Design of a Society of Automotive Engineers Regular Curved Retroreﬂector for Enhancing Optical Efﬁciency and Working Area

crystals

Article Design of a Society of Automotive Engineers Regular Curved Retroreﬂector for Enhancing Optical Efﬁciency and Working Area

Lanh-Thanh Le 1,2, Hien-Thanh Le 1,2, Jetter Lee 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] (J.L.) 2 Department of Technology, Dong Nai Technology University, Bien Hoa, Dong Nai 830000, Vietnam 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]; Tel.: +886-7-381-4526

Received: 28 September 2018; Accepted: 28 November 2018; Published: 30 November 2018

Abstract: A highly efficient regular curved retroreflector is proposed to meet the requirements of the US Society of Automotive Engineers (SAE) regulations. It is demonstrated that 28% higher retroreflection efficiency and 33% more working area can be accomplished with the new designed retroreflector when compared with the commercial ones used in modern vehicles.

Keywords: optical design; curved retroreflector; US Society of Automotive Engineers (SAE) regulations

1. Introduction A retroreflector, also called a reflex reflector, can reflect light [1–3] back along a vector that is parallel or nearly parallel to but opposite in direction from the light source [4,5], no matter what the incident light angle is [2]. Because of their high tolerance to the direction of incident waves [6], retroreflectors have been used extensively in many applications instead of plane mirrors [2], such as free-space optical communications networks [4], satellites, road signs [7], vehicles [8], and clothing [9,10]. Retroreflectors on cars or clothing increase their visibility in the dark [2], so that traffic accidents can be reduced [6,11,12]. Common vehicle signage is composed of cube-corner retroreflectors (CCRs) [13]. According to the regulations of the US Society of Automotive Engineers (SAE), vehicle signage needs to return light back to the observer located 0.2◦ above the light source [14], ◦ and the coefficient of luminous intensity RI should be more than certain values within a 20 angle of light incidence. The measure of vehicle signage performance RI is decided by the ratio of the strength of the reflected light (retroreflected light intensity) to the amount of light that falls on the retroreflector (incident light illuminance) [13–15], as shown in Figure1.R A is the measure of retroreflection efficiency, defined as the ratio of the flux of incident light to the total flux of a reflected cone. Vehicle signage appears brighter as its RI value increases [10,14,15]. In the design of commercial retroreflectors for modern vehicles, outlook smoothness is usually first considered rather than efficiency. Therefore, it is often necessary for a retroreflector to be made with a curved surface fitting the outlook of the application, such as the corner of a vehicle. However, cube-corner structures are usually distorted or even destroyed to complete the curve, so their effective working area and reflection efficiency are influenced seriously, and that could lead to the retroreflector not complying with SAE regulations [6,16].

Crystals 2018, 8, 450; doi:10.3390/cryst8120450 www.mdpi.com/journal/crystals Crystals 2018, 8, 450 2 of 16 effective working area and reflection efficiency are influenced seriously, and that could lead to the retroreflector not complying with SAE regulations [6,16]. Based on pin-bundling technology, thethe tooling of a reflexreflex reflectorreflector mold can be produced, and it can serve as a testingtesting samplesample or forfor massmass production.production. In In this this study, a reflexreflex reflectorreflector sample was designed and produced by bundled metal pins for SA SAEE regulations. A curved curved retroreflector retroreflector with new cube-corner structure is proposed and demonstrated.demonstrated. By use of genetic algorithms for optimization, the angles and positions of thethe pinspins serveserve asas thethe optimizingoptimizing parameters to enhanceenhance thethe performanceperformance of a curved retroreflector.retroreflector. Compared with conventionalconventional retroreflectors, retroreflectors, it is found that 28% higher retroreflectionretroreflection efficiencyefficiency andand 33%33% moremore workingworking areaarea cancan bebe accomplishedaccomplished withwith ourour proposedproposed one. one.

Figure 1. IllustrationIllustration of of characteristic characteristic re retroreflectiontroreflection of reflexreflex reflector.reflector.

RA isis the the measure measure of of retroreflection retroreflection efficiency, efficiency, defineddefined as the ratio of the fluxflux of incident light to the total fluxflux ofof reflectedreflected light.light. RI (coefficient(coefficient of luminous intensity) is used to definedefine the reflectionreflection ◦ efficiencyefficiency at certain observationobservation anglesangles (upward(upward ofof 0.20.2°).).

2. Principles 2. Principles The SAE standard is to reduce deaths and injuries resulting from trafﬁc accidents by providing The SAE standard is to reduce deaths and injuries resulting from traffic accidents by providing adequate illumination of roadways and enhancing the conspicuousness of motor vehicles on public adequate illumination of roadways and enhancing the conspicuousness of motor vehicles on public roads so that their presence is perceived and their signals understood in both daylight and darkness or roads so that their presence is perceived and their signals understood in both daylight and darkness other conditions of reduced visibility [14,17]. The value of the standard in each test case is detailed in or other conditions of reduced visibility [14,17]. The value of the standard in each test case is detailed Table1[12,15,17]. in Table 1 [12,15,17].

Table 1. Minimum mcd (millicandela)/incident lux for a white reflex reflector. SAE, Society of Table 1. Minimum mcd (millicandela)/incident lux for a white reflex reflector. SAE, Society of Automotive Engineers. Automotive Engineers. ◦ Observation US SAE Regulation Entrance Angle ( ) ◦ Entrance Angle (°) ObservationAngle ( ) USRequirement SAE Regulation 0◦ 10◦ Up 10◦ Down 20◦ Left 20◦ Right 10° Angle (°) MinimumRequirement coefficient of 0° 10° Up 20° Left 20° Right Down 0.2 luminous intensity RI 1680 1120 1120 560 560 Minimum(mcd/incident coefficient lux) of 0.2 luminous intensity RI 1680 1120 1120 560 560 A corner-cube retroreflector(mcd/incident is a kindlux) of reflex reflector and its working mechanism is based on groups of three perpendicular planes, as shown in Figure2. Usually, the dihedral angle between any A corner-cube retroreflector is a kind of reflex reflector and its working mechanism is based on pair of reflecting faces is made to be exactly 90◦, so that the reflected beam is exactly antiparallel to groups of three perpendicular planes, as shown in Figure 2. Usually, the dihedral angle between any the incident beam. If the angles differ from 90◦ by any amount, the reflected beam will be split into pair of reflecting faces is made to be exactly 90°, so that the reflected beam is exactly antiparallel to multiple beams to achieve the required application. the incident beam. If the angles differ from 90° by any amount, the reflected beam will be split into multiple beams to achieve the required application. Crystals 2018, 8, 450 3 of 16

(a) (b) (c)

