based on the device concept of Fig. 1, these actuators make up a key component of the adaptive self-tracking mechanism. Namely, the solar induced mechanical positioning of the lightguide coupling feature. In Section 4 we present an experimental demonstration of light activated FTIR using the PCM actuators of Section 3. As will be explained, this demonstration of FTIR closely resembles the operation of the actuator required for lightguide coupling and provides a useful proof of principle demonstration of the actuator’s function. Finally, in Section 5 we present a summary and conclusion.
2. Some preliminary optical considerations of a self-tracking planar concentrator device
In this section we propose and describe some basic optical considerations of a self-tracking planar concentrator device. Many aspects and optical design trade-offs remain the same as those of a static planar micro-optic solar concentrator , and have not been reiterated in detail here. Instead, we will focus on particular design aspects and issues that are important for the self-tracking concept of Fig. 1. The two optical issues most critically important to extending the planar concentrator for self-tracking are 1) lens design and performance over a range of incidence angles, and 2) design and performance of the lightguide coupling features over a range of incidence angles. These two issues are discussed in this section.
2.1 Lens design
A self-tracking planar concentrator must be capable of efficient lightguide coupling over a broad range of incidence angles. Although very wide field of view (FOV) lenses (such as the fisheye lens) exist, their geometry is impractical for concentration due to the fact that all wide angle lenses have an entrance pupil diameter much smaller than their physical lens diameter. Lens designs for concentration require a high utilization of their pupil area-to-physical area ratio, which practically limits FOV. Constraints on lens complexity and cost limit the realistic FOV further. As mentioned in Section 1, one possible application of a self-tracking concentrator is to combine it with a polar-aligned single-axis mechanical tracker, such as those sometimes used with Silicon panels . Under these circumstances, the self-tracking mechanism would be used to provide fine-tuning of the alignment and to cover seasonal variations in solar elevation; which would require an angular field of approximately ± 23.5° . Plano-convex singlet lenses will have large off-axis aberrations for this range of incidence and are not likely to be suitable. Two-element plano-convex designs, however, have been shown to have good performance with low F-numbers over this angle range [7,8].
2.2 Lightguide coupling
Light is coupled into the lightguide by an array of dichroic reflective facets. This concept is similar to that of the planar microoptic concentrator where an array of 30°/30°/120° triangular facets are used to coupling . This structure is ideal for normal incidence light since it provides efficient coupling without outcoupling from secondary reflections. However, light of sufficient incidence angle at the facet will not be confined by TIR within the lightguide.
Assuming an air-clad lightguide and an elastomeric coupling region with reflective facets on the bottom, the critical angle within the elastomeric coupling medium for light after reflecting from the reflective facet is given byEq. (1) to calculate the maximum incidence angle in air that can be coupled into the lightguide. From the law of reflection, the angle of a ray incident on either side of the 30°/30° facet array is related to the ray angle after reflection byEq. (1) and Eq. (2) and using Snell’s law, we can calculate the maximum ray angle of incidence in air, θin air max,30/30, below which all light is coupled into the lightguide:Equation (3) can also be used to define the minimum F/# lens that could be used with the system. Due to the fixed limit on incidence angle for the 30/30 facets, the minimum F/# of the lens for complete coupling will increase with field angle:Eq. (4) the cosine factor is due to lens aperture obliquity. As shown by the blue minimum F/# curve in Fig. 2(c) , there is only a very limited angle range for which low F/# lens can be efficiently coupled. For larger incidence angles, the facet angles should be tuned to match the chief ray angle, θi, at the facet (in the elastomeric medium). The ideal facet angles, α1 and α2, as a function of the chief ray angle areEq. (5) and Eq. (6) provide optimal coupling by maintaining the unique condition that the 30°/30° facets provide for normal incidence. Namely, that the chief ray reflecting from the shallower facet (facet 1, defined by angle α1) is exactly parallel to the steeper adjacent facet (facet 2, defined by angle α2), and marginal rays reflecting at shallower angles strike the adjacent facet at a grazing incidence and subsequently match the angle of the steeper marginal ray. This can be seen in Fig. 2(a) and 2(b) for normal incidence and 25° (in air) off-axis light respectively. The angular limits that satisfy lightguide coupling for off-axis light are given byEquation (7) and Eq. (8) represent the lower and upper limits on incidence angle for light that satisfies the TIR condition in the lightguide. The lower bound angle of incidence given by Eq. (7) is limited by shallow angle reflections from facet 1 (solid red or solid green rays in Fig. 2(b). The upper bound angle of incidence given by Eq. (8) is limited by steeper angle reflections from facet 2 (dashed green ray in Fig. 2(b)). With a tuned facets the minimum F/# is given byFigure 2(c) shows the minimum F/# possible as a function of field angle with both tuned facets (red curve) and the 30°/30° fixed normal incidence facets (blue curve). As shown, tuned facets allow for efficient coupling over ± 23.5° incidence with a lens F/# < 2. In practical terms, a tuned facet array requires a more complex fabrication and alignment to the lens. However this system can be made insensitive to misalignment simply by increasing the F/# of the lens.
