research article solar divergence collimators for optical...

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2013 Article ID 610173 10 pageshttpdxdoiorg1011552013610173

Research ArticleSolar Divergence Collimators for Optical Characterisation ofSolar Components

D Fontani P Sansoni E Sani S Coraggia D Jafrancesco and L Mercatelli

Consiglio Nazionale delle Ricerche National Institute of Optics INO Largo E Fermi 6 50125 Firenze Italy

Correspondence should be addressed to P Sansoni paolasansoniinoit

Received 14 November 2012 Accepted 21 December 2012

Academic Editor Ho Chang

Copyright copy 2013 D Fontani et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Experimentation and laboratory optical tests on solar components are central aspects of the research on renewable energiesThe key element of the proposed testing systems is a solar divergence collimator which exactly reproduces in laboratory thesunlight divergence while commercial solar simulators are mainly aimed to replicate intensity and spectrum of the sun Precisesolar divergence reproduction is essential to correctly assess the optical properties and to simulate the operative conditionsof a solar collecting device Optical characterisation and experimentation can give information about production quality andhomogeneitymoreover specific tests can address the serial production of solar components detecting defects type and location ForConcentrating Photovoltaic systems appropriate tests can analyze solar concentrators of various shapes dimensions and collectionfeatures Typically to characterise a solar component the most important and commonly examined quantities are collectionefficiency image plane analysis and angle dependence

1 Introduction

Solar energy concentration on reduced size surfaces typicallyphotovoltaic cells or more rarely optical fibres representsa recent field of application within the renewable energystudies These technologies and solar plants appear to bequite promising for energetic supply [1ndash4] Optical systemsfor solar light concentration on reduced size surfaces wereanalyzed and experimented in our research laboratory since1997 [5ndash9] Our work on renewable energies includes threemain research lines optics to concentrate and transfer solarlight by optical fibres solar concentrators coupled to Pho-toVoltaic cells (Concentrating PhotoVoltaic systems) andfinally sunlight collectors coupled to various devices Thesesolar components can be applied in the photovoltaic field orfor internal illumination

Laboratory experimentation and optical measurements[5ndash7] on commercial solar components or samples realizedfrom customized optical designs represent crucial aspects ofthese researches Optical characterization tests [10ndash12] can

give information about production quality and realisationhomogeneity of solar devices constituents Dedicated andadapted measurements can address the serial productionof solar components individuating type and location ofrealisation imperfections For Concentrating PhotoVoltaicapplications suitable optical measurements can control thehomogeneity of collector production comparing the opticalfeatures among the different samples Finally to check thefidelity of reproduction of the original design the opticalcharacterization can be used to compare the measured valuesof optical properties to the nominal values belonging to theoptical project of the component

Solar simulators are often employed to optically charac-terise solar components in fact they aremore frequently usedto test absorbers than collectors However due to the recenttechnological improvements in Concentrating Photovoltaics(CPV systems) there is an increasing request of employingsolar simulators to test CPV components

Commercial solar simulators [13ndash15] are essentiallydesigned for experimentations on plane solar panels or single

2 International Journal of Photoenergy

Photodetector

Sample

Collimation lens

S

Source

Integrating sphere

Figure 1 Scheme of collimator S1 (for image tests and focused imagemeas on small components)

cells without collection optical system In principle a solarsimulator is a device that can reproduce on limited areas theconditions of solar irradiation with specific spectral charac-teristics and irradiance uniformity The solar simulators onthe market perform a quite good reproduction of spectraldistribution and intensity of the solar emission up to 200x forcontinuous light and up to 5000x for pulsed light The maindrawback of these solar simulators is that the output light hasa divergence larger than the solar one semi-angle divergenceof few degrees while the solar value is around 025∘ Themost sophisticated so very expensive device present on themarket can produce a collimated beam with divergence half-angle 24∘ and diameter 610158401015840or divergence half-angle 12∘ anddiameter 1210158401015840

Image light distribution is another crucial aspect thatmust be taken into account especially for the experimen-tation on concentrating photovoltaic components In orderto minimise the thermal stresses and to maximise the con-version efficiency the CPV cells require adequate irradianceuniformity over the cell surface

This paper proposes a solar divergence collimator ableto exactly reproduce the solar divergence and to provide anextremely uniform beam Our solar divergence collimatoris applied to test solar components in a laboratory set-up whose main advantages are flexibility and versatility Apossible engineering of our test system to obtain a closedand fixed instrument would lose its ability to adapt the teststo specific requirements of the solar application or particularcharacteristics of the examined sample

2 Solar Divergence Collimators

The optical collimator reproducing the solar divergencerepresents the core of every laboratory set-up employed tocharacterize solar components The principal layouts for ouroptical tests are presented in Figures 1 2 3 and 4The sourceis always realized by a white light illuminator coupled by anoptical fibre to an integrating sphere The solar divergence isaccurately reproduced combining the sphere output diameterS to the focal distance 119891

119862of the collimation optics which can

be a lens or a mirrorThe solar divergence collimator can be realized in axis

(S1-S2) if the examined collectors have reduced dimensionsCollimator S1-S2 is presented in Figures 1 and 2 showingthe two optical configurations used for image tests andcollection efficiency assessmentThe setup of S1-S2 includes acollimation lens with focal length119891

119862= 700mmand diameter

119889119862= 90mm

Photodetector

MaskCollimationS

Source

Integrating sphere

Mirror

lens

Figure 2 Scheme of collimator S2 (for entering light measurementon small components)

For practical reasons the test of solar collectors withdiameter exceeding 80mm is realized employing the solardivergence collimator L1-L2 in Figures 3 and 4 To clarifythe schemes in Figures 3 and 4 the values of 119891

119862and

119889119862do not respect the real proportions whereas they are

correctly proportioned in Figures 1 and 2 Collimator L1-L2 has two spherical mirrors with 119891

119862= 1500mm and

119889119862= 250mm The first acts as collimation mirror while the

second is a concentrating mirror (indicated as ldquoMirrorrdquo inS2 Figure 2 and L2 Figure 4) In collimator L1-L2 the opticalaxis is deflected once (L1 Figure 3) or twice (L2 Figure 4)over the measurement plane The bent configuration of L1-L2 introduces some optical errors and aberrations on thecollimated beam