Figure 2. (a) Corner-cube retroreflector composed of groups of pins; (b) a group of pins; (c) reflecting Figure 2. (a) Corner-cube(a) retroreflector composed( ofb) groups of pins; (b) a group of (pins;c) (c) reflecting surfaces of pin group (green lines show inner region). surfaces of pin group (green lines show inner region). Figure 2. (a) Corner-cube retroreflector composed of groups of pins; (b) a group of pins; (c) reflecting Through an array of pins, a corner-cube retroreflector can be produced, which is shown in Figure2. surfacesThrough of an pin array group of (green pins, alines corner-cube show inner retrorefle region). ctor can be produced, which is shown in Figure The orientation of each face is given by the unit normal nˆ1, nˆ2, and nˆ3 to each face. The reflection 2. The orientation of each face is given by the unit normal 𝑛, 𝑛, and 𝑛 to each face. The reflection→ fromThrough each face an reverses array of that pins, component a corner-cube of the retrorefle light’s velocityctor can vectorbe produced, that is normalwhich is to shown the face. in Figure Let V⃗ from→ each0 face reverses that component of the light's velocity vector that is normal to the face. Let 𝑉 2. The orientation of each face is given by the unit normal 𝑛, 𝑛, and 𝑛 to each face. The 0reflection and V𝑉⃗ be the directions of a ray before and after reflection,reflection, respectively, withwith the vector VV’ given by from→ → each face→ reverses that component of the light's velocity vector that is normal to the face. Let 𝑉⃗ 𝑉′⃗0 = 𝑉⃗′0 −− 2(𝑉⃗.𝑛)𝑛, where 𝑛 is the normal to the face. Applying the above formula three times yields Vand= 𝑉V⃗ be 2(theV )directionsnˆ, where n ôfis a the ray normal before toand the after face. reflec Applyingtion, respectively, the above formula with the three vector times V’ yields given theby directionthe direction of the of reflectedthe reflected beam beam for afor particular a particular order order of reflection. of reflection. Formulas Formulas for thefor directionthe direction of the of 𝑉′⃗ = 𝑉⃗′ − 2(𝑉⃗.𝑛)𝑛, where 𝑛 is the normal to the face. Applying the above formula three times yields reflectedthe reflected rays rays after after the threethe three reflections reflections are givenare given by Chandler’s by Chandler's formula: formula: the direction of the reflected beam for a particular order of reflection. Formulas for the direction of ⃗ the reflected rays after the three reflect→ 𝑡⃗ions =→ 𝑞⃗ are →+ 2 given𝑎⃗(→α𝑎⃗ -by β→ 𝑏Chandler's + γ→𝑐⃗) formula: (1) t = q 2 a α a − β b + γ c (1) where 𝑡⃗ is the final direction and 𝑞⃗ is𝑡⃗ the= 𝑞⃗ original+ 2𝑎⃗(α𝑎⃗ direction;- β𝑏⃗ + γ𝑐⃗ )α , β, γ are the small angles by which(1) the angles between the three mirrors exceed right angles, and 𝑎⃗, 𝑏⃗, and 𝑐⃗ are normal to the three where →𝑡⃗ is the final direction and→ 𝑞⃗ is the original direction; α, β, γ are the small angles by which wheremirrorst takenis the in final order direction in a right-hand and q is thesense. original Equati direction;on (1) is αvalid, β, γ toare the the first small order angles when by the which mirrors the the angles between the three mirrors exceed right angles,→ and→ 𝑎⃗, 𝑏→⃗, and 𝑐⃗ are normal to the three anglesare nearly between mutually the three perpendicular. mirrors exceed α is the right angle angles, between and a the, b faces, and whosec are normal normals to are the 𝑏 three⃗ and mirrors 𝑐⃗. The mirrors taken in order in a right-hand sense. Equation (1) is valid to the first order when the mirrors takennormals in ordermay be in strictly a right-hand perpendicula sense. Equationr; that is, (1)they is do valid not to need the firstto include order whenthe small the deviations mirrors are caused nearly are nearly mutually perpendicular. α is the angle between the faces whose normals→ are→ 𝑏⃗ and 𝑐⃗. The by the dihedral-angle offsets.α The directions of the reflected rays were computedb by applyingc the law mutuallynormals may perpendicular. be strictly perpendiculais the angler; that between is, they the do faces not need whose to normalsinclude the are smalland deviations. The normals caused of reflection three times. mayby the be dihedral-angle strictly perpendicular; offsets. The that directions is, they do of not the needreflected to include rays were the smallcomputed deviations by applying caused the by law the The unit normals to the faces can be computed as follows (see Figure 3). Let the normals to the dihedral-angleof reflection three offsets. times. The directions of the reflected rays were computed by applying the law of faces without dihedral-angle offsets be the unit vectors 𝚤̂, 𝚥̂, and 𝑘 along the three coordinates x, y, reflectionThe unit three normals times. to the faces can be computed as follows (see Figure 3). Let the normals to the and Thez, respectively. unit normals If tothe the angle faces betwee can ben computed the xz plane as follows and the (see yz Figure plane3 ).is Let(π/2) the + normals δ, this can to the be faces without dihedral-angle offsets be the unit vectors 𝚤̂, 𝚥̂, and 𝑘 along the three coordinates x, y, facesexpressed without by dihedral-anglen = ı̂ + ȷ̂ ; offsets𝑛 = 𝚥 bê + the𝚤̂ unit;𝑛 = vectors 𝑘 . Forıˆ, ˆsmall, and kânglesalong theδ, these three coordinatesexpressions xare, y, andquitez, and z, respectively. If the angle betwee n the xz plane and the yz plane is (π/2) + δ, this can be respectively.adequate. Offsets If the in angle the other between two thedihedralxz plane angles and can the beyz planesimilarly is ( πrepresented./2) + δ, this can be expressed by expressed by n = ı̂ + ȷ̂ ; 𝑛 = 𝚥̂ + 𝚤̂ ;𝑛 = 𝑘 . For small angles δ, these expressions are quite δ δ ˆ nˆ1 = ıˆ + 2 ˆ; nˆ2 = ˆ + 2 ıˆ; nˆ3 = k. For small angles δ, these expressions are quite adequate. Offsets in the otheradequate. two dihedralOffsets in angles the other can two be similarly dihedral represented. angles can be similarly represented.

Figure 3. Normal to the reflecting faces with dihedral-angle offsets. Figure 3. Normal to the reflecting reﬂecting faces with dihedral-angle offsets. Crystals 2018, 8, 450 4 of 16

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 Figure4; we see that cos θA = √ ; √ 2 sin θ = √1 ; cos λ = √2 ; sin λ = √1 . The normals in the xyz coordinate system can be given in the A 2 A 3 A 3 coordinate system of the symmetry axis by rotating the original coordinate system around the z-axis of θA and around the y-axis of –λA. This brings the x-axis along the axis of the matrix form, and the total rotation is given by

