applied sciences

Article Enhancement of ECE SuperPin Curved Reflex Reflector by the Use of Double Pins with Corner Cubes

Lanh-Thanh Le 1,2, Hien-Thanh Le 1,2, Ming-Jui Chen 1, Guo-Feng Luo 1, Hsing-Yuan Liao 1, Hsin-Yi Ma 3 and Hsiao-Yi Lee 1,4,*

1 Department of Electrical Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 80778, Taiwan; [email protected] (L.-T.L.); [email protected] (H.-T.L.); [email protected] (M.-J.C.); [email protected] (G.-F.L.); [email protected] (H.-Y.L.) 2 Department of Technology, Dong Nai Technology University, Bien Hoa 830000, Dong Nai, Viet Nam 3 Department of Industrial Engineering and Management, Minghsin University of Science and Technology, Hsinchu 30401, Taiwan; [email protected] 4 Department of Graduate Institute of Clinical Medicine, Kaohsiung Medical University, Kaohsiung 807, Taiwan * Correspondence: [email protected]



Received: 17 February 2019; Accepted: 11 April 2019; Published: 15 April 2019


Abstract: A new, highly efficient curved reflex reflector is proposed to meet the requirement of EU ECE (Economic Commission for Europe) regulations based on the commercial design provided by an automotive company which has been in mass production. We used double pins with corner cubes which served as the building element of a SuperPin curved retro-reflector to enhance reflectivity performance. Our experiment outcomes indicated 46% higher retro-reflection efficiency and 33% larger working areas compared with the commercial design.

Keywords: optics design; double pins with corner cubes; SuperPin curved retro-reflector; EU ECE regulations (Economic Commission for Europe)

1. Introduction Reflex reflectors, usually composed of cube-corner arrays [1], can reflect light back along vectors that are nearly parallel but with a direction opposite to the incident light [2,3]. Reflex reflectors attached on cars or clothing can increase visibility in the dark for safety [4] and have been applied extensively in vehicle applications [5]. For instance, regular reflex reflectors [6–8], as shown in Figure1a, can diverge the reflected energy into multiple light beams with equal emitting angle intervals [9]. It is also the most commonly used retro-reflecting device for vehicles currently [7,10]. In contrast to regular reflectors, the SuperPin reflex reflector not only reflects light beams but also concentrates them to amplify the light intensity of signals for observers, as shown in Figure1b [ 11]. Owing to the highly effective retro-reflection ability, SuperPin retro-reflectors have been replacing regular retroreflectors in vehicle application markets [5,12]. According to regulations of the ECE (Economic Commission for Europe), vehicle signage needs to return light back to an observer located at 0.33 degrees above the light source [13], and the coefficient of luminous intensity RI should be greater than threshold values within 20◦ angle of light incidence [5,14]. The vehicle signage performance RI is evaluated by the ratio of the strength of the reflected light (retro-reflected light intensity) to the amount of light that falls on the retro-reflector (incident light illuminance), as shown in Figure1. RA is the measure of retro-reflection efficiency, defined as the ratio

Appl. Sci. 2019, 9, 1555; doi:10.3390/app9081555 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 1555 2 of 15 of the flux of incident light to the total flux of the reflected cone [12,15]. Consequently, vehicle signage wouldAppl. Sci. be2019 observed, 9, x to be brighter as its RI value increases [13,16]. 2 of 14 It is usual for reflex reflectors to have a curved shape; for example, to fit the corner of a vehicleIt is [1 usual–5,17]. for Cube-corner reflex reflectors structures to have are, a thus, curved distorted shape; to for complete example, the to curve, fit the so corner that their of a e vehicleffective working[1–5,17]. areaCube-corner and reflection structures efficiency are, arethus, aff ected,distorte thusd to leading complete to the the retro-reflector curve, so that being their against effective EU workingECE regulations area and [5 ,reflection11,17]. efficiency are affected, thus leading to the retro-reflector being against EU ECEIn thisregulations paper, a[5,11,17]. curved reflex reflector with a new cube-corner structure is proposed and demonstrated.In this paper, By using a curved genetic reflex algorithms reflector for with optimization, a new cube-corner the angles andstructure the positions is proposed of the pins,and whichdemonstrated. serve as theBy using building genetic elements algorithms of corner-cube for optimi reflectors,zation, the play angles a role and as the the parameters positions of to the enhance pins, whichthe performance serve as the of abuilding curved reflex elements reflector. of corner-cub Comparede withreflectors, conventional play a role retro-reflectors, as the parameters it is found to enhancethat a 46% the higher performance retro-reflection of a curved efficiency reflex and reflector. 33% larger Compared working with area conventional can be accomplished retro-reflectors, with our it isoptimized found that design. a 46% higher retro-reflection efficiency and 33% larger working area can be accomplished with our optimized design.

(a) (b)

FigureFigure 1. Retro-reflected 1. Retro-reflected light bylight (a) by the ( Economica) the Economic Commission Commission for Europe for (ECE) Europe regular (ECE) reflex regular reflector, andreflex (b) the reflector, ECE SuperPin and (b) reflex the ECE reflector. SuperPin reflex reflector.

2. Principles 2. PrinciplesThe EU ECE standard is designed to reduce injuries and deaths resulting from traffic accidents by providingThe EU adequate ECE standard illumination is designed of the roadway to reduce and inju byries enhancing and deaths the conspicuityresulting from of motor traffic vehicles accidents on publicby providing roads so adequate that their il presencelumination is perceived, of the roadway in daylight, and darknessby enhancing and other the conspicuity conditions of of reduced motor vehiclesvisibility. on A public white reflexroads reflectorso that their provides presence an observation is perceived, angle in daylight, of 0.33◦ darkness(EU ECE and regulations), other conditions not less ofthan reduced 1680 millicandela visibility. /luxA white at a light reflex entrance reflec angletor provides of 0◦, not an less observation than 1120 millicandelaangle of 0.33/lux° of(EU light ECE at 1regulations),◦ up and 10◦ notdown less and than not 1680 less thanmillicandela/lux 560 millicandela at a /luxlight including entrance the angle entrance of 0°, angle not less at 20 than◦ left 1120 and millicandela/lux20◦ right. [5]. of light at 1° up and 10° down and not less than 560 millicandela/lux including the entranceThe corner-cubeangle at 20° retro-reflectorleft and 20° right. (CCR) [5]. is based on groups of three perpendicular planes, as shown in FigureThe 2corner-cube. Conventionally, retro-reflector the dihedral (CCR) angle is based between on groups any pair of of three reflecting perpendicular faces is made planes, to beas shownalmost exactlyin Figure 90 2.◦ [Conventionally,1], so that the reflected the dihedral beam isangle exactly between antiparallel any pair to theof reflecting incident beamfaces is [13 made]. If the to beangles almost diff exactlyer from 90° 90 ◦[1],by so an that amount, the reflected the reflected beam is beam exactly will antiparallel be converged to the or incident diverged beam in multiple [13]. If thebeams angles to achieve differ from the required90° by an application amount, the [1 reflecte]. d beam will be converged or diverged in multiple beamsThrough to achieve an arraythe requ of pins,ired application corner-cube [1]. retro-reflectors can be produced as shown in Figure2. The orientation of each face is given by the normal unit nˆ1, nˆ2, and nˆ3 for each face. The reflection from each face reverses the component of the light’s velocity vector that is normal to the face. Let →V and →V0 be the directions of a ray before and after reflection, respectively, with the vector V given by →V=→V0 0 − 2(→V nˆ) nˆ, where nˆ is normal to the face. Applying the above formula three times yields the direction of ·

(a) (b) Appl. Sci. 2019, 9, x 2 of 14

It is usual for reflex reflectors to have a curved shape; for example, to fit the corner of a vehicle [1–5,17]. Cube-corner structures are, thus, distorted to complete the curve, so that their effective working area and reflection efficiency are affected, thus leading to the retro-reflector being against EU ECE regulations [5,11,17]. In this paper, a curved reflex reflector with a new cube-corner structure is proposed and demonstrated. By using genetic algorithms for optimization, the angles and the positions of the pins, which serve as the building elements of corner-cube reflectors, play a role as the parameters to enhance the performance of a curved reflex reflector. Compared with conventional retro-reflectors, it is found that a 46% higher retro-reflection efficiency and 33% larger working area can be accomplished with our optimized design.

