Open Access
Add to BibSonomy
Abstract
Since the first full LED headlamp was introduced in 2007, technology has evolved to now provide enhanced performance, improved security, and memorable aesthetics. Further miniaturization has been continuously pursued to allow more advanced design options, but LED headlamp height has been stalled at around 40–60 mm for some years. Recently a total internal reflection-based low-beam module achieved an optical opening down to 20 mm. However, the small opening came with a housing envelope height that was larger than 40–60 mm. Conventional LED single modules are still more attractive in terms of cost and overall compactness, especially for low-cost, low-beam headlamps. A demanding question remains about the minimum achievable limit of a single-module LED low-beam projection headlamp consisting of an LED source, an elliptical reflector, a cutoff baffle, and a projection lens. Here, we answer that question using an analytical approach rather than attempt to base it on current applied design trials or parametric studies. First, we analytically investigated the baseline optical properties of an LED low-beam module in terms of geometrical optics and photometrical luminance transfer. During the analysis, we employed the ratio of the focal distances ($m$) of the elliptical reflectors as a design variable to efficiently consider geometrical similarities. Then we confirmed and extended the analytical results by numerical simulation, using ray-tracing software. Based on the results from the analytical and numerical analysis with low-beam regulations, we finally determined a suitable range of $m$ (0.15–0.17), which satisfied the regulations, and found the best achievable height of a single module when $m \sim{0.15}$ is 46 mm. The precise number will differ depending on the geometrical and ray-emitting properties of the LED applied, but our study provides a valid general framework for designing LED-based low-beam headlamps.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. INTRODUCTION
Automotive headlamps have steadily evolved to provide enhanced performance, improved security, and memorable aesthetics. These features have appeared in tandem with technical advances in lighting, especially the emergence of new light sources: halogen, high-intensity discharge, and LED [1–5]. Since the first LED headlamp was introduced in 2007 [4], LED technology has allowed the headlamps to become distinctive design elements, while enabling intelligent headlight control features such as adaptive driving beam [5,6] and adaptive front-lighting systems [7]. Recently, innovative headlamps have been introduced with laser headlights and micro-LEDs. Laser lights easily double the drivers’ distance visibility, with less electric power [8,9]. The micro-pixel LED headlamp is a high-resolution lighting system that offers a maximum range of functions [5]. The laser headlight and micro-LED headlamps can also be much smaller than LEDs and traditional bulbs, allowing more compact and therefore more aesthetic design options. However, because these two options are still relatively unaffordable, LED headlamps are still the most favored light especially for low-beam headlamps.
The light intensity distribution of low-beam headlamps for normal nighttime driving is designed to limit light directed toward the eyes of other road users to control glare, according to the ECE R112 regulation [10]. The regulation calls for small regions of high intensity, with larger regions of mid or very low intensity, and well specified transitions [10,11]. The most prominent transient region is the cutoff line preventing significant amounts of light from being cast into the eyes of drivers of preceding or oncoming cars. Figure 1 shows the low-beam patterns on a road and a test wall.
Fig. 2. Required luminous intensities at reference angular positions and zones used in the low passing-beam photometric requirements (indicated for right-hand traffic) [10]. Angular positions are expressed in degree (U) up or (D) down from H-H, respectively, (R) right or (L) left from ${\rm{V}} {-} {\rm{V}}.\;{\rm{I}}*$ is the actual measured value at points 50R.
This unique low-beam illumination pattern requires complicated optical designs for LEDs, which have light distribution patterns that are different from traditional headlamp light sources. In terms of system types, there are three main kinds of LED low-beam headlamps: projection type, refraction type, and reflection. Among the three, the projection type is the most widely used, usually consisting of a reflector, a baffle, and a projection lens.
In recent years multiple optical designs have been reported in efforts to improve projection types. These can be categorized into four areas: those that improve lighting efficiency [12,13], reduce color dispersion [14,15], enhance the contrast of the cutoff line [16,17], and miniaturize the optics module [18,19]. The latter is especially in demand due to recent trends in styling toward slim or low-profile automotive lighting.
Miniaturization of the optical module has been achieved through various innovative optical approaches, including the use of freeform or segmented mirrors [12,20], the use of micro-lenses [21], the use of multiple optical modules [22], and the use of total internal reflection (TIR) lenses [23–25]. Several approaches have successfully reduced the height of the optical opening, which is the height of the projection lens, down to around 20 mm by using a TIR lens or multi-source/module approaches [24–26]. The reported compact modules can provide the ECE R112 beam profile with a luminance equivalent to a conventional LED low-beam module of 40–60 mm height, which is the reported minimum [18,24]. In spite of the small ${\sim}{{20}}\;{\rm{mm}}$ opening, the overall envelope height of the optical modules was still around 40–60 mm or even larger [24–26]. In addition, the conventional single module is still more attractive in terms of cost and overall compactness. Parametric studies have been reported that reference the design of a single-module LED low-beam headlamp with compact size and high photometry performance [27,28]. However, as far as we are aware, no publication has yet provided an analytical analysis of the minimum achievable height of a single-module LED low-beam projection headlamp.