 0      x cos λA 0 sin λA cos θA sin θA 0 x  0   Figure 4. Direction of symmetry axis.    y =  0 1 0  − sin θA cos θA 0  y  (2) z0 − sin λ 0 cos λ 0 0 1 z It is desirable to have the unit Anormals givenA in the coordinate system of the symmetry axis of the corner cube, since the incidenceFigure angle 4. Direction of the la ofser symmetry beam is axis. given with respect to this axis. The Substituting the values of the sines and cosines and multiplying the matrices, we get symmetry axis is in the direction of the vector x = y = z = 1, as shown in Figure 4; we see that cos θ x0 = √1 (x + y + z); y0 = √1 (y − x); z0 = √1 (2z − x − y). In Figure5, the ( x, y, z) axes represent the It3 is desirable to have2 √the unit normals 6 given in the coordinate system of the symmetry axis of = ; sin θ = ; cos λ = ; sin λ =0 0 . The0 normals in the xyz coordinate system can be given in theoriginal√ corner coordinate cube,√ since system the √incidence and the (x angle, y√, z )of axes the arelaser the beam rotated is given coordinates. with respect to this axis. The symmetrythe coordinate axis systemis in the of direction the symmetry of the axisvector by xrotating = y = z =the 1, originalas shown coordinate in Figure system4; we see around that costhe θz- axis of θA and around the y-axis√ of –λA. This brings the x-axis along the axis of the matrix form, and = ; sin θ = ; cos λ = ; sin λ = . The normals in the xyz coordinate system can be given in the√ total rotation√ is given by√ √ the coordinate system of the symmetry axis by rotating the original coordinate system around the z- 𝑥′ cos λ 0sinλ cos θ sin θ 0 𝑥 axis of θA and around the y-axis of –λA. This brings the x-axis along the axis of the matrix form, and 𝑦′ = 010−sinθ cos θ 0𝑦 (2) the total rotation is given by 𝑧′ −sin λ 0 cos λ 001𝑧 𝑥′ cos λ 0sinλ cos θ sin θ 0 𝑥 Substituting the values of the sines and cosines and multiplying the matrices, we get 𝑥 = 𝑦′ = 010 −sinθ cos θ 0𝑦 (2) 𝑥+𝑦+𝑧; 𝑦 = 𝑦−𝑥; 𝑧 = 2𝑧 − 𝑥 −𝑦. In Figure 5, the (x, y, z) axes represent the √ √ 𝑧′ −sin λ√ 0 cos λ 001 𝑧 original coordinate system and the (x’, y’, z’) axes are the rotated coordinates. Substituting the values of theFigureFigure sines 4.4. DirectionDirectionand cosines ofof symmetrysymmetry and multiplying axis.axis. the matrices, we get 𝑥 = 𝑥+𝑦+𝑧; 𝑦 = 𝑦−𝑥; 𝑧 = 2𝑧 − 𝑥 −𝑦. In Figure 5, the (x, y, z) axes represent the √ √ √ It is desirable to have the unit normals given in the coordinate system of the symmetry axis of original coordinate system and the (x’, y’, z’) axes are the rotated coordinates. 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 4; 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 around the z- axis of θA and around the y-axis of –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 0 0 0 Figure𝑦′ = 5. RelationshipRelationship010 of of x,x, y,y, z and−sin xx’,, yy’,θ, zz’ coordinatecoordinatecos θ 0 axes.axes.𝑦 (2) 𝑧′ −sin λ 0 cos λ 001𝑧 0 0 The incident beam after reﬂection at the front face is in a direction given by the angles θ and φ Substituting0 0 0 the values of the sines and cosines and multiplying the matrices, we get 𝑥 = in the (x , y , z ) coordinateFigure system 5. Relationship (see Figure of 6x,). y, z and x’, y’, z’ coordinate axes. 𝑥+𝑦+𝑧; 𝑦 = 𝑦−𝑥; 𝑧 = 2𝑧 − 𝑥 −𝑦. In Figure 5, the (x, y, z) axes represent the √ √ √ original coordinate system and the (x’, y’, z’) axes are the rotated coordinates.

Figure 6. Direction angle of reflected beam.

Figure 6. Direction angle of reflected reﬂected beam.

Figure 5. Relationship of x, y, z and x’, y’, z’ coordinate axes.

Figure 6. Direction angle of reflected beam. Crystals 2018, 8, 450 5 of 16

A second rotation of the coordinate system must be performed to get the normals to the faces in the coordinate system of the laser beam. By rotating the coordinate system around the x0-axis of θ0 and then around the new z0-axis of φ’, we get       x00 cos φ0 sin φ0 0 1 0 0 x0  00   0 0  0 0  0   y =  − sin φ cos φ 0  0 cos θ sin θ  y  (3) z00 0 0 1 0 − sin θ0 cos θ0 z0

The relationship of the (x0, y0, z0) and (x00, y00, z00) coordinate axes is given in Figure7. The x0 axis is the symmetry axis of the reflector, the y0, z0 plane is parallel to the front face, and the x00 axis is parallel to the beam after it enters the cube corner. In this study, we used a Hollow corner cube, and the reflections can be done for all six possible sequences of reflections by taking the incident beam, given by the vectors x00 = −1, y00 = z00 = 0, and reflecting it from each normal to the faces in the (x00, y00, z00) coordinate system. The y00 and z00 coordinates of the reflected beam give the deviations from the incident direction.

0 0 0 00 00 00 Figure 7. Relationship of xx’,, yy’,, zz’ and xx”,, yy”,, zz” axes.axes.

The beamincident spread beam at after normal reflection√ incidence at the when frontall face dihedral is in a direction angles are given offset by by the an angles equal θ′ amount and ϕ′ γ 4 δ δ ◦ isin giventhe (x’, by y’, the z’) formulacoordinate= system3 6 n (see, where Figure 6).is the angle by which the dihedral angles exceed 90 and γAis second the angle rotation between of the the coordinate incident system ray and must the reflectedbe performed ray. Lightto get passesthe normals through to the CCRs faces and in 0 therethe coordinate is a change system in the of direction the laser of beam. reflection. By rotati The directionng the coordinate of the incident system beam around is determined the x’-axis byof θ ' 0 0 0 0 ◦ and φthenin around the (x , ythe, z new) coordinate z’-axis of system. ϕ’, we get The values of γ are shown in Table2. At δ = 0.09, γ = 0.2 (SAE regulations).𝑥′′ cos ϕ′ sin ϕ′ 0 10 0𝑥′ Based on the𝑦′′ above = computation−sin ϕ′ cos theory, ϕ′ 0 the optical0 cos simulationsθ′ sin θ′ through 𝑦 TracePro′ software(3) (Lambda Research𝑧′′ Corporation001 of Littleton, MA, USA)0−sin show thatθ′ CCRscos withθ′ equal𝑧′ dihedral angles can reflectThe six relationship beams with of equal the reflection(x’, y’, z’) angleand (x”,γ with y”, z”) respect coordinate to the incidentaxes is given beam, in as Figure shown 7. inThe Figure x’ axis8. Whenis the thesymmetry dihedral axis angle of the is 90.09 reflector,◦, it can the be y’, found z’ plan thate γisbecomes parallel 0.2to ◦the, which front fitsface, SAE and regulations the x” axis and is compliesparallel to with the beam the mathematical after it enters analysis the cube shown corner in. TableIn this2. study, we used a Hollow corner cube, and the reflections can be done for all six possible sequences of reflections by taking the incident beam, givenTable by the 2. Angles vectors between x” = −1, incident y” = z” ray = 0, and and retroreflected reflecting it ray fromγ with each respect normal to δ to, which the faces is the in dihedral the (x”, y”, z”) coordinateangle of retroreflector system. The corner y” and cube z” surface coordinates with 90◦ ofas the the reference.reflected beam give the deviations from the incident direction. δ (◦) 0 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 The beam◦ spread at normal incidence when all dihedral angles are offset by an equal amount is γ ( ) 0 0.05 0.07 0.09 0.13 0.14 0.16 0.19 0.20 given by the formula γ = √6 n δ, where δ is the angle by which the dihedral angles exceed 90° and δ (◦) 0.1 0.11 0.12 0.13 0.14 0.15 0.64 0.7 γ is the angleγ (◦ )between 0.23 the incident 0.26 ray 0.28 and the 0.30 reflected 0.33 ray. Light 0.35 passes 1.50 through 1.62 CCRs and there is a change in the direction of reflection. The direction of the incident beam is determined by θ′ and ϕ′ in the (x’, y’, z’) coordinate system. The values of γ are shown in Table 2. At δ = 0.09, γ = 0.2° (SAE The angle between the incident ray and the retroreflected ray γ is closely related to δ, which is regulations). the dihedral angle of retroreflector corner cube surface with 90◦ as the reference. As shown in Table2, Based on the above computation theory, the optical simulations through TracePro software for example, when δ is controlled to be 0.09◦, the retroreflected beam angle γ becomes 0.2◦, as required (Lambda Research Corporation of Littleton, MA, USA) show that CCRs with equal dihedral angles by the SAE standards. can reflect six beams with equal reflection angle γ with respect to the incident beam, as shown in Figure 8. When the dihedral angle is 90.09°, it can be found that γ becomes 0.2°, which fits SAE regulations and complies with the mathematical analysis shown in Table 2.