(a) (b)

Figure 1. Retro-reflected light by (a) the Economic Commission for Europe (ECE) regular reflex reflector, and (b) the ECE SuperPin reflex reflector. Appl. Sci. 2019, 9, 1555 3 of 15

2.the Principles reflected beam for a particular order of reflection. Formulas for the direction of the reflected rays afterThe the EU three ECE reflections standard areis designed given by to Chandler’s reduce inju formula:ries and deaths resulting from traffic accidents by providing adequate illumination of the roadway and by enhancing the conspicuity of motor vehicles on public roads so that their presence→t = →q + is2 perceived,→α(α→α β→b in+ daylight,γ→c ) darkness and other conditions(1) − of reduced visibility. A white reflex reflector provides an observation angle of 0.33° (EU ECE regulations),where →t is thenot finalless direction;than 1680 →millicandela/luxq is the original direction:at a light entranceα, β, γ are angle the smallof 0°, anglesnot less by than which 1120 the ° ° millicandela/luxangles between of the light three at mirrors1 up and exceed 10 down right anglesand not and less→a ,than→b , and 560→c millicandela/luxare normal to the including three mirrors the ° ° entrancetaken in angle order at in 20 a right-hand left and 20 sense. right. Equation [5]. (1) is valid at the first-order when the mirrors are nearly The corner-cube retro-reflector (CCR) is based on groups of three perpendicular planes, as mutuallyAppl. Sci. 2019 perpendicular., 9, x The angle α is the angle between the faces whose normals are →b , and →c .3 The of 14 shown in Figure 2. Conventionally, the dihedral angle between any pair of reflecting faces is made to normals may be strictly perpendicular; that is, they do not need to include the small deviations caused be almost exactly 90° [1], so that the reflected beam is exactly antiparallel to the incident beam [13]. If by theThrough dihedral-angle an array off sets.of pins, The corner-cube directions of retro-reflec the reflectedtors rays can were be produced computed as by shown applying in Figure the law 2. the angles differ from 90° by an amount, the reflected beam will be converged or diverged in multiple ofThe reflection orientation three of times. each face is given by the normal unit , , and for each face. The reflection beamsfrom to each achieve face thereverses requ iredthe componentapplication of[1]. the light's velocity vector that is normal to the face. Let and be the directions of a ray before and after reflection, respectively, with the vector V' given by =′- 2(. ) , where is normal to the face. Applying the above formula three times yields the direction of the reflected beam for a particular order of reflection. Formulas for the direction of the reflected rays after the three reflections are given by Chandler's formula:

= + 2(α − β + γ) (1) where is the final direction; is the original direction: α, β, γ are the small angles by which the angles between the three mirrors exceed right angles and , , and are normal to the three

mirrors taken in order in a right-hand sense. Equation (1) is valid at the first-order when the mirrors (a) (b) are nearly mutually perpendicular. The angle α is the angle between the faces whose normals are , and Figure. The 2. normals(a) A flat corner-cubemay be strictly retro-reflector perpendicular; composed th ofat groups is, they of pins;do not and need (b) a groupto include of pins the and small deviationsits reflecting caused surfaces by the of thedihedral-angle pin groups (red offsets. inner region).The directions of the reflected rays were computed by applying the law of reflection three times. TheThe unitunit normalsnormals toto the the faces faces can can be be computed computed as as follows follows and and as as shown shown in in Figure Figure3. 3. Let Let the the ˆ ˆ kˆ normalsnormals toto thethe facesfaces withoutwithout dihedral-angledihedral-angle ooffsetsffsets be the unit vectors ı,̂ ,̂, andand along along the the three three α π coordinatescoordinates x, x, y, y, and and z, z, respectively. respectively. If If the the angle angle between between the the zx zx plane plane and and the the zy zy plane plane is is α= =( (π/2)/2)+ + δ1, the xz plane and the xy plane is β = (π/2) + δ2, the yz plane and the yx plane is γ = (π/2)+ δ3, shown δ1, the xz plane and the xy plane is β = (π/2) + δ2 , the yz plane and the yx plane is γ = (π/2)+ δ3, shown inin Figure Figure3 b;3b; this this can can be be expressed expressed by by Equations Equations (2)–(4), (2)–(4),

δ δ n = ı ̂ + 1 ȷ ̂ ; = ̂ + 1 ̂ ; ˆ= (2) nb1 = ˆı + ; nb2 = ˆ + ˆı; nb3 = k (2) 2 2 n = ı ̂ + ȷ ̂ ; = ̂ + ̂ ; = (3) δ δ 2 2 ˆ nb1 = ˆı + ; nb2 = ˆ + ˆı; nb3 = k (3) 2 2 (4) n = ı ̂ + ȷ ̂ δ; = ̂ + δ̂ ; = 3 3 ˆ nb1 = ˆı + ; nb2 = ˆ + ˆı; nb3 = k (4) 2 2 For small angles δ, the above expressions are quite adequate. Offsets in the other two dihedral For small angles δ, the above expressions are quite adequate. Offsets in the other two dihedral angles can be similarly represented. angles can be similarly represented. It is desirable to have the unit normals given in the coordinate system of the symmetry axis of the corner cube since the incidence angle of the laser beam is given with respect to this axis. The symmetry 1 axis is in the direction of the vector x = y = z = 1, as shown in Figure3c; we see that cos θA= ; √2 1 √2 1 sin θA = ; cos λA = ; sin λA = . The normals in the xyz coordinate system can be given in the √2 √3 √3 coordinate system of the symmetry axis by rotating the original coordinate system about the z axis by

(a) (b) (c)

Figure 3. (a) Normal to the reflecting faces with dihedral-angle offsets; (b) angle between each

plane: α = (π/2)+ δ1, ;β = (π/2)+ δ2 ; γ = (π/2)+ δ3 ; and (c) direction of symmetry axis.

It is desirable to have the unit normals given in the coordinate system of the symmetry axis of the corner cube since the incidence angle of the laser beam is given with respect to this axis. The

symmetry axis is in the direction of the vector x = y = z = 1, as shown in Figure 3c; we see that cos θ= √ ; sin θ = ; cos λ = ; sin λ = . The normals in the xyz coordinate system can be given in the √ √ √ √ coordinate system of the symmetry axis by rotating the original coordinate system about the z axis by θA and about the y axis by −λA. This brings the x axis along the axis of the matrix form, and the total rotation is given by: Appl. Sci. 2019, 9, x 3 of 14

Figure 2. (a) A flat corner-cube retro-reflector composed of groups of pins; and (b) a group of pins and its reflecting surfaces of the pin groups (red inner region).

Through an array of pins, corner-cube retro-reflectors can be produced as shown in Figure 2.

