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    Solar Energy 86 (2012) 877885Design of dome-shaped non-imaging Fresnel lenses takingchromatic aberration into account

    Atsushi Akisawa a,, Masao Hiramatsu b, Kouki Ozaki b

    a Institute of Engineering, Tokyo University of Agriculture and Technology, Koganei, Tokyo, JapanbR&D Department, Technology Division, Daido Metal Co., Ltd., Inuyama, Aichi, Japan

    Received 13 June 2011; received in revised form 8 September 2011; accepted 19 December 2011Available online 23 January 2012

    Communicated by: Associate Editor Avi KribusAbstract

    Concentration PV system is a technology for providing solar-based electricity at very high conversion efficiency of 40%. It needs solarconcentration of 500 suns or more, for which the authors developed dome-shaped non-imaging Fresnel lenses with a certain acceptancehalf angle. As conventional design method uses only one wave length, the performance suffers from chromatic aberration. In this paper, anew design method is proposed. One of the points is that it uses two kinds of design wave length which covers a given range of solarspectrum for the concentration. The other is that new design points are located on the corners of prisms while the conventional pointis at the center of prisms. Numerical examples with the concentration ratio of 500 were designed and optical efficiency was examined byray tracing simulation. The results indicate that the lens based on the conventional way has dish-like shape and the lenses designed by theproposed method have relatively deep dome shape in contrast. The optical efficiency of the new design is better than that of the conven-tional one at the incident angle equal to the acceptance half angle. It was concluded that the proposed method could produce more effec-tive solar concentrator with a certain tolerance of solar incident angle. 2011 Elsevier Ltd. All rights reserved.

    Keywords: Non-imaging Fresnel lens; Concentration photovoltaic system; Chromatic aberration; Dome shape; Optical efficiency1. Introduction

    Renewable energies are expected to increase the installa-tion to reduce fossil fuel consumption. Especially solar PVsystems have been adopted worldwide. However, conven-tional Si-based PV cells have the efficiency of approximately20%atmost. To utilizemuchmore solar energy, it is essentialto improve the PV efficiency significantly. One technologicalcandidate to attain such a high efficiency is concentration PVsystems (CPV) which concentrates solar irradiation onto thePV cell by lenses or mirrors with the concentration ratio of500 sums ormore. The cell with quite high energy conversionefficiency of 40% has been developed for CPV (Kurt, 2009).0038-092X/$ - see front matter 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.solener.2011.12.017

    Corresponding author. Tel./fax: +81 42 388 7226.E-mail address: (A. Akisawa).New Energy and Industrial Technology DevelopmentOrganization (NEDO), a governmental agency to supporttechnological development in Japan, once committedlaunching a project of developing CPV about 10 yearsago. In the project, the authors were involved in the designand the production of dome shaped lenses of 500 suns(Akisawa and Kashiwagi, 2005). One of the features is thatthe dome shaped lenses have undercut prisms which cannotbe produced by ordinary mold injection technique. One ofthe authors successfully developed a production process fordome shaped lenses in the project (Hiramatsu et al., 2003).While most of CPVs use flat shaped lenses, Japanese CPVsimplement dome shaped lenses thanks to the NEDOproject.

    The design of shaped Fresnel lenses was proposed byLeutz et al. (1999) and Leutz and Suzuki (2001) based on

  • Fig. 2. Photo of a manufactured dome shaped lens (500 suns).

    878 A. Akisawa et al. / Solar Energy 86 (2012) 877885the theory of non-imaging optics. It allows Fresnel lenseswith curved surface, for example, arch shape or dome shape.Dome shaped Fresnel lens array was also developed byPiszczor et al. (1991) for solar concentrator prior to them.In contrast, most of CPV use flat type Frenel lenses withpoint focus. Xie et al. (2011) surveys various types of Fresnellenses for solar concentrator applications. The advantage ofnon-imaging Fresnel lenses is to have acceptance half angleto collect sun light effectively. In other words, the lenses areinsensitive to the incident direction to some extent. Ryu et al.(2006) proposed a new type of Fresnel lens concentratorwhich unites many modular Fresnel lenses into one piecein flat shape. It has allowance of the incident angle withnot so high concentration ratio of 9-121 suns.

