Asymmetric Double Freeform Surface Lens for Integrated LED Automobile Headlamp

micromachines

Article Asymmetric Double Freeform Surface Lens for Integrated LED Automobile Headlamp

Hui Zhang 1, Dengfei Liu 1,2, Yinwan Wei 1,2 and Hong Wang 1,2,*

1 Engineering Research Center for Optoelectronics of Guangzhou Province, School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China; [email protected] (H.Z.); eedﬂ[email protected] (D.L.); [email protected] (Y.W.) 2 Guangdong Provincial Engineering Research Center for Wide Bandgap Semiconductor Chips and Application, Zhongshan Institute of Modern Industrial Technology, South China University of Technology, Zhongshan 528437, China * Correspondence: [email protected]; Tel.: +86-20-87111557

Abstract: We propose a design method of asymmetric double freeform surface lens for an integrated LED automobile headlamp and develop an integrated LED automobile optical system. A single asymmetric double freeform surface lens is designed to redistribute rays emitting from the light source for realizing both low and high beams. Moreover, a freeform surface reflector is used to improve the energy efficiency of high beams. The prism placed in the optical path can suppress chromatic dispersion on the edge of the target plane. Simulation and experimental results show that the illumination values and color temperature of the key points can fully meet the requirements of United Nations Economic Commission for Europe vehicle regulations (ECE) R112, 48, and 128. The volume of the whole optical system comprised of freeform surface elements is smaller than that of the low beam system of a traditional headlamp, resulting in saved space, in which other electronic Citation: Zhang, H.; Liu, D.; Wei, Y.; devices can be installed for the safety of the driver, which indicates that the proposed method is Wang, H. Asymmetric Double practical in the field of automobile lighting. Freeform Surface Lens for Integrated LED Automobile Headlamp. Micromachines 2021, 12, 663. https:// Keywords: asymmetric double freeform surface lens; LED; integrated automobile headlamp; freeform doi.org/10.3390/mi12060663 surface optics

Academic Editors: W.B. Lee and Lihua Li 1. Introduction Received: 5 May 2021 LEDs have gradually entered our lives due to their advantages of energy saving, Accepted: 4 June 2021 high energy efficiency, long lifespan, and miniaturization [1,2]. In the past decade, LEDs Published: 5 June 2021 have been used increasingly as light sources in automobile headlamps for their excellent properties [3–6]. Since low-beam requirements are completely different from those of high Publisher’s Note: MDPI stays neutral beams, the traditional optical systems of low and high beams in headlamps are designed with regard to jurisdictional claims in separately, mainly including projection and reflection types. In general, projection-type published maps and institutional affil- optical systems deflect by lenses and reflection type by reflectors [7]. It is easy to form iations. a clear cutoff line but hard to improve the energy efficiency for projection types with a baffle plate; conversely, the reflection type without a baffle plate is more efficient but has a dim cutoff line. Previously, Cvetkovic et al. presented a simultaneous multiple surface (SMS) 3D method for automobile low and high beam headlamps, whose optical efficiency Copyright: © 2021 by the authors. is more than 75% [8,9]. Domhardt et al. designed a combined lens for LED-based low Licensee MDPI, Basel, Switzerland. beam headlamp but needed large space to install lenses for high energy efficiency [10]. This article is an open access article Ge et al. used an elliptical and parabolic reflector to design a low beam headlamp that distributed under the terms and had high energy efficiency [5]. Hsieh et al. proposed a modular design for an LED conditions of the Creative Commons vehicle projector headlamp that provided the cutoff line of low beams without a baffle Attribution (CC BY) license (https:// plate [11]. Chu et al. proposed a low beam headlamp with a compound ellipsoidal reflector creativecommons.org/licenses/by/ that achieved the highest energy efficiency in the existing literature [12]. In the past, 4.0/).

Micromachines 2021, 12, 663. https://doi.org/10.3390/mi12060663 https://www.mdpi.com/journal/micromachines Micromachines 2021, 12, 663 2 of 16

our research group has proposed several optical systems for headlamps. For example, an optical system with a single freeform surface lens [13], a low chromatic dispersion headlamp system using a parabolic reflector and micro-lens array [14], a LED motorcycle headlight using a combined lens [15], etc. More separate design methods for low and high beams can be found in references [16–21]. In recent years, compact headlamp design has become more and more fashionable [22]. The integrated headlamp reduces its volume by sharing some optical elements between low- and high-beam systems, allowing the designs of integrated headlamps to fit with the trend of compact design. However, few studies in the literature have been reported about the integrated headlamp. Hung et al. designed an integrated headlamp incorporating a digital micromirror device [23]. Wu et al. presented a modular LED headlamp system based on a freeform reflector [24]. Borocki et al. recommended a single optical system with both a low beam and a high beam, in which switching between the low beam and high beam was achieved by a removable shutter [25]. M. Rice et al. proposed an integrated headlamp based on a projective low- beam system, in which the light emitted from the high-beam source was reflected by the lower plane of the baffle plate and deflected by the lens to form the illumination distribution of high beams [26]. In previous studies, most of the headlamps were designed individually, which may increase the complexity and volume of the headlamp. Existing integrated headlamps with a removable shutter may affect the reliability of the headlamp. Therefore, it is necessary to study a simple and small-volume headlamp system. In this paper, we proposed a method of designing an asymmetric double freeform surface lens (ADFSL) and developed an integrated LED automobile optical system. On the premise of meeting the requirements of ECE R112, 48, and 128 [27–29], this new integrated LED headlamp system can greatly improve the compactness of the optical system and suppress chromatic dispersion at the edge of the target illumination area. Just one lens is needed to achieve low and high beams, which means that this new headlamp system can save a lot of space. A freeform surface reflector focusing light is proposed to improve energy efficiency. Furthermore, a prism is placed in the optical path to reduce the chromatic dispersion further, which can provide comfortable and safe lighting for the driver. Compared to the traditional, separated headlamp and integrated headlamp, the proposed headlamp has only one single lens to achieve low and high beams, reducing the volume of the automobile headlamp. Furthermore, the color distribution on the target plane using ADFSL and prism is more stable.