The orientation of each face is given by the normal unit 𝑛, 𝑛, and 𝑛 for each face. The reflection from each face reverses the component of the light's velocity vector that is normal to the face. Let 𝑉⃗ and 𝑉⃗ be the directions of a ray before and after reflection, respectively, with the vector V' given by 𝑉⃗=𝑉⃗′- 2(𝑉⃗. 𝑛) 𝑛, where 𝑛 is normal to the face. Applying the above formula three times yields the direction of the reflected beam for a particular order of reflection. Formulas for the direction of the reflected rays after the three reflections are given by Chandler's formula:

𝑡⃗ = 𝑞⃗ + 2𝑎⃗(α𝑎⃗ − β𝑏⃗ + γ𝑐⃗) (1) where 𝑡⃗ is the final direction; 𝑞⃗ is the original direction: α, β, γ are the small angles by which the angles between the three mirrors exceed right angles and 𝑎⃗, 𝑏⃗, and 𝑐⃗ are normal to the three mirrors taken in order in a right-hand sense. Equation (1) is valid at the first-order when the mirrors are nearly mutually perpendicular. The angle α is the angle between the faces whose normals are 𝑏⃗, and 𝑐⃗. The normals may be strictly perpendicular; that is, they do not need to include the small deviations caused by the dihedral-angle offsets. The directions of the reflected rays were computed by applying the law of reflection three times. The unit normals to the faces can be computed as follows and as shown in Figure 3. Let the Appl. Sci. 2019, 9, 1555 4 of 15 normals to the faces without dihedral-angle offsets be the unit vectors 𝚤̂, 𝚥̂, and 𝑘 along the three coordinates x, y, and z, respectively. If the angle between the zx plane and the zy plane is α = (π/2) + θδ1, theand xz about plane the and y axisthe xy by planeλ . is This β = brings (π/2) + the δ2 , xthe axis yz along plane the and axis the of yx the plane matrix is γ form, = (π/2)+ and δ3 the, shown total A − A rotationin Figure is 3b; given thisby: can be expressed by Equations (2)–(4),

      n λ= ı ̂ + ȷ ̂ ; 𝑛λ = 𝚥̂ + θ𝚤̂ ; 𝑛 = 𝑘θ (2)  x0   cos A 0 sin A  cos A sin A 0  x         y0  =  0 1 0  sin θA cos θA 0  y  (5)    n = ı ̂ + ȷ ̂ ; 𝑛 = 𝚥̂ −+ 𝚤̂ ; 𝑛 = 𝑘   (3)  z   sin λ 0 cos λ  0 0 1  z  0 − A A (4)1 Substituting the valuesn of the= ı ̂ sines+ ȷ and ̂ ; 𝑛 cosines = 𝚥̂ + and 𝚤̂ ; multiplying𝑛 = 𝑘 the matrices, we obtain x0= √3 1 1 (x + y + z); y0= (y x); z0= (2z x y). In Figure4a, the unprimed axes represent the original For small angles√2 −δ, the above√6 expressions− − are quite adequate. Offsets in the other two dihedral coordinateangles can be system similarly and therepresented. primed axes are the rotated coordinates.

Appl. Sci. 2019, 9, x 4 of 14 axis by θA and about the y axis by −λA. This brings the x axis along the axis of the matrix form, and the total rotation is given by:

𝑥′ cos λ 0sinλ cos θ sin θ 0 𝑥 𝑦′ = 010 −sinθ cos θ 0 𝑦 (5) 𝑧 𝑧′ −sin λ 0 cos λ 001 Substituting the values of the sines and cosines and multiplying the matrices, we obtain 𝑥= (a) (b) (c) √ (𝑥+𝑦+𝑧); 𝑦= (𝑦−𝑥); 𝑧= (2𝑧 − 𝑥 −𝑦). In Figure 4a, the unprimed axes represent the original FigureFigure 3. 3.(a √()a Normal) Normal to to the the reflecting√ reflecting faces faces with with dihedral-angle dihedral-angle offsets; offsets; (b) angle(b) angle between between each plane:each coordinateαplane:= (π /system2) α+ =δ (1π; β /2)+and= (δπ 1,the/ 2);β+ =primed δ(2π;/2)+γ = δ(axesπ2 ;/ 2)γ += are δ(π3;/2)+ the and δ rotated (3c ;) and direction ( ccoordinates.) direction of symmetry of symmetry axis. axis.

It is desirable to have the unit normals given in the coordinate system of the symmetry axis of the corner cube since the incidence angle of the laser beam is given with respect to this axis. The

symmetry axis is in the direction of the vector x = y = z = 1, as shown in Figure 3c; we see that cos θ= √ ; sin θ = ; cosλ = ; sin λ = . The normals in the xyz coordinate system can be given in √ √ √ √ the coordinate system of the symmetry axis by rotating the original coordinate system about the z

(a) (b) (c)

FigureFigure 4. (4.a )( Relationshipa) Relationship of x,of y, x, z andy, z xand0, y 0x',, z 0y',coordinate z' coordinate axes; axes; (b) the (b direction) the direction of incident of incident beam after reflection;beam after and reflection; (c) the relationship and (c) the of relationship x0, y0, z0 and ofx”, x', y”,y', z' z” and axes. x", y", z" axes.

TheThe incident incident beam beam after after reflection reflection at at the the front front face face is is in in a a direction direction given given by by the the angles angles θ′θ0 andand ϕ′φ0 inin the the primed primed coordinate coordinate system, system, as as shown shown in in Figure Figure 44b.b. AA second second rotation rotation of of the the coordinate coordinate system system must must be be performed performed to to get get the the normals normals to to the the faces faces in in thethe coordinate coordinate system system of of the the laser laser beam. beam. By By rotati rotatingng the the coordinate coordinate system system about about the the x' x0 axisaxis by by θθ' 0andand thenthen about about the the new new z' z 0axisaxis by by ϕφ',0 we, we obtain: obtain:       𝑥′′ cos ϕ′ φ sin ϕ′φ 0 10 0 𝑥′  x00   cos 0 sin 0 0  1 0 0  x0  𝑦′′ = −sin ϕ′ cos ϕ′ 0 0 cos θ′ sin θ′  𝑦′ (6)  y00  =  φ φ  θ θ  y     sin 0 cos 0 0  0 cos 0 sin 0  0  (6) 𝑧′′   −0010−sinθ′ cos θ′  𝑧′  z00 0 0 1 0 sin θ0 cos θ0 z0 The relationship of the primed and double-primed coordinate− axes is given in Figure 4c. The x' axis isThe the relationshipsymmetry axis of theof the primed reflector, and double-primedthe y', z' plane is coordinate parallel to axes the front is given face, in and Figure the4 x"c. Theaxis xis0 parallelaxis is theto the symmetry beam after axis it of enters the reflector, the corner the cube y0, z.0 Inplane this isstudy, parallel we toused the a front hollow face, corner and the cube; x” axisthe reflectionsis parallel can to the be done beam for after all itsix enters possible the sequence corner cube.s of reflections In this study, by taking we used the aincident hollow beam, corner given cube; bythe the reflections vectors x"= can –1, be y"= done z" = for 0, alland six reflecting possible it sequences from each of of reflections the normals by to taking the faces the incidentin the double- beam, primed coordinate system. The y" and z" coordinates of the reflected beam give the deviations from the incident direction. The beam spread at normal incidence when all dihedral angles are offset by the same amount is given by the formula ε1 = √6 n δ1 , ε2 = √6 n δ2 , ε3 = √6 n δ3, where δ is the angle by which the dihedral angles exceed 90° and ε is the angle between the incident and the reflected rays. When the light passes through CCRs, there will be a change in the direction of reflection. The direction of the incident beam is determined by θ′ and ϕ′ in the primed coordinate system. Based on the above mathematical theory, the optical simulations through the TracePro software (Lambda Research Corporation of Littleton, Massachusetts, USA) show that CCRs with the same dihedral angle can reflect six beams with the same reflection angle ε with respect to the incident beam. When the dihedral angle is δ1 = 0.095°; (α = 90.095°); δ2 = 0.095°; (β = 90.095°); δ3 = 0.12° (γ = 90.12°), the reflected beams can be found that ε1= 0.33°, ε2 = ε3 = 0.31°, which fit EU ECE regulation requirements. The simulation result is shown in Figure 5c. Appl. Sci. 2019, 9, 1555 5 of 15 given by the vectors x” = –1, y” = z” = 0, and reflecting it from each of the normals to the faces in the double-primed coordinate system. The y” and z” coordinates of the reflected beam give the deviations from the incident direction. The beam spread at normal incidence when all dihedral angles are offset by the same amount is 4 √ 4 √ 4 √ given by the formula ε1 = 3 6 n δ1, ε2 = 3 6 n δ2, ε3 = 3 6 n δ3, where δ is the angle by which the dihedral angles exceed 90◦ and ε is the angle between the incident and the reflected rays. When the light passes through CCRs, there will be a change in the direction of reflection. The direction of the incident beam is determined by θ0 and φ0 in the primed coordinate system. Based on the above mathematical theory, the optical simulations through the TracePro software (Lambda Research Corporation of Littleton, Massachusetts, USA) show that CCRs with the same dihedral angle can reflect six beams with the same reflection angle ε with respect to the incident beam. When the dihedral angle is δ1 = 0.095◦;(α = 90.095◦); δ2 = 0.095◦;(β = 90.095◦); δ3 = 0.12◦ (γ = 90.12◦), the reflected beams can be found that ε1= 0.33◦, ε2 = ε3 = 0.31◦, which fit EU ECE regulation requirements. The simulation result is shown in Figure5c. Appl. Sci. 2019, 9, x 5 of 14

(a) (b) (c)

FigureFigure 5. (5.a()a Set-up) Set-up for opticalfor optical simulations simulations of corner-cube of corner-cube retro-reflectors retro-reflectors (CCRs); ( b(CCRs);) the orientation (b) the of theorientation corner cube; of the and corner (c) the cube; retro-reflected and (c) the beams retro-reflected intensity beams distribution. intensity distribution.