The preceding analysis does not take into account facet deformations due to the PCM actuator, and assumes an overall flat-based facet array. A device based on the concentrator concept of Fig. 1 will place the facet array on or within a transparent flexible layer, which is actively pressed against the lightguide at the coupling location. Such a deflection will deform the facet angles where the material is bent or stretched. However, we speculate that the majority of the coupling area will remain essentially flat since the actuator is pressing firmly with a flat top against the planar glass lightguide. Residual deformations in the facet array when pressed against the lightguide can be either measured or estimated through finite element analysis and incorporated into the design of the facet array and the tolerance requirements of the concentrator design.
Finally, regarding the design and required performance of the multilayer dichroic coating over the required angle range; our expectation is that the coating can be designed with a wide enough tolerance in the transition wavelength from reflection/transmission to allow for the desired ± 23.5° incidence. Assuming an F/2 lens, the range of incidence angles on the tuned facets vary from ~9deg to ~36 deg in PDMS (or ± 18 deg a center design angle). In addition, questions regarding coating adhesion and the impact of cracking in the coating will need to be investigated. These open questions will be investigated and addressed further in a subsequent paper describing demonstration of the self-tracking concentrator.
3. PCM actuator array
In this section we move away from the conceptual analysis of the self-tracking concentrator and focus on the fabrication and testing of a solar activated in-plane actuator. This actuator is an in-plane deflector capable of expanding vertically at the location of focused infrared sunlight. When integrated beneath a flexible dichroic facet array patterned onto a transparent elastomer, it becomes the self-adaptive coupling feature for the self-tracking concentrator. Here we present fabrication and characterization of a paraffin wax actuator array towards the goal of realizing a self-adaptive lightguide coupling feature.
3.1 Fabrication of paraffin wax actuator arrays
We fabricated the two devices shown in Fig. 3 to examine their function as candidate structures for the solar activated in-plane deflector. This actuator structure should ideally expand at the location of focused infrared sunlight to position the reflective facets for lightguide coupling. Here we have fabricated the actuator structure without the integrated dichroic reflector. Without it, these devices are not yet capable of lightguide coupling and are instead solar light activated in-plane deflectors. We will use them to examine their optical-mechanical characteristics and potential for the self-adaptive coupling mechanism.
To account for the missing dichroic reflector in terms of actuation energy, we illuminated these devices through an external cold mirror to remove the visible spectrum from the actuation light from a solar simulator. For our demonstration devices we used honeycomb arrays with two different cell sizes- 2.3mm (Fig. 3(a) and Fig. 3(c)) and 0.75mm (Fig. 3(b) and Fig. 3(d)). The 2.3mm array is a commercial polycarbonate honeycomb array from Plascore with 3mm thickness and 2.45mm cell separation. The 0.75mm array is a steel laser cut part, 2mm thick with 0.9mm cell separation. The honeycomb arrays were chosen to provide a lateral confinement for the expansion of the paraffin wax. In the future it would be desirable to have a fully continuous array without the rigid structure to avoid discrete actuation. This may be possible in the future by creating a paraffin/elastomer composite, which has been suggested for in-plane actuators without rigid confinement .