2. Design Method The optical system of the new integrated headlamp is shown in Figure1. The whole system consists of an ADFSL, a freeform surface reflector, a prism, a baffle, and two LEDs. The optical system of the low beam includes a LED source, an upper half of the ADFSL, and a baffle plate. Correspondingly, the optical system of the high beam comprises a freeform surface reflector, a prism, the lower half of the ADFSL, and a LED source. Rays emitting from the low beam LED source are partially blocked by the baffle plate and then redistributed by the ADFSL, forming a low beam with a clear cutoff line on the target plane. On the other hand, rays from the high beam LED source are focused on a point by the freeform surface reflector and then deflected by the prism. Finally, the remaining rays will be redistributed by the ADFSL to form the illumination distribution of the high beam. The implementation of the low and high beams will be described in detail below. Micromachines 2021, 12, 663 3 of 16

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Figure 1. Optical system of the integrated LED automobile headlamp.

2.1. Optical System of the Low Beam Mode Figure 1. Optical system of the integrated LED automobile headlamp. FigureOver 1. Optical the past system decade, of the a series integrated of regulations LED automobile have been headlamp. introduced for driver’s safety. 2.1. Optical System of the Low Beam Mode Low beam is mainly used for good road lighting and cannot cause glare to the opposing 2.1.Over Optical the past System decade, a of series the of Low regulations Beam have Mode been introduced for driver’s safety. drivers.Low beam isAccording mainly used for to good the road ECE lighting R112 and regulations, cannot cause glare the to thetested opposing points and the cutoff line are showndrivers.Over According in Figure the to past the 2. ECE decade, R112 regulations, a series the of tested regulations points and the have cutoff linebeen are introduced for driver’s safety. shown in Figure2. Low beam is mainly used for good road lighting and cannot cause glare to the opposing drivers. According to the ECE R112 regulations, the tested points and the cutoff line are shown in Figure 2.

Figure 2. Tested2. Tested points andpoints regions and of low regions beam. of low beam. It can be found that the light shape of the low beam has a wide horizontal spread for both sides,It can which be can found provide that a big the angle light of view shape for drivers. of the Moreover, low thebeam lighting has spot a wide horizontal spread for of the low beam is “dark on the left but bright on the right”. The measuring plane is 25 m bothin front sides, of the headlamp which forcan testing provide the illuminances a big angle on key of points. view Each for optical drivers. element Moreover, the lighting spot ofhasFigure the a specific low 2. Tested function beam topoints is ensure “dark and a qualified on regions the low left beam of butlow on thebright beam. measuring on the plane. right”. Concretely, The measuring plane is 25 m the upper half of the ADFSL is used to realize the ellipse lighting spot, and the baffle plate inblocks front the strayof the light headlamp to form a clear for cutoff testing line. In our the laboratory, illuminances a low beam on system key for points. Each optical element haslaser headlampa Itspecific can withoutbe function found ellipsoid that to reflector ensure the (Figurelight a qualified 3shape) was designed, of low the andbeam low the constructionbeamon the has measuring a wide horizontalplane. Concretely, spread for wasboth also sides, adopted which in the integrated can provide headlamp fora big the low angle beam forof theview compactness for drivers. of the Moreover, the lighting spot theoptical upper system. half of the ADFSL is used to realize the ellipse lighting spot, and the baffle plate blocksof the lowthe straybeam light is “dark to form on athe clear left cutoff but bright line. Inon our the laboratory, right”. The a measuringlow beam system plane isfor 25 m laserin front headlamp of the headlamp without ellipsoid for testing reflector the illuminances (Figure 3) was on designed, key points. and Each the constructionoptical element washas aalso specific adopted function in the to integrated ensure a headlampqualified low for thebeam low on beam the measuringfor the compactness plane. Concretely, of the opticalthe upper system. half of the ADFSL is used to realize the ellipse lighting spot, and the baffle plate blocks the stray light to form a clear cutoff line. In our laboratory, a low beam system for laser headlamp without ellipsoid reflector (Figure 3) was designed, and the construction was also adopted in the integrated headlamp for the low beam for the compactness of the optical system.

Figure 3. Low beam system without an ellipsoid reflector.

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Figure 1. Optical system of the integrated LED automobile headlamp.

2.1. Optical System of the Low Beam Mode Over the past decade, a series of regulations have been introduced for driver’s safety. Low beam is mainly used for good road lighting and cannot cause glare to the opposing drivers. According to the ECE R112 regulations, the tested points and the cutoff line are shown in Figure 2.

Figure 2. Tested points and regions of low beam.

It can be found that the light shape of the low beam has a wide horizontal spread for both sides, which can provide a big angle of view for drivers. Moreover, the lighting spot of the low beam is “dark on the left but bright on the right”. The measuring plane is 25 m in front of the headlamp for testing the illuminances on key points. Each optical element has a specific function to ensure a qualified low beam on the measuring plane. Concretely, the upper half of the ADFSL is used to realize the ellipse lighting spot, and the baffle plate blocks the stray light to form a clear cutoff line. In our laboratory, a low beam system for laser headlamp without ellipsoid reflector (Figure 3) was designed, and the construction

Micromachines 2021, 12, 663 was also adopted in the integrated headlamp for the low4 ofbeam 16 for the compactness of the optical system.