By using the different different angles between each pair of facets, we can move the three retro-reflected retro-reflected raysrays on the toptop intointo oneone directiondirection and and the the other other three three into into another another direction, direction, as as shown shown in in Figure Figure5c. 5c. In Inthis this way, way, we dramaticallywe dramatically improve improve the optical the optica performancel performance of a corner of a corner cube, because cube, because the retro-reflected the retro- reflectedenergy in energy a given directionin a given is tripled.direction We is call tripled. this techique We call SuperPin this techique technology. SuperPin The experimenttechnology. beam The experimentpattern retro-reflected beam pattern from retro-reflected the SuperPin from corner the is SuperPin shown in corner next section. is shown in next section.

3. Experimental Setups and Analysis 3. Experimental Setups and Analysis In order to investigate the property of a curved reflex reflector, a commercialized CCCR (curved In order to investigate the property of a curved reflex reflector, a commercialized CCCR (curved corner cube retroreflector) for a car was used for testing, as shown in Figure6. The 146 34 mm sample corner cube retroreflector) for a car was used for testing, as shown in Figure 6. The× 146 × 34 mm is made of PMMA (poly methyl methacrylate) and composed of 2.75-mm sized corner-cube arrays. The sample is made of PMMA (poly methyl methacrylate) and composed of 2.75-mm sized corner-cube product is provided by OWL LIGHT AUTOMOTIVE MFG. CORP (Lukang, Chunghua, Taiwan) and it arrays. The product is provided by OWL LIGHT AUTOMOTIVE MFG. CORP (Lukang, Chunghua, has been in mass production for automotives in the EU. The experimental setup for CCCR testing is Taiwan) and it has been in mass production for automotives in the EU. The experimental setup for shown in Figure7. In the optical setup, a 532 nm diode-pumped solid state (DPSS) laser operated with CCCR testing is shown in Figure 7. In the optical setup, a 532 nm diode-pumped solid state (DPSS) a 5 mW output acted as the light source. The distance between the laser and the curved reflex reflector laser operated with a 5 mW output acted as the light source. The distance between the laser and the was set to be 30.5 meters to measure the reflected light spot. Based on the laser spectrum specification, curved reflex reflector was set to be 30.5 meters to measure the reflected light spot. Based on the laser its coherence length is calculated to be about 0.5 mm, which is less than the corner-cube dimension spectrum specification, its coherence length is calculated to be about 0.5 mm, which is less than the of 2.75 mm in the experiments. Therefore, the retro-reflected output spots were spatially incoherent, corner-cube dimension of 2.75 mm in the experiments. Therefore, the retro-reflected output spots and the laser can be considered as an incoherent light source for the following retro-reflector testing were spatially incoherent, and the laser can be considered as an incoherent light source for the followingexperiments. retro-reflector The laser light testing had experiments. an incident angle The laser of 0◦ lightwith had respect an incident to the car angle driving of 0 direction,° with respect as it shone on the commercialized CCCR with a spot area of 520 mm2. As a result, several retro-reflected to the car driving direction, as it shone on the commercialized CCCR with a spot area of 520 mm2. As alight result, spots several can be retro-reflected found on the light black spots screen can located be found 30.5 on meters the black away screen from the located test sample. 30.5 meters A Minolta 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 obtained. During experiments, the anterior, central and posterior regions of the CCCR were investigated. Their locations and the car’s driving direction are presented in Figure 8. Initially, the laser light was adjusted to be parallel with the driving direction and focus on the central part of each region. The reflected outputs are shown in Figure 9a–c, respectively. It can be found that the reflected light spots become gloomy as the test region shifted from the front part to the end part of the CCCR. The curved shape of the CCCR seems to have caused interferences regarding its functions. Appl. Sci. 2019, 9, 1555 6 of 15

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 obtained. During experiments, the anterior, central and posterior regions of the CCCR were Appl. Sci. 2019, 9, x 6 of 14 Appl.investigated.Appl. Sci.Sci. 20192019,, 99,, Their xx locations and the car’s driving direction are presented in Figure8. 66 ofof 1414

Figure 6. The commercial SuperPin curved reflex reflector. FigureFigure 6. 6. TheThe commercialcommercial SuperPin SuperPin cu curvedcurvedrved reflex reflexreflex reflector. reflector.reflector.

Figure 7. Experimental setup for curved corner-cube retro-reflector (CCCR) testing. FigureFigure 7. 7. ExperimentalExperimental setupsetup forfor curved curved corner corner-cubecorner-cube-cube retro-reflector retro-reflectorretro-reflector (CCCR)(CCCR) testing.testing.

Figure 8. The test regions of CCCR; each testing area is 520 mm22.. FigureFigure 8.8. TheThe testtest regionsregions ofof CCCR;CCCR; eacheach testingtesting areaarea isis 520520 mmmm22.. Initially, the laser light was adjusted to be parallel with the driving direction and focus on the central part of each region. The reflected outputs are shown in Figure9a–c, respectively. It can be found that the reflected light spots become gloomy as the test region shifted from the front part to the end part of the CCCR. The curved shape of the CCCR seems to have caused interferences regarding Commercialized its functions.CommercializedCommercialized reflex reflector reflexreflex reflectorreflector

(a) (b) (c) ((aa)) ((bb)) ((cc)) Figure 9. The retro-reflected outputs by (a) anterior, (b) central, and (c) posterior regions FigureFigure 9.9. TheThe retro-reflectedretro-reflected outputsoutputs byby ((aa)) anterior,anterior, ((bb)) central,central, andand ((cc)) posteriorposterior regionsregions of the commercial SuperPin CCCR. ofof thethe commercialcommercial SuperPinSuperPin CCCR.CCCR. Appl. Sci. 2019, 9, x 6 of 14

Figure 6. The commercial SuperPin curved reflex reflector.

Figure 7. Experimental setup for curved corner-cube retro-reflector (CCCR) testing.

Appl. Sci. 2019, 9, 1555 7 of 15 Figure 8. The test regions of CCCR; each testing area is 520 mm2.

Commercialized reflex reflector

(a) (b) (c)

Appl.Figure Sci. 2019 9.,,Figure 9,, The xx retro-reflected9. The retro-reflected outputs outputs by (a) by anterior, (a) anterior, (b) central, (b) central, and and (c) posterior(c) posterior regions regions of the 7 of 14 commercialof the SuperPin commercial CCCR. SuperPin CCCR. In order to enhance the performance of the.SuperPin CCCR, a single beam parallel with driving directionIn order was to used enhance to probe the performance the reflecting of surfaces the.SuperPin of the CCCR,posterior a single region beam by optical parallel simulations. with driving As directionshown in was Figure used 9, tothe probe anterior the and reflecting the central surfaces regions of the areas posterior have a region higher by performance optical simulations. than the rest. As shownIn contrast, in Figure at the9, the upper anterior position and (0.33°) the central of the regions posterior areas area have of a CCCR, higher there performance is almost than no thereflected rest. Inlight. contrast, Therefore, at the it upper can be position concluded (0.33 that◦) the of the post posteriorerior area area cannot of CCCR, meet ECE there regulation is almost requirements. no reflected light.In Therefore, order to it rescue can be the concluded posterior that region, the posterior the rela areationship cannot between meet ECE the incident regulation light requirements. location of CCRIn and order its retro-reflected to rescue the posteriorlight direction region, is investigated. the relationship The betweensimulation the experiments incident light of rays location shining of CCRon face and #1, its retro-reflectedface #2, and face light #3 direction are conducted, is investigated. respectively. The simulation Their resulted experiments reflected of light rays intensity shining ondistribution face #1, face are #2,shown and in face Figures #3 are 10–12. conducted, Comparing respectively. Figure 9 Theirwith Figure resulted 10, reflected Figure 11 light and Figure intensity 12, distributionit can be understood are shown inthat Figures the #1 10 and–12 .#3 Comparing reflecting Figuresurfacessurfaces9 with inin thethe Figures posteriorposterior 10–12 regionregion, it can dodo be understoodnotnot functionfunction thatnormally, the #1 andso that #3 three reflecting light surfaces spots are in missed the posterior in the output region screen. do not functionIf the pin normally, group structures so that threecould light spots are missed in the output screen. If the pin group structures could be reconstructed, the be reconstructed, the coefficient of luminous intensity RII andand thethe reflectionreflection efficiencyefficiency RRA wouldwould bebe coeimproved.fficient of luminous intensity RI and the reflection efficiency RA would be improved.