The verification of the solar divergence reproduction canbe preliminary performed comparing the obtained beamdiameter with the expected value In practice we realise areference target a circle with the exact beam dimensions atthe distance of the concentrating mirror (ldquoMirrorrdquo in Figures4 and 2) The reference target is placed at this distance onthe beam axis The set-up L2 (or S2) projects a beam on itwhich should correspond to the target circle A more precisecontrol of beamproperties and solar divergence reproductionis represented by the beam measurements described inSection 4

Concerning the optical quality of the beams it is impor-tant to remark that the optical layout of S1-S2 is bent oncein Figure 2 but the measured quantity is the entering lightwhich is filtered (by the mask) in the axial collimator Thenthe mirror bending the optical axis concentrates the lightover the photodetector In collimator L1-L2 the collimationmirror deflects the optical axis realizing a bent collimatorwith two axes forming an angle 120572 Then the concentratingmirror focuses the light on the sensor introducing a seconddeflection of the optical axis (Figure 4) The crucial bend isthe first one since it affects the quality of the collimated beamwith solar divergence Moreover the use of an integrationsphere and the precision in realizing its aperture S representtwo other sources of optical errors

3 Aberrations of Collimated Beams

The collimators under study are of two types S1-S2 containsa collimation lens while L1-L2 has a collimation mirror ina bent configuration Both collimators generate a series of

International Journal of Photoenergy 3

PhotodetectorCollimation

S

Source

Integrating sphere

mirror

Sample

Figure 3 Scheme of set-up L1 (for image tests and focused imagemeas on large components)

Photodetector

Mask

Collimation

SSource

Integrating sphere

mirror

Mirror

Figure 4 Scheme of set-up L2 (for entering light measurement onlarge components)

aberrations that contribute to degrade the definition of theimage on the detector The value of these aberrations mustbe quantified in order to identify the specific contributiongenerated by the sample under test The use of collimator S1-S2 allows limiting the aberrations by an appropriate choicefor the collimation lens which should be a lens with fieldcorrection and optimized for the used spectral bandwidthOn the other hand employing collimator L1-L2 the aberra-tions mainly depend on the collimator angle 120572 and on thesurface type of the collimation mirror In L1-L2 of Figures3 and 4 the collimation mirror was chosen to be sphericalbecause it is easy and cheap to be realized The aberrationstudy was carried out considering a spherical mirror of focallength 1500mm and an ideal lens with focal length 250mmwhich represents the component under test The ideal lensallows analyzing the aberrations of the wave front comingout from the collimation mirror in the position where thesolar collectors are usually tested The aberrations of thebeam generated by L1-L2 are reported in Figure 5 as standardZernike coefficients 119862

119885 considering three collimator angles

120572 5∘ 15∘ and 25∘ The actual angle of the collimator L1-L2 used in our laboratory for collector tests is 15∘ and thelaboratory set-up allows angles up to 23∘ The values ofspherical aberration coma astigmatism and field curvatureare plotted versus the entrance pupil diameter of the test lens(in millimetres) which corresponds to the beam diameterunder examination

The 119862119885

values plotted in Figure 5 indicate that themain contribution is represented by the astigmatism and it

improves with the diameter of the collimated beam For beamdiameter lower than 150mm and 120572 le 15∘ the 119862

119885coefficients

are such that the effect of the single aberrations on the qualityof the image produced by the lens is negligible The imagemaintains high uniformity in intensity

The degradation of image definition was estimated sim-ulating a collimator L1-L2 with a ray-tracing optical designsoftware which provided simulations reproducing the profileof the image Sg of our sourceThe profiles of the image Sg aredisplayed in Figures 6(a) and 6(b) for angles 120572 up to 25∘ andfor two beam diameters In Figure 6(a) the beam diameteris 150mm while Figure 6(b) refers to a beam diameter of250mm that corresponds to the total width of the solardivergence beam For120572 le 15∘ the image keeps the rectangularshape hence it can be concluded that our collimator L1-L2 isa very good test system for sample diameters up to 150mmwith 120572 = 15∘

As final validation the reliability of the off-axis collimatorL1-L2 to test solar collectors was experimentally verifiedThischeck is reported in Figure 7 comparing the characteristicsof the image produced by an ideal lens without aberrationswith the image generated by a real solar collector Thecomparison of these two optical elements is useful to evaluatethe contribution of the aberrations characterizing the off-axis spherical mirror in order to separate them from thecontributions due to the tested collector

Figure 7 compares the profile of a real image to the profileof a simulated image The measured image was acquiredby a CCD camera with a Fresnel lens of diameter 180mmand focal length 195mm The simulated curve in Figure 7is obtained for a lens with the same optical features butconsidered an ideal lens without aberrations For the real lensthe aberrations contribution is visible on the image profilewhich results enlarged at the bottom andmore smoothed andrestricted at the top of the curve The shape of the ideal lensimage is almost rectangular while themeasured image profileapproaches a bell shape It can thus be concluded that forthe examined measurements the aberrations of collimator L1-L2 can be considered negligible It is necessary to repeat thiscomparison operation at every new collector test in order toverify the degree of interaction of the measurement systemwith the parameters of the sample to be measured

4 Measurements of Collimated Beams

The research is completed by a set of experimental mea-surements examining the solar divergence beam generatedby collimators S1-S2 and L1-L2 The detection is preformedsampling the beam by a photodiode (of side 4mm) displacedon the vertical plane XY The sensor is mounted on amotorized translation stage which is shifted by anothertranslation stage that is perpendicularly mounted Suitablesampling step and speed were chosen to reach a good trade-off between high definition of acquired image and acceptablelength of measurement time The beam of collimator S1-S2has diameter 90mm hence it can be completely sampled byour detection system which has a maximum excursion of150mm For collimator L1-L2 the beam has diameter 250mm


0

005

01

015

02

025

03

035

04

50 100 150 200 250

Beam diameter (mm)