Here, we first analytically investigate the baseline optical properties of the projection-type LED low-beam headlamp in terms of geometrical optics and photometrical luminance transfer. Then we confirm and extend the analytical results by numerical simulation using ray-tracing software. Based on the results from the analytical and numerical analysis, we derive the minimum achievable height of a single module and then we propose some possible design methods for reducing the optical height further, below the minimum.
2. REGULATION AND ANALYSIS MODEL
A. Regulations for Automotive Low-beam Headlamps
A headlight is a light lamp attached to the front of a vehicle to illuminate the road ahead, providing either a low beam or a high beam depending on the road conditions. A low beam (also called passing beam, dipped beam, meeting beam) is used for normal nighttime driving, and by design limits light directed toward the eyes of other road users, to control glare. A high beam (also called main beam, driving beam, full beam) is used to provide a bright, center-weighted distribution of light with no particular control of the light directed toward other road users’ eyes.
Fig. 4. Optical conjugation relationship of the conventional projection module with key design parameters (${L_1}$, ${L_2}$, ${L_3}$, and $D$).
Over years a series of regulations have been introduced that limit the light distribution of each beam. According to the most widely applied regulation, ECE R 112 [10], the low beam should have a sharp, asymmetric cutoff to prevent significant amounts of light from being cast into the eyes of drivers of preceding or oncoming cars. The light pattern in the regulation is characterized by small regions of high intensity, large regions of mid or very low, and well specified transitions called the cutoff line. The required luminous intensity [candela (cd)] at specific points or in segment areas (called zones) are specified as shown in Fig. 2. The luminous intensity produced by the lamp is measured at 25 m distance using a photometer head unit measuring illuminance in lux. Headlamp developers often use a simpler version of the required luminous intensities for initial or preliminary evaluation purposes. Figure 3 shows a simpler version we adopted for the present analysis. Table 1 lists some of the requirements along the V-V axis of the simpler version.
Table 1. Simpler Version of the Light Field Distribution Regulation Along the Vertical (${\rm{V}} - {\rm{V}}$) Axis
B. Analysis Model
A conventional low-beam headlamp consists of an LED source, a reflector, a cutoff baffle, and a projection lens. The reflector is basically an ellipsoid which efficiently collects the light radiating from the LED located at its first focus (${F_1}$) and forms an intermediate image (or illuminance) at the second focus (${F_2}$). The projection lens then conjugates the intermediate image to a target (or far-field) plane 25 m away by locating its focus close to ${F_2}$. A baffle located near the focus of the projection lens slightly modulates the illuminance profile by cutting or reflecting some portion of the light converging to ${F_2}$. To achieve the beam regulation mentioned above, there is a small offset or defocus of the projection lens from the second focus (${F_2}$).
Figure 4 shows the conceptual conjugation relationship from the LED to the target plane via the projection lens. In terms of construction, the key parameters of the modules are the distances between the elements (${L_1}$, ${L_2}$, and ${L_3}$) and the diameter of the projection lens $D$ (Fig. 5).
3. FORMATION OF AN INTERMEDIATE IMAGE WITH AN ELLIPTICAL REFLECTOR
A. Geometrical Parameters and Selection of the Main Analysis Parameter
Figure 5 shows a cross section of an elliptical reflector with a major axis ${{2}}a$, a minor axis ${{2}}b$, and the inter-focal distance $2c = 2\sqrt {{a^2} - {b^2}}$. The reflector focuses any ray from the first focus (${F_1}$) with an emittance angle (${{\theta}}$) to the second focus (${F_2}$) with an incidence angle ($\gamma$), via reflection at a point $P$ with a uniform optical path length, i.e., $\overline {{F_1}P} + \overline {P{F_2}} = r + r^\prime = 2a$. An ellipse is also represented by the first and second focal distances given by ${f_1} = a - c$ and ${f_2} = a + c$, respectively, or by the numerical eccentricity $e = c/a$.
Most studies utilize a set of conventional geometrical parameters such as ($a$, $b$, $c$), (${f_1}$, ${f_2}$), or (${{{L}}_1}$, ${{{L}}_2}$) to design the elliptical mirrors of headlamps [13,27–30]. However, to efficiently consider geometