ECE/SAE Dual Functional Superpin Plus Curved Reflex Reflector By

applied sciences

Article ECE/SAE Dual Functional SuperPin Plus Curved Reﬂex Reﬂector by Use of New Structured Corner Cubes

Hien-Thanh Le 1,2, Lanh-Thanh Le 1,2, Ming-Jui Chen 1, Thanh-Hong Lam 3, Hsing-Yuan Liao 1, Guo-Feng Luo 1, Yung-Cheng Li 4 and Hsiao-Yi Lee 1,5,*

1 Department of Electrical Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 80778, Taiwan; [email protected] (H.-T.L.); [email protected] (L.-T.L.); [email protected] (M.-J.C.); [email protected] (H.-Y.L.); [email protected] (G.-F.L.) 2 Department of Technology, Dong Nai Technology University, Bien Hoa 810000, Dong Nai, Viet Nam 3 Department of Computer Science, Vietnamese-German University, Thu Dau Mot 820000, Binh Duong, Viet Nam; [email protected] 4 Department of Materials Science and Engineering, National Tsing Hua University, No. 101, Section 2, Kuang-Fu Road, Hsinchu 30013, Taiwan; [email protected] 5 Department of Graduate Institute of Clinical Medicine, Kaohsiung Medical University, Kaohsiung 807, Taiwan * Correspondence: [email protected]

Received: 31 October 2019; Accepted: 2 January 2020; Published: 8 January 2020

Abstract: We propose and demonstrate, using optical experiments, a new reflex reflector structure called SuperPin Plus. The structure is composed of special pin groups with dihedral-angle offsets in corner cubes. One of the specular features brought by this new design is that it can comply with both the US SAE (US Society of Automotive Engineers) standard and the EU ECE (Economic Commission for Europe) standard, so that manufacturing costs of reflex reflector for both European and American automobile markets can be reduced. By using genetic algorithms for optimization, the angles and the positions of the pins, which are the building elements of corner cube reflectors, serve as the parameters to tune up the performance of the SuperPin Plus curved reflex reflector. Compared with conventional ECE flat regular retro-reflectors, we found that not only can we achieve a 41% higher retro-reflection efficiency with the ECE SuperPin Plus flat reflex reflector, but that SuperPin Plus can also act as a reflex reflector within SAE standards. In addition, we demonstrate that the retro-reflection efficiency is 30.5% higher (SAE standard) and 42.7% higher (ECE standard), and that a 32% increase in working area can be achieved if double pin groups are used to construct the corner cubes instead of a single pin arrangement, in a curved SuperPin Plus reflex reflector.

Keywords: optics design; double pins with corner cubes; SuperPin Plus curved retro-reﬂector; EU ECE regulations (Economic Commission for Europe); US SAE regulation (US Society of Automotive Engineers)

1. Introduction A reflex reflector is an optical device that allows light to be reflected in a direction that is parallel to that of the source [1–3]. The corner cube array is the typically used structure and such an array can be built up through pin grouping to generate the expected retro-reflected light [4–6]. Reflex reflectors on cars or signage can increase visibility in the dark for safety [7,8], so they have been applied extensively in vehicle applications [9]. Due to their high tolerance to the direction of incident waves [10–12] retroreflectors have been used extensively in many applications instead of

Appl. Sci. 2020, 10, 454; doi:10.3390/app10020454 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 of 15

extensively in vehicle applications [9]. Due to their high tolerance to the direction of incident waves Appl.[10–12] Sci. 2020retroreflectors, 10, 454 have been used extensively in many applications instead of plane mirrors2 [13]. of 16 For instance, regular reflex reflectors [14–16], as shown in Figure 1a, can diverge the reflected energy planeinto multiple mirrors light [13]. beams For instance, with equal regular emitting reflex reflectorsangle intervals [14–16 [17–19],], as shown and inthese Figure are1 currentlya, can diverge the most the reflectedcommonly energy used intoretro-reflecting multiple light devices beams for with vehicles equal [2 emitting0,21]. In angle contrast intervals to regular [17–19 reflex], and reflectors, these are currentlySuperPin thereflex most reflectors commonly not only used reflect retro-reflecting light beams devices but also for vehiclesconcentrate [20, 21them]. In to contrast amplify to the regular light reflexintensity reflectors, of signals SuperPin for observers, reflex reflectors as shown not in only Figure reflect 1b [22]. light Owing beams butto the also highly concentrate effective them retro- to amplifyreflection the ability, light intensitySuperPin of retro-reflectors signals for observers, have been as shown replacing in Figure regular1b[ retroreflectors22]. Owing to thein vehicle highly eapplicationffective retro-reflection markets [17,21,23]. ability, SuperPin retro-reflectors have been replacing regular retroreflectors in vehicleAccording application to regulations markets [17 ,of21 ,the23]. US Society of Automotive Engineers (SAE) and EU Economic CommissionAccording for toEurope regulations (ECE), ofreflex the USreflectors Society for of vehi Automotivecles need to Engineers return light (SAE) to an and observer EU Economic located Commissionat 0.2 degrees for (SAE Europe regulations) (ECE), reflex and reflectors 0.33 degrees for vehicles (ECE needregulations) to return above light tothe an light observer source located [23], atrespectively. 0.2 degrees Therefore, (SAE regulations) corner cube and arrays 0.33 composed degrees (ECE of pins regulations) need to be designed above the and light produced source with [23], respectively.different specification Therefore, for corner the cuberequirements arrays composed of ECE and of pins SAE need reflex to bereflectors, designed respectively. and produced In with this dipaper,fferent a specificationnew reflex reflector for the requirementsstructure called of ECESuperP andin SAE Plus reflex is proposed reflectors, for respectively. fitting both Inthe this ECE paper, and aSAE new regulations, reflex reflector shown structure in Figure called 1c. SuperPin SuperPin Plus’s Plus isprinciple proposed is based for fitting on the both structure the ECE of SuperPin and SAE regulations,[24], which was shown developed in Figure by1c. the SuperPin difference Plus’s in the principle value of is dihedral based on angle. the structure of SuperPin [ 24], whichThe was reflex developed reflector by can the switch difference its function in the value from of ECE dihedral to SAE angle. or SAE to ECE just by rotating pins groupThe 45° reflex in structure, reflector so can one switch type itsof pin function is enou fromgh to ECE handle to SAE the or production SAE to ECE of justECE by and rotating SAE reflex pins reflectors. Flat SuperPin Plus reflex reflectors and curved SuperPin Plus reflex reflectors with the new group 45◦ in structure, so one type of pin is enough to handle the production of ECE and SAE reflex reflectors.corner cube Flat structure SuperPin Plusare proposed reflex reflectors and anddemons curvedtrated SuperPin to meet Plus the reflex ECE/SAE reflectors dual with function the new cornerrequirements cube structure through are experiments. proposed and By demonstrated using genetic to algorithms meet the ECE for /optimization,SAE dual function we use requirements the angles throughand the experiments.positions of Bythe using pins genetic serving algorithms as the buildi for optimization,ng elements we of usecorner the anglescube andreflectors the positions as the ofparameters the pins servingto enhance as the the building performa elementsnce of the of SuperPin corner cube Plus reflectors curved reflex as the reflector. parameters Compared to enhance with theconventional performance regular of the retro-reflectors, SuperPin Plus curvedit is foun reflexd that reflector. not only Compared can 41% with higher conventional retro-reflection regular retro-reflectors,efficiency be achieved it is found with thatthe ECE not onlySuperPin can 41% Plus higher flat reflex retro-reflection reflector, but e ffitheciency SuperPin be achieved Plus can with also theact as ECE a SAE SuperPin reflex Plusreflector. flat reflex It is shown reflector, that but a 32 the% SuperPin larger working Plus can area also can act be as achieved a SAE reflex if double reflector. pin Itgroups is shown are thatused a to 32% construct larger workingcorner cubes area instead can be achievedof the single if double pin arrangement pin groups arein a usedcurved to constructSuperPin cornerPlus reflex cubes reflector. instead of the single pin arrangement in a curved SuperPin Plus reflex reflector.

(a) (b)

Figure 1. Cont. Appl. Sci. 2020, 10, 454 3 of 16 Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 15

(c)

FigureFigure 1.1.The The formulaformula ofof retro-reflectedretro-reflected lightlight byby ((aa)) thethe EUEU EconomicEconomic CommissionCommission forfor EuropeEurope (ECE)(ECE) regularregular inin ([([16],16], FigureFigure1 ),1), ( (bb)) the the ECE ECE SuperPin SuperPin inin ([([24],24], Figure Figure1 ),1), and and ( c(c)) the the ECE ECE and and US US Society Society ofof AutomotiveAutomotive Engineers Engineers (SAE) (SAE) SuperPin SuperPin Plus Plus reflex reflex reflector, reflector, an an extension extension of of SuperPin SuperPin [24 [24].].

AccodingAccoding toto thethe standardsstandards ofof SAESAE andand ECE,ECE, thethe coecoefficientfficient ofof luminous luminous intensityintensityR RI I shouldshould bebe higherhigher thanthan thethe thresholdthreshold valuesvalues withinwithin thethe 2020°◦ angle angle ofof lightlight incidenceincidence [23[23–25].–25]. TheThe vehiclevehicle signagesignage performanceperformance RRII isis evaluated evaluated by by the the ratio ratio of of the the strength strength of ofthe the reflected reflected light light ϕRLIφ (retro-reflectedRLI (retro-reflected light lightintensity) intensity) to the to amount the amount of light of light that that falls falls on onthe the retro-reflector retro-reflector ϕILIφ ILI(incident(incident light light illuminance), illuminance), as asshown shown in inFigure Figure 1.1 Th. Thee minimum minimum coefficients coe fficients of ofluminous luminous intensity intensity RI RrequiementI requiement for forEU EU ECE ECE or US or USSAE SAE standards standards are are shown shown in inTable Table 1.1 .RRA Ais isthe the measure measure of of retro-reflection retro-reflection efficiency, efficiency, defineddefined asas thethe ratioratio ofof thethe fluxflux of of incident incident light lightφ ϕ11 toto thethe totaltotal fluxflux ofof the the reflected reflected cone coneφ ϕ22 [[18,23].18,23]. Consequently,Consequently, vehiclevehicle signagesignage wouldwould bebe observedobserved toto bebe brighterbrighter asas itsitsR RII valuevalue increasesincreases [[23].23]. ItIt isis usualusual forfor reflexreflex reflectorsreflectors toto havehave aa curvedcurved shape;shape; forfor example,example, toto fitfitthe the corner corner of of a a vehicle vehicle [ 1[1–5,18].–5,18]. CornerCorner cubecube structuresstructures areare thusthus distorteddistorted toto completecomplete thethe curve,curve, soso thatthat theirtheir activeactive workingworking areaarea andand reflectionreflection eefficiencyfficiency areare a affected,ffected, thus thus leading leading to to a a retro-reflector retro-reflector that that is is against against regulations regulations [19 [19,25].,25].

TableTable 1.1. MinimumMinimum mcdmcd (millicandela)(millicandela)/incident/incident luxlux forfor aa whitewhite reﬂexreflex reﬂector. reflector.

MinimumMinimum Coeﬃ Coefficientcient of Luminous of Luminous Intensity Intensity RI RI RegulationRegulationObservation Observation (Mcd(Mcd/Incident/Incident Lux) Lux) RequirementRequirement Angle (◦Angle) (°) EntranceEntrance Angle Angle (◦) (°) 0 10 Up 10 Down 20 Left 20 Right ◦ 0° ◦ 10° Up ◦ 10° Down ◦ 20° Left 20°◦ Right SAE 0.2 1680 1120 1120 560 560 ECESAE 0.330.2 16801680 1120 1120 11201120 560560 560560 ECE 0.33 1680 1120 1120 560 560

2.2. PrinciplesPrinciples AA cornercorner cube cube retro-reflector retro-reflector (CCR) (CCR) is is based based on on groups groups of of three three perpendicular perpendicular planes, planes, as shownas shown in Figurein Figure2. Conventionally, 2. Conventionally, the dihedralthe dihedral angle angle between betwee anyn pairany pair of reflecting of reflecting faces faces is made is made to be to 90 be◦ [90°1], so[1], that so thethat reflected the reflected beam beam is exactly is exactly contradictory contradi directionalctory directional to the incidentto the incident beam [ 13beam]. If the[13]. angles If the dianglesffer from differ 90 ◦fromby a 90° specific by a amount,specific amount, the reflected the reflected beam will beam be converged will be converged or diverged or indiverged multiple in beamsmultiple to achievebeams to the achieve required the application required application [1]. We can [1]. move We the can three move retro-reflected the three retro-reflected rays on the top rays into on onethe directiontop into andone thedirection other threeand the into other another three direction into another by using direction the different by using angles the between different each angles pair ofbetween facets. Ineach this pair way, of thefacets. optical In this performance way, the optica of a cornerl performance cube can of be a corner improved cube as can the be retro-reflected improved as energythe retro-reflected in a given direction energy in is tripled;a given thisdirection is called is tripled; superpin this technology is called [superpin24]. The superpintechnology technology [24]. The issuperpin characterized technology by the uniqueis characterized structure ofby cornerthe uniq cubesue tostructure concentrate of corner the retroreflected cubes to concentrate light into two the zonesretroreflected insteads light of six into zones, two shown zones in insteads Figure2 ofc. Thesix zones, SuperPin shown Plus in structure Figure was2c. The developed SuperPin based Plus structure was developed based on the superpin technology with the same specification of the pins. Appl. Sci. Sci. 20202020,, 1010,, x 454 FOR PEER REVIEW 4 of 15 16

The experiment beam pattern retro-reflected from the superpin plus corner is shown in the next section.on the superpin technology with the same speciﬁcation of the pins. The experiment beam pattern retro-reﬂectedAppl. Sci. 2020, 10 from, x FOR the PEER superpin REVIEWplus corner is shown in the next section. 4 of 15

The experiment beam pattern retro-reflected from the superpin plus corner is shown in the next section.

(a) (b) (c)

Figure 2. ((aa)) A A 3D 3D design design of of flat flat corner corner cube cube SuperPin SuperPin Plus Plus retro-reflector; retro-reflector; ( (b)) a a group group of pins and its reflecting surfaces (blue line inner region); and (c) SuperPin retroreflected light pattern [24]. reflecting surfaces(a) (blue line inner region); and ((cb)) SuperPin retroreflected light pattern(c) [24].

ThroughFigure 2. an (a )array A 3D designof pins, of flatcorner corner corner cube cube cube retro-refl retro-reflectorsSuperPin ectorsPlus retro-reflector; can can be be produced, produced, (b) a group as as ofshown shown pins and in in itsFigure Figure 22.. The direction reflecting of surfaces the reflectedreflected (blue line rays inner after region); the reflectionsreflections and (c) SuperPin areare givengiven retroreflected byby Chandler’sChandler’s light pattern formula:formula: [24].

Through an array of pins, corner𝑡⃗ cube= 𝑞⃗ +retro-refl 2𝑎⃗(α𝑎⃗ −ectors β𝑏⃗ + canγ𝑐⃗) be produced, as shown in Figure 2.(1) →t = →q + 2→a (α→a β→b + γ→c ) (1) The direction of the reflected rays after the reflections are given by Chandler’s formula: where 𝑡⃗ is the final direction; 𝑞⃗ is the original direction;− α, β, and γ are the small angles, by which ⃗ thewhere angles→t is between the final direction;the three →qmirrorsis the originalexceed𝑡⃗ = 𝑞⃗ + direction;right2𝑎⃗(α𝑎 ⃗angles; − β𝑏α ,+β andγ,𝑐 and⃗) 𝑎⃗γ, 𝑏are⃗, and the small𝑐⃗ are angles,normal byto whichthe(1) three the mirrors taken in the order in a right-hand sense. The unit normals to the faces can be computed as angleswhere between 𝑡⃗ is the the final three direction; mirrors 𝑞⃗exceed is the original right angles; direction; and →αa,, β→b, ,and and γ→c areare the normal small toangles, the three by which mirrors follows, as shown in Figure 3. Let the normals to the faces without dihedral-angle offsets be the unit takenthe angles in the orderbetween in athe right-hand three mirrors sense. exceed The unitright normalsangles; and to the 𝑎⃗, faces𝑏⃗, and can 𝑐⃗ are be computednormal to the as follows,three vectors 𝚤̂, 𝚥̂, and 𝑘 along the three coordinates x, y, and z, respectively. If the angle between the zx asmirrors shown intaken Figure in 3the. Let order the normalsin a right-hand to the facessense. without The unit dihedral-angle normals to the o facesffsets can be thebe unitcomputed vectors asiˆ , jˆ, plane, and the zy plane is α = (π/2) + δ1, the xz plane and the xy plane is β = (π/2) + δ2, the yz plane andfollows,kˆ along as the shown three in coordinates Figure 3. Let x, the y, and normals z, respectively. to the faces If without the angle dihedral-angle between the zxoffsets plane, be andthe unit the zy andvectors the yx 𝚤 planê, 𝚥̂, and is γ𝑘 = along (π/2) the + δ three3, shown coordinates in Figure x, 3b;y, and this z, can respectively. be expressed If the by angle Equations between (2)–(4), the zx plane is α = (π/2) + δ1, the xz plane and the xy plane is β = (π/2) + δ2, the yz plane and the yx plane is γ plane,π andδ the zy plane is α = (π/2) + δ1, the xz plane and the xy plane is β = (π/2) + δ2, the yz plane = ( /2) + 3, shown in Figure3b;n this= ı ̂ can+ be ȷ ̂ expressed; 𝑛 = 𝚥̂ + by 𝚤 Equationŝ ; 𝑛 = 𝑘 (2)–(4), (2) and the yx plane is γ = (π/2) + δ3, shown in Figure 3b; this can be expressed by Equations (2)–(4), δ δ n = ı ̂ + 1ȷ ̂ ; 𝑛 = 𝚥̂ + 1 𝚤̂ ; 𝑛 =ˆ 𝑘 (3) nnˆ == ı ̂î++ ȷ ̂ˆj;; n𝑛ˆ2 == 𝚥jˆ̂ ++ 𝚤iˆ̂ ;;n ˆ3𝑛= =k 𝑘 (2) (2) 1 2 2 nn == ı ̂ı ̂ ++ ȷȷ ̂ ̂ ;; 𝑛𝑛 = 𝚥̂ ̂ + 𝚤𝚤̂ ̂ ;; 𝑛𝑛 == 𝑘𝑘 (3)(4) δ2 δ2 nˆ1 = î + ˆj; nˆ2 = jˆ+ iˆ; nˆ3 = kˆ (3) 2 2 n = ı ̂ + ȷ ̂ ; 𝑛 = 𝚥̂ + 𝚤̂ ; 𝑛 = 𝑘 (4) δ δ nˆ = î + 3 ˆj; nˆ = jˆ+ 3 iˆ; nˆ = kˆ (4) 1 2 2 2 3

(a) (b) (c)

Figure 3. (a) The(a )dihedral-angle offsets; (b) the angle(b) between each plane; and (c) the(c) symmetry axis direction.FigureFigure 3. 3.( a(a)) TheThe dihedral-angledihedral-angle offsets; oﬀsets; (b ()b the) the angle angle between between each each plane; plane; and (c and) the ( csymmetry) the symmetry axis axisdirection. direction. The retro-reflected beam spread angle at normal beam incidence when all dihedral angles are offset byThe the retro-reflected same amount beam is given spread by theangle formulas at normal (5)–(7), beam incidence when all dihedral angles are offset by the same amount is given by the formulas (5)–(7), Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 16

ε1 = 4/3 √6 n δ1 (5)

ε2 = 4/3 √6 n δ2 (6)

ε3 = 4/3 √6 n δ3 (7) where δ is the dihedral angles of corner cubes and ε is the angle between the incident ray and the reflected rays, thus there will be several retro-reflected rays generated, once one ray is incident on CCR. The direction of the incident beam is determined by θ′ and ϕ′ in the primed coordinate system. By adjusting the angles between each pair of facets, we can set the six retro-reflected rays with equal angle intervals or let them propagate in almost contradictory directions, such as the simulation results performed by regular, SuperPin, and SuperPin Plus retro-reflectors, as shown in Figure 4a–c.

(α = β = γ = 90.09°) (α = β = 90.01°< γ = 90.12°) (α = β = 90.012°>γ = 90.01°) Appl. Sci. 2020, 10, 454 5 of 16

The retro-reﬂected beam spread angle at normal beam incidence when all dihedral angles are oﬀset by the same amount is given by the formulas (5)–(7),

ε1 = 4/3 √6 n δ1 (5)

ε2 = 4/3 √6 n δ2 (6)

ε3 = 4/3 √6 n δ3 (7) where δ is the dihedral angles of corner cubes and ε is the angle between the incident ray and the

reflected rays, thus there will be several retro-reflected rays generated, once one ray is incident on (a) (b) (c) CCR. The direction of the incident beam is determined by θ0 and φ0 in the primed coordinate system. ByFigure adjusting 4. Relationship the angles between between dihedral each pairangles of and facets, the wereflected can set beam the sixdirection. retro-reflected (a) The reflected rays with equal angleintensity intervals distribution or let by them a regular propagate retro-reflector. in almost (b) contradictory The reflected intensity directions, distribution such as by the a simulationSuperPin results performedretro-reflector. by ( regular,c) The reflected SuperPin, intensity and SuperPindistribution Plus by a retro-reflectors, SuperPin Plus retro-reflector. as shown in Figure4a–c.

Figure 4. Relationship between dihedral angles and the reflected beam direction. (a) The reflected Afterintensity analyzing distribution the values by aof regular the angles retro-reflector. α, β, and ( bγ), Thewe concluded reflected intensity the influence distribution of incident by a SuperPin angle on the valueretro-reflector. and position (c) The of reflectedthe reflected intensity beams. distribution In case by 1: aα SuperPin = β = γ, Plusthe retro-reflector.reflected beam is divided into six small beams that are symmetrical with each other in a circle, known as regular structure, shown inAfter Figure analyzing 4a. In case the 2: values α = β < of γ the, the angles reflectedα, β beams, and γ converged, we concluded into two the influencesymmetric of groups incident on angle the topon theand value bottom and (three position beams of the on reflected the top and beams. three In beams case 1: onα = theβ =bottom),γ, the reflected known beamas the isSuperPin divided into structure,six small shown beams in Figure that are 4b. symmetrical In case 3: α with = β > each γ, the other reflected in a circle, beams known converged as regular to four structure, beams at shown the in top andFigure bottom4a. In positions case 2: α (two= β beams< γ, the on reflected the top an beamsd two converged beams on intothe bottom) two symmetric and two groups beams onat the the top left andand right bottom locations (three beams(one beam on the on top the and left threeand one beams beam on on the the bottom), right), known asas thethe SuperPinSuperPin structure,Plus shown in Figure4b. In case 3: α = β > γ, the reflected beams converged to four beams at the top and bottom positions (two beams on the top and two beams on the bottom) and two beams at the left and right locations (one beam on the left and one beam on the right), known as the SuperPin Plus structure, shown in Figure4c. The SuperPin Plus structure, which is accomplished by our proposal, will reduce manufacturing costs as well as be more advantageous as it can be used in both the European and American markets. When the dihedral angles δ1 = 0.12◦;(α = 90.12◦); δ2 = 0.12◦;(β = 90.12◦); and δ3 = 0.01◦ (γ = 90.01◦), the CCR is called the SuperPin Plus type, where the reflected beam angle can be calculated as ε1 = ε2 = 0.33◦, ε3 = 0.2◦, and the luminous intensity RI meets EU ECE and US SAE regulation requirements. In Figure5, the simulation results through the TracePro software (Lambda Research Corporation of Littleton, Massachusetts, USA) can verify the above ε and δ relation formulas. In Figure5b,d, the retro-reflected light can reach up to 0.2 ◦, and up to 0.33◦ through the CCR shown in Figure5a and the 45 ◦ rotated CCR, shown in Figure5c respectively. Therefore, the SuperPin Plus design Appl. Sci. 2020, 10, 454 6 of 16 can simultaneously meet SAE and ECE standards by using pins with the same specifications. For the requirements of the SAE standard, the direction of CCR is determined by the original orientation, shownAppl. Sci. in2020 Figure, 10, x5 FORa. For PEER ECE REVIEW standards, we only need to rotate the CCR at a 45-degree angle, as shown6 of 15 in Figure5c. The results are detailed in Figure5b,d.

(a) (b)

Figure 5. (a) The orientation of the corner cube reflectorreflector forfor EUEU EconomicEconomic Commission for Europe (ECE)(ECE) regulations.regulations. ((bb)) TheThe reflected reflected intensity intensity distribution distribution accomplished accomplished by by the the corner corner cube cube reflector reflector for ECEfor ECE regulations. regulations. (c) The (c) orientationThe orientation of the cornerof the cubecorner reflector cube reflector for US Society for US of Society Automotive of Automotive Engineers ° (SAE)Engineers regulation, (SAE) regulation, which is the which 45◦ rotated is the 45 corner rotated cube corner reflector cube for reflector ECE regulations. for ECE regulations. (d) The reflected (c) The intensityreflected distributionintensity distribution accomplished accomplished by the corner by the cube corner reflector cube for reflector SAE regulations. for SAE regulations.

3. Experimental Setups and Analysis In order toto demonstratedemonstrate the performance of the SuperPin Plus CCR, the pin element for corner cubes with 2.75 2.75 mm mm cross cross sectional sectional size size and and dihedral dihedral angles angles δ1δ =1 0.12°;= 0.12 (α◦; =( α90.12°);= 90.12 δ◦2) ;=δ 0.12°;2 = 0.12 (β ◦=; (90.12°);β = 90.12 and◦); δ and3 = 0.01°δ3 = 0.01(γ =◦ 90.01°)(γ = 90.01 are ◦made) are madeby CNC by CNCprocess process and bundled and bundled as a flat as aarray flat arraytesting testing CCR CCRsample, sample, as shown as shown in Figure in Figure 6. In6. optical In optical testing testing pr processes,ocesses, the the sample sample is is te testedsted for for ECE regulationregulation verificationverification first,first, andand thenthen itit is rotated 4545◦° for SAE regulation measurement.measurement. For comparison, one flatflat SAE regular CCR and one flatflat ECE regularregular CCRCCR areare alsoalso putput inin anan opticaloptical setupsetup toto test.test. The optical setup for reflexreflex reflectorreflector regulation testing is established,established, as shown in Figure7 7,, withwith aa 633633 nmnm diodediode laser operated operated with with a a 5 5 mW mW output output acting acting as as the the light light source, source, and and the thedistance distance between between the laser the laser and andthe curved the curved reflex reflex reflector reflector set to 30.5 set to m 30.5 to measure m to measure the reflected the reflected light spot. light Based spot. on Basedthe laser on spectrum the laser spectrumspecification, specification, its coherence its coherencelength is calculated length is to calculatedbe about to0.5 be mm, about which 0.5 mm,is less which than the is less corner than cube the cornerdimension cube of dimension 2.75 mm ofin 2.75the experiments. mm in the experiments. Therefore, Therefore,the retro-reflected the retro-reflected output spots output were spots spatially were spatiallyincoherent, incoherent, and the laser and thecan laser be considered can be considered as an incoherent as an incoherent light source light sourcefor thefor following the following retro- retro-reflectorreflector testing testing experiments. experiments. The laser light had an incident angle of 0° with respect to the car driving direction, as it shone on the tested CCR with a spot area of 520 mm2. As a result, several retro-reflected light spots can be found on the black screen located 30.5 m away from the test sample. A Minolta T10 illuminance meter was used to measure the illuminance of the sample and of the retro-reflected light spot in order to get the incident light illuminance (in lux) and the retro-reflected light intensity (in candela). The coefficient of luminous intensity RI and retro-reflection efficiency RA of the test sample can be Appl. Sci. 2020, 10, 454 7 of 16

Appl. Sci. 2020, 10The, x FOR laser PEER light hadREVIEW an incident angle of 0◦ with respect to the car driving direction, as it shone 7 of 15 Appl. Sci. 2020on the, 10, tested x FOR CCR PEER with REVIEW a spot area of 520 mm2. As a result, several retro-reflected light spots can be 7 of 15 obtainedfound through on the calculation black screen of located the measured 30.5 m away data from theto ensure test sample. that A the Minolta tested T10 CCRs illuminance can pass meter US SAE regulationsobtainedwas through and used EU to calculation measure ECE regulations. the illuminanceof the measured of the sample data and to ensure of the retro-reflected that the tested light spotCCRs inorder can pass to get US SAE regulationsThe thetesting incidentand EUoutput light ECE illuminance light regulations. patterns (in lux) of and the the ECE retro-reflected SuperPin light Plus intensity CCR, (in the candela). SAE SuperPin The coefficient Plus CCR, of luminous intensity RI and retro-reflection efficiency RA of the test sample can be obtained through the flatThe ECEcalculation testing regular output of CCR, the measured light and patternsthe data flat to SAE ensureof the regular that ECE the CCRSu testedperPin are CCRs shown Plus can passCCR, in Figure US the SAE SA8a–d, regulationsE SuperPin respectively. and EUPlus Based CCR, onthe theflat measuredECEECE regular regulations. data CCR, in andFigure the flat8, compar SAE regularing the CCR light are reflection shown in performanceFigure 8a–d, respectively.of RI between Based the regularon the measuredCCRsThe and testing datathe outputSuperPin in Figure light Plus patterns8, compar CCR, of thetheing ECE result the SuperPin lights show reflection Plus that CCR, the theperformance light SAE reflection SuperPin of Plus performanceRI CCR,between the of theregular new CCRsdesignthe flat and ECEis higher the regular SuperPin than CCR, that and Plus of the the CCR, flat regular SAE the regular resultones. sIn CCR show detail, are that shown the the R inI valueslight Figure reflection 8ofa–d, the respectively. flat performance SuperPin Plus of Based on the measured data in Figure8, comparing the light reflection performance of R between samplethe new under design ECE is higher working than conditionsthat of the regularat 0°, 10 ones.°U, 10In °detail,D, 20° theL, and RI values 20°R ofare the 20,002 flatI SuperPin millicandela Plus the regular CCRs and the SuperPin Plus CCR, the results show that the light reflection performance (mcd)/lux,sample under 10,214 ECE mcd/lux, working 7863 conditions mcd/lux, at 7318 0°, 10mc°U,d/lux, 10° D,and 20 8871°L, and lux/mcd, 20°R arerespectively, 20,002 millicandela shown in of the new design is higher than that of the regular ones. In detail, the RI values of the flat SuperPin I ° ° Figure(mcd)/lux, 8ePlus The 10,214 sample R values mcd/lux, under of ECE the 7863 working flat mcd/lux, SuperPin conditions 7318 Plus at0 mc◦ ,sample 10d/lux,◦U, 10 ◦ underD,and 20 ◦8871L, the and lux/mcd,SAE 20◦R areworking 20,002 respectively, millicandelamode at shown0 , 10 U,in 10Figure°D, 20 8e(mcd)°L, The and/lux, RI 20values 10,214°R are mcd of 12,318the/lux, flat 7863 mcd/lux, SuperPin mcd/lux, 73186227 Plus mcd mcd/lux,sample/lux, and under 4442 8871 the luxmcd/lux,/ mcd,SAE respectively,working 4586 mcd/lux, mode shown at inand 0°, 104904°U, lux/mcd,10°D, 20Figure °respectively,L, and8e The 20°RRI shownvaluesare 12,318 of in the Figure flat mcd/lux, SuperPin 8f. The 6227 Plus measured samplemcd/lux, under coefficients 4442 the SAEmcd/lux, of working luminous 4586 mode mcd/lux, intensity at 0◦, 10◦ U,and RI of 4904 the 10 D, 20 L, and 20 R are 12,318 mcd/lux, 6227 mcd/lux, 4442 mcd/lux, 4586 mcd/lux, and 4904 lux/mcd, SuperPinlux/mcd, respectively,Plus◦ CCR◦ are shown ◦all higher in Figure than the 8f. regulaThe measuredtion requirement coefficients of ECEof luminous and SAE, intensity shown RinI Tableof the respectively, shown in Figure8f. The measured coe fficients of luminous intensity R of the SuperPin SuperPin Plus CCR are all higher than the regulation requirement of ECE andI SAE, shown in Table 1. Based Pluson the CCR data are all shown higher thanin Figure the regulation 8, we requirementcan conclude of ECE that and the SAE, retro-reflection shown in Table1. efficiency Based on of the SuperPin1. Basedthe onPlus data the CCR showndata isshown in Figure41% inhigher8, weFigure can comparing conclude 8, we can that to theco thenclude retro-reflection ECE that regular the e ffi retro-reflection ciencyone, of and the SuperPincan efficiencyhave Plus the ofsame the regulationSuperPinCCR Pluslevel is 41% CCRas higherthe is SAE 41% comparing regular higher to one, thecomparing ECErespectively. regular to one, the and ECE can haveregular the same one, regulation and can level have as the the same regulationSAE level regular as the one, SAE respectively. regular one, respectively.

Figure 6. The flat SuperPin Plus corner cube retro-reflector (CCR) sample built by pin array. Figure 6.Figure The flat 6. The SuperPin ﬂat SuperPin Plus Plus corner corner cube cube retro-reflector retro-reﬂector (CCR) (CCR) sample sample built bybuilt pin by array. pin array.

FigureFigure 7. Ex 7.perimentalExperimental setup setup for for testing testing samples samples (ﬂat (flat and and curve). curve). Figure 7. Experimental setup for testing samples (flat and curve).

(a) ECE SuperPin Plus (d) SAE regular CCR (a) ECE SuperPinCCR Plus (b) SAE SuperPin Plus CCR (c) ECE regular CCR (d)retroreflected SAE regular light CCR retroreflected light pattern. retroreflectedCCR light (b) SAE SuperPin Plus CCR retroreflected(c) ECE regular light pattern.CCR retroreflectedpattern. light retroreflectedpattern. light retroreflected light pattern. retroreflected light pattern. pattern. pattern. Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 15

obtained through calculation of the measured data to ensure that the tested CCRs can pass US SAE regulations and EU ECE regulations. The testing output light patterns of the ECE SuperPin Plus CCR, the SAE SuperPin Plus CCR, the flat ECE regular CCR, and the flat SAE regular CCR are shown in Figure 8a–d, respectively. Based on the measured data in Figure 8, comparing the light reflection performance of RI between the regular CCRs and the SuperPin Plus CCR, the results show that the light reflection performance of the new design is higher than that of the regular ones. In detail, the RI values of the flat SuperPin Plus sample under ECE working conditions at 0°, 10°U, 10°D, 20°L, and 20°R are 20,002 millicandela (mcd)/lux, 10,214 mcd/lux, 7863 mcd/lux, 7318 mcd/lux, and 8871 lux/mcd, respectively, shown in Figure 8e The RI values of the flat SuperPin Plus sample under the SAE working mode at 0°, 10°U, 10°D, 20°L, and 20°R are 12,318 mcd/lux, 6227 mcd/lux, 4442 mcd/lux, 4586 mcd/lux, and 4904 lux/mcd, respectively, shown in Figure 8f. The measured coefficients of luminous intensity RI of the SuperPin Plus CCR are all higher than the regulation requirement of ECE and SAE, shown in Table 1. Based on the data shown in Figure 8, we can conclude that the retro-reflection efficiency of the SuperPin Plus CCR is 41% higher comparing to the ECE regular one, and can have the same regulation level as the SAE regular one, respectively.

Figure 6. The flat SuperPin Plus corner cube retro-reflector (CCR) sample built by pin array.

Appl. Sci. 2020, 10, 454 8 of 16 Figure 7. Experimental setup for testing samples (flat and curve).

(a) ECE SuperPin Plus (d) SAE regular CCR CCR (b) SAE SuperPin Plus CCR (c) ECE regular CCR Appl. Sci. 2020, 10, x FOR PEER REVIEW retroreflected light8 of 15 retroreflected light retroreflected light pattern. retroreflected light pattern. pattern. pattern.

Figure 8. Comparison of the coefficient of luminous intensity(f) CoefficientsRI between of theluminous flat regular intensity CCR RI of and the the (e) Coefficients of luminous intensity RI of the commercaial flat SuperPin Plus CCR. commercaial flat SAE regular CCR and the Flat flat ECE regular CCR and the Flat SuperPin Plus CCR sample. SuperPin Plus CCR sample. In order to extend the ECE/SAE dual functional advantage from a flat SuperPin Plus CCR to a curvedFigure SuperPin 8. Comparison Plus CCR, of the the coefficient SuperPin of luminous Plus pin intensity elements R areI between connected the flat side regular by side CCR with and the their tips flat SuperPin Plus CCR. touching the curved plane of a commercial curved CCR, serving as the initial design of the curved SuperPin Plus CCR. The commercial curved regular CCR made of PMMA (polymethyl methacrylate) In order to extend the ECE/SAE dual functional advantage from a flat SuperPin Plus CCR to a shown in Figure9 provided by OWL LIGHT AUTOMOTIVE MFG. CORP (Lukang, Chunghua, Taiwan) curved SuperPin Plus CCR, the SuperPin Plus pin elements are connected side by side with their tips is used as the reference to design a SuperPin Plus curved retro-reflector. The commercial curved regular touching the curved plane of a commercial curved CCR, serving as the initial design of the curved CCR and the initial SuperPin Plus curved CCR design are shown in Figure9a,b, respectively. The cross SuperPin Plus CCR. The commercial curved regular CCR made of PMMA (polymethyl methacrylate) section working surface of the design is 146 mm 34 mm. Through TracePro software simulation, shown in Figure 9 provided by OWL LIGHT AUTOMOTIVE× MFG. CORP (Lukang, Chunghua, the anterior, central, and posterior regions of the ECE (SAE) SuperPin Plus curved CCR result in their Taiwan) is used as the reference to design a SuperPin Plus curved retro-reflector. The commercial retro-reflected light intensity distributions for an incident beam in the driving direction, as shown curved regular CCR and the initial SuperPin Plus curved CCR design are shown in Figure 9a and in Figure 10. The locations of the probing regions and the car’s driving direction of the CCRs are Figure 9b, respectively. The cross section working surface of the design is 146 mm × 34 mm. Through presented in Figure 11. As the simulation results are shown in Figure 10, the anterior and the central TracePro software simulation, the anterior, central, and posterior regions of the ECE (SAE) SuperPin regions areas can reflect light up to 0.2 and up to 0.33 , but the posterior area can not. Therefore, we Plus curved CCR result in their retro-reflected◦ light intensity◦ distributions for an incident beam in conclude that it is difficult for the posterior area to meet ECE or SAE regulation requirements. the driving direction, as shown in Figure 10. The locations of the probing regions and the car’s driving direction of the CCRs are presented in Figure 11. As the simulation results are shown in Figure 10, the anterior and the central regions areas can reflect light up to 0.2° and up to 0.33°, but the posterior area can not. Therefore, we conclude that it is difficult for the posterior area to meet ECE or SAE regulation requirements.

(a) (b)

Figure 9. (a) The commercial regular curved reflex reflector sample. (b) The pin and the primary curved SuperPin Plus reflector design composed of pins. Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 15

(f) Coefficients of luminous intensity RI of the (e) Coefficients of luminous intensity RI of the commercaial commercaial flat SAE regular CCR and the Flat flat ECE regular CCR and the Flat SuperPin Plus CCR sample. SuperPin Plus CCR sample.

Figure 8. Comparison of the coefficient of luminous intensity RI between the flat regular CCR and the flat SuperPin Plus CCR.

In order to extend the ECE/SAE dual functional advantage from a flat SuperPin Plus CCR to a curved SuperPin Plus CCR, the SuperPin Plus pin elements are connected side by side with their tips touching the curved plane of a commercial curved CCR, serving as the initial design of the curved SuperPin Plus CCR. The commercial curved regular CCR made of PMMA (polymethyl methacrylate) shown in Figure 9 provided by OWL LIGHT AUTOMOTIVE MFG. CORP (Lukang, Chunghua, Taiwan) is used as the reference to design a SuperPin Plus curved retro-reflector. The commercial curved regular CCR and the initial SuperPin Plus curved CCR design are shown in Figure 9a and Figure 9b, respectively. The cross section working surface of the design is 146 mm × 34 mm. Through TracePro software simulation, the anterior, central, and posterior regions of the ECE (SAE) SuperPin Plus curved CCR result in their retro-reflected light intensity distributions for an incident beam in the driving direction, as shown in Figure 10. The locations of the probing regions and the car’s driving direction of the CCRs are presented in Figure 11. As the simulation results are shown in Figure 10, the anterior and the central regions areas can reflect light up to 0.2° and up to 0.33°, but the posterior area can not. Therefore, we conclude that it is difficult for the posterior area to meet ECE or SAE Appl.regulation Sci. 2020 requirements., 10, 454 9 of 16

(a) (b) Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 15 Appl. Sci.FigureFigure2020, 10 9.9., x (( FORa)) TheThe PEER commercialcommercial REVIEW regularregular curvedcurved reflexreflex reflectorreflector sample.sample. (b) The pinpin andand thethe primaryprimary9 of 15 curvedcurved SuperPinSuperPin PlusPlus reflectorreflector designdesign composedcomposed ofof pins.pins.

((aa)) ((bb)) (c()c )

((dd)) ((ee)) (f()f)

FigureFigureFigure 10. 10. 10. The TheThe RRI IR andandI and intensityintensity intensity distributionsdistributions distributions onon onanterior,anterior, anterior, central,central, central, andand and posterior posterior posterior regions, regions, regions, which which which are are are shownshownshown in: in: in:( a(a–– (cac)– )SAE cSAE) SAE SuperPin SuperPin SuperPin PlusPlus Plus curved;curved; curved; (d– (fd)) – ECEECEf) ECE SuperPinSuperPin SuperPin Plus Plus Plus curved. curved. curved.

Figure 11. The areas for testing of SuperPin Plus curve (each area is 520 mm2). Figure 11. The areas for testing of SuperPin Plus curve (each area is 520 mm2). Figure 11. The areas for testing of SuperPin Plus curve (each area is 520 mm2). In order to remedy the ineffective posterior working area of the commercial design, two groups In order to remedy the ineffective posterior working area of the commercial design, two groups of pins were connected as the double pins group to compose the SuperPin Plus curved CCR, as shown of pins were connected as the double pins group to compose the SuperPin Plus curved CCR, as shown in Figure 12. Fifteen pieces of double-pin groups were arranged in parallel to the car driving direction in Figure 12. Fifteen pieces of double-pin groups were arranged in parallel to the car driving direction to form the primary curved CCR; one pin group touches the curve reference surface, and the other toone form is freethe primaryto translate curved in the CCR; car drivingone pin directio group n.touches The height the curve difference reference between surface, the neighboringand the other one is free to translate in the car driving direction. The height difference between the neighboring pins in a group of double pins and the double pin group are named di and Di, respectively. pins in a group of double pins and the double pin group are named di and Di, respectively. Appl. Sci. 2020, 10, 454 10 of 16

In order to remedy the ineﬀective posterior working area of the commercial design, two groups of pins were connected as the double pins group to compose the SuperPin Plus curved CCR, as shown in Figure 12. Fifteen pieces of double-pin groups were arranged in parallel to the car driving direction to form the primary curved CCR; one pin group touches the curve reference surface, and the other one is free to translate in the car driving direction. The height diﬀerence between the neighboring pins in a Appl.group Sci. of 2020 double, 10, x FOR pins PEER and REVIEW the double pin group are named di and Di, respectively. 10 of 15

Figure 12. TheThe height height difference diﬀerence between the neighb neighboringoring pins in a double-pin group.

The object object function function f fdefineddefined by by Equation Equation 8 (8)was was determined determined in the in optimization the optimization process. process. The Theoptimization optimization process process enco encompassedmpassed three three fragments. fragments. Object function: The equation that describes the value of the object function of the optimization program established by genetic algorithms isis asas follows:follows: 𝑓(𝑖, 𝑗) ∑ r𝑤 (𝑚 −𝑡) +𝑤𝑗(𝑚 −𝑡) =X ,n 2 (8) f (i, j)= w (m t )2 + wj m t (8) = i i i j j where wi is the weight parameter of the iobject,j 1 function,− mj is the value− of the measured target, which is determined by the intensity sensor through each optimal loop when running the program, and tj where wi is the weight parameter of the object function, mj is the value of the measured target, which is is the optimization target defined with a value corresponding to the retro-reflective light intensity on determined by the intensity sensor through each optimal loop when running the program, and tj is the theoptimization retroreflector target plane. defined with a value corresponding to the retro-reflective light intensity on the retroreflectorLuminous plane. intensity function: In order to improve the primary curved CCR further, the add-on ray tracingLuminous simulation intensity tool function: OptisWork In order (Optis to improveSAS, La theFarlede, primary France), curved embedded CCR further, in SolidWorks the add-on mechanicalray tracing design simulation software, tool OptisWorkwas used to (Optis search SAS, for suitable La Farlede, variable France), parameters embedded to get in an SolidWorks optimized curvedmechanical CCR, design using software,di to elevate was its used performance to search for and suitable Di to fit variable the reference parameters curve to for get the an outlook optimized of curved CCR smoothly. The constraint of each variable parameter is determined by the curvature of curved CCR, using di to elevate its performance and Di to fit the reference curve for the outlook of thecurved curved CCR CCR smoothly. surface. The The constraint lighting performances of each variable, such parameter as intensity is determined distributions, by the illumination curvature uniformity,of the curved and CCR optical surface. efficiencies The lighting of curved performances, CCR, can such be accomplished as intensity distributions, to meet targets illumination by using optimization.uniformity, and In the optical study, effi theciencies luminous of curved intensity CCR, function can be serves accomplished as the object to function, meet targets and the by usingvalue ° Roptimization.I at the upper In 0.33 the study, is targeted the luminous to be maximum intensity in function the solution serves searching as the object process. function, We andsearch the for value an approximation of the luminous intensity (RI) I(φ, a, b, c) as the object function, which is at the polar RI at the upper 0.33◦ is targeted to be maximum in the solution searching process. We search for an Φ angleapproximation in Equation of the (9), luminous where K intensity is the number (RI) I( ϕof, a,functions. b, c) as the object function, which is at the polar angle Φ in Equation (9), where K is the number of functions. I(φ,x,y,z) = Imax∑ 𝑥𝑐𝑜𝑠 (φ–yk) (9)

Xk In order to set the target value of the optimization, thezk simulation experiment with a flat I(ϕ, x, y, z) = Imax xkcos (ϕ y ) (9) regulated CCR was exercised to find the reflected klight=1 power −as kthe reference by a 1000 lumen incidentIn order beam. to The set the resulting target value power of was the optimization, 850 lm and this the simulationwas used as experiment the target withfor the a flat subsequent regulated searchingCCR was exercisedof the optimized to find the curved reflected CCR. light By powerrunning as the referencescheme in by optimization a 1000 lumen steps, incident manually beam. Thelimited resulting to 600 powersearching was steps 850 lm to andquickly this find was useda better as thesolution, target the for best thesubsequent results were searching determined of the in stepoptimized 18 (SAE curved curve) CCR. and By step running 79 (ECE the scheme curve). in The optimization final intensity steps, sensor manually values limited were to 600shown searching to be 742.51steps to lm quickly (SAE curve) find a betterand 802.1 solution, lm (ECE the bestcurve), results which were were determined also the output in step powers 18 (SAE reflected curve) and by step the optimized curved CCR. In the initial optimization process, the mathematical equation for the intensity distribution of reflected light entered into the program is expressed in the measurement value of the intensity sensor. The luminous intensity RI is defined by I (φ, a, b, c) at the polar angle of φ, shown in Equation (9). The target of the optimization process was defined as a value corresponding to the retro-reflective light intensity on the retro-reflector plane. During the optimization, to have the curved CCR meet the requirement of the ECE (0.33°) and SAE 0.2°) standard and maximum reflection efficiency, the values of δ and di were found through the workflows shown in Figures 13 and 14, respectively. Appl. Sci. 2020, 10, 454 11 of 16

79 (ECE curve). The final intensity sensor values were shown to be 742.51 lm (SAE curve) and 802.1 lm (ECE curve), which were also the output powers reflected by the optimized curved CCR. In the initial optimization process, the mathematical equation for the intensity distribution of reflected light entered into the program is expressed in the measurement value of the intensity sensor. The luminous intensity RI is defined by I (ϕ, a, b, c) at the polar angle of ϕ, shown in Equation (9). The target of the optimization process was defined as a value corresponding to the retro-reflective light intensity on the retro-reflector plane. During the optimization, to have the curved CCR meet the requirement of the ECE (0.33◦) and SAE 0.2◦) standard and maximum reflection efficiency, the values Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 15 Appl.of δ andSci. 2020 di ,were 10, x FOR found PEER through REVIEW the workflows shown in Figures 13 and 14, respectively. 11 of 15

Figure 13. The designing flow chart of CCR used for SuperPin Plus. FigureFigure 13. 13. TheThe designing designing flow ﬂow chart chart of of CCR CCR used used for for SuperPin SuperPin Plus ..

Figure 14. The optimization process flow ﬂow chart. Figure 14. The optimization process flow chart.

As the optimization is terminated by the program,program, the optimized curved CCR with the same As the optimization is terminated by the program, the optimized curved CCR with the same curve as the commercial one was obtained. After After the the optimization optimization process, the optimized curved CCR curve as the commercial one was obtained. After the optimization process, the optimized curved CCR was analyzedanalyzed forfor comparison comparison with with the the commercial commercial reflector reflector by simulations.by simulations. The The distance distance from from the light the was analyzed for comparison with the commercial reflector by simulations. The distance from the sourcelight source to the to curved the curved CCR is CCR set as is 30.5 set m, as and 30.5 the m, diameter and the ofdiameter the laser of beam the laser is 25 mm.beam The is 25 curved mm. CCRThe light source to the curved CCR is set as 30.5 m, and the diameter of the laser beam is 25 mm. The iscurved kept with CCR its is carkept driving with its direction car driving at 0◦, 10direction◦ (up, down) at 0°, vertically,10° (up, down) and 20 vertically,◦ (left, right) and horizontally 20° (left, right) with curved CCR is kept with its car driving direction at 0°, 10° (up, down) vertically, and 20° (left, right) thehorizontally incident light,with respectively,the incident to light, perform respectively, the optical to tests perform of SAE the and optical ECE regulations. tests of SAE The and resulting ECE horizontally with the incident light, respectively, to perform the optical tests of SAE and ECE intensityregulations. distributions The resulting by 0 ◦intensityincident distributions light to the anterior, by 0° incident central, andlight posterior to the anterior, regions sequentiallycentral, and regulations. The resulting intensity distributions by 0° incident light to the anterior, central, and areposterior shown regions in Figures sequentially 15 and 16 are. The shown results in Figures showed 15 that and the 16. optimized The results curved showed CCR that could the optimized contribute posterior regions sequentially are shown in Figures 15 and 16. The results showed that the optimized muchcurved higher CCR sucouldfficient contribute light intensity much thanhigher that sufficient of the commercial light intensity design than (no ethatffective of the retro-reflection commercial curved CCR could contribute much higher sufficient light intensity than that of the commercial atdesign 0.2◦ (SAE),(no effective 0.33◦ (ECE)retro-reflection up), as shown at 0.2° in(SAE), Figure 0.33° 15c (ECE) for regular up), as SAE shown curved in Figure CCR 15c and for shown regular in design (no effective retro-reflection at 0.2° (SAE), 0.33° (ECE) up), as shown in Figure 15c for regular FigureSAE curved 16c for CCR regular and ECE shown curved in Figure CCR. Additionally, 16c for regular it was ECE demonstrated curved CCR. that Additionally,RI and RA are it alsowas SAE curved CCR and shown in Figure 16c for regular ECE curved CCR. Additionally, it was increaseddemonstrated significantly that RI inand all regions,RA are andalso aincreased larger retro-reflection significantly working in all regions, area is accomplished and a larger through retro- demonstrated that RI and RA are also increased significantly in all regions, and a larger retro- thereflection optimal working design. area is accomplished through the optimal design. reflection working area is accomplished through the optimal design.

(a) (b) (c) (a) (b) (c)

Figure 15. The RI and intensity distributions on anterior, central, and posterior regions, which are Figure 15. The RI and intensity distributions on anterior, central, and posterior regions, which are shown in: (a–c) Optimized ECE SuperPin Plus curved CCR. shown in: (a–c) Optimized ECE SuperPin Plus curved CCR. Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 15

Figure 13. The designing flow chart of CCR used for SuperPin Plus.

Figure 14. The optimization process flow chart.

As the optimization is terminated by the program, the optimized curved CCR with the same curve as the commercial one was obtained. After the optimization process, the optimized curved CCR was analyzed for comparison with the commercial reflector by simulations. The distance from the light source to the curved CCR is set as 30.5 m, and the diameter of the laser beam is 25 mm. The curved CCR is kept with its car driving direction at 0°, 10° (up, down) vertically, and 20° (left, right) horizontally with the incident light, respectively, to perform the optical tests of SAE and ECE regulations. The resulting intensity distributions by 0° incident light to the anterior, central, and posterior regions sequentially are shown in Figures 15 and 16. The results showed that the optimized curved CCR could contribute much higher sufficient light intensity than that of the commercial design (no effective retro-reflection at 0.2° (SAE), 0.33° (ECE) up), as shown in Figure 15c for regular SAE curved CCR and shown in Figure 16c for regular ECE curved CCR. Additionally, it was demonstrated that RI and RA are also increased significantly in all regions, and a larger retro- Appl.reflection Sci. 2020 working, 10, 454 area is accomplished through the optimal design. 12 of 16

(a) (b) (c)

FigureFigure 15.15. The RRI and intensity distributions on anterior, central,central, andand posteriorposterior regions,regions, whichwhich areare Appl. Sci. 2020, 10, x FOR PEERI REVIEW 12 of 15 Appl. Sci.shownshown 2020 in:,in: 10 , ( ax– FORc)) OptimizedOptimized PEER REVIEW ECEECE SuperPinSuperPin PlusPlus curvedcurved CCR.CCR. 12 of 15

(a) (b) (c) (a) (b) (c) Figure 16. The RI and intensity distributions on anterior, central, and posterior regions, which are shownFigure in: 16.16. ( aThe–c) OptimizedRII and intensity SAE SuperPin distributions Plus curvedon anterior, CCR. central, and posterior regions, which areare shownshown in:in: (a–c) Optimized SAE SuperPin PlusPlus curvedcurved CCR.CCR. The optimization results shown in Figures 15 and 16, that demonstrate the intensity distributions on theThe posterior optimization regions resultsresults were shownshown improved. inin Figures We 1515comp andared 1616,, thatwith demonstrate the results theshown intensity in Figure distributions 10 the posterioron thethe posterior posterior regions regions regionshave werereflected were improved. improved. beams We on comparedWe top, comp as ared withshown thewith resultsin theFigures results shown 15c inshown and Figure 16c.in 10 Figure theIn posteriororder 10 theto demonstrateregionsposterior have regions that reﬂected the have optimized beams reflected on SuperPin top, beams as shown Pluson intop,cu Figuresrved as CCRshown 15c can and in meet 16Figuresc. SAE In order and15c toECEand demonstrate requirements 16c. In order that and theto performoptimizeddemonstrate better SuperPin that than the the Plus optimized commercial curved CCRSuperPin samples, can meet Plus we SAEcu prototrved and CCRyped ECE can requirementsand meet tested SAE the and SuperPin performECE requirements Plus better in practical than and the experiments,commercialperform better samples, as than shown the we commercialin prototyped Figure 17. samples, and The tested retro-re we the prototflected SuperPinyped outputs and Plus tested inon practical the the screen SuperPin experiments, by thePlus commercial in as practical shown regularinexperiments, Figure curved 17. Theas CCRsshown retro-reﬂected shown in Figure in outputs Figure 17. The on18a–d retro-re the screenandflected the by optimized the outputs commercial oncurved the regular screen CCR curved bywere the presented CCRs commercial shown in inregular Figure curved 18a–d andCCRs the shown optimized in Figure curved 18a–d CCR wereand presentedthe optimized in Figure curved 19a–d, CCR respectively, were presented resulted in Figures 19a-d, respectively, resulted in RI values for rotational angles of 0°, 10°U, 10°D, 20°L, and ° ° ° ° 20inFigures°RR,I valuesas shown19a-d, for respectively,in rotational Figures 20 angles resultedand 21. of 0 Atin◦, 10theRI◦ valuesU, posterior 10◦D, for 20 arearotational◦L, andof the 20 anglescommercial◦R, as shownof 0 ,curved 10 inU, Figures 10CCRD, 20sample,20 andL, and 21 it. At20° theR, as posterior shown in area Figures of the 20 commercial and 21. At curvedthe posterior CCR sample, area of itthe can commercial be found thatcurved the RCCRvalues sample, were it can be found that the RI values were 0 mcd/lux. However, the RI of the optimal curved SuperPinI Plus CCR0can mcd be sample/ lux.found However, was that muchthe theR I improved.valuesRI of thewere optimal 0 mcd/lux. curved However, SuperPin the Plus RI of CCR the sampleoptimal was curved much SuperPin improved. Plus CCR sample was much improved.

Figure 17. TheThe SuperPin SuperPin Plus Plus curv curveded CCR sample—output of the optimized design. Figure 17. The SuperPin Plus curved CCR sample—output of the optimized design.