Spherical aberration

5 deg

15 deg

25 deg

(a)

50 100 150 200 250

Beam diameter (mm)

Coma

5 deg

15 deg

25 deg

minus 8

minus 7

minus 6

minus 5

minus 4

minus 3

minus 2

minus 1

0

(b)

0

10

20

30

40

50

60

70

80

90

50 100 150 200 250

Beam diameter (mm)

Astigmatism

5 deg

15 deg

25 deg

minus 10

(c)

0

50 100 150 200 250

Beam diameter (mm)

Field curvature

5 deg

15 deg

25 deg

minus 08

minus 07

minus 06

minus 05

minus 04

minus 03

minus 02

minus 01

(d)

Figure 5 Aberrations as Zernike coefficients for 120572 = 5∘ minus 25∘

therefore the measurement procedure is more complicatedTwo photodiodes are mounted at a horizontal distance of150mm on the same translation stage and they are displacedtogether In this way two parallel sampling are obtained incorrespondence of the left and right portion of the beamTo take into account possible differences between the twosensors the double sampling is repeated exchanging thephotodiodesThe final image is then calculated averaging theresults of the two measurements

Figure 8 shows the solar divergence beam measured oncollimator S1-S2 the left picture presents a 3D plot while theright picture reports a 2D image of the beam AnalogouslyFigure 9 presents the 2D and 3D plots of the measurementson the beam of collimator L1-L2

In themeasurements on the collimated beam of L1-L2 thevertical sampling range is 150mmwhile the beam diameter is250mm so the images represent only the central portion ofthe beam Nevertheless the sampling is sufficient to contain

the beam in the horizontal direction and the aberrationsaffect this central band of the solar divergence beam

By a practical point of view in our laboratory set-up L1-L2 the minimum collimator angle 120572 is 15∘ This is the valueusually employed for the solar component tests because itminimizes the aberration effects The beam in Figure 9 doesnot show aberration effects which result to be lower than thedetection sensitivity

It can be concluded that both collimators are appropriateto test solar components the optical quality of the solardivergence beams is very high for S1-S2 and high for L1-L2 For collimator S1-S2 inside the diameter of 90mm thebeammaintains very high uniformity in intensity with profilevariations within 10 of the maximum value For the beamof collimator L1-L2 the data fluctuations are lower than 10in the diameter 180mm and lower than 20 in the diameter210mm Consequently the maximum useful diameter foraccurate measurements on the beam obtained with L1-L2 can


0

50

100

150

200

250

300

0 02 04 06 08 1 12 14

Imag

e p

rofi

le (

au

)

Image dimension (mm)

Beam diameter 150 mm

0∘

15∘20∘

25∘

(a)

0

50

100

150

200

250

300

0 02 04 06 08 1 12 14

Imag

e p

rofi

le (

au

)



0∘

15∘20∘

25∘

(b)

Figure 6 Image profiles for beam diameter 150mm (a) or 250mm (b)

0

50

100

150

200

250

300

0 05 1

Imag

e p

rofi

le (

au

)


Real lens

Ideal lens

minus 1 minus 05

Figure 7 Profiles of simulated and detected images

be considered 210mm while high accuracy measurementsshould be performed within the diameter of 180mm

Two aspects could be improved in the described opticalsystems that reproduce the solar divergence The first aspectconcerns the precise value chosen for the beam divergencethe solar divergence as total angular aperture ranges from05253∘ (Aphelion) to 05421∘ (Perihelion)The second aspectis the reproduction of the solar spectrum typically performedusing halogen or Xenon lamps Figure 10 presents the spec-tra of the light emitted by several sources comparing themeasurements to the sunlight spectrum All measurementsare performed coupling the source to the integrating sphereThe examined lamps cover the wavelength range of the solarspectrum (300 nmndash1500 nm) but with a different spectraldistribution Moreover in laboratory we use an optical fibrethat selects almost the visible light (350 nmndash800 nm) whichis typically the range of use and test of solar componentsTheinternal source of the two illuminators is a halogen lampwith

an ellipticmirror its spectrumcorresponds to the illuminatorwithout optical fibre (in Figure 10)

In our laboratories the solar divergence beams of Figures8 and 9 are successfully applied as testing light to characterizesolar components In particular we developed test configura-tions and procedures to test solar collectors with maximumdiameterdiagonal 240mm For such reduced sizes the exam-ined samples typically have various shapes dimensions andcollection characteristicsTherefore each solar image presentsdifferent light levels and uniformity features which requirethe use of appropriate instrumentation and measurementsprocedures

The described optical measurements on solar collectorsconsider image plane analysis angle dependence collectionefficiency and spot size The proposed characterization pro-vides optical properties and collection performances whichare crucial to optimise a solar exploitation device Howeveron the base of the specific solar application it can be useful toexamine other aspects or assess specific quantities significantfor the examined case [16ndash21]

5 Image Plane Analysis

Considering the characterisation of a CPV solar collectorsome preliminary studies on the focal distance 119891 are essen-tial both for image analyses and for collection efficiencyassessment It is essential to assess the position of eachfocal plane measuring the experimental values of 119891 for eachcollector sample The focal plane definition is dictated bycollector design and solar system application Solar collec-tors are optically designed as nonimaging systems with themain purpose of maximizing the focused energy within thenominal image Therefore the focal plane can simply beindividuated bymaximizing the collected light over thewholeexamined plane (for absorber size exceeding the nominal


(a)

(b)

Figure 8 Measurement of the S1-S2 beam 3D and 2D plots

image) If the dimension of the absorber is crucial as incase of photovoltaic cells (or optical fibres) the image planecan be defined maximizing the light concentrated over adetector with shape and size of the real absorber After thedetermination of the focal distance several experimentalmeasurements can then be performed to examine the imagegenerated by each sample of a solar collector production Inparticular for Concentrating PhotoVoltaic applications it isfundamental to analyze the light distribution in the imageplane