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FigureFigure 3.DoubleLow 3. Low beam systemfreeform beam without system surface an ellipsoid without lens reflector. an(DFSL) ellipsoid has reflector.many advantages over single freeform sur- faceDouble lens. freeform For example, surface lens it (DFSL) can achieve has many an advantages accurate over distribution single freeform of light and suppress chro- surfacematic lens. dispersion For example, by it canits achieveinner anand accurate outer distribution freefor ofm light surfaces and suppress [15]. The deflection factor C (0 ≤ chromatic dispersion by its inner and outer freeform surfaces [15]. The deflection factor C (0C≤ ≤C 1),≤ 1), an an important important factor factor in DFSL, in isDFSL, used to representis used the toangular represent deflection the ratio angular deflection ratio of two offreeform two freeform surfaces. surfaces. It It is worthis worth noting noting that θ, ϕ are that zenith θ angle, ϕ and are azimuth zenith angle, angle and azimuth angle, re- respectively, and α is theα angle between the discrete points on the target plane and positive Xspectively, axis (Figure4). Theand ray’s angle is afterthe passingangle through between the inner the freeform discrete surface points could be on the target plane and posi- denotedtive X as axis follows: (Figure 4). The ray’s angle after passing through the inner freeform surface θ = Cθ + (1 − C)θ 1 0 2 (1) could be denoted as follows:ϕ1 = Cϕ + (1 − C)α

FigureFigure 4. Sketch 4. Sketch of the light of deﬂectionthe light of thedeflection asymmetric of double the freeform asymmetric surface lens. double freeform surface lens. To construct the ADFSL, the mapping relationship between certain angle rays on the target plane and discrete points of the target plane should be calculated. Figure5 shows the division of the target illumination area. Toθθ simplify=+− the calculation and θ generate 10CC(1 ) 2 qualiﬁed illumination distribution, the lighting zone is set as an ellipse and divided into I, (1) II, III zones. E1, E2, E3 are the corresponding illuminancesϕϕ=+−CC of zone(1 I, II, III, respectively, )α and the semi-major axis is a, and the semi-minor axis,1 b. Similarly, the semi-major and semi-minor axes are equally divided into three parts, with ai, bi being the semi-major axis and semi-minorTo construct axis of the the divided ADFSL, sub-ellipse, the respectively. mapping On relationship the other hand, the between target certain angle rays on the target plane and discrete points of the target plane should be calculated. Figure 5 shows the division of the target illumination area. To simplify the calculation and generate qualified illumination distribution, the lighting zone is set as an ellipse and divided into I, II, III zones. E1, E2, E3 are the corresponding illuminances of zone I, II, III, respectively, and the semi-major axis is a, and the semi-minor axis, b. Similarly, the semi-major and semi-

minor axes are equally divided into three parts, with ai , bi being the semi-major axis and semi-minor axis of the divided sub-ellipse, respectively. On the other hand, the target α α illumination area is divided into n parts along the direction , where i is the angle between ith part and the positive X axis.

Figure 5. Division of the target plane for low beam.

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Double freeform surface lens (DFSL) has many advantages over single freeform surface lens. For example, it can achieve an accurate distribution of light and suppress chromatic dispersion by its inner and outer freeform surfaces [15]. The deflection factor C (0 ≤ C ≤ 1), an important factor in DFSL, is used to represent the angular deflection ratio of two freeform surfaces. It is worth noting that θ , ϕ are zenith angle and azimuth angle, respectively, and α is the angle between the discrete points on the target plane and positive X axis (Figure 4). The ray’s angle after passing through the inner freeform surface could be denoted as follows:

Figure 4. Sketch of the light deflection of the asymmetric double freeform surface lens.

θθ=+− θ 10CC(1 ) 2 ϕϕ=+−α (1) 1 CC(1 ) To construct the ADFSL, the mapping relationship between certain angle rays on the target plane and discrete points of the target plane should be calculated. Figure 5 shows the division of the target illumination area. To simplify the calculation and generate qualified illumination distribution, the lighting zone is set as an ellipse and divided into I, II, III zones. E1, E2, E3 are the corresponding illuminances of zone I, II, III, respectively, and the semi-major axis is a, and the semi-minor axis, b. Similarly, the semi-major and semi-

minor axes are equally divided into three parts, with ai , bi being the semi-major axis Micromachines 2021, 12, 663 5 of 16 and semi-minor axis of the divided sub-ellipse, respectively. On the other hand, the target α α illumination area is divided into n parts along the direction , where i is the angle illuminationbetween areaith ispart divided and into then parts positive along the X direction axis. α, where αi is the angle between ith part and the positive X axis.

FigureFigure 5. Division 5. Division of the target of the plane target for low plane beam. for low beam.

I0 is the central intensity of the LED source; I(θ), the intensity distribution of light in the θ direction; θ, the angle between the emergent light and the optical axis; and the relationship between I(θ) and I0 can be expressed as follows:

I(θ) = I0 cos θ (2)

According to the conservation of energy, we obtain [30]

2 2 R θ1 1 R αn a1b1 2π I0· cos θ· sin θdθ = E1· 2 2 dα 0 2 0 b1 cos α+a1 sin α 2 2 2 2 R θ2 1 R αn a2b2 a1b1 2π I0· cos θ· sin θdθ = E2· 2 2 − 2 2 dα (3) θ1 2 0 b2 cos α+a2 sin α b1 cos α+a1 sin α 2 2 2 2 R θ3 1 R αn a3b3 a2b2 2π I0· cos θ· sin θdθ = E3· 2 2 − 2 2 dα θ2 2 0 b3 cos α+a3 sin α b2 cos α+a2 sin α

By solving the above integral equation, the mapping relationship between θi and the illumination area on the target plane can be acquired. According to the conservation of energy, the relationship between the azimuth angle ϕj and αj can be expressed as follows:

2 2 R θ1 R ϕj+1 1 R αj+1 a1b1 I0· cos θ· sin θdθdϕ = E1· 2 2 dα 0 ϕj 2 αj b1 cos α+a1 sin α 2 2 2 2 R θ2 R ϕj+1 1 R αj+1 a2b2 a1b1 I0· cos θ· sin θdθdϕ = E2· 2 2 − 2 2 dα (4) θ1 ϕj 2 αj b2 cos α+a2 sin α b1 cos α+a1 sin α 2 2 2 2 R θ3 R ϕj+1 1 R αj+1 a3b3 a2b2 I0· cos θ· sin θdθdϕ = E3· 2 2 − 2 2 dα θ2 ϕj 2 αj b3 cos α+a3 sin α b2 cos α+a2 sin α

By solving the above equation, the relationship between ϕj and αj is obtained. ( x = a cos α (i,j) i j (5) y(i,j) = bi sin αj

The coordinates of the points on the target plane can be calculated by Equation (5). Then, we obtain the mapping relationship between the light emitting from the source and the points on the target plane. Next, the proﬁle of ADFL is calculated by iteration. The initial points of the ﬁrst and second freeform surfaces are set as L1 and L2, respectively. Micromachines 2021, 12, 663 6 of 16

After the initial points are given, the normal vector of the initial points can be obtained according to the vector form of refraction law,

→ → → noout − nin In N = (6) → → noout − n In in

Micromachines 2021, 12, 663 → → → 6 of 16 Micromachines 2021, 12, 663 where In is the unit vector of the incident ray, Out is the unit vector of outgoing ray, N is 6 of 16

the normal vector, no is the refractive index in the outgoing space, and nin is the refractive index in the incident space. All coordinates of the discrete points on the freeform surface can be calculated by iteration of the normal vector, which stipulates that the intersection pointthe first of the and next incidentsecond ray freeform and the normal surfaces plane ofis the generated. last point is theThen, next pointby fixing on the the value of θ and the first and second freeform surfaces is generated. Then, by fixing the value of θ and curve.changing The expression the value of the of normal ϕ , the plane coordinates at any point can of bethe obtained discrete by Equation points (6).on Byboth freeform surfaces changingfixing the value the of valueϕ and changing of ϕ , the value coordinates of θ, the initial of curve the discrete of the first andpoints second on both freeform surfaces freeformcan be surfacesacquired is generated. by iteration Then, byof fixingthe normal the value ofveθctor.and changing Readers the can value find of ϕ ,the detailed iteration cantheprocess coordinates be acquired in reference of the discreteby iteration 15. points After on of bothimporting the freeform normal surfacesthe data ve canctor. to be modeling acquired Readers by iteration software,can find the upperdetailed half iteration of processofthe the ADFSL normal in vector.reference can Readersbe obtained 15. can After find by the importinglofting detailed iterationcurve, theprocess as data shown in to [15 ].modelingin After Figure importing 6. software, the upper half of the data to modeling software, the upper half of the ADFSL can be obtained by lofting thecurve, ADFSL as shown can in Figure be obtained6. by lofting curve, as shown in Figure 6.

Figure 6. The upper half of the double freeform surface lens. Figure 6. The upper half of the double freeform surface lens. FigureThe 6. The curved upper baffle half of plate the doublewith 45 freeform degrees surface is chosen lens. to form the clear cutoff line, as shownThe curvedin Figure bafﬂe 7. plate with 45 degrees is chosen to form the clear cutoff line, as shownThe in Figure curved7. baffle plate with 45 degrees is chosen to form the clear cutoff line, as shown in Figure 7.

FigureFigure 7. The7. The bafﬂe baffle plate. plate. 2.2. Optical System of the High Beam Mode 2.2.The Optical high beam System of the of automobile the High headlamp Beam Mode is mainly used for bad road lighting since Figure 7. The baffle plate. it providesThe enough high beam illumination of the on automobile the target area [headlamp31]. In addition, is mainly the regulations used requirefor bad road lighting since it provides enough illumination on the target area [31]. In addition, the regulations require 2.2.the Optical target plane System center of the area High with Beam maximum Mode illumination. The test area of the high beam is shownThe in high Figure beam 8. of the automobile headlamp is mainly used for bad road lighting since it provides enough illumination on the target area [31]. In addition, the regulations require the target plane center area with maximum illumination. The test area of the high beam is shown in Figure 8.

Figure 8. Test points and regions of the high beam.

The traditional design uses an ellipsoidal reflector to focus the rays emitted from the source, while part of the rays emitted from the high beam source will be blocked by the Figurelow beam 8. Test source points due and to regions the volume of the highof the beam. LED source. It will cause significant energy losses, as shown in Figure 9a. Therefore, the construction in Figure 1 is adopted to improve lightThe efficiency traditional and illumination. design uses Rays an ellipsoidal emitted from reflector the high to beam focus source the rays focus emitted on a point from the source,on Z axis while by the part freeform of the surfacerays emitted reflector, from as shownthe high in Figurebeam 9b.source will be blocked by the low beam source due to the volume of the LED source. It will cause significant energy losses, as shown in Figure 9a. Therefore, the construction in Figure 1 is adopted to improve light efficiency and illumination. Rays emitted from the high beam source focus on a point on Z axis by the freeform surface reflector, as shown in Figure 9b.

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the first and second freeform surfaces is generated. Then, by fixing the value of θ and changing the value of ϕ , the coordinates of the discrete points on both freeform surfaces can be acquired by iteration of the normal vector. Readers can find the detailed iteration process in reference 15. After importing the data to modeling software, the upper half of the ADFSL can be obtained by lofting curve, as shown in Figure 6.

Figure 6. The upper half of the double freeform surface lens.

The curved baffle plate with 45 degrees is chosen to form the clear cutoff line, as shown in Figure 7.

Figure 7. The baffle plate.

2.2. Optical System of the High Beam Mode

Micromachines 2021, 12, 663 The high beam of the automobile headlamp is mainly used7 of 16 for bad road lighting since it provides enough illumination on the target area [31]. In addition, the regulations require the target plane center area with maximum illumination. The test area of the high beam is the target plane center area with maximum illumination. The test area of the high beam is shownshown in Figure in Figure8. 8.

FigureFigure 8. Test 8. pointsTest points and regions and of theregions high beam. of the high beam. The traditional design uses an ellipsoidal reflector to focus the rays emitted from the source, whileThe parttraditional of the rays emitteddesign from uses the highan ellipsoidal beam source will reflector be blocked to by thefocus low the rays emitted from the beam source due to the volume of the LED source. It will cause significant energy losses, Micromachines 2021, 12, 663 assource, shown in while Figure9 a.part Therefore, of the the rays construction emitted in Figure from1 is th adoptede high to improve beam lightsource wi7 llof be16 blocked by the efficiencylow beam and illumination. source due Rays to emitted the fromvolume the high of beam the source LED focus source. on a point It onwill Z cause significant energy axislosses, by the as freeform shown surface in Figure reflector, 9a. as shown Therefore, in Figure 9theb. construction in Figure 1 is adopted to improve light efficiency and illumination. Rays emitted from the high beam source focus on a point on Z axis by the freeform surface reflector, as shown in Figure 9b.

(a) (b) Figure 9. (aFigure) Integrated 9. (a) Integrated headlamp headlamp based based on onellipsoidal ellipsoidal reflectorreflector and and (b) sketch(b) sketch of the freeformof the freeform reflector. reflector. Due to the symmetry of the reflector, only half of the freeform surface reflector was Duedesigned. to the An symmetry initial point isof given the andreflector, the normal only vector half of of the the initial freeform point can besurface obtained reflector was designed.according An initial to the vector point form is ofgiven the reflection and the law, normal which canvector be expressed of the asinitial point can be obtained according to the vector form of the→ reflection→ law, which can be expressed as → out − In N =   (7) → →  out −outIn − In = N  (7) → → out− In → where In, Out are the unit vectors of the incident ray and outgoing ray, respectively, and N is the normal vector. The initial curve and profile of the freeform surface reflector can be whereobtained In , Out by an are iteration the unit process. vectors of the incident ray and outgoing ray, respectively, and N isFreeform the normal surface vector. reflector The converges initial curve rays emitted and profile from the of source the freeform to another focussurface reflector on the Z axis. Therefore, the focus on the Z axis can be seen as a light source without can bevolume obtained that by does an not iteration block the process. rays from the low beam source and will illuminate the Freeformtarget plane. surface Similar reflector to the process converges of low beam rays design, emitted the lighting from spot the of source the high to beam another focus on theis Z set axis. as an Therefore, ellipse, whose the semi-major focus axison the and semi-minorZ axis can axis be are seen equally as divideda light into sourcem without parts. Accordingly, a , b are the semi-major and semi-minor axes of ith part, respectively, volume that does not blocki i the rays from the low beam source and will illuminate the target plane. Similar to the process of low beam design, the lighting spot of the high beam is set as an ellipse, whose semi-major axis and semi-minor axis are equally divided into m

parts. Accordingly, ai , bi are the semi-major and semi-minor axes of ith part, respectively, 0 ≤ i ≤ m. At the same time, the target plane is also divided into n parts along theα α direction, i is the angle between ith part and the X axis, and then the target plane is divided into mn× lattices, as shown in Figure 10. According to the energy conservation, we can obtain the mapping relations.

Figure 10. Division of the target plane for high beam.

θϕ α 22 22 ij++111 j + 1 abii++11 ab ii I θϕ ddθ ϕ = Ek − dα θϕ(,)  α 0 i 2 222 (8) ij j α + ααα+ 2sinbaiiii++11cosa sinb cos

where E0∙ki is the illumination value, and ki is the illuminance control factor on the ith part. Generally, the closer to the original point, the greater the value of the ki. I(,θ ϕ ) is the intensity distribution of the light focused by the freeform surface reflector. After calculating Equation (8), the mapping relationship can be acquired, and the profile of the lower half of the ADFSL is calculated by the normal vector iteration.

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(a) (b) Figure 9. (a) Integrated headlamp based on ellipsoidal reflector and (b) sketch of the freeform reflector.

Due to the symmetry of the reflector, only half of the freeform surface reflector was designed. An initial point is given and the normal vector of the initial point can be obtained according to the vector form of the reflection law, which can be expressed as   − = out In N  (7) out− In   where In , Out are the unit vectors of the incident ray and outgoing ray, respectively, and N is the normal vector. The initial curve and profile of the freeform surface reflector

Micromachines 2021, 12, 663 can be obtained by an iteration process. 8 of 16 Freeform surface reflector converges rays emitted from the source to another focus on the Z axis. Therefore, the focus on the Z axis can be seen as a light source without 0volume≤ i ≤ m. Atthat the does same time, not theblock target the plane rays is also from divided the into lown parts beam along source the α and will illuminate the direction, αi is the angle between ith part and the X axis, and then the target plane is dividedtarget into plane.m × n Similarlattices, as to shown the inprocess Figure 10 .of According low beam to the design, energy conservation, the lighting spot of the high beam weis canset obtainas an the ellipse, mapping whose relations. semi-major axis and semi-minor axis are equally divided into m 2 2 2 2 ! Z θi+1 Z ϕj+1 Z αj+1 a b parts. Accordingly,1 a , i+b1 i +are1 the semi-majorai bi and semi-minor axes of ith part, respec- I(θ,ϕ)dθdϕ = E0·ki· i i − dα (8) θ ϕ 2 α b cos2 α + a sin2 α b cos2 α + a sin2 α i j tively, 0 ≤j i ≤ m. Ati +the1 samei+ time,1 thei target planei is also divided into n parts along theα where E ·k is the illumination value, and k is the illuminance control factor on the direction,0 αi is the angle betweeni ith part and the X axis, and then the target plane is ith part. Generally,i the closer to the original point, the greater the value of the ki. I(θ, ϕ) isdivided the intensity into distribution mn× of lattices, the light focusedas shown by the in freeform Figure surface 10. A reﬂector.ccording After to the energy conservation, calculating Equation (8), the mapping relationship can be acquired, and the proﬁle of the lowerwe can half ofobtain the ADFSL the is mapping calculated by relations. the normal vector iteration.

FigureFigure 10. Division10. Division of the target of the plane target for high plane beam. for high beam. Similar to the low beam lens construction method, the whole ADFSL can be built in Micromachines 2021, 12, 663 8 of 16 the modeling software. As shown in Figure 11, the diameter and thickness of the lens are θϕ α 22 22 ij++1164 mm and 30 mm, respectively. j + 1 ab ab θ ϕ = 1 ii++11 − ii α I(,)θϕ dd E 0ki d (8) θϕ  α 2 I0 +I 222 ij j α + 1 2 ααα+ Similar to the2sin low beam lensα construction+baiiiiδ++11cos method,α cosa the sin2 whole ADFSLb cos can be built in sin( ) = n sin( )· 0 (9) the modeling software. As shown in2 Figure 11, the2 diameterI1+I 2 and thickness of the lens are cos 2 64where mm and E 300∙ kmm,i is therespectively. illumination value, and ki is the illuminance control factor on the ith part. Generally, the closer to the original point, the greater the value of the ki. I(,θ ϕ ) is the intensity distribution of the light focused by the freeform surface reflector. After calculating Equation (8), the mapping relationship can be acquired, and the profile of the lower half of the ADFSL is calculated by the normal vector iteration.