FigureFigure 10. The 10. CCCRThe CCCR #1 reflecting #1 reflecting surface surface in the inin posterior thethe posterior region is regionregion hit by isis a hithit simulated byby aa simulatedsimulated laser beam laserlaser (left ) and thebeam resulting (left) and retro-reflected the resulting light retro-reflected intensity distributions light intensity (right distributions). (right).

FigureFigure 11. The 11. CCCRThe CCCR #2 reflecting #2 reflecting surface surface in the in posterior the posterior region is regionregion hit by isis a hithit simulated byby aa simulatedsimulated laser beam laserlaser (left ) and thebeam resulting (left) and retro-reflected the resulting light retro-reflected intensity distributions light intensity (right distributions). (right).

Appl. Sci. 2019, 9, x 7 of 14

In order to enhance the performance of the.SuperPin CCCR, a single beam parallel with driving direction was used to probe the reflecting surfaces of the posterior region by optical simulations. As shown in Figure 9, the anterior and the central regions areas have a higher performance than the rest. In contrast, at the upper position (0.33°) of the posterior area of CCCR, there is almost no reflected light. Therefore, it can be concluded that the posterior area cannot meet ECE regulation requirements. In order to rescue the posterior region, the relationship between the incident light location of CCR and its retro-reflected light direction is investigated. The simulation experiments of rays shining on face #1, face #2, and face #3 are conducted, respectively. Their resulted reflected light intensity distribution are shown in Figures 10–12. Comparing Figure 9 with Figure 10, Figure 11 and Figure 12, it can be understood that the #1 and #3 reflecting surfaces in the posterior region do not function normally, so that three light spots are missed in the output screen. If the pin group structures could be reconstructed, the coefficient of luminous intensity RI and the reflection efficiency RA would be improved.

Figure 10. The CCCR #1 reflecting surface in the posterior region is hit by a simulated laser beam (left) and the resulting retro-reflected light intensity distributions (right).

Figure 11. The CCCR #2 reflecting surface in the posterior region is hit by a simulated laser Appl. Sci. 2019, 9, 1555 8 of 15 beam (left) and the resulting retro-reflected light intensity distributions (right).

Appl. Sci. 2019, 9, x 8 of 14

FigureFigure 12. The12. The CCCR CCCR #3 reflecting #3 reflecting surface surface in the in posteriorthe posterior region region is hit is by hit a simulatedby a simulated laser beamlaser beam (left) and( theleft) resulting and the resulting retroreflected retroreflected light intensity light distributionsintensity distributions (right). (right). 4. Optics Design and Verification 4. Optics Design and Verification In order to remedy the ineffective posterior working area of the commercial design, two groups of In order to remedy the ineffective posterior working area of the commercial design, two groups pins were connected together as the double pins group to compose the CCCR, as shown in Figure 13. of pins were connected together as the double pins group to compose the CCCR, as shown in Figure Fifteen pieces of double-pin groups were arranged in parallel to the car driving direction to compose 13. Fifteen pieces of double-pin groups were arranged in parallel to the car driving direction to the primary CCCR; one pin group touches the curve reference surface and the other one is free to compose the primary CCCR; one pin group touches the curve reference surface and the other one is translate in the car driving direction. The height difference between the neighboring pins in a group of free to translate in the car driving direction. The height difference between the neighboring pins in a double pins and the double pin group are named di and Di, respectively. group of double pins and the double pin group are named di and Di, respectively.

Figure 13. The height difference difference between the neighboringneighboring pins in aa double-pin group.group.

f The object function f defineddefined by the Equation (7) was determined in the optimization process. TheThe optimizationoptimization processprocess encompassedencompassed threethree fragments.fragments. Object function: The equation that describes the value of the object function of the optimization programprogram establishedestablished byby geneticgenetic algorithmsalgorithms isis asas follows:follows:

n r 𝑓(𝑖, 𝑗) = ∑X, 𝑤(𝑚 −𝑡) +𝑤𝑗(𝑚 −𝑡2) (7) f (i, j) = w (m t )2 + wj m t (7) i i − i j − j where wi is the weight parameter of thei, jobject=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 is wherethe optimizationwi is the weight target parameter defined with of the a objectvalue function, correspondingmj is the to value the retroreflective of the measured light target, intensity which on is determinedthe retroreflector by the plane. intensity sensor through each optimal loop when running the program, and tj is the optimizationLuminous intensity target defined function: with In a valueorder correspondingto improve the to primary the retroreflective CCCR further, light intensitythe add-on on ray the retroreflectortracing simulation plane. tool OptisWork (Optis SAS, La Farlede, France), embedded in SolidWorks mechanicalLuminous design intensity software, function: was used In order to search to improve suitable the variable primary parameters CCCR further, to get the an add-on optimized ray tracingCCCR, simulationusing di to tool elevate OptisWork its performance (Optis SAS, and La D Farlede,i to fit the France), reference embedded curve infor SolidWorks the outlook mechanical of CCCR designsmoothly. software, The constraint was used of to each search variable suitable parameter variable parameters is determin toed get by an the optimized curvature CCCR, of the using CCCR di surface. The lighting performances, such as intensity distributions, illumination uniformity and optical efficiencies of CCCR, can be accomplished to meet targets by using optimization. In the study, the luminous intensity function serves as the object function, and the value RI at the upper 0.33° is targeted to be maximum in the solution searching process. We search for an approximation of the luminous intensity (RI) I(φ,a,b,c) as object function, which is at the polar angle Φ in the form:

I(φ,x,y,z) = Imax∑ 𝑥𝑐𝑜𝑠 (φ–yk) (8) where K is the number of functions to sum and xk, yk, zk are the function coefficients that we expect. For brevity, coefficients are written as vectors x = (x1, x2,...,xk), y = (y1,y2,...,yk), z= (z1,z2,...,zk). The interval range of the coefficients is: a = [0,0.81], b = [–1,1], c = [0,100]. Discrete optimization algorithms will work on the finite subsets where the possible values will be: x* ϵ {0, 0.001,0.002,...0.81}, y* ϵ {–1, 0.9,0.8,0.7, ..., -1}, z* ϵ{0, 1, 2, ...,100}. Appl. Sci. 2019, 9, 1555 9 of 15

to elevate its performance and Di to fit the reference curve for the outlook of CCCR smoothly. The constraint of each variable parameter is determined by the curvature of the CCCR surface. The lighting performances, such as intensity distributions, illumination uniformity and optical efficiencies of CCCR, can be accomplished to meet targets by using optimization. In the study, the luminous intensity function serves as the object function, and the value RI at the upper 0.33◦ is targeted to be maximum in the solution searching process. We search for an approximation of the luminous intensity (RI) I(φ,a,b,c) as object function, which is at the polar angle Φ in the form:

Xk zk I(φ, x, y, z) = Imax xkcos (φ–yk) (8) k=1 where K is the number of functions to sum and xk, yk, zk are the function coefficients that we expect. For brevity, coefficients are written as vectors x = (x1, x2,...,xk), y = (y1,y2,...,yk), z= (z1,z2,...,zk). The interval range of the coefficients is: a = [0,0.81], b = [ 1,1], c = [0,100]. Discrete optimization algorithms − will work on the finite subsets where the possible values will be: x*  {0, 0.001,0.002,...0.81}, y*  {1, Appl. Sci. 2019, 9, x 9 of 14 0.9,0.8,0.7, ..., 1}, z* {0, 1, 2, ...,100}. − The components in the OptisWork optimization softwaresoftware have been configuredconfigured to incorporate three elements: the the light light source, source, intensity sensor sensor and and CCCR. The interspace between the CCCR and the surface sourcesource hadhad been been fixed fixed as as stated stated by by ECE ECE standards standards as as the the interval interval of theof the intensity intensity sensor. sensor. For Forthe the rapid rapid finishing finishing of theof the optimization, optimization, Di Disi is initially initially set set to to be be constant constant and and eacheach double-pindouble-pin group was assigned a value of di asas aa variable.variable. Based on the lengthwise extent and bend of the curved surface, dualdual pinspins hadhad 1515 groups groups that that comprised comprised 15 15 variables variables of ofdi (fromdi (fromd1 dto1 tod15 d).15). This This is is illustrated illustrated in inFigure Figure 13. 13. The The constraints constraints of each of each variable variable of di areof di determined are determined by the by curvature the curvature of thecontact of the surface.contact surface.Each variable Each hasvariable a non-identical has a non-identical limitation oflimitation height values of height and is values contingent and onis thecontingent situation on of the situationsurface that of the merit surface should that fluctuate merit should from fluctuate 0.01–0.81 from mm. 0.01–0.81 The territory mm. ofThe a CCCRterritory which of a CCCR has extreme which hascurvature extreme will curvature have the will highest have altitude the highest value. altitu Ourde optimal value. goalOur shouldoptimal focus goal onshould the posterior focus on area, the whereposterior the area, lowest where reflectivity the lowest is achieved, reflectivity and improveis achieved, the reflectivityand improve of light.the reflectivity As shown of in light. Figure As8, shownthe restriction in Figure was 8, determinedthe restriction by was the locationdetermined of each by the region. location of each region. In orderorder toto set set the the target target value value of the of optimization, the optimization, the simulation the simulation experiment experiment with a flat with regulated a flat regulatedCCR was exercisedCCR was to exercised find the reflected to find lightthe reflected power as thelight reference power byas athe 1000 reference lumen incident by a 1000 beam. lumen The incidentresulting beam. power The was 850resulting lm and power was used was as850 the lm target and for was the used subsequent as the searchingtarget for ofthe the subsequent optimized searchingCCCR. By of running the optimized the scheme CCCR. in optimization By running steps, the sche manuallyme in optimization limited to 500 steps, searching manually steps limited to quickly to 500find searching a better solution, steps to thequickly best find results a better were solution, determined the inbest step results 139, aswere shown deter inmined Figure in 14 step. The 139, final as shownintensity in sensorFigure value14. The was final shown intensity to be sensor 810.27 value lm, which was shown was also to thebe output810.27 lm, power which reflected was also by the outputoptimized power CCCR. reflected by the optimized CCCR.

Figure 14. TheThe recorded recorded value for the intensit intensityy sensor versus running cycles.

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 (8). The target of the optimization process was defined as a value corresponding to the retroreflective light intensity on the retro-reflector plane. During the optimization, to have the CCCR meet the requirement of the ECE standard at 0.33° and maximum reflection efficiency, the values of δ and di were found through the workflows shown in Figures 15 and 16, respectively.

Appl. Sci. 2019, 9, x 9 of 14

The components in the OptisWork optimization software have been configured to incorporate three elements: the light source, intensity sensor and CCCR. The interspace between the CCCR and the surface source had been fixed as stated by ECE standards as the interval of the intensity sensor. For the rapid finishing of the optimization, Di is initially set to be constant and each double-pin group was assigned a value of di as a variable. Based on the lengthwise extent and bend of the curved surface, dual pins had 15 groups that comprised 15 variables of di (from d1 to d15). This is illustrated in Figure 13. The constraints of each variable of di are determined by the curvature of the contact surface. Each variable has a non-identical limitation of height values and is contingent on the situation of the surface that merit should fluctuate from 0.01–0.81 mm. The territory of a CCCR which has extreme curvature will have the highest altitude value. Our optimal goal should focus on the posterior area, where the lowest reflectivity is achieved, and improve the reflectivity of light. As shown in Figure 8, the restriction was determined by the location of each region. In order to set the target value of the optimization, the simulation experiment with a flat regulated CCR was exercised to find the reflected light power as the reference by a 1000 lumen incident beam. The resulting power was 850 lm and was used as the target for the subsequent searching of the optimized CCCR. By running the scheme in optimization steps, manually limited to 500 searching steps to quickly find a better solution, the best results were determined in step 139, as shown in Figure 14. The final intensity sensor value was shown to be 810.27 lm, which was also the output power reflected by the optimized CCCR.

Appl. Sci. 2019, 9, 1555 10 of 15 Figure 14. The recorded value for the intensity sensor versus running cycles. In the initial optimization process, the mathematical equation for the intensity distribution of 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. 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 (8). The The luminous intensity RI is defined by I(φ, a, b, c) at the polar angle of φ, shown in Equation (8). The target of the optimization process was defined as a value corresponding to the retroreflective light target of the optimization process was defined as a value corresponding to the retroreflective light intensity on the retro-reflector plane. During the optimization, to have the CCCR meet the requirement intensity on the retro-reflector plane. During the optimization, to have the CCCR meet the of the ECE standard at 0.33◦ and maximum reflection efficiency, the values of δ and di were found requirement of the ECE standard at 0.33° and maximum reflection efficiency, the values of δ and di through the workflows shown in Figures 15 and 16, respectively. were found through the workflows shown in Figures 15 and 16, respectively.

Appl. Sci. 2019, 9, x 10 of 14

Figure 15. CCRCCR design design flow flow chart.

Figure 16. FlowFlow chart chart of of optimization optimization process.

As the optimization is terminated by the program, the optimized CCCR with the same curve as the commercial commercial one was obtained. After After the the optimization optimization process, process, the the optimized optimized CCCR CCCR was was analyzed analyzed for comparison withwith thethe commercial commercial reflector reflector by by simulations. simulations. The The distance distance from from the the light light source source to the to theCCCR CCCR is set is asset 30.5 as 30.5 meters meters and and the the diameter diameter of laser of laser beam beam is 25 ismm. 25 mm. The The CCCR CCCR is kept is kept with with its carits cardriving driving direction direction at 0at◦, 0°, 10 ◦10°(up, (up, down) down) vertically, vertically, and and 20 20°◦ (left, (left, right) right) horizontally horizontally withwith the incident light, respectively,respectively, to to perform perform the opticalthe optical tests of test ECEs regulations.of ECE regulations. The resulting The intensity resulting distributions intensity distributionsby 0◦ incident by light 0° incident to the anterior, light to centralthe anterior, and posterior central and regions posterior sequentially regions sequentially are shown in are Figure shown 17. inThe Figure results 17. showed The results that theshowed optimized that the CCCR optimize can contributed CCCR can much contribute greater much effective greater light effective intensity light than intensitythat of the than commercial that of the design commercial (no effective design retro-reflection (no effective atretro-reflection 0.33◦ up), as shown at 0.33° in up), Figure as 17shownc,f. The in Figurecandela 17c values and shownFigure in17f. Figure The candela17 showed values that show the lightn in reflectionFigure 17 intensityshowed ofthat the the optimal light reflection design is intensity4.36% (anterior of the area)optimal and design 16.7% (central is 4.36% area) (anterio higherr area) than theand commercial 16.7% (central design area) at 0 ◦higherlight incidence.than the commercialIn addition, design it was demonstratedat 0° light incidence. that RI Inand addition,RA are alsoit was increased demonstrated significantly that R inI and all regions, RA are also and increaseda larger retro-reflection significantly in working all regions, area is and accomplished a larger retro-reflection through the optimal working design. area is With accomplished 0◦, 10◦ (up, throughdown) vertical, the optimal and 20design.◦ (left, With right) 0°, horizontal 10° (up, down) incident vertical, light, theand retroflection 20° (left, right) results horizontal data R Iincidentand RA light,achieved the retroflection by the optimized results CCCR, data theRI and primary RA achieved CCCR, andby the the optimized commercial CCCR, CCCR the are primary calculated CCCR, and andshown the in commercial Figures 18 andCCCR 19 individuallyare calculated for and comparison. shown in Figure 18 and Figure 19 individually for comparison.