The key element of our optical tests system is the solardivergence collimator reproducing the divergence of sunlightrays It can be of two types collimator S1-S2 (Figures 1and 2) for small components with diameterdiagonal lowerthan 80mm or collimator L1-L2 (Figures 3 and 4) forlarger samples up to diameters of 240mm Figures 1 and 3show the two optical systems S1 and L1 used for the imageplane analysis The difference between the two layouts is thecollimation optics a lens with focal length 119891

119862700mm in S1

Figure 1 or a spherical mirror with 11989111986215m in L1 Figure 3

Figure 11 illustrates the laboratory practical realization ofsolar divergence collimator L1

The source for L1-L2 and S2-S2 is realized by a white lightilluminator coupled to an integrating sphere using an optical

(a)

(b)

Figure 9 Measurement of the L1-L2 beam for 120572 = 15∘ 3D and 2Dplots

fibreThe solar divergence is simulated combining the sphereoutput diameter 119878 to the focal distance 119891

119862of the collimation

optics The beam with solar divergence impinges on thesample under test and a camera visualizes the generatedimage The sensor used to estimate the focal distance andto examine the image plane is a CCD camera while forthe measurement of collection efficiency the sensor is aphotodetector Size and shape of the photodetector shouldcorrespond to those of the absorber

The high-definition camera is mounted on a mechan-ical support that is usually displaced by a high-precisionmicrometric translation stage to keep a good stability ofthe detection system and to allow a precise estimation ofthe focal distance Beside the high precision the translationstage should have high reproducibility of the positions andlarge excursion In our laboratory optical system we use aCMOS camerawith an external chip which allows examiningcollectors with very short focal distances Figure 12 shows theCMOS camera testing a component with a diameter of fewcentimetres The image saturation is a critical parameter inthese tests First of all the source level should be adaptedto obtain a good image for the camera acquisition Thedetection parameters can be properly chosen to evidencedifferent aspects of the image analysis For instance the imagesaturation must be avoided when determining the beam


0

500

1000

1500

2000

2500

3000

300 600 900 1200 1500 1800

Wavelength (nm)

Xenon lampKL2500 illuminator

KL1500 illuminator

Spec

tral

irr

adia

nce

(W

m2)

Sun (air mass = 1)

Illuminator source (halogen lamp + elliptic mirror)

Figure 10 Lamp light (measuredwith integrating sphere) comparedto the sunlight

Optical fiber

Integrating sphere

Mirror

Sensor

Light source

Translation stage

Figure 11 Practical realization of configuration L1 (for large com-ponents)

profile On the other hand the image saturation can be usefulto emphasize image borders

It is important to remark that all these measurementsare very sensitive to misalignments between collector planeand camera array plane Therefore mounting stability andalignment accuracy are essential elements to obtain reliableand reproducible results

To consider some defocusing effects the mentionedanalysis can be repeated examining the parallel planes locatedbefore and after the focal position Moreover dedicated

Figure 12 CMOS camera examining a small solar collector

measurements can investigate the dependence on specificparameters of interest

6 Angle Dependence Study

Suitably designed and especially realized configurations arededicated to examine angular properties and the angulardependences of the tested components These angular mea-surements assess how collector features and performancesare affected by rotations tilts and angular misalignmentsin general These crucial aspects are connected to collectionefficiency performance tracking errors and Field of Viewaperture of the optical system In the worse case the angularmisalignment can cause bad illumination over the photo-voltaic cell generating thermal stresses

Since every collector has its specific collection geometryit is consequently characterized by specific angular effects andangle dependencies which can be examined by appropriatetests Furthermore typically each application has specificangular requirements that can be experimented or verified inlaboratory by suitable tests on angle dependence

Finally these angular analyses can be combined withimage plane studies or collection efficiency assessment tocomplete the research and to provide a more realistic sim-ulation Investigating the interactions between the separatelytested aspects this experimentation represents a better simu-lation of the real working conditions

The angular tests basically require a tilt or a rotation stagewhich is combined to the instrumentation used for imageplane analyses or collection efficiency tests

By a practical point of view for the simulation of mount-ing errors or angular misalignments only the collector isrotated while in the tracking error tests both collector anddetector are rotated with the same reference plane

7 Collection Efficiency Test

For the applications of sunlight exploitation the essentialquantity to be considered is the collection efficiency Themeasurements are performed on a white light collimator thatreproduces the solar divergence assessing the efficiency ofsunlight collection The collection efficiency is obtained as


Optical fiber

Integrating sphere

Mirror 1

Mirror 2

Mask

Sensor

Light source

Figure 13 Practical realization of configuration L2 (for largecomponents)

ratio between the light focusedwithin the nominal image andthe light inside the entrance aperture of the collector Thesetwo quantities are separately measured The focused light ismeasured using collimator S1 of Figure 1 (for small collectors)or collimator L1 (for large collectors) shown schematically inFigure 3 and practically in Figure 11 For this measurementthe sensor is a photodetector with dimensions correspondingto the nominal image obtained from the optical project of thetested collector The beam with solar divergence illuminatesthe sample under test which is located at the focal distanceto maximize the collected light

The second measurement concerns the light enteringthrough the collector entrance aperture It is performed usingcollimator S2 in Figure 2 (for small collectors) or collimatorL2 (for large collectors) reported as scheme in Figure 4and as laboratory set-up in Figure 13 The beam with solardivergence impinges on a suitablemask composed of a screenwith a hole reproducing shape and size of collector entranceaperture The light passing through the mask is concentratedby a spherical mirror and measured by a photodetector

In general the optical tests are aimed to verify quality andhomogeneity of collector production and reproducibility ofthe collector fabrication process Every test checks produc-tion homogeneity and reproducibility for the specific aspectexamined by the test but probably themost significant resultsare represented by collection efficiency assessment and focaldistance measurement

The essential optoelectronic instrumentation employedto assess the collection efficiency is a photodiode with largedynamic amplifier a mask (simulating the collector entranceaperture) a concentrating mirror (spherical mirror) anda translation stage Optical systems S1 of Figure 1 and S2Figure 2 are used to measure collectors with maximumdiagonaldiameter 80mm Components of larger dimensionsare tested with configurations L1 of Figure 3 and L2 Figure 4