FigureFigure 11. 11. TheThe asymmetric asymmetric double double freeform freeform surface surface lens. lens. ′ + I12I αδ+ αcos sin( )= n sin( ) 2 I + I′ (9) 22cos 12 2 Although DFSL can reduce chromatic dispersion on the target plane, there is still serious chromatic dispersion at the edge due to the large deflection angle. To obtain a light pattern with a stable color distribution, a prism was added to the optical system to reduce the deflection angle of the ADFSL. Figure 12 shows an optical path in the prism. The prism can deflect rays based on refraction law, and the deflection angle between the incident and outgoing ray is δ . Formula (9) presents the calculation of the deflection angle of the prism [32].

Figure 12. Optical path in the prism.

3. Simulation After calculation and optimization, the whole system of the integrated headlamp is introduced into the optical simulation software LightTools [33], as shown in Figure 13. The volume of the whole system is 91 × 64 × 64 mm3, which is smaller than all the separately designed headlamp systems. The low beam source placed at the origin is KW H4L531.TE of OSRAM company and 6R brightness with 1300 lm luminous flux is selected [34]. On the other hand, the high beam source placed at a focus of the freeform surface reflector is KW H4L531.TE and 7R brightness with 1500 lm luminous flux is selected. Low and high beam sources comply with the ECE R48 and ECE R128 regulations [28,29].

Micromachines 2021, 12, 663 8 of 16

Similar to the low beam lens construction method, the whole ADFSL can be built in the modeling software. As shown in Figure 11, the diameter and thickness of the lens are 64 mm and 30 mm, respectively.

Figure 11. The asymmetric double freeform surface lens. ′ + I12I αδ+ αcos sin( )= n sin( ) 2 I + I′ (9) 22cos 12 2 Micromachines 2021, 12, 663 Although DFSL can reduce chromatic dispersion on9 ofthe 16 target plane, there is still serious chromatic dispersion at the edge due to the large deflection angle. To obtain a light pattern with a stable color distribution, a prism was added to the optical system to reduce Although DFSL can reduce chromatic dispersion on the target plane, there is still theserious deflection chromatic dispersion angle atof the the edge ADFSL. due to the Figure large deflection 12 shows angle. Toan obtain optical a light path in the prism. The prism patterncan deflect with a stable rays color based distribution, on refraction a prism was added law, to theand optical the system deflection to reduce angle between the incident the deflection angle of the ADFSL. Figure 12 shows an optical path in the prism. The prism andcan deflect outgoing rays based ray on is refraction δ . Formula law, and the (9) deflection presents angle the between calculation the incident of the deflection angle of the prismand outgoing [32]. ray is δ. Formula (9) presents the calculation of the deflection angle of the prism [32].

Figure 12. Optical path in the prism. Figure 12. Optical path in the prism. 3. Simulation After calculation and optimization, the whole system of the integrated headlamp is 3.introduced Simulation into the optical simulation software LightTools [33], as shown in Figure 13. The volume of the whole system is 91 × 64 × 64 mm3, which is smaller than all the separately designedAfter headlamp calculation systems. The and low beamoptimization, source placed atthe the originwhole is KW system H4L531.TE of the integrated headlamp is introducedof OSRAM company into and the 6R brightnessoptical with simulation 1300 lm luminous softwa flux isre selected LightTools [34]. On the [33], as shown in Figure 13. other hand, the high beam source placed at a focus of the freeform surface reflector is KW Micromachines 2021, 12, 663 3 9 of 16 TheH4L531.TE volume and 7R of brightness the whole with 1500 system lm luminous is 91 flux × is 64 selected. × 64 Low mm and, highwhich beam is smaller than all the sepa- ratelysources comply designed with the headlamp ECE R48 and ECE systems. R128 regulations The [low28,29]. beam source placed at the origin is KW H4L531.TE of OSRAM company and 6R brightness with 1300 lm luminous flux is selected [34]. On the other hand, the high beam source placed at a focus of the freeform surface reflector is KW H4L531.TE and 7R brightness with 1500 lm luminous flux is selected. Low and high beam sources comply with the ECE R48 and ECE R128 regulations [28,29].

Figure 13. 13.Optical Optical system system of the of integrated the integrated headlamp headlamp in simulation in software.simulation software.

Before the simulation, the freeform surface reflector is set as an aluminum alloy with a reflectivity of 90% and the lens material is PMMA with a refractive index of 1.49. The baffle plate is set as a perfect absorber to absorb all rays that hit it. The exact illuminance values on key points and the specified regions in the prescribed area can be read in the software. The simulation results are shown in the figures and tables below. Figures 14 and 15 show the illumination and color distribution of the low beam, respectively. Figure 16 shows the illumination distribution of the high beam. Figure 17a shows the color distribution of a high beam with a prism, and Figure 17b shows the color distribution without a prism. Tables 1 and 2 show the simulated illuminance values on the target plane of low and high beams, respectively.

Figure 14. The illumination distribution of low beam.

Figure 15. The color distribution of low beam.