    It is a nature of lenses to have chromatic aberration,which may cause degradation of the concentration whenthe lenses are applied for solar concentrators. In the shapedlens design method proposed by Leutz, wave length of 550nm is adopted to design prisms. It is likely that the lensperformance suffers from chromatic aberration. The objec-tive of this paper is to improve the design method for domeshaped non-imaging Fresnel lenses taking chromatic aberra-tion into account explicitly. Further techniques for improv-ing concentration performance are also discussed andexamined with ray-tracing simulations.2. Non-imaging Fresnel lenses

    2.1. Edge ray principle

    The purpose of the proposed dome shaped lenses is to col-lect sun light as much as possible on the absorber. The objec-tive of ordinary lenses is to enlarge images, for instance, withdefinite focus for clear image formation. In contrast, imageformation is not required for the dome shaped lenses becausecollecting solar incident rays onto the absorber is essential,whatever the image is. This feature results in an advanta-geous characteristic of having acceptance half angle. Theacceptance half angle, h, is defined as the angle where solar


    acceptance half angle



    Fig. 1. Principle of designing non-imaging Fresnel lens with acceptancehalf angle.incident rays coming in between +h and h is captured onthe absorber. In other words, the ray at +h goes to an edgeof the absorber while the ray at h reaches the other edge.Rays between +h andh arrive at somewhere on the absor-ber, which is enough for the purpose of collecting sun light.Fig. 1 shows the principle of the lens design, which is so-called Edge ray principle. Because Fresnel lenses consistof many prisms, each prism is required to have appropriateshape incorporating this principle.2.2. Dome shaped lens

    Ordinary Fresnel lenses have flat surface and grooves onone side either upper face or lower face. However, theoreti-cally their acceptance half angle is considered zero becausethe main purpose is image formation. Contrary to theirshape, prisms of non-imaging Fresnel lenses basically haveinclined surface on both upper and lower sides to hold agiven acceptance half angle. It causes that the lenses havecurved shape looking like a dome in three dimensions ifthe lenses have smooth surface of the upper side. The authorsmanufactured dome shaped Fresnel lenses actually andtested the performance. Fig. 2 shows a photo of the domeshaped lens made of acrylic plastic material (PMMA).3. New design method of dome shaped lenses

    3.1. Coping with chromatic aberration

    Although chromatic aberration is inevitable for lenses,conventional way of designing non-imaging Fresnel lensesdoes not take the effect into account. Rays of single wavelength are used for the design, which is regarded as neglect-ing chromatic aberration in the design process. Chromaticaberration eventually degrades the lens performance whensolar irradiation is applied to the lenses. For imagingoptics, some lenses are compounded so that the effect ofchromatic aberration is canceled, which is so-calledachromatic lens. Leutz and Ries (2003) examined anachromatic dome-shaped Fresnel lens which consists of

  • A. Akisawa et al. / Solar Energy 86 (2012) 877885 879two layers having different refractive indices. In contrast,the attempt of this study is to propose Fresnel lenses withone layer coping with chromatic aberration. because non-imaging lenses need no clear focus, non-imaging Fresnellenses is intrinsically considered insensitive to chromaticaberration. The requirement is that lights of different wavelength should arrive at somewhere on the absorber, notarrive at the focal point as is the case of imaging optics.

    The proposed way of designing dome-shaped Fresnellenses consists of the following three steps.

    (1) Determining upper and lower wave length to captureon the absorber. Each wave length is correspondingto different refractive index.

    (2) Assigning the longer wave length coming at +h (cen-ter side) to get the edge of right hand side.

    (3) Assigning the shorter wave length coming at h(outer side) to get the edge of left hand side.

    Fig. 3 indicates the behavior of the rays showing that theshorter wave length coming at +h is expected to arrive atthe edge of left hand side on the absorber. Similarly thelonger wave length coming at h is predicted to get theother edge of the absorber. Therefore, light in the rangeof wave length can be fully captured by the absorber eventhough there occurs chromatic aberration. It should benoted that the proposed non-imaging Fresnel lenses candeal with chromatic aberration not by canceling the effectbut by accepting the effect.absorber

    single wave length


    + -

    Fig. 3. Edge rays considering chromatic aberration into acco3.2. Decoupling lens height with acceptance half angle

    Shaped non-imaging Fresnel lenses for solar collectingdevices were designed by Leutz et al. as mentioned before.According t