The currentmirrors available in our laboratory have diameter250mmand they allow testing samples withmaximumdiam-eter 240mmThephotodetector used in our laboratory set-upis a squared photodiode of side 18mm In the measurementof entering light the image diameter of the source S onthe photodiode exceeds 15mm therefore the photodiodeshould have suitable dimensions This is due to the fact thatthe source diameter S is dictated by the requirements ofsolar divergence reproduction and by the focal length ofcollimation optics

An important aspect is to utilize the central portion ofthe collimated beam characterized by higher uniformityThereflectivity of the concentrating mirror should be assessedespecially because they typically are large mirrors withdiameters of 200ndash300mm Moreover the reflectivity is notconstant over the reflecting surface hencewe usually estimatean average value which is successively employed to rescalethe detection Finally the entering light measurement canbe replaced by a light density assessment if the beam ishomogeneous enough

8 Image Size Measurement

A simple and low-cost methodology allows evaluating thelight concentrated into a fibre or over a photovoltaic cellThisexperimental measurement assesses image spot dimensionand light distribution within the focused image The opticalset-up for this image control includes a white light sourcereproducing the solar divergence The beam impinges on thetested collector and a detection system is located in its imageplane It consists of a photodiode combined to a multi holesmask Figure 14 shows an example of themulti holemaskwith8 hole diameters 119889 with approximate step of 01mm suitablefor images of few millimetres The mask moves in front ofthe detector and it allows measuring the light intensity Idcorresponding to the encircled image of the collector whichis the luminous intensity focused inside a hole This imageanalysis can verify if the collector production is homogeneousfor what concerns the light distribution inside the imageThe results are expressed in percentage as ratio between theencircled image light and the total light in the focal planeSome measurements results appear particularly interestingthe diameter corresponding to the nominal image of thecollector and the value corresponding to the absorber (corediameter of the optical fibre or photovoltaic cell area)

The technique to determine the image diameter Di isbased on the measurement of the encircled image light IdThevalue ofDi is obtainedwhen the Id values start to saturatethus indicating that the hole diameter119889 is exceedingDi SomeId results measured using a multi-hole mask are reported inFigure 15 the Id values are plotted versus the hole diameter119889 For verification and comparison Figure 15 also reports thecorresponding values estimated from an image acquired bya CMOS camera Considering a saturation threshold of 95for the curve in Figure 15 the value of image diameter Di is16mm

In this test the translation stage moves the multi-holesmask behind the collector which maintains its position In


Figure 14 Example of Multi hole mask

07

075

08

085

09

095

1

1 11 12 13 14 15 16 17 18 19 2 21

Enci

rcle

d im

age l

ight

()

Hole diameter (mm)

EstimationDetection

Figure 15 Measurement and calculation of the encircled imagelight

fact the most critical point for this measurement is the align-ment of each hole The multi-hole mask should be moved inthe image plane keeping the hole in the focal position whichis practically obtained maximizing the photodiode outputsignal

This procedure can be appliedwhen the image is unusablefor the camera in case of very luminous or extremely poorsignal

9 Conclusions

Since 1997 within our researches on renewable energieswe studied and experimented solar concentrators for smallsurfaces Our laboratory developed fibre-coupled collectorsConcentration PhotoVoltaic (CPV) systems and optical sys-tems coupled to various devices These solar componentswere designed to be applied in the photovoltaic sector or forinternal lighting

For simulating the real working conditions of a directexposition to the sun collimators with solar divergence are

employed in the optical systems to test solar componentsThe solar divergence is reproduced combining the outputdiameter of an integrating sphere to the focal distance ofa collimation lens The solar divergence collimator can berealized in axis for small collectors While collectors withdiameterdiagonal gt80mm are tested using two large spheri-calmirrorswith focal length 15m In this case the collimationmirror deflects the optical axis realizing a bent collimatorwith two axes forming an angle 120572 This bent configurationintroduces some optical errors on the collimated beam withsolar divergence In the bent collimator the beam aberrationsdepend on the angle 120572 Measurements of the solar divergencebeams have evidenced that both collimators are appropriateto test solar components The collimated beams do not showaberration effects that are lower than the detection sensitivityThe optical quality of the solar divergence beam is veryhigh for the unbent collimator and high for bent collimatorBesides high accuracymeasurements can be performed in thecentral part of the beam of the bent collimator

Optical characterization and experimentation are crucialaspects for the development of every sunlight exploitationdevice and in particular for CPV systems Optical tests canverify quality and homogeneity of solar components produc-tion or compare themeasured values of optical features to thenominal values estimated in the optical design

The core of our optical testing systems is a solar diver-gence collimator which produces a beam with solar diver-gence and elevated illumination uniformity The examinedcollectors can have various shape dimensions and con-centration features Hence each image presents differentlight levels and concentration features which require theuse of appropriate hardware and procedures The describedoptical tests allow determining image plane analysis angledependence collection efficiency and image dimensionsThementioned features represent an exemplificative and basicoptical characterization for sunlight exploitation howevereach solar application requires adapting the tests to examinethe significant quantities and aspects

Our research group developed optical systems andmethodologies to characterize solar components of reducedsize (max diameterdiagonal 240mm) This dimensionallimitation on the examinable samples is only due to theactual size of our laboratory the sample size can be increasedextending the optical system and using mirrors with largerdiameter In alternative samples larger than 240mm can beexamined in portions averaging and combining the resultsto obtain the optical characterisation of the componentAnother important case is the test of high-concentrationcollectors the solution can be either to use a reduced sourceemission or to choose suitable sensors and acquisition param-eters However the major advantage of using a laboratory set-up is its adaptability to sample features and solar applicationneeds

Acknowledgment

The authors wish to thank Dr D Ferruzzi for her funda-mental contribution to develop the ray-tracking simulations


of solar divergence collimators in order to assess beamaberrations and beam profile errors

References

[1] R M Swanson ldquoThe promise of concentratorsrdquo Progress inPhotovoltaics vol 8 pp 93ndash111 2000

[2] W T Welford and R Winston High Collection NonimagingOptics Academic Press San Diego Calif USA 1989

[3] US Department of EnergyElectric Power Research Institute(EPRI) ldquoRenewable energy technology characterisationsrdquo Top-ical Report TR-109496 1997

[4] A Luque Solar Celle and Optics for Photovoltaic ConcentrationThe Adam Higler Series on Optics and Optoelectronics Tayloramp Francis New York NY USA 1989

[5] P Sansoni F Francini andD Fontani ldquoOptical characterisationof solar concentratorrdquo Optics and Lasers in Engineering vol 45no 3 pp 351ndash359 2007

[6] P Sansoni F Francini D Fontani L Mercatelli and DJafrancesco ldquoIndoor illumination by solar light collectorsrdquoLighting Research and Technology vol 40 no 4 pp 323ndash3322008

[7] F Francini D Fontani D Jafrancesco L Mercatelli and PSansoni ldquoOptical control of sunlight concentratorsrdquo in Highand Low Concentration for Solar Electric Applications vol 6339of Proceeding of SPIE San Diego Calif USA September 2006

[8] P Sansoni D Fontani F Francini D Jafrancesco and GLongobardi ldquoOptical design and development of fibre coupledcompact solar collectorsrdquo Lighting Research and Technology vol39 no 1 pp 17ndash30 2007

[9] C Ciamberlini F Francini G Longobardi M Piattelli and PSansoni ldquoSolar system for exploitation of the whole collectedenergyrdquoOptics and Lasers in Engineering vol 39 no 2 pp 233ndash246 2003

[10] P Maddalena A Parretta A Sarno and P Tortora ldquoNoveltechniques for the optical characterization of photovoltaicmaterials and devicesrdquoOptics and Lasers in Engineering vol 39no 2 pp 165ndash177 2003

[11] A Parretta P Grillo P Maddalena and P Tortora ldquoMethodformeasurement of the directionalhemispherical reflectance ofphotovoltaic devicesrdquo Optics Communications vol 186 no 1ndash3pp 1ndash14 2000

[12] P Horta M J Carvalho M C Pereira andW Carbajal ldquoLong-term performance calculations based on steady-state efficiencytest results analysis of optical effects affecting beam diffuse andreflected radiationrdquo Solar Energy vol 82 no 11 pp 1076ndash10822008

[13] D L Fain ldquoDesign considerations for precision solar simula-tionrdquo Applied Optics vol 3 no 12 pp 1389ndash1396 1964

[14] I Powell ldquoNew concept for a system suitable for solar simula-tionrdquo Applied Optics vol 19 no 2 pp 329ndash334 1980

[15] C Domınguez I Anton and G Sala ldquoConcentrator photo-voltaics solar simulatorrdquo in Frontiers in Optics p JThA1 OpticalSociety of America Rochester NY USA 2008

[16] J L Balenzategui and F Chenlo ldquoMeasurement and analysis ofangular response of bare and encapsulated silicon solar cellsrdquoSolar Energy Materials and Solar Cells vol 86 no 1 pp 53ndash832005

[17] D C Miller and S R Kurtz ldquoDurability of Fresnel lenses areview specific to the concentrating photovoltaic applicationrdquo

Solar Energy Materials and Solar Cells vol 95 no 8 pp 2037ndash2068 2011

[18] H Zhai Y J Dai J Y Wu R Z Wang and L Y ZhangldquoExperimental investigation and analysis on a concentratingsolar collector using linear Fresnel lensrdquo Energy Conversion andManagement vol 51 no 1 pp 48ndash55 2010

[19] D Jing H Liu X Zhang L Zhao and L Guo ldquoPhotocatalytichydrogen production under direct solar light in a CPC basedsolar reactor reactor design and preliminary resultsrdquo EnergyConversion and Management vol 50 no 12 pp 2919ndash29262009

[20] W T Xie Y J Dai and R Z Wang ldquoNumerical and exper-imental analysis of a point focus solar collector using highconcentration imaging PMMAFresnel lensrdquo Energy Conversionand Management vol 52 no 6 pp 2417ndash2426 2011

[21] B Perers ldquoAn improved dynamic solar collector test method fordetermination of non-linear optical and thermal characteristicswithmultiple regressionrdquo Solar Energy vol 59 no 4ndash6 pp 163ndash178 1997

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

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International Journal ofPhotoenergy


Carbohydrate Chemistry

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Journal of

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Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

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Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


Photodetector

Sample

Collimation lens

S

Source

Integrating sphere

Figure 1 Scheme of collimator S1 (for image tests and focused imagemeas on small components)

cells without collection optical system In principle a solarsimulator is a device that can reproduce on limited areas theconditions of solar irradiation with specific spectral charac-teristics and irradiance uniformity The solar simulators onthe market perform a quite good reproduction of spectraldistribution and intensity of the solar emission up to 200x forcontinuous light and up to 5000x for pulsed light The maindrawback of these solar simulators is that the output light hasa divergence larger than the solar one semi-angle divergenceof few degrees while the solar value is around 025∘ Themost sophisticated so very expensive device present on themarket can produce a collimated beam with divergence half-angle 24∘ and diameter 610158401015840or divergence half-angle 12∘ anddiameter 1210158401015840

Image light distribution is another crucial aspect thatmust be taken into account especially for the experimen-tation on concentrating photovoltaic components In orderto minimise the thermal stresses and to maximise the con-version efficiency the CPV cells require adequate irradianceuniformity over the cell surface

This paper proposes a solar divergence collimator ableto exactly reproduce the solar divergence and to provide anextremely uniform beam Our solar divergence collimatoris applied to test solar components in a laboratory set-up whose main advantages are flexibility and versatility Apossible engineering of our test system to obtain a closedand fixed instrument would lose its ability to adapt the teststo specific requirements of the solar application or particularcharacteristics of the examined sample

2 Solar Divergence Collimators

The optical collimator reproducing the solar divergencerepresents the core of every laboratory set-up employed tocharacterize solar components The principal layouts for ouroptical tests are presented in Figures 1 2 3 and 4The sourceis always realized by a white light illuminator coupled by anoptical fibre to an integrating sphere The solar divergence isaccurately reproduced combining the sphere output diameterS to the focal distance 119891