Micromachines 2021, 12, 663 9 of 16 Micromachines 2021, 12, 663 9 of 16

Figure 13. Optical system of the integrated headlamp in simulation software. Figure 13. Optical system of the integrated headlamp in simulation software. Before the simulation, the freeform surface reflector is set as an aluminum alloy with Before the simulation, the freeform surface reflector is set as an aluminum alloy with Micromachines 2021, 12, 663 a reflectivity of 90% and the lens material is PMMA with 10a ofrefractive 16 index of 1.49. The a reflectivity of 90% and the lens material is PMMA with a refractive index of 1.49. The baffle plate is set as a perfect absorber to absorb all rays that hit it. The exact illuminance baffle plate is set as a perfect absorber to absorb all rays that hit it. The exact illuminance values on key points and the specified regions in the prescribed area can be read in the valuesBefore on the key simulation, points the freeformand the surface specified reflector isregions set as an aluminumin the prescribed alloy with a area can be read in the software. The simulation results are shown in the figures and tables below. reflectivitysoftware. of 90%The and simulation the lens material results is PMMA are with sh aown refractive in the index figures of 1.49. The and baffle tables below. plate isFigures set as a perfect 14 and absorber 15 toshow absorb the all rays illumination that hit it. The exactand illuminance color distribution values of the low beam, re- on keyFigures points and 14 the specifiedand 15 regionsshow in the the prescribedillumination area can and be read color in the distribution software. of the low beam, respectively. Figure 16 shows the illumination distribution of the high beam. Figure 17a Thespectively. simulation resultsFigure are shown16 shows in the figuresthe illumination and tables below. distribution of the high beam. Figure 17a showsFigures the 14 color and 15 distribution show the illumination of a high and colorbeam distribution with a ofprism, the low and beam, Figure 17b shows the color shows the color distribution of a high beam with a prism, and Figure 17b shows the color respectively.distribution Figure without 16 shows a the prism. illumination Tables distribution 1 and of 2 the show high beam. the Figuresimulated 17a illuminance values on showsdistribution the color distribution without of a a prism. high beam Tables with a prism, 1 and and 2 Figure show 17b the shows simulated the color illuminance values on distributionthe target without plane a prism.of low Tables and1 and high2 show beams, the simulated respectively. illuminance values on the targetthe target plane of plane low and of high low beams, and respectively. high beams, respectively.

Figure 14. The illumination distribution of low beam. FigureFigure 14. 14.The illuminationThe illumination distribution distribution of low beam. of low beam.

FigureFigure 15. 15.The colorThe distributioncolor distribution of low beam. of low beam. Figure 15. The color distribution of low beam.

Micromachines 2021, 12, 663 10 of 16

Table 1. Simulated illuminance values of low beam on the target plane.

Required Illuminance in Simulated illuminance in Point on Target Plane Lux Lux HV ≤0.7 0.28 Micromachines 2021, 12, 663 10 of 16 B50L ≤0.4 0.00 75L ≤12 6.50 Table 1. Simulated illuminance50L values of low beam on the target ≤plane.15 13.36 75R Required Illuminance in ≥15Simulated illuminance in 41.50 Point on Target Plane 50R Lux ≥12 Lux 40.48 HV ≤0.7 0.28 B50L 50V ≤0.4 ≥6 0.00 35.08 75L 25L ≤12 ≥2 6.50 5.22 50L 25R ≤15 ≥2 13.36 5.67 75R ≥15 41.50 50R Zone I ≥12 ≤2E * 40.48 √ 50VZone III ≥6 ≤0.7 35.08 √ 25L ≥2 5.22 Micromachines 2021, 12, 663 Zone IV ≥3 11 of 16 √ 25R ≥2 5.67 E * is the actual measurement of the value at point 50R. Zone I ≤2E * √ Zone III ≤0.7 √ Zone IV ≥3 √ E * is the actual measurement of the value at point 50R.

Figure 16. The illumination distribution of high beam with prism. FigureFigure 16. The16. illuminationThe illumination distribution distribution of high beam with of prism. high beam with prism.

(a) (b)

FigureFigure 17. 17. ((aa)) The The color color distribution ofof high high beam beam with with a prisma prism and and (b )(b without) without a prism. a prism.

Table 1. Simulated illuminance values of low beam on the target plane.

Point on Target Plane Required Illuminance in Lux Simulated illuminance in Lux HV (a) ≤0.7 0.28 (b) B50L ≤0.4 0.00 Figure 17.75L (a) The color distribution≤12 of high beam with a 6.50prism and (b) without a prism. 50L ≤15 13.36 75R ≥15 41.50 50R ≥12 40.48 50V ≥6 35.08 25L ≥2 5.22 25R ≥2 5.67√ Zone I ≤2E * √ Zone III ≤0.7 √ Zone IV ≥3 E * is the actual measurement of the value at point 50R.

Micromachines 2021, 12, 663 12 of 16

Table 2. Simulated illuminance values of high beam on the target plane.

Point on Target Plane Required Illuminance in Lux Simulated Illuminance in Lux

Emax ≥48 and ≤240 80.80 HV ≥0.8 Emax 74.81√ 0–1125L, 1125R ≥24 √ 0–2250, 2250R ≥6

Figures 14 and 15 indicate that the integrated headlamp system with a single ADFSL could ensure the quality of the low beam. The illumination width of the low beam can reach 12 m, which can provide a large angle of view for drivers. Furthermore, the cutoff line with the blue edge does not appear, which means that the inherent problem of the cutoff line with the blue edge in traditional projection designs can be solved by this method. The color temperature of the low beam is stable on the target plane, and the color on the target plane is close to white. As shown in Table1, the simulation values of the low beam fully meet the requirements of ECE R112 regulations; Figure 16 shows that the illumination distribution of the high beam can comply with the requirements of ECE R112 regulations. Furthermore, the highest value of the high beam is 80.8 lux, providing sufﬁcient illumination when the road lighting is poor. Figure 17 shows the color distribution of the high beam. The color distribution with a prism is more stable, as compared to the color distribution without a prism, which means that adding a prism to the optical path can largely suppress chromatic dispersion on the edge. Table2 demonstrates that the simulation values of the high beam satisfy the requirements of ECE R112 regulations. In short, the light shape of the low beam and high beam and simulation values of the key points fully comply with the requirements of ECE R112; Moreover, the chromatic dispersion can be largely suppressed by using a new integrated optical system. Here, we must present a simple analysis of the installation error. The error of the low beam and high beam source position mounting is ±0.3 mm and 0.5 mm, respectively. In other words, when position error is greater than the above values, the performance will no longer satisfy the ECE R112 regulations. Therefore, proper installment of the optical elements is very important for achieving optimal performance.