Table 2. Angles between incident ray and retroreflected ray γ with respect to δ, which is the dihedral angle of retroreflector corner cube surface with 90° as the reference.

δ (°) 0 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 γ (°) 0 0.05 0.07 0.09 0.13 0.14 0.16 0.19 0.20 δ (°) 0.1 0.11 0.12 0.13 0.14 0.15 0.64 0.7 γ (°) 0.23 0.26 0.28 0.30 0.33 0.35 1.50 1.62

The angle between the incident ray and the retroreflected ray γ is closely related to δ, which is the dihedral angle of retroreflector corner cube surface with 90° as the reference. As shown in Table 2, for example, when δ is controlled to be 0.09°, the retroreflected beam angle γ becomes 0.2°, as required by the SAE standards. Crystals 2018, 8, 450 6 of 16

((a)) ((b))

Figure 8.8. ((aa)) SetupSetup forfor opticalopticaloptical simulationssimulationssimulations ofof cube-cornercube-cornercube-corner retroreflectorsretroreflectorsretroreflectors (CCRs).(CCRs).(CCRs). ( (b)) ReflectedReflectedReflected beambeam ◦ intensityintensity distributiondistribution byby CCRsCCRCCRs withwith dihedraldihedral angleangle 90.0990.09°.. 3. Optical Setup and Analysis 3. Optical Setup and Analysis In order to investigate the properties of a curved reflex reflector, a commercialized one with InIn orderorder toto investigateinvestigate thethe propertiesproperties ofof aa curvcurved reflex reflector, a commercialized one with corner-cube structure for cars was used for testing, shown in Figure9. The sample is made of PMMA corner-cube structure for cars was used for testing, shown in Figure 9. The sample is made of PMMA (Poly Methyl Methacrylate) with size 146 mm × 34 mm, provided by Owl Light Automotive Products (Poly(Poly MethylMethyl Methacrylate)Methacrylate) withwith sizesize 146146 mmmm ×× 3434 mm,mm, providedprovided byby OwlOwl LightLight AutomotiveAutomotive ProductsProducts Mfg. Corp., which has been in mass production for vehicles in the USA. The experimental setup for Mfg. Corp., which has been in mass production for vehicles in the USA. The experimental setup for curved reflex reflector testing is shown in Figure 10. In the optical setup, a semiconductor laser with curved reflex reflector testing is shown in Figure 10. In the optical setup, a semiconductor laser with wavelength 635 nm acted as the light source, and its distance from the curved reflex reflector was set to wavelength 635 nm acted as the light source, and its distance from the curved reflex reflector was set be 30.5 m to measure the reflected light spot. The laser light with an incident angle of 0◦ with respect toto bebe 30.530.5 mm toto measuremeasure thethe reflectedreflected lightlight spot.spot. ThThe laser light with an incident angle of 0° with to the car driving direction was incident on the commercialized curved reflex reflector. As a result, respect to the car driving direction was incident on the commercialized curved reflex reflector. As a several retroreflected light spots could be found on the black screen located 30 m away from the test result, several retroreflected light spots could be found on the black screen located 30 m away from sample. A Minolta T10 illuminance meter was used to measure the illuminance on the sample and the thethe testtest sample.sample. AA MinoltaMinolta T10T10 illuminanceilluminance metermeter wawas used to measure the illuminance on the sample retroreflected light spot, in order to get the incident light illuminance (in lux) and the retroreflected and the retroreflected light spot, in order to gett thethe incidentincident lightlight illuminanceilluminance (in(in lux)lux) andand thethe light intensity (in candela). Coefficient of luminous intensity RI and retroreflection efficiency RA of retroreflected light intensity (in candela). Coefficient of luminous intensity RII andand retroreflectionretroreflection the test sample can thus be worked out. During the experiments, the anterior, central, and posterior efficiency RA ofof thethe testtest samplesample cancan thusthus bebe workedworked out.out. During the experiments, the anterior, central, regions of the sample were investigated with the car driving direction, and these are presented in and posterior regions of the sample were investigated with the car driving direction, and these are Figure 11. presented in Figure 11. Initially, the laser light was adjusted to be parallel with the driving direction and aimed at the Initially,Initially, thethe laserlaser lightlight waswas adjustedadjusted toto bebe parallelparallel withwith thethe drivingdriving directiondirection andand aimedaimed atat thethe central part of the region. The resulted reflected outputs are shown in Figure 12a–c. While observing central part of the region. The resulted reflected outputs are shown in Figure 12a–c. While observing the output signals, it was found that the reflected light spots became weaker and weaker as the test thethe outputoutput signals,signals, itit waswas foundfound thatthat thethe reflectedreflected lightlight spotsspots becamebecame weakerweaker andand weakerweaker asas thethe testtest region shifted from the front part to the end part of the tested curved corner-cube retroreflector (CCCR). region shifted from the front part to the end part ofof thethe testedtested curvedcurved corner-cubecorner-cube retroreflectorretroreflector Accordingly, it is evident that its curved shape had an influence on its performance. (CCCR).(CCCR). Accordingly,Accordingly, itit isis evidentevident thatthat itsits curvcurved shape had an influence on its performance.

Figure 9. Commercial curved reﬂex reﬂector. Figure 9. CommercialCommercial curvedcurved reflexreflex reflector.reflector. Crystals 2018, 8, 450 7 of 16

FigureFigureFigure 10.10. 10. ExperimentalExperimentalExperimental Experimental setupsetup setup forfor for curvedcurved curved cornercornercorner-cube corner-cube-cube-cube retroreflectorretroreflector retroreﬂector retroreflector (CCCR) (CCCR) (CCCR) testing. testing. testing.

22 FigureFigureFigure 11. 11. 11. TestTest Test regions regions regions of of of CCCR; CCCR; CCCR; each each each testing testing testing area area area isis is 490490 490 mmmm mm2..2 .