The cells of the honeycomb array were filled with Merck Paraffin wax (melting temperature of 42-44°C), and 4% (by wt.) carbon black (Cancarb Thermax N991). Carbon black acts as a broadband light absorber to generate the heat for phase change in the Paraffin wax within each cell of the array when illuminated with focused and filtered infrared light from a solar simulator. A 300μm layer of Sylgard 184 polydimethylsiloxane (PDMS) was glued onto the tops of the filled honeycomb arrays using a thin layer flexible ultraviolet (UV) adhesive (Norland Optical Adhesive NOA68) to act as the transparent deflector. Methyl Siloxanes do not show characteristic absorption bands in the UV or visible spectrum but have several absorption bands in the NIR. Using data from , we estimate a transmission of >80% in a 300um layer of Sylgard 184 from 700nm to 1800nm. Transmission could be improved by switching to elastomers with better infrared transmission, such as GE RTV 615.
3.2 Paraffin wax actuator characterization
To test the paraffin wax actuator devices, we passed light from a 300W solar simulator (Sciencetech SF300) and AM1.5 filter through a Thorlabs 2” cold mirror (cut off wavelength 700 nm) and a 30mm focal length achromatic lens (Thorlabs). This test setup is shown in Fig. 4(a) . Threshold actuation energy was found by varying the diameter of the lens aperture. The aperture required for actuation was found to be 15mm, providing 33mW of focused infrared optical power on the sample measured with a thermal detector. This value is roughly 1/3 of the power available in the 700nm-2500nm AM1.5 solar spectrum and indicates that the commercially available cold mirror, with its passband designed for 700-1200nm light, is suboptimal for transmitting the full infrared spectrum for heating.
Since the PDMS layer is glued to the honeycomb array, each actuator can be described theoretically by the deflection of a circular plate of radius ra with clamped edges under a uniformly distributed load. The differential equation describing this has a simple analytical solution  described by
We incorporated a coaxial white light interferometer shown in Fig. 4(a) into the setup by reflection from the cold mirror to measure device deflections. The setup uses identical 30mm lenses in each arm of the interferometer in a Linnik configuration. To generate the broadband light for the measurements, we used a pulsed 6W Fianium supercontinuum light source with 60MHz repetition rate. The source was attenuated and bandpass filtered (500nm-850nm) with a beam power of 14mW. The bandwidth of the light is further filtered (600-650nm) before entering the camera to adjust the size of the coherence envelope and measurement resolution. By scanning the reference arm we used the position and visibility of the low coherence fringes to create steady state 3D profiles of the PDMS surface.
Figure 4(b) shows measured device deflections for the two devices. For both devices the initial unheated surface profile is subtracted from the heated state profile to measure deflection. The maximum deflections for the 2.3mm and 0.75mm cell devices were 64μm and 51μm respectively. Using these measured values and the cell diameter; the theoretical estimations for the profile given by Eq. (10) were calculated and shown as solid lines in Fig. 4(b). The measured profile for the 0.75mm cell is less complete than the 2.3mm device since surface slopes were too large to be measured outside of the base and peak. Aside from this, the profile appears to match the theoretical prediction reasonably well for the 0.75mm device. The profile for the 2.3mm does not appear to match the prediction as well. This is probably due to the large size of the cell, which is significantly larger than the infrared spot from the solar simulator and may be causing non-uniform or incomplete melting of the paraffin in the cell.
For this actuator to be used effectively as the coupling mechanism for the self-adaptive concentrator of Fig. 1, it must have reliable and reversible deflections. To examine this, we made several repeated actuations of the devices and measured the deflections. In all cases we found that the deflection heights for heated and unheated states were consistent (<5μm variation) and reversible with the exception of the first full actuation after fabrication. On the first actuation, we found that the actuator returned to an unheated state with additional sag of ~10μm (0.75mm cells) and ~30μm (2.3mm cells) below the steel array structure. We believe this is due to imperfect filling of the paraffin reservoirs, which allows for a settling upon first use. Subsequent actuations repeatably returned to the same unheated profile, which poses no issue for its use as a reactive coupling mechanism.
4. Solar induced FTIR demonstration
The solar activated PCM actuators described in Section 3 do not yet contain the integrated dichroic facets necessary for lightguide coupling. Despite this, we can demonstrate the fundamentally similar effect of solar induced FTIR, where the in-plane actuator is used to strip light guided by TIR. This effect is similar to lightguide coupling because it places the same simple functional requirement on the actuator: a solar induced contact region between the PDMS layer of the actuator and an air-glass TIR planar interface. In this case the base of a dove prism. In this section we describe this experiment and present results demonstrating solar induced FTIR using the actuator described in Section 3.
4.1 Setup and demonstration of solar light induced FTIR
We set up the experiment shown in Fig. 5(a) and 5(b) to demonstrate the solar light induced FTIR capabilities of the paraffin actuator devices. TIR in a dove prism can be frustrated (FTIR) by placing it over one of the actuator devices with an air space cladding between the two. When the solar simulator is off, light passes through the dove prism by TIR as shown in Fig. 5(a). When the solar simulator is focused through the dove prism onto the device below, actuation causes the PDMS layer to press against the base of the dove prism, frustrating the TIR at the location of the contact as shown in Fig. 5(b). The size of the FTIR region is determined by the shape and volume of the expanding membrane, and by the size of the airspace between the dove prism and actuator. At the time of this experiment we did not have a reliable method to directly measure the size of the air-space between the dove prism and the PDMS layer. However, we can estimate it by measuring the size of actuated contact area between the PDMS and the dove prism, and by making some assumptions about the shape of the expansion. If we assume that the deflected membrane has a trapezoidal cylinder or “conical frustrum” shape  when pressed against the dove prism, we can estimate the air-space thickness to be:Fig. 5(c) for the 0.75mm cell.
The inset image of Fig. 5(c) shows an image of the visible FTIR contact area between the PDMS and the dove prism; seen as a dark central area (slight change in contrast) within the actuator cell looking down through the roof of the dove prism. This image is taken coaxial with the solar light using the camera shown in Fig. 4(a). Although the bandpass filter removes most of the solar simulator light from the image, a bright reflection can still be seen in the inset image where light from the elliptical focus hits the steel array structure. For this deflection, the diameter of the contact area is approximately 76% of the cell diameter. From this value we can the estimate size of the air-space to be ~22μm from Eq. (13). A large rFTIR/ra ratio is important since it determines the active fill factor of the array.
Figure 6 shows FTIR reversibility (Media 1) and tracking (Media 2) capabilities for the two devices using a camera to observe the image through the angled facets of the dove prism. The camera is tilted at an angle to observe the change from TIR to FTIR within the dove prism. Because of the oblique perspective, the circular FTIR regions appear elliptical. Although the cold mirror filters out the majority of the visible light, the red focus spot is visible to the camera in Fig. 6 and allows us to easily measure the device activation and deactivation times. The relative brightness of the bright spot from scattered actuator light and the dark FTIR spot are sensitive to both the angle of the camera and the location on the bottom of the dove prism. This accounts for the difference in spot brightness between the 0.75mm cell device (Fig. 6(a) and Fig. 6(b)) and the 2.3mm cell device (Fig. 6(c) and Fig. 6(d)). As shown, both devices exhibit reversible FTIR and tracking of the solar focus when activated by the filtered solar simulator light. Tracking is demonstrated in Fig. 6 by lateral movement of the actuator and prism using a micrometer adjustment of a mechanical translation stage.