4. Experiment To study the illumination performance of the experiment, the optical samples were processed and assembled according to the results of the optical simulation software, and the GO-HD5 automobile lighting test system was used for testing the illuminance values of the key points and specified regions. According to ECE R112 regulations, the test starts after the light source is steady. The lighting spot of the low beam and color temperature test of the point 50 V are shown in Figure 18, and the lighting spot of the high beam and color temperature test of the point HV are shown in Figure 19. The test illumination values of the low beam and high beam measurement screens are shown in Tables3 and4, respectively. From Figure 18a, there is a straight cutoff line with no stray light above, and the color temperature is stable on the measuring screen. Slight chromatic dispersion appears near the cutoff line, which is different from the simulation results. Additionally, it still meets the ECE regulations. Compared with the traditional low beam, the chromatic dispersion near the cutoff line is much slighter. The test results of illuminance were slightly different from the simulations, due to the slight error of the shield’s place and the absorption of mechanical objects. However, all illuminance values at the required points can fit with the regulations. According to ECE regulations, the color test results for the 50 V point must be within the white light range. The color test result at point 50 V is 5160 K, as shown in Figure 18b, and is quite qualified. The low beam lighting spot has a smooth transition that provides drivers with visual comfort. Micromachines 2021, 12, 663 13 of 16

(a)

(b)

Figure 18. Figure(a) The lighting18. (a) The spot lighting and (b) testspot results and ( ofb) color test results of the point of color 50 V of for the low point beam. 50V for low beam.

Table 3. Tested illuminance values of low beam on the target plane.

Point on Target Plane Required Illuminance in Lux Tested Illuminance in Lux HV ≤0.7 0.42 B50L ≤0.4 0.00 75L ≤12 7.36 50L ≤15 13.25 75R ≥15 32.32 50R ≥12 30.26 (a) 50V ≥6 34.26 25L ≥2 6.32 25R ≥2 6.85 Zone I ≤2E * √ Zone III ≤0.7 √ Zone IV ≥3 √ E * is the actual measurement of the value at point 50R.

(b)

Figure 19.Figure(a) The 19. lighting (a) The spot lighting and (spotb) test and results (b) test of results color of of the color point of HVthe point for high HV beam. for high beam.

2 Micromachines 2021, 12, 663 14 of 16

Table 3. Tested illuminance values of low beam on the target plane.

Point on Target Plane Required Illuminance in Lux Tested Illuminance in Lux HV ≤0.7 0.42 B50L ≤0.4 0.00 75L ≤12 7.36 50L ≤15 13.25 75R ≥15 32.32 50R ≥12 30.26 50V ≥6 34.26 25L ≥2 6.32 25R ≥2 6.85√ Zone I ≤2E * √ Zone III ≤0.7 √ Zone IV ≥3 E * is the actual measurement of the value at point 50R.

Table 4. Tested illuminance values of high beam on the target plane.

Point on Target Plane Required Illuminance in Lux Tested Illuminance in Lux

Emax ≥48 and ≤240 70.36 HV ≥0.8 Emax 65.34√ 0–1125L, 1125R ≥24 √ 0–2250L, 2250R ≥6

It can be inferred from Figure 19a and Table4 that the lighting spot is nearly elliptic and the central area is the brightest, which meets the ECE regulations. The color of the high beam is almost white, indicating that adding a prism could reduce chromatic dispersion at the edge of the target area and stabilize the color temperature. Similar to the test low beam results, the high beam test results in Table4 are lower than the simulation results. The maximum illuminance of the high beam is 70.36 lux, less than simulation results but still much greater than the regulation requires, and can provide sufﬁcient illumination for the ground. Similarly, the color test results for the HV point must be within the white light range. The color test result of the HV point is 5560 K, as shown in Figure 19b, which complies with the regulations.

5. Discussion According to the simulation and experimental results, it can be found that both illuminance values of the required points and the color temperature distributions are qualiﬁed. The comparison of the new integrated headlamp system with the traditional headlamp system is shown in Table5.

Table 5. The comparison of the new integrated headlamp with traditional headlamp.

Chromatic Dispersion Items Volume Cost Low Beam High Beam Cutoff Line on the Target Plane Slight New integrated Small Low Qualified Qualified chromatic Slight headlamp system dispersion Traditional A little serious projection Large High Qualified Qualified chromatic A little serious headlamp system dispersion

The volume of the new integrated LED headlamp is 91 × 64 × 64 mm3, much smaller than that of the traditional headlamp. The ADFSL has a diameter of 64 mm, as large as the traditional low beam lens, which means saving space for installing the high beam system Micromachines 2021, 12, 663 15 of 16

and its cooling system. Compared with the high beam without prism, the new headlamp with ADFSL and prism has a more uniform color distribution due to the light deﬂection of the prim. Both low and high beams are qualiﬁed. Since the new integrated headlamp has only one optical system, it costs less than the traditional headlamp with two optical systems. By using an asymmetric double freeform surface lens, the cutoff line of the new integrated headlamp has less chromatic dispersion than that of the traditional headlamp using a single freeform surface or aspheric surface lens, providing comfortable lighting for oncoming drivers. These advantages make the new integrated headlights acceptable in the headlamp market.

6. Conclusions We proposed a method to design the asymmetric double freeform surface lens and the integrated LED headlamp optical system. The construction algorithms of the optical elements were presented in detail. Simulation and experimental results show that a good light pattern can be obtained with the selected source, and the values of key points and speciﬁed regions can fully comply with the standards of ECE R112, 48, and 128. Moreover, color uniformity on the target plane is improved by the freeform surface lens and the prism. The volume of the whole optical system is smaller than that of the traditional headlamp, saving space to install other electronic devices safely, such as distance sensors, to help drivers gain better control of the distances between vehicles. Moreover, the freeform surface optical system has high compactness and manufacturing feasibility.

Author Contributions: The work presented here was carried out in collaboration between all authors. Conceptualization and methodology, H.Z., D.L. and H.W.; validation and analysis, writing, H.Z. and Y.W.; supervision, H.W. All authors have read and agreed to the published version of the manuscript. Funding: This work was funded by Science and Technologies Plan Projects of Guangdong Province (Nos.2017B010112003, 2020B010171001), and Guangzhou Municipal Science and Technology Plan Projects (Nos.201604046021, 201905010001), and Science and Technology Development Special Fund Projects of Zhongshan City (Nos.2019AG014,2019AG042,2020AG023). Data Availability Statement: The data presented in this study are included in the article. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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