((aa(a)) ) ((bb(b)) ) ((cc()c) ) Figure 12. Retroreflected outputs by (a) anterior, (b) central, and (c) posterior region of the commercial CCCR. FigureFigureFigure 12.12. 12. RetroreflectedRetroreflected Retroreflected outputsoutputs outputs byby by ((a a()a) anterior,)anterior, anterior, ((b b(b)) central,)central, central, andand and ((c c()c) posterior)posterior posterior regionregion region ofof of thethe the commercialcommercial commercial CCCR.InCCCR.CCCR. order to improve the poor performance of the commercial CCCR, a single ray antiparallel to the driving direction was set to probe the reflecting surfaces of the posterior region by optical simulations. In order to improve the poor performance of the commercial CCCR, a single ray antiparallel to The labeledInIn order order input to to improve improve reflecting the the surfacepoor poor performance performance and the resulting of of the the commercial idealcommercial reflected CCCR, CCCR, light a a intensitysingle single ray ray distribution antiparallel antiparallel are to to the driving direction was set to probe the reflecting surfaces of the posterior region by optical theshownthe driving driving in Figures direction direction 13–15 was .was set set to to probe probe the the reflectin reflectingg surfaces surfaces of of the the posterior posterior region region by by optical optical simulations.simulations.simulations. The TheThe labeled labeledlabeled input inputinput reflecting reflectingreflecting surface surfacesurface and andand the thethe resulting resultingresulting ideal idealideal reflected reflectedreflected light lightlight intensity intensityintensity distributiondistributiondistribution areare are shownshown shown inin in FiguresFigures Figures 13–15.13–15. 13–15. Crystals 2018, 8, 450 8 of 16

Figure 13. CCCR #1 reflecting surface in the posterior region is hit by simulated laser Figure 13. CCCRFigure #1 13. reﬂecting CCCR #1 surfacereflecting in surface the posterior in the posterior region isregion hit by is hit simulated by simulated laser laser beam (left) and beamFigure (left 13.) CCCRand the #1 resulting reflecting retroreflected surface in the light posterior intensity region distributions is hit by simulated(right). laser the resultingbeam retroreﬂected (left) and the light resulting intensity retroreflected distributions light ( rightintensity). distributions (right). beam (left) and the resulting retroreflected light intensity distributions (right).

Figure 14. CCCR #2 reflecting surface in the posterior region is hit by simulated laser Figure 14. CCCR #2 reflecting surface in the posterior region is hit by simulated laser Figure 14. CCCRbeamFigure #2(left 14. reﬂecting) CCCRand the #2 resulting surface reflecting inretroreflected surface the posterior in the light posterior region intensity is region hit distributions by is simulatedhit by simulated(right laser). beamlaser (left) and beam (left) and the resulting retroreflected light intensity distributions (right). the resultingbeam retroreﬂected (left) and lightthe resulting intensity retroreflected distributions light (right intensity). distributions (right).

Figure 15. CCCR #3 reflecting surface in the posterior region is hit by simulated laser Figure 15. CCCR #3 reflecting surface in the posterior region is hit by simulated laser beamFigure (left 15.) CCCRand the #3 resulting reflecting retroreflected surface in the light posterior intensity region distributions is hit by simulated(right). laser Figure 15. CCCRbeam ( #3left reflecting) and the resulting surface inretroreflected the posterior light region intensity is hit distributions by simulated (right laser). beam (left) and Comparingbeam Figure (left) and 12c the with resulting Figure retroreflected 14, it can lightbe seen intensity that distributions reflecting surfaces(right). 1 and 3 in the the resultingComparing retroreflected Figure 12c light with intensity Figure distributions14, it can be ( rightseen ).that reflecting surfaces 1 and 3 in the posteriorComparing region didFigure not 12cfunction, with Figureso that 14, four it canlight be spots seen were that reflectingmissed and surfaces only two 1 and light 3 inspots the posterior region did not function, so that four light spots were missed and only two light spots posterior region did not function, so that four light spots were missed and only two light spots Comparing Figure 12c with Figure 14, it can be seen that reflecting surfaces 1 and 3 in the posterior region did not function, so that four light spots were missed and only two light spots reached the output screen. By means of a genetic algorithm to search for better pin group structures, it could be reached the output screen. By means of a genetic algorithm to search for better pin group structures, it could be possible to revive the disabled reflecting surfaces to elevate the coefficient of luminous intensity RI and reflection efficiency RA.

4. Optics Design and Verification In the proposed CCCR structure, two group of pins were connected as a double-pin group, shownCrystals in Figure2018, 8, 45016, which served as the building element to construct a primary CCCR, as 9shown of 16 in Figure 17. Fifteen pieces of double-pin groups were arranged parallel to the car driving direction to compose reachedreachedthe primary thethe outputoutput CCCR, screen.screen. one ByBy meansmeanspin group ofof aa geneticgenetic touching alalgorithm the tocurve search reference for bettertter pinpinsurface groupgroup andstructures,structures, the other one possible to revive the disabled reflecting surfaces to elevate the coefficient of luminous intensity RI and free to translateitit couldcould beinbe possiblepossiblethe car totodriving reviverevive thethedirection. disabled Thereflecting height surfaces differences to elevate between the coefficient the neighboring of luminous pins in reflection efficiency RA. a group ofintensityintensity double RRII andandpins reflectionreflection and the efficiencyefficiency double-pin RRAA.. group are named di and Di, respectively, as shown in Figure4. Optics18. In Designorder to and further Verification improve the primary CCCR, the add-on ray tracing simulation tool 4. Optics Design and Verification OptisWorks (Optis SAS, La Farlede, France), embedded in SolidWorks mechanical design software, In theInIn proposed thethe proposedproposed CCCR CCCRCCCR structure, structure,structure, two twotwo group groupgroup of pins ofof pins were were connected connected as aas double-pin a double-pin group, group, shown was used to search suitable di to elevate its performance and Di to smoothly fit the reference curve of in Figureshownshown 16 ,inin which FigureFigure served 16,16, whichwhich as the servedserved building asas thethe elementbuildingbuilding toelement construct to construct a primary a primary CCCR, CCCR, as shown as shown in Figure in 17. the outlookFifteenFigure pieces of 17. CCCR. ofFifteen double-pin piecesThe oflighting groups double-pin wereperformance groups arranged were parallelarrangedarrangedof the to parallelparallelCCCR, the car toto such drivingthethe carcar as drivingdriving direction intensity directiondirection to composedistribution, toto illuminationthe primarycomposecompose uniformity, CCCR, thethe primaryprimary one and CCCR, pinCCCR, optical group oneone pin pin touchingefficiency, groupgroup touchingtouching the ca curven be thethe reference accomplishedcurvecurve referencereference surface surfacesurface to and meet and theand targets otherthethe otherother one by oneone free means to of optimization.translatefreefree to into translatetranslate the car driving inin thethe carcar direction. drivingdriving direction.direction. The height TheThe differences heightheight differencesdifferences between betweenbetween the neighboring thethe neighboringneighboring pins pinspins in a inin group a group of double pins and the double-pin group are named di and Di, respectively, as shown in of doublea group pins of anddouble the pins double-pin and the double-pin group are group named ared namedand D d,i respectively,and Di, respectively, as shown as shown in Figure in 18. Figure 18. In order to further improve the primary CCCR,i thei add-on ray tracing simulation tool In orderFigure to further18. In order improve to further the primaryimprove CCCR,the prim theary add-onCCCR, the ray add-on tracing ray simulation tracing simulation tool OptisWorks tool OptisWorks (Optis SAS, La Farlede, France), embedded in SolidWorks mechanical design software, (Optis SAS, La Farlede, France), embedded in SolidWorks mechanical design software, was used to was used to search suitable dii toto elevateelevate itsits performanceperformance andand DDii toto smoothlysmoothly fitfit thethe referencereference curvecurve ofof searchthethe suitable outlookoutlookd i oftoof elevateCCCR.CCCR. itsTheThe performance lightinglighting performanceperformance and Di to smoothlyofof thethe CCCR,CCCR, fit the suchsuch reference asas intensityintensity curve distribution, ofdistribution, the outlook of CCCR.illuminationillumination The lighting uniformity,uniformity, performance andand opticaloptical of the efficiency, CCCR,efficiency, such cacan as be intensity accomplished distribution, to meet illuminationtargets by means uniformity, of and opticaloptimization. efficiency, can be accomplished to meet targets by means of optimization.