Commercial ECE Commercialregular curved ECE regularCCR curved CCR

(a) (b) (c) (a) (b) (c)

Optimized ECE OptimizedSuperPin Plus ECE SuperPincurved CCR Plus curved CCR

(d) (e) (f) (d) (e) (f) Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 15

(a) (b) (c)

Figure 16. The RI and intensity distributions on anterior, central, and posterior regions, which are shown in: (a–c) Optimized SAE SuperPin Plus curved CCR.

The optimization results shown in Figures 15 and 16, that demonstrate the intensity distributions on the posterior regions were improved. We compared with the results shown in Figure 10 the posterior regions have reflected beams on top, as shown in Figures 15c and 16c. In order to demonstrate that the optimized SuperPin Plus curved CCR can meet SAE and ECE requirements and perform better than the commercial samples, we prototyped and tested the SuperPin Plus in practical experiments, as shown in Figure 17. The retro-reflected outputs on the screen by the commercial regular curved CCRs shown in Figure 18a–d and the optimized curved CCR were presented in Figures 19a-d, respectively, resulted in RI values for rotational angles of 0°, 10°U, 10°D, 20°L, and 20°R, as shown in Figures 20 and 21. At the posterior area of the commercial curved CCR sample, it can be found that the RI values were 0 mcd/lux. However, the RI of the optimal curved SuperPin Plus CCR sample was much improved.

Appl. Sci. 2020, 10Figure, 454 17. The SuperPin Plus curved CCR sample—output of the optimized design. 13 of 16

Commercial ECE regular curved CCR

(a) (b) (c)

Optimized ECE SuperPin Plus curved CCR

Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 15 (d) (e) (f) Figure 18. The intensity distributions on anterior, central, and posterior regions, which are shown in: (Figurea)–(c) Commercial 18. The intensity curved distributions regular curved on anterior, CCR (ECE); central, (d–f and) SuperPin posterior Plus regions, curved which CCR are(ECE). shown in: (a–c) Commercial curved regular curved CCR (ECE); (d–f) SuperPin Plus curved CCR (ECE).

Commercial regular SAE curved CCR

(a) (b) (c)

Optimized SAE SuperPin Plus curved CCR

(d) (e) (f)

FigureFigure 19. 19. TheThe intensity intensity distributions distributions on on anterior, anterior, central, central, and and posterio posteriorr regions, regions, which which are are shown shown in: in: ((aa)–(–cc)) Commercial Commercial curved curved regular regular curved curved CCR CCR (SAE); (SAE); ( d(d–f–)f) SuperPin SuperPin Plus Plus curved curved CCR CCR (SAE). (SAE).

Figure 20. Comparison of the commercial regular CCR with the optimized design SuperPin Plus CCR’s coefficient of luminous intensity RI by region. (ECE curved CCR).

Figure 21. Comparison of the commercial regular CCR and the optimized design SuperPin Plus CCR’s

coefficient of luminous intensity RI by region. (SAE curved CCR). Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 15

Figure 18. The intensity distributions on anterior, central, and posterior regions, which are shown in: (a)–(c) Commercial curved regular curved CCR (ECE); (d–f) SuperPin Plus curved CCR (ECE).

Commercial regular SAE curved CCR

(a) (b) (c)

Optimized SAE SuperPin Plus curved CCR

(d) (e) (f)

Appl. Sci.Figure2020 19., 10 ,The 454 intensity distributions on anterior, central, and posterior regions, which are shown in:14 of 16 (a)–(c) Commercial curved regular curved CCR (SAE); (d–f) SuperPin Plus curved CCR (SAE).

Figure 20.20. ComparisonComparison ofof the the commercial commercial regular regular CCR CCR with wi theth optimizedthe optimized design design SuperPin SuperPin Plus CCR’s Plus I CCR’scoeﬃcient coefficient of luminous of luminous intensity intensityRI by region. RI by region. (ECE curved (ECE curved CCR). CCR).

Figure 21. Comparison of the commercial regular CCR and the optimized design SuperPin Plus CCR’s Figure 21. ComparisonComparison of of the the commercial commercial regular regular CCR CCR and and the the optimized optimized design design SuperPin SuperPin Plus CCR’s coefficient of luminous intensity RI by region. (SAE curved CCR). coeﬃcient of luminous intensity RI by region. (SAE curved CCR).

4. Conclusions and Discussions One of the most crucial advantages of this research on the SuperPin Plus curved reflex-reflector can decrease the production cost of the reflex reflector severely, as the design can reflect one incident beam as two groups of beams to 0.20◦ and 0.33◦, respectively, as shown in Figure5. This allows the SuperPin Plus to meet both SAE and ECE standards while using the same type of pins with the same dimension and shape. Function switching between SAE and ECE standards only needs CCRs to rotate 45◦. The new optimal CCR design is shown to surpass the performance of the typical one. By using double-pin groups to build the SuperPin Plus curved CCR, reflection efficiency can be improved. Through using OptisWork software to find out the optimized SuperPin Plus curved CCR, RI can be increased further; however, this does sacrifice the reflection efficiency, RA. Using an efficient working area ratio, reflection efficiency RA, and coefficient of luminous intensity RI as the evaluation indices of curved CCR to compare a commercial regular curved CCR with the proposed new design. It can be inferred that the optimized SuperPin Plus curved CCR redistributes the reflected light beam energy of the initial SuperPin Plus curved CCR design, which takes more energy from other retro-reflected beams into the up 0.2◦ (SAE) or up 0.33◦ (ECE). After computer simulations and optical experiments, we demonstrated that the proposed SuperPin Plus curved CCR is not only above the SAE and ECE standard but also has a 32% larger working area and much better reflection efficiency than the commercial CCR, whose posterior region is not effective at all. Appl. Sci. 2020, 10, 454 15 of 16

Based on the data in Figures 20 and 21, it can be computed that the ratio of averaged RI of the optimized SuperPin Plus SAE curved CCR to that of the commercial SAE curved CCR is (10,172/7,380, 0◦), (8,489/5,972, 10◦U), (7,826/5,268, 10◦D), (7,479/5,322, 20◦L), and (6,678/4,427, 20◦D), which means 27.4% (0◦), 29.6% (10◦U), 32.7% (10◦D), 28.8% (20◦L), and 33.7% (20◦R) higher retro-reflection efficiency can be accomplished by the proposed SuperPin Plus SAE curved CCR. In addition, the ratio of averaged RI of the optimized SuperPin Plus ECE curved CCR to that of the commercial ECE curved CCR is (13,446/8,145, 0◦), (11,306/6,203, 10◦U), (10,194/5,888, 10◦D), (9,451/5,457, 20◦L), and (9,139/5,093, 20◦D), which means 39.4% (0◦), 45.1% (10◦U), 42.2% (10◦D), 42.3% (20◦L), and 44.28% (20◦R) higher retro-reflection efficiency can be accomplished by the proposed SuperPin Plus ECE curved CCR. In conclusion, we proposed a reflex reflector with a new corner cube structure. Compared with conventional ECE regular retro-reflectors, we found that not only can a 41% higher retro-reflection efficiency be achieved with the ECE SuperPin Plus flat reflex reflector, but also that the SuperPin Plus can act as a reflex reflector for the SAE standard. By using genetic algorithms for optimization, the angles and the positions of the pins considered as the building parameters of corner cube reflectors can influence the performance of a curved reflex reflector. It is demonstrated that 32% larger working area can be increased if double pin groups are used to construct corner cubes instead of the single pin arrangement in a curved SuperPin Plus reflex reflector. The yield rate of the mold production of the optimized design is less than the commercialized design as, through the pin composition method, the precision of the pin height control is even more necessary. In order to overcome the technical problems, we are conducting a study into molding by ultra-high precision casting. Moreover, a product that is accomplished by our proposed reflex reflector will reduce manufacturing costs so as to be more advantageous for both the European and American markets.

Author Contributions: H.-T.L., L.-T.L., T.-H.L. and H.-Y.L. carried out the experiment and wrote the manuscript with support from Y.-C.L., and H.-Y.L. fabricated the sample and G.-F.L. helped supervise the project. M.-J.C. and H.-Y.L. conceived the original idea, supervised the project. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Ministry of Science and Technology (MOST 108-2622-E-992-013 –CC3). Conﬂicts of Interest: The authors declare that they have no conﬂict of interest.

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