Paraffin actuators are notoriously slow making them difficult to use in some applications. As shown in Fig. 6, FTIR response time is significantly affected by the size of the actuator cell. With an airspace of approximately 20 μm between the dove prism and the inactivated PDMS layer, full actuation times of 3 sec and 10 sec were required for the 0.75 mm cell and 2.3 mm cell respectively. Similarly, deactivation times for the two devices were found to be 2 sec and 6 sec for the 0.75 mm and 2.3 mm devices respectively. Although these response times are slow compared to other potential mechanisms, the growth rate of the paraffin in response to lateral movement of the stimulus is the limiting actuation speed. The sun’s angular velocity of roughly 0.2 mrad/sec corresponds to a lateral translation of 7 μm/sec with a 30 mm focal length lens. Using an optical coherence tomographic (OCT) setup (not shown) and heating laser, we measured the paraffin growth rate to be >10 μm/sec, which is suitable for tracking the sun with this device.
In this paper we have presented a candidate solar induced actuation mechanism for an adaptive self-tracking concentrator. Previous works on self-tracking concentrators have shown potential of the concept, but viable candidates for the adaptive mechanism remain a challenge. Towards the goal of an effective self-tracking mechanism, we have presented a proof of principle demonstration of a reversible in-plane PCM actuator activated by focused sunlight, and described a concept for its use as a self-tracking mechanism in a planar solar concentrator. Experimental results suggest that when combined with a tuned-angle dichroic facet array and a two-element lens array, the in-plane PCM actuator can be used for high efficiency coupling over ± 23.5° with a lens F/# <2, and could be used in combination with coarse single axis tracking for a simplified and potentially low-cost solar concentrator.
As with any solar concentrator technology, cost benefits are critically important. At the early stage of this work it is difficult to accurately predict the manufacturing costs of such a device, but we can describe a basic hypothesis for a cost advantage. We suggest that cost savings from 1) reduced PV material due to moderate levels of concentration and 2) the reduction from accurate two-axis tracking to coarse single-axis tracking outweigh the additional costs incurred from materials, parts, and complexity of manufacture.
Further, we can consider the materials used for our concept device. Paraffin wax is an inexpensive and common by-product of the petroleum refining process. Similarly, carbon black is also a common and inexpensive material produced by combustion of heavy petroleum products and also more recently from recycling of rubber automotive tires. PDMS, the elastomer we currently use is extremely convenient for prototype fabrication, but it is not common for industrial applications and would likely be substituted by another transparent and flexible polymer in a commercial device. Finally, of the components required by our concept, the dichroic mirror coating is the most likely to be considered too costly, as it is often deemed too expensive for other solar concentrators. However, there are reasons to believe that multilayer coatings are not out of reach. One example is the cool mirror material made by 3M . This material is a commercial multilayer polymer for solar concentration with a cost of ~$20/m2 . Further, its multilayer design is similar to that required for our application, since it reflects useful light for Silicon PV and transmits the heat producing mid-infrared and UV light. Although it’s unclear if this material could be processed for our device, its existence suggests that we should not discount the possibility of inexpensive multilayer coatings suitable for solar spectrum splitting.
With experimental measurements using a solar simulator we have shown reversible in-plane deflections of >50μm using 33mW of infrared light (>700nm) focused by a 30mm lens diameter. Since this power represents approximately 1/3 of the available energy in the 700nm-2500nm portion of the solar spectrum, we believe that lens size or the spectral bandwidth required for heat actuation can be reduced. The paraffin wax used had a melting temperature of 43C. Paraffin waxes with melting temperatures between 25C and 100C are commercially available allowing for further tuning of the actuation energy threshold.
Finally, by placing this device below a dove prism, we have demonstrated solar activated FTIR- an effect fundamentally similar to that needed for a solar induced lightguide coupler, and have shown reversibility, repeatability and tracking capability for this device. We found the device response times to be greatly dependent on cell size with FTIR activation and removal times of 3sec and 2 sec for the smaller of the two devices tested. Growth rate of the actuator was found to be >10μm/sec, compatible with the sun’s lateral position velocity using a 30mm focal length. With simple materials and fabrication, and high potential coupling efficiency over a broad range of angles, this approach appears to be a promising candidate for a self-tracking planar solar concentrator.
The authors would like to thank Arno Bouwens of the EPFL Laboratoire d’optique biomédicale for assistance with the OCT measurement.
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