Figure 16. Double-pin group.

FigureFigure 16. 16. Double-pinDouble-pin group. group.

Figure 17. Primary CCCR constructed by double-pin groups.

FigureFigure 17. 17.Primary PrimaryPrimary CCCR CCCRCCCR constructed constructedconstructed byby by double-pindouble-pin double-pin groups.groups. groups.

Figure 18. Height difference di between neighboring pins in a double-pin group. Crystals 2018, 8, 450 10 of 16

The object function f defined by Equation (4) was determined in the optimization process. The optimization process encompassed three fragments. Object function: The equation that describes the value of the object function of the optimization program established by the genetic algorithm is as follows: q ( )= n ( − )2 + − 2 f i, j ∑i,j=1 wi mi ti wj mj tj (4) where wi is the level of curvature of a curved retroreflector that has 15 variables from w1 to w15, and the constraint of each variable is determined by the curvature of the CCCR surface; 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 the optimization target defined with a value corresponding to the retroreflective light intensity on the retroreflector plane. Luminous intensity function: We searched for an approximation of the luminous intensity (RI) I(Φ, a, b, c) at the polar angle of Φ in the form:

k (ϕ ) = zk (ϕ − I , x, y, z Imax ∑k=1 xkcos yk (5)

Here, 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 finite subsets where the possible values will be x* {0, 0.001, 0.002, ... , 0.81}, y* {−1, 0.9,0.8,0.7, . . . , -1}, z* {0, 1, 2, . . . , 100}. The components in OptisWorks were configured to incorporate light source, intensity sensor, and CCCR. The space between the CCCR and the surface source was set to fit the required testing conditions of SAE standards. In the initial CCCR building, there were 15 groups of double pins, so it comprised 15 variables di (from d1 to d15), illustrated in Figure 18. The constraint of each variable di is determined by the curvature of the CCCR surface. Each variable has a non-identical limitation of height values and is dependent on the surface curve. The resulting merit fluctuated 0.01–0.81 mm. The territory of CCCR with extreme curvature will have the highest altitude value. Our focus was on improving the reflection properties of the end area. In order to set the target value of the optimization, we conducted a simulation experiment with a flat regular CCR to find the reflected light power as referenced by 1000 lumen incident beam. The resulting reflected light power was 850 lm, and it was used as the target for subsequent searches for optimized CCCR. Through running the scheme in the optimization process, the best results were determined in the step 25. The recorded data of intensity sensor versus running cycles are shown in Figure 19. The final intensity sensor data was shown as 737.52 lm, which was also the output power of the optimized CCCR. Figure 18. Height difference di between neighboring pins in a double-pin group.

The object function f defined by Equation (4) was determined in the optimization process. The optimization process encompassed three fragments. Object function: The equation that describes the value of the object function of the optimization program established by the genetic algorithm is as follows:

𝑓𝑖, 𝑗 = ∑, 𝑤𝑚 −𝑡 +𝑤𝑚 −𝑡 (4) where wi is the level of curvature of a curved retroreflector that has 15 variables from w1 to w15, and the constraint of each variable is determined by the curvature of the CCCR surface; 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 the optimization target defined with a value corresponding to the retroreflective light intensity on the retroreflector plane. Luminous intensity function: We searched for an approximation of the luminous intensity (RI) I (Φ, a, b, c) at the polar angle of Φ in the form:

I(φ,x,y,z) = Imax∑ 𝑥𝑐𝑜𝑠 φ–yk) (5)

Here, 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 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}. The components in OptisWorks were configured to incorporate light source, intensity sensor, and CCCR. The space between the CCCR and the surface source was set to fit the required testing conditions of SAE standards. In the initial CCCR building, there were 15 groups of double pins, so it comprised 15 variables di (from d1 to d15), illustrated in Figure 18. The constraint of each variable di is determined by the curvature of the CCCR surface. Each variable has a non-identical limitation of height values and is dependent on the surface curve. The resulting merit fluctuated 0.01–0.81 mm. The territory of CCCR with extreme curvature will have the highest altitude value. Our focus was on improving the reflection properties of the end area. In order to set the target value of the optimization, we conducted a simulation experiment with a flat regular CCR to find the reflected light power as referenced by 1000 lumen incident beam. The resulting reflected light power was 850 lm, and it was used as the target for subsequent searches for optimized CCCR. Through running the scheme in the optimization process, the best results were determined in the step 25. The recorded data of intensity sensor versus running cycles are shown in Figure 19. The final intensity sensor data was shown as 737.52 lm, which was also the output power Crystals 2018, 8, 450 11 of 16 of the optimized CCCR.

In the initial optimizationFigureFigure 19. Recorded 19. process,Recorded data the data of mathemat of intensity intensity sensor sensorical versusequation versus running running for cycles. the cycles. intensity distribution of reflected lightIn thewas initial entered optimization into the process, program the mathematical that is expressed equation forin thethe intensity measurement distribution value of of the intensityreflected sensor. light The was luminous entered into intensity the program RI is that defined is expressed by I( inφ, the a, measurementb, c) at the polar value ofangle the intensity of φ shown in Equationsensor. (5). The The luminoustarget of intensity the optimization RI is defined byprocess I(ϕ, a, b ,wac) ats thedefined polar angle with of aϕ valueshown corresponding in Equation (5). to the retroreflectiveThe target light of theintensity optimization on the process retroreflector was defined plane. with a During value corresponding the optimi tozation, the retroreflective to have the CCCR light intensity on the retroreflector plane. During the optimization, to have the CCCR meet the meet the requirements of SAE standards◦ at 0.2° and maximum reflection efficiency, the values of δ requirements of SAE standards at 0.2 and maximum reflection efficiency, the values of δ and di were and di werefound found through through the workflows the workflows shown in Figures show n20 in and Figures 21, respectively. 20 and 21, respectively.

FigureFigure 20. 20. ReflectorReﬂector designdesign ﬂowchart. flowchart.

Figure 21. Flowchart of optimization process.

Before optimization, the di values shown in Table 3 were selected by a random process from the height difference constraint by the optics design software. The constraints of each variable di were determined by the surface curve of the commercial reflex reflector shown in Figure 10. As shown in Table 4, each variable has a different limitation of height values in the range of 0.01 mm to about 0.81 mm. As the optimization was executed and terminated by the program, the optimized CCCR with the same curve of the commercial one was produced. The di and Di of the optimized CCCR (after optimization) and those of the primary CCCR (before optimization) are listed in Table 4 and Table 5, respectively. In the initial optimization process, the mathematical equation for the intensity distribution of reflected light was entered into the program that 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 (5). The target of the optimization process was defined with a value corresponding to the retroreflective light intensity on the retroreflector plane. During the optimization, to have the CCCR meet the requirements of SAE standards at 0.2° and maximum reflection efficiency, the values of δ and di were found through the workflows shown in Figures 20 and 21, respectively.

Crystals 2018, 8, 450 12 of 16 Figure 20. Reflector design flowchart.

Figure 21. Flowchart of optimization process. Figure 21. Flowchart of optimization process.