(a) (b) (c)

(d) (e) (f) Appl. Sci. 2019, 9, x 10 of 14

Figure 15. CCR design flow chart.

Figure 16. Flow chart of optimization process.

As the optimization is terminated by the program, the optimized CCCR with the same curve as the commercial one was obtained. After the optimization process, the optimized CCCR was analyzed for comparison with the commercial reflector by simulations. The distance from the light source to the CCCR is set as 30.5 meters and the diameter of laser beam is 25 mm. The CCCR 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 ECE regulations. The resulting intensity distributions by 0° incident light to the anterior, central and posterior regions sequentially are shown in Figure 17. The results showed that the optimized CCCR can contribute much greater effective light intensity than that of the commercial design (no effective retro-reflection at 0.33° up), as shown in Figure 17c and Figure 17f. The candela values shown in Figure 17 showed that the light reflection intensity of the optimal design is 4.36% (anterior area) and 16.7% (central area) higher than the commercial design at 0° light incidence. In addition, it was demonstrated that RI and RA are also increased significantly in all regions, and a larger retro-reflection working area is accomplished through the optimal design. With 0°, 10° (up, down) vertical, and 20° (left, right) horizontal incident light, the retroflection results data RI and RA achieved by the optimized CCCR, the primary CCCR, Appl.and Sci. 2019the ,commercial9, 1555 CCCR are calculated and shown in Figure 18 and Figure 19 individually 11for of 15 comparison.

(a) (b) (c)

Appl. Sci. 2019, 9, x 11 of 14

(d) Figure 17. Intensity(e) distributions and RI for 0° incident(f) light beam on anterior, central and posterior regions of the commercial CCCR, which are shown in (a)–(c) respectively, and those Figure 17. Intensity distributions and RI for 0◦ incident light beam on anterior, central and posterior of the optimized CCCR are shown in (d)–(f). regions of the commercial CCCR, which are shown in (a)–(c) respectively, and those of the optimized CCCR are shown in (d)–(f). .

Appl. Sci. 2019, 9, x 11 of 14

Figure 17. Intensity distributions and RI for 0° incident light beam on anterior, central and posterior regions of the commercial CCCR, which are shown in (a)–(c) respectively, and those of the optimized CCCR are shown in (d)–(f). Figure 18. Comparison of theFigure reflection 18. Comparison coefficient RofI ofthe commercial reflection CCCR, primaryFigure CCCR 19. andComparison of the reflection optimized CCCR. . coefficient RI of commercial CCCR, efficiency RA of commercial CCCR, primary primary CCCR and optimized CCCR. CCCR and optimized CCCR.

In order to demonstrate that the optimized SuperPin CCCR can really meet ECE requirements and perform better than the commercial samples, it is prototyped and tested in practical experiments, as shown in Figure 20. Through the proposed experimental setup in Figure 7, the retro-reflected outputs on the screen by two commercial CCCRs with the same part number (commercial CCCR 1 and commercial CCCR 2) and the optimized CCCR are presented in Figure 21 while the resulting RI values in rotational angles of 0°, 10°U, 10°D, 20°L, 20°R are obtained through optical measuring and shown in Figure 22. At the posterior area of the two commercial CCCR samples, it could be found that their RI values were both 0 mcd/lux. However, the RI of the optimal CCCR sample was shown to be much improved. According to the bar chart shown in Figure 22, the RI values of the optimal CCCR sample at 0°, 10°U, 10°D, 20°L, 20°R are 11,051 mcd/lux, 9394 mcd/lux, 7736 mcd/lux, 7183 Figure 18. Comparison of theFigure reflection 19. Comparison ofFigure the reflection 19. Comparison efficiency Rof ofthe commercial reflection CCCR, primary CCCR and mcd/lux, and 7515 lux/mcd,A respectively, and they were all over EU ECE regulation standards. coefficient RI of commercialoptimized CCCR, CCCR. efficiency RA of commercial CCCR, primary primary CCCR and optimized CCCR. CCCR and optimized CCCR.

In order to demonstrate that the optimized SuperPin CCCR can really meet ECE requirements and perform better than the commercial samples, it is prototyped and tested in practical experiments, as shown in Figure 20. Through the proposed experimental setup in Figure 7, the retro-reflected outputs on the screen by two commercial CCCRs with the same part number (commercial CCCR 1 and commercial CCCR 2) and the optimized CCCR are presented in Figure 21 while the resulting RI values in rotational angles of 0°, 10°U, 10°D, 20°L, 20°R are obtained throughFigure optical 20. The measuringprototyped SuperPinand CCCR of the optimized design. shown in Figure 22. At the posterior area of the two commercial CCCR samples, it could be found that their RI values were both 0 mcd/lux. However, the RI of the optimal CCCR sample was shown to be much improved. According to the bar chart shown in Figure 22, the RI values of the optimal CCCR sample at 0°, 10°U, 10°D, 20°L, 20°R are 11,051 mcd/lux, 9394 mcd/lux, 7736 mcd/lux, 7183 mcd/lux, and 7515 lux/mcd, respectively, and they were all over EU ECE regulation standards. Commercial CCCR

(a) (b) (c)

Figure 20. The prototyped SuperPin CCCR of the optimized design.

Commercial CCCR

(a) (b) (c) Appl. Sci. 2019, 9, x 11 of 14 Appl. Sci. 2019, 9, x 11 of 14

Figure 17. Intensity distributions and RI for 0° incident light beam on anterior, central and Figure 17. Intensity distributions and RI for 0° incident light beam on anterior, central and posterior regions of the commercial CCCR, which are shown in (a)–(c) respectively, and those posterior regions of the commercial CCCR, which are shown in (a)–(c) respectively, and those of the optimized CCCR are shown in (d)–(f). of the optimized CCCR are shown in (d)–(f). . .