119862of the collimation optics which can

be a lens or a mirrorThe solar divergence collimator can be realized in axis

(S1-S2) if the examined collectors have reduced dimensionsCollimator S1-S2 is presented in Figures 1 and 2 showingthe two optical configurations used for image tests andcollection efficiency assessmentThe setup of S1-S2 includes acollimation lens with focal length119891

119862= 700mmand diameter

119889119862= 90mm

Photodetector

MaskCollimationS

Source

Integrating sphere

Mirror

lens

Figure 2 Scheme of collimator S2 (for entering light measurementon small components)

For practical reasons the test of solar collectors withdiameter exceeding 80mm is realized employing the solardivergence collimator L1-L2 in Figures 3 and 4 To clarifythe schemes in Figures 3 and 4 the values of 119891

119862and

119889119862do not respect the real proportions whereas they are

correctly proportioned in Figures 1 and 2 Collimator L1-L2 has two spherical mirrors with 119891

119862= 1500mm and

119889119862= 250mm The first acts as collimation mirror while the

second is a concentrating mirror (indicated as ldquoMirrorrdquo inS2 Figure 2 and L2 Figure 4) In collimator L1-L2 the opticalaxis is deflected once (L1 Figure 3) or twice (L2 Figure 4)over the measurement plane The bent configuration of L1-L2 introduces some optical errors and aberrations on thecollimated beam

The verification of the solar divergence reproduction canbe preliminary performed comparing the obtained beamdiameter with the expected value In practice we realise areference target a circle with the exact beam dimensions atthe distance of the concentrating mirror (ldquoMirrorrdquo in Figures4 and 2) The reference target is placed at this distance onthe beam axis The set-up L2 (or S2) projects a beam on itwhich should correspond to the target circle A more precisecontrol of beamproperties and solar divergence reproductionis represented by the beam measurements described inSection 4

Concerning the optical quality of the beams it is impor-tant to remark that the optical layout of S1-S2 is bent oncein Figure 2 but the measured quantity is the entering lightwhich is filtered (by the mask) in the axial collimator Thenthe mirror bending the optical axis concentrates the lightover the photodetector In collimator L1-L2 the collimationmirror deflects the optical axis realizing a bent collimatorwith two axes forming an angle 120572 Then the concentratingmirror focuses the light on the sensor introducing a seconddeflection of the optical axis (Figure 4) The crucial bend isthe first one since it affects the quality of the collimated beamwith solar divergence Moreover the use of an integrationsphere and the precision in realizing its aperture S representtwo other sources of optical errors

3 Aberrations of Collimated Beams

The collimators under study are of two types S1-S2 containsa collimation lens while L1-L2 has a collimation mirror ina bent configuration Both collimators generate a series of



S

Source

Integrating sphere

mirror

Sample


Photodetector

Mask

Collimation

SSource

Integrating sphere

mirror

Mirror





The 119862119885



119885coefficients








0

005

01

015

02

025

03

035

04

50 100 150 200 250

Beam diameter (mm)


5 deg

15 deg

25 deg

(a)

50 100 150 200 250

Beam diameter (mm)

Coma

5 deg

15 deg

25 deg

minus 8

minus 7

minus 6

minus 5

minus 4

minus 3

minus 2

minus 1

0

(b)

0

10

20

30

40

50

60

70

80

90

50 100 150 200 250

Beam diameter (mm)

Astigmatism

5 deg

15 deg

25 deg

minus 10

(c)

0

50 100 150 200 250

Beam diameter (mm)

Field curvature

5 deg

15 deg

25 deg

minus 08

minus 07

minus 06

minus 05

minus 04

minus 03

minus 02

minus 01

(d)









0

50

100

150

200

250

300

0 02 04 06 08 1 12 14

Imag

e p

rofi

le (

au

)



0∘

15∘20∘

25∘

(a)

0

50

100

150

200

250

300

0 02 04 06 08 1 12 14

Imag

e p

rofi

le (

au

)



0∘

15∘20∘

25∘

(b)


0

50

100

150

200

250

300

0 05 1

Imag

e p

rofi

le (

au

)


Real lens

Ideal lens

minus 1 minus 05










(a)

(b)




119862700mm in S1




(a)

(b)







0

500

1000

1500

2000

2500

3000

300 600 900 1200 1500 1800

Wavelength (nm)


KL1500 illuminator

Spec

tral

irr

adia

nce

(W

m2)

Sun (air mass = 1)



Optical fiber

Integrating sphere

Mirror

Sensor

Light source

Translation stage
















Optical fiber

Integrating sphere

Mirror 1

Mirror 2

Mask

Sensor

Light source














07

075

08

085

09

095

1

1 11 12 13 14 15 16 17 18 19 2 21

Enci

rcle

d im

age l

ight

()

Hole diameter (mm)

EstimationDetection




9 Conclusions







Acknowledgment




References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



S

Source

Integrating sphere

mirror

Sample


Photodetector

Mask

Collimation

SSource

Integrating sphere

mirror

Mirror





The 119862119885



119885coefficients








0

005

01

015

02

025

03

035

04

50 100 150 200 250

Beam diameter (mm)


5 deg

15 deg

25 deg

(a)

50 100 150 200 250

Beam diameter (mm)

Coma

5 deg

15 deg

25 deg

minus 8

minus 7

minus 6

minus 5

minus 4

minus 3

minus 2

minus 1

0

(b)

0

10

20

30

40

50

60

70

80

90

50 100 150 200 250

Beam diameter (mm)

Astigmatism

5 deg

15 deg

25 deg

minus 10

(c)

0

50 100 150 200 250

Beam diameter (mm)

Field curvature

5 deg

15 deg

25 deg

minus 08

minus 07

minus 06

minus 05

minus 04

minus 03

minus 02

minus 01

(d)









0

50

100

150

200

250

300

0 02 04 06 08 1 12 14

Imag

e p

rofi

le (

au

)



0∘

15∘20∘

25∘

(a)

0

50

100

150

200

250

300

0 02 04 06 08 1 12 14

Imag

e p

rofi

le (

au

)



0∘

15∘20∘

25∘

(b)


0

50

100

150

200

250

300

0 05 1

Imag

e p

rofi

le (

au

)


Real lens

Ideal lens

minus 1 minus 05










(a)

(b)




119862700mm in S1




(a)

(b)







0

500

1000

1500

2000

2500

3000

300 600 900 1200 1500 1800

Wavelength (nm)


KL1500 illuminator

Spec

tral

irr

adia

nce

(W

m2)

Sun (air mass = 1)



Optical fiber

Integrating sphere

Mirror

Sensor

Light source

Translation stage
















Optical fiber

Integrating sphere

Mirror 1

Mirror 2

Mask

Sensor

Light source














07

075

08

085

09

095

1

1 11 12 13 14 15 16 17 18 19 2 21

Enci

rcle

d im

age l

ight

()

Hole diameter (mm)

EstimationDetection




9 Conclusions







Acknowledgment




References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0

005

01

015

02

025

03

035

04

50 100 150 200 250

Beam diameter (mm)


5 deg

15 deg

25 deg

(a)

50 100 150 200 250

Beam diameter (mm)

Coma

5 deg

15 deg

25 deg

minus 8

minus 7

minus 6

minus 5

minus 4

minus 3

minus 2

minus 1

0

(b)

0

10

20

30

40

50

60

70

80

90

50 100 150 200 250

Beam diameter (mm)

Astigmatism

5 deg

15 deg

25 deg

minus 10

(c)

0

50 100 150 200 250

Beam diameter (mm)

Field curvature

5 deg

15 deg

25 deg

minus 08

minus 07

minus 06

minus 05

minus 04

minus 03

minus 02

minus 01

(d)









0

50

100

150

200

250

300

0 02 04 06 08 1 12 14

Imag

e p

rofi

le (

au

)



0∘

15∘20∘

25∘

(a)

0

50

100

150

200

250

300

0 02 04 06 08 1 12 14

Imag

e p

rofi

le (

au

)



0∘

15∘20∘

25∘

(b)


0

50

100

150

200

250

300

0 05 1

Imag

e p

rofi

le (

au

)


Real lens

Ideal lens

minus 1 minus 05










(a)

(b)




119862700mm in S1




(a)

(b)







0

500

1000

1500

2000

2500

3000

300 600 900 1200 1500 1800

Wavelength (nm)


KL1500 illuminator

Spec

tral

irr

adia

nce

(W

m2)

Sun (air mass = 1)



Optical fiber

Integrating sphere

Mirror

Sensor

Light source

Translation stage
















Optical fiber

Integrating sphere

Mirror 1

Mirror 2

Mask

Sensor

Light source














07

075

08

085

09

095

1

1 11 12 13 14 15 16 17 18 19 2 21

Enci

rcle

d im

age l

ight

()

Hole diameter (mm)

EstimationDetection




9 Conclusions







Acknowledgment




References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0

50

100

150

200

250

300

0 02 04 06 08 1 12 14

Imag

e p

rofi

le (

au

)



0∘

15∘20∘

25∘

(a)

0

50

100

150

200

250

300

0 02 04 06 08 1 12 14

Imag

e p

rofi

le (

au

)



0∘

15∘20∘

25∘

(b)


0

50

100

150

200

250

300

0 05 1

Imag

e p

rofi

le (

au

)


Real lens

Ideal lens

minus 1 minus 05










(a)

(b)




119862700mm in S1




(a)

(b)







0

500

1000

1500

2000

2500

3000

300 600 900 1200 1500 1800

Wavelength (nm)


KL1500 illuminator

Spec

tral

irr

adia

nce

(W

m2)

Sun (air mass = 1)



Optical fiber

Integrating sphere

Mirror

Sensor

Light source

Translation stage
















Optical fiber

Integrating sphere

Mirror 1

Mirror 2

Mask

Sensor

Light source














07

075

08

085

09

095

1

1 11 12 13 14 15 16 17 18 19 2 21

Enci

rcle

d im

age l

ight

()

Hole diameter (mm)

EstimationDetection




9 Conclusions







Acknowledgment




References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


(a)

(b)




119862700mm in S1




(a)

(b)







0

500

1000

1500

2000

2500

3000

300 600 900 1200 1500 1800

Wavelength (nm)


KL1500 illuminator

Spec

tral

irr

adia

nce

(W

m2)

Sun (air mass = 1)



Optical fiber

Integrating sphere

Mirror

Sensor

Light source

Translation stage
















Optical fiber

Integrating sphere

Mirror 1

Mirror 2

Mask

Sensor

Light source














07

075

08

085

09

095

1

1 11 12 13 14 15 16 17 18 19 2 21

Enci

rcle

d im

age l

ight

()

Hole diameter (mm)

EstimationDetection




9 Conclusions







Acknowledgment




References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0

500

1000

1500

2000

2500

3000

300 600 900 1200 1500 1800

Wavelength (nm)


KL1500 illuminator

Spec

tral

irr

adia

nce

(W

m2)

Sun (air mass = 1)



Optical fiber

Integrating sphere

Mirror

Sensor

Light source

Translation stage
















Optical fiber

Integrating sphere

Mirror 1

Mirror 2

Mask

Sensor

Light source














07

075

08

085

09

095

1

1 11 12 13 14 15 16 17 18 19 2 21

Enci

rcle

d im

age l

ight

()

Hole diameter (mm)

EstimationDetection




9 Conclusions







Acknowledgment




References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Optical fiber

Integrating sphere

Mirror 1

Mirror 2

Mask

Sensor

Light source














07

075

08

085

09

095

1

1 11 12 13 14 15 16 17 18 19 2 21

Enci

rcle

d im

age l

ight

()

Hole diameter (mm)

EstimationDetection




9 Conclusions







Acknowledgment




References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



07

075

08

085

09

095

1

1 11 12 13 14 15 16 17 18 19 2 21

Enci

rcle

d im

age l

ight

()

Hole diameter (mm)

EstimationDetection




9 Conclusions







Acknowledgment




References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of










Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

research article solar divergence collimators for optical...

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