Before optimization, the di values shown in Table3 were selected by a random process from the Beforeheight optimization, difference constraint the di values by the optics shown design in Table software. 3 were The constraintsselected by of a each random variable processdi were from the height differencedetermined constraint by the surface by curvethe optics of the commercialdesign software. reﬂex reﬂector The constraints shown in Figure of each 10. As variable shown di were determinedin Table by 4the, each surface variable curve has a of different the commercial limitation of re heightflex valuesreflector in the shown range ofin 0.01Figure mm 10. to about As shown in 0.81 mm. As the optimization was executed and terminated by the program, the optimized CCCR Table 4, each variable has a different limitation of height values in the range of 0.01 mm to about 0.81 with the same curve of the commercial one was produced. The di and Di of the optimized CCCR mm. As (afterthe optimiza optimization)tion andwas those executed of the and primary terminated CCCR (before by the optimization) program, arethe listedoptimized in Tables CCCR4 with the sameand curve5, respectively. of the commercial one was produced. The di and Di of the optimized CCCR (after optimization) and those of the primary CCCR (before optimization) are listed in Table 4 and Table 5, Table 3. Height variable d before and after optimization. respectively. i

di (mm) d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12 d13 d14 d15 Region Anterior Region Central Region Posterior Region Min (mm) 0.01 0.05 0.1 0.15 0.18 0.3 0.5 0.55 0.6 0.65 0.7 0.7 0.73 0.74 0.75 Max (mm) 0.15 0.2 0.25 0.3 0.4 0.6 0.7 0.75 0.78 0.78 0.81 0.81 0.81 0.81 0.81

Table 4. Constraints of height variable di in optimization process.

d (mm) d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12 d13 d14 d15 Region Anterior Region Central Region Posterior Region Before 0.15 0.2 0.25 0.3 0.4 0.6 0.7 0.75 0.78 0.78 0.81 0.81 0.81 0.81 0.81 optimization After 0.11 0.18 0.14 0.23 0.28 0.56 0.62 0.70 0.68 0.78 0.77 0.74 0.78 0.80 0.80 optimization

Table 5. Height variable Di before and after optimization.

Di (mm) D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 D15 Region Anterior Region Central Region Posterior Region Before 0.17 0.3 0.45 0.75 0.89 1.37 1.66 1.88 2 2.13 2.26 2.57 2.74 3.15 3.43 optimization After 0.07 0.12 0.31 0.52 0.61 0.81 1.04 1.18 1.32 1.35 1.49 1.83 1.96 2.35 2.63 optimization

After ending the solution search, the optimized CCCR was analyzed to compare with the commercial one by simulations. The distance from the light source to the CCCR was 30 m, CCCR was kept in the car driving direction, 0◦, 10◦ (up, down) vertical and 20◦ (left, right) horizontal with the incident light, to proceed with optical tests of SAE regulations. The resulting intensity distributions

After ending the solution search, the optimized CCCR was analyzed to compare with the commercial one by simulations. The distance from the light source to the CCCR was 30 m, CCCR was After ending the solution search, the optimized CCCR was analyzed to compare with the Crystals 2018, 8, 450 ° ° ° 13 of 16 keptcommercial in the car one driving by simulations. direction, The0 , 10distance (up, fromdown) the vertical light source and 20to the (left, CCCR right) was horizontal 30 m, CCCR with was the incidentkept in light, the car to drivingproceed direction, with optical 0°, 10 tests° (up, of down)SAE regulations. vertical and The 20° resulting(left, right) intensity horizontal distributions with the ° ◦ byby incident0 0lightlight light,incident incident to proceed to to anterior, anterior, with opticalcentral, central, tests and and of posterio posterior SAE regulations.r regions sequentiallysequentiallyThe resulting areare intensity shown shown distributions in in Figure Figure 22 22,, whichwhichby 0 °demonstrate light demonstrate incident that to that anterior,R RI Iandand Rcentral, RAA increasedincreased and posterio significantly significantlyr regions in allsequentiallyall regions,regions, andareand moreshown more retroreflection inretroreflection Figure 22, ◦° ◦° ◦ ° workingworkingwhich areademonstrate area was was accomplished accomplished that RI and throughR throughA increased the the newsignificantly design.design. WithWithin all 0 0regions,,, 10 10 (up, (up, and down) down) more vertical verticalretroreflection and and 20 20 (left,(left,working right) right) horizontalarea horizontal was accomplished incident incident light, light, through the the retroflection retroflection the new design. resultsresults With for for R RI0Iand° and, 10 R° RA(up,Aachieved achieved down) by verticalby the the optimized optimizedand 20° CCCR,CCCR,(left, right)the the primary horizontal primary CCCR, CCCR, incident and and light,the the commercial commercialthe retroflection CCCR CCCR results were for calculatedcalculated RI and R and Aand achieved are are shown shown by the in in Figuresoptimized Figures 23 23 andandCCCR, 24 24individually individuallythe primary for forCCCR, comparison. comparison. and the commercial CCCR were calculated and are shown in Figures 23 and 24 individually for comparison.

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

(d()d ) ((e) (f()f )

(g()g ) ((h) (i() i)

◦ Figure 22. ReflectedReﬂected light light intensity intensity distributions distributions and and RI Rforfor 0° 0incidentincident light light beam beam on ( ona) anterior, (a) anterior, (b) Figure 22. Reflected light intensity distributions and RI forI 0° incident light beam on (a) anterior, (b) (central,b) central, and and(c) posterior (c) posterior regions regions of (d– off) (thed– f)commercial the commercial CCCR CCCRand (g– andi) the (g –optimizedi) the optimized CCCR, central, and (c) posterior regions of (d–f) the commercial CCCR and (g–i) the optimized CCCR, CCCR,respectively. respectively. respectively.

Figure 23. Comparison of reﬂection coefﬁcient RI of commercial CCCR, primary CCCR, and optimized CCCR. Figure 23. Comparison of reflection coefficient RI of commercial CCCR, primary CCCR, and

Figureoptimized 23. CCCR.Comparison of reflection coefficient RI of commercial CCCR, primary CCCR, and optimized CCCR. CrystalsFigure2018, 823., 450 Comparison of reflection coefficient RI of commercial CCCR, primary CCCR, and14 of 16 optimized CCCR.

Figure 24. Comparison of reflection efficiency RA of commercial CCCR, primary CCCR, and

Figureoptimized 24. CCCR.Comparison of reflection efficiency RA of commercial CCCR, primary CCCR, and optimized CCCR. FigureFigureIn 24.orderComparison 24. toComparison demonstrate of reflection of reflectionthat efficiency the efficiencyoptimized RA of commercial R ACCCR of commercial CCCR,can really primary CCCR, meet CCCR, primary SAE and requirements optimizedCCCR, and CCCR. and performoptimizedIn order better CCCR.to than demonstrate the commercial that thesample, optimized it was CCCRprototyped can reallyand tested meet inSAE practical requirements experiments, and performshownIn in order better Figure to than demonstrate 25. Throughthe commercial thatthe proposed the optimizedsample, experimental it CCCRwas prototyped can setup really in and meet Figure tested SAE 10, requirements thein practical retroreflected experiments, and performoutputs shownbetteron screenIn than inorder Figure by the theto commercial 25. demonstratecommercial Through sample, the CCCRthat proposed the it and was optimized the prototypedexperimental optimi CCCRzed and setup CCCR can tested in really areFigure in practicalpresented meet 10, the SAE experiments, retroreflectedin requirementsFigure 26, shown outputsand and the in performonFigureresulting screen 25 better .R ThroughbyI at the rotationalthan commercial thethe proposedcommercial angles CCCR of experimental 0° sample,, and10° U, the 10 it optimi ° setupwas D, 20 prototypedzed in° L, Figure andCCCR 20 10 °andare, R the were presentedtested retroreflected calculated in practical in Figure outputsand experiments, are 26, onshown and screen the in shownresultingbyFigure the incommercial27. FigureR I at rotational 25. CCCRThrough angles and the the of proposed optimized0°, 10° U, experimental 10 CCCR° D, 20 are° L, presented setup and 20 in° Figure R in were Figure 10, calculated the26, retroreflected and theand resulting are shown outputs RI inat ◦ ◦ ◦ ◦ ◦ onFigurerotational screen 27. by angles the commercial of 0 , 10 U, CCCR 10 D, 20andL, the and optimi 20 Rzed were CCCR calculated are presented and are shownin Figure in Figure26, and 27 the. resulting RI at rotational angles of 0°, 10° U, 10° D, 20° L, and 20° R were calculated and are shown in Figure 27.

Figure 25. Prototyped CCCR of the optimized design. Figure 25. Prototyped CCCR of the optimized design.

Figure 25. Prototyped CCCR of the optimized design.

Commercial CommercialCCCR CCCR Commercial

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

(a) (b) (c)

Optimized OptimizedCCCR CCCR Optimized

CCCR (d) (e) (f) (d) (e) (f) Figure 26. ReﬂectedReflected light distribution for 0◦° incident light beam on anterior, central,central, andand posteriorposterior

Figureregions 26. ofof ((Reflecteda–c)) thethe commercialcommercial light distribution CCCRCCCR andandfor 0 (( d–f°d–f incident)) thethe optimizedoptimized light beam CCCR,CCCR, on anterior, respectively.respectively. central, and posterior (d) (e) (f) regions of (a–c) the commercial CCCR and (d–f) the optimized CCCR, respectively. Figure 26. Reflected light distribution for 0° incident light beam on anterior, central, and posterior regions of (a–c) the commercial CCCR and (d–f) the optimized CCCR, respectively. Crystals 2018, 8, 450 15 of 16

Figure 27. ComparisonFigure 27. Comparison of coefﬁcient of of luminouscoefficient intensity of luminous RI between intensity the commercialRI between samplethe and the optimized prototypedcommercial sample sample (region and the by optimized region). prototyped sample (region by region).

5. Discussion of the Results 5. DiscussionIn the study, of the a curved Results retroreflector with 120 mm × 28 mm reflecting area was built by 15 arrays of double-pinIn the study, groups, a curved and retroreflector each pin cross-section with 120 mm size × was 28 mm 5.56 reflecting mm. It was area demonstrated was built by 15 that arrays the CCCRof double-pin could retroreflect groups, and one each incident pin cross-section beam as six beams,size was as shown5.56 mm. in FigureIt was 12demonstrated. In the optimization that the process,CCCR could the heightretroreflect differences one incidentdi among beam the as pin six groupsbeams, as were shown set asin variables.Figure 12. InIn orderthe optimization to find the optimalprocess, heightthe height difference differences under d thei among limit of the computer pin groups memory, were only set as 15 variables. sets of di were In order used. to Therefore, find the theoptimal retroreflector height difference structure under was controlled the limit and of computer could be adjustedmemory, in only one dimension15 sets of only,di were resulting used. inTherefore, the annoying the retroreflector staircase effect. structure However, was controll if the heighted and ofcould all double-pinbe adjusted groupsin one dimension was allowed only, to changeresulting independently in the annoying during staircase the effect. optimization However, procedure, if the height we of believe all double-pin that the groups staircase was effect allowed can beto change diminished independently and more during complex the curved optimization retroreflector procedure, design we can believe be accomplished. that the staircase If the effect CCCR can hasbe diminished a curved outlook,and more the complex height curved between retroreflector each pin group design due can to be surface accomplished. curvature If the would CCCR affect has opticala curved characteristics, outlook, the height leading between to lower each reflection pin grou efficiencyp due to and surface even failingcurvature to pass would SAE affect regulations. optical Bycharacteristics, using double-pin leading groups to lower to build reflection the primary efficie CCCR,ncy and reflection even failing efficiency to canpass be SAE improved. regulations. Through By OptisWorksusing double-pin software groups to produceto build the the primary optimized CCCR, CCCR, reflection RI can efficiency be increased can further,be improved. but sacrificing Through reflectionOptisWorks efficiency software RA to, as produce shown inthe Figures optimized 23 and CCCR, 24. RI can be increased further, but sacrificing reflection efficiency RA, as shown in Figures 23 and 24. 6. Conclusions

6. ConclusionsServing as an efficient working area ratio, reflection efficiency RA and coefficient of luminous intensity R as evaluation indices for a commercial CCCR and a proposed new design are compared. ServingI as an efficient working area ratio, reflection efficiency RA and coefficient of luminous It can be concluded that the optimized CCCR redistributed the reflected light beam energy of the intensity RI as evaluation indices for a commercial CCCR and a proposed new design are compared. ◦ primaryIt can be CCCR,concluded which that shared the optimized more energy CCCR in the redist 0.2ributedup-reflected the reflected beam by light taking beam energy energy from of the otherprimary five CCCR, reflected which beams. shared After more computer energy simulations in the 0.2° andup-reflected optical experiments, beam by taking it was energy demonstrated from the thatother the five proposed reflected CCCR beams. not After only computer exceeded simulati SAE standards,ons and optical listed inexperiment Table1, buts, it also was had demonstrated 33% more workingthat the proposed area and muchCCCR better not only reflection exceeded efficiency SAE standa thanrds, the commerciallisted in Table one, 1, whosebut also posterior had 33% region more wasworking not effectivearea and atmuch all, better as shown reflection in Figures efficiency 26 and than 27 .the Based commercial on the one, data whose in Figure posterior 27, it canregion be computedwas not effective that the at ratio all, as of shown average in R IFiguresof the optimized26 and 27. CCCRBased toon thatthe ofdata the in commercial Figure 27, it CCCR can be is (13419/9470, 0◦), (5900/4263, 10◦ U), (3916/2832, 10◦ D), (4218/2983, 20◦ L), and (4354/3080, 20◦ D), computed that the ratio of average RI of the optimized CCCR to that of the commercial CCCR is ◦ ◦ ◦ ◦ ◦ which(13419/9470, means 0 29.43%°), (5900/4263, (0 ), 27.75% 10° U), (10 (3916/2832,U), 27.67% 10 (10° D),D), (4218/2983, 29.27% (20 20L),° L), and and 29.26% (4354/3080, (20 R) 20 higher° D), retroreflectionwhich means 29.43% efficiency (0°), can 27.75% be accomplished (10° U), 27.67% by the (10 proposed° D), 29.27% CCCR. (20° L), and 29.26% (20° R) higher retroreflection efficiency can be accomplished by the proposed CCCR. Author Contributions: L.-T.L. conducted the simulation and wrote the paper. H.-T.L. designed the simulation cases,Author discussed Contributions: the results L.T.L. with conducted J.L. and revised the simulation the paper. and H.-Y.M. wrote had the helpful paper. discussionH.T.L. designed with H.-Y.L. the simulation and help revise the paper. cases, discussed the results with J.L. and revised the paper. H.Y.M. had helpful discussion with H.Y.L. and help revise the paper. Crystals 2018, 8, 450 16 of 16

Funding: 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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