Figure 18. Comparison of the reflection Figure 19. Comparison of the reflection Figure 18. Comparison of the reflection Figure 19. Comparison of the reflection coefficient RI of commercial CCCR, efficiency RA of commercial CCCR, primary coefficient RI of commercial CCCR, efficiency RA of commercial CCCR, primary Appl.primary Sci. 2019 CCCR, 9, 1555 and optimized CCCR. CCCR and optimized CCCR. 12 of 15 primary CCCR and optimized CCCR. CCCR and optimized CCCR. In order to demonstrate that the optimized SuperPin CCCR can really meet ECE requirements In order to demonstratedemonstrate that the optimized SuperPinSuperPin CCCR can really meet ECE requirements and perform better than the commercial samples, it is prototyped and tested in practical experiments, and perform better than the commercial samples, it is prototyped prototyped and and tested tested in in practical practical experiments, experiments, as shown in Figure 20. Through the proposed experimental setup in Figure 7, the retro-reflected as shown in Figure 2020.. Through Through the the proposed expe experimentalrimental setup setup in in Figure 77,, thethe retro-reflectedretro-reflected outputs on the screen by two commercial CCCRs with the same part number (commercial CCCR 1 outputs on the screen by two commercial CCCRs withwith the same part number (commercial CCCR 1 and commercial CCCR 2) and the optimized CCCR are presented in Figure 21 while the resulting RI and commercial CCCR 2) and the optimized CCCR are presented in Figure 21 while the resulting RI and commercial CCCR 2) and° the° optimized° CCCR° are° presented in Figure 21 while the resulting RI values in rotational angles of 0 ,° 10 U,° 10 D,° 20 L,° 20 R° are obtained through optical measuring and values in rotational angles of 0 , 1010 U, 10 D, 20 L, 20 R are obtained through optical measuring and shown in Figure 22. At the posterior◦ ◦ area ◦of the◦ two commercial◦ CCCR samples, it could be found shown inin FigureFigure 22 22.. AtAt the the posterior posterior area area of of the th twoe two commercial commercial CCCR CCCR samples, samples, it could it could be found be found that that their RI values were both 0 mcd/lux. However, the RI of the optimal CCCR sample was shown thattheir theirRI values RI values were were both both 0 mcd 0 /mcd/lux.lux. However, However, the R theI of R theI of optimal the optimal CCCR CCCR sample sample was shownwas shown to be to be much improved. According to the bar chart shown in Figure 22, the RI values of the optimal to be much improved. According to the bar chart shown in Figure 22, the RI values of the optimal much improved. According° ° ° to the° bar chart° shown in Figure 22, the RI values of the optimal CCCR CCCR sample at 0 ,° 10 U,° 10 D,° 20 L,° 20 R° are 11,051 mcd/lux, 9394 mcd/lux, 7736 mcd/lux, 7183 CCCRsample sample at 0 , 10 atU, 0 , 10 10D,U, 20 10L,D, 20 20RL, are 20 11,051R are mcd 11,051/lux, mcd/lux, 9394 mcd 9394/lux, mcd/lux, 7736 mcd 7736/lux, mcd/lux, 7183 mcd 7183/lux, mcd/lux, and◦ 7515◦ lux/mcd,◦ respectively,◦ ◦ and they were all over EU ECE regulation standards. mcd/lux,and 7515 and lux/ mcd,7515 respectively,lux/mcd, respectively, and they wereand they all over were EU all ECE over regulation EU ECE regulation standards. standards.

FigureFigure 20. 20. TheThe prototyped prototyped SuperPin SuperPin CCCR CCCR of of the the optimized optimized design. design. Figure 20. The prototyped SuperPin CCCR of the optimized design.

Commercial CCCR Commercial CCCR

Appl. Sci. 2019, 9, x (a) (b) (c) 12 of 14 (a) (b) (c)

Optimized CCCR

(d) (e) (f)

FigureFigure 21. 21. TheThe light light distribution distribution for a 00◦° incidentincidentlight light beam beam on on anterior, anterior, central central and posteriorand posterior regions regionsof the commercial of the commercial CCCRs, which CCCRs, are shownwhich in are (a)–( shownc) respectively, in (a)–(c and) respectively, those of the optimizedand those SuperPin of the optimizedCCCR are SuperPin shown in CCCR (d)–(f ).are shown in (d)–(f).

Figure 22. Comparison of the coefficient of luminous intensity RI between the commercial sample and the optimized prototyped sample (region by region).

5. Conclusions and Discussions A new optimal CCCR design which improves the performance and working area of the previous commercial one is proposed. We have demonstrated that the parameter of height difference between pin groups in a CCCR unit has an impact on the reflected light performance. In experiments, the curved retroreflector with a 120 × 28 mm reflecting area was built by 15 arrays of double-pin groups, and each pin cross-section size is 5.56 mm. It is demonstrated that a SuperPin CCCR can retro-reflect one incident beam as six beams, as shown in Figure 5c. If a CCCR has a curved region, the height between each group of pins due to surface curvature would affect optical characteristics, leading to lower reflection efficiency and even failing to pass ECE regulations. By using double-pin groups to build the primary SuperPin CCCR, reflection efficiency can be improved. Through using OptisWork software to find out the optimized SuperPin CCCR, RI can be increased further, but by sacrificing reflection efficiency RA, as shown in Figures 18 and 19. Using an efficient working area ratio, reflection efficiency RA and coefficient of luminous intensity RI as the evaluation indices of CCCR to compare a commercial SuperPin CCCR with the proposed new design, it can be inferred that the optimized Appl. Sci. 2019, 9, x 12 of 14

Optimized CCCR

(d) (e) (f)

Figure 21. The light distribution for a 0° incident light beam on anterior, central and posterior Appl. Sci.regions2019, 9 ,of 1555 the commercial CCCRs, which are shown in (a)–(c) respectively, and those of the13 of 15 optimized SuperPin CCCR are shown in (d)–(f).

Figure 22. Comparison of the coefficient of luminous intensity RI between the commercial sample and Figure 22. Comparison of the coefficient of luminous intensity RI between the commercial sample and the optimized prototyped samplesample (region(region byby region).region).

5. Conclusions and Discussions A new optimal CCCR design which improves the pe performancerformance and working area of the previous commercial one is proposed. We have demonstrated that the parameter of height difference difference between pin groups in aa CCCRCCCR unitunit hashas anan impactimpact onon thethe reflectedreflected lightlight performance.performance. In experiments,experiments, the curved retroreflectorretroreflector with a 120 × 2828 mm mm reflecting reflecting area was built by 15 15 arra arraysys of of double-pin double-pin groups, groups, × and each pin cross-section size is 5.56 mm. It is demonstrated that a SuperPin CCCR can retro-reflect retro-reflect one incident beam as six beams, as shown in FigureFigure5 5c.c. IfIf aa CCCRCCCR hashas aa curvedcurved region,region, thethe heightheight between each group of pins due to surface curvaturecurvature would aaffectffect opticaloptical characteristics,characteristics, leading to lower reflectionreflection eefficiencyfficiency and even failingfailing toto passpass ECEECE regulations.regulations. By using double-pin groups to build the primary SuperPin CCCR, re reflectionflection eefficifficiencyency can be improved. Through using OptisWork software to findfind out thethe optimizedoptimized SuperPin CCCR, RI can be increased further, but by sacrificingsacrificing reflectionreflection eefficiencyfficiency R RAA, as shown shown in Figures Figures 18 andand 19.19. Using Using an an efficient efficient working working area area ratio, ratio, reflection reflection eefficiencyfficiency RA and coefficient coefficient of luminous intensity RI as the evaluation indices of CCCR to compare a commercial SuperPin CCCR with the proposed new design, it can be inferred that the optimized SuperPin CCCR redistributes the reflected light beam energy of the primary SuperPin CCCR, which shares more energy into the 0.33◦ up-reflected beam by taking energy from the other five reflected beams. After computer simulations and optical experiments, it is demonstrated that the proposed SuperPin CCCR is not only above the ECE standard but also has a 33% larger working area and much better reflection efficiency than the commercial one, whose posterior region is not effective at all, as shown in Figures 18 and 19. Based on the data in Figure 22, it can be computed that the ratio of averaged RI of the optimized SuperPin CCCR to that of the commercial CCCR is (14929/8930, 0◦), (12689/5983, 10◦U), (10450/4822, 10◦D), (9704/5715, 20◦L) and (10152/5894, 20◦D), which means 40.1% (0◦), 52.85% (10◦U), 53.05% (10◦D), 41.1% (20◦L), and 42% (20◦R) higher retro-reflection efficiency can be accomplished by the proposed SuperPin CCCR. One of the most important advantages of this research outcome is that the new design of the SuperPin CCCR can enhance transportation safety. On the other hand, to produce our proposed design Appl. Sci. 2019, 9, 1555 14 of 15 with the highest accuracy and optimal efficiency, it is essential to have an advanced CNC (computer numerical control). Consequently, the commercial price of this design will be slightly higher than previous ones. In conclusion, we proposed a curved reflex reflector with a new cube-corner structure. By using genetic algorithms for optimization, the angles and the positions of the pins considered as building elements of corner-cube reflectors can enhance the performance of a curved reflex reflector. Compared with conventional retro-reflectors, it is found that a 46% higher retro-reflection efficiency and 33% larger working area can be accomplished with our optimized design. The yield rate of the mold production of the optimized design is less than the commercialized design because, 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.

Author Contributions: The authors of the present work made equal contributions to all of its parts. Funding: This research received no external funding. Acknowledgments: This work was supported by the Ministry of Science and Technology of the Republic of China, project MOST 106-2221-E-992-347. Conflicts of Interest: The authors declare no conflict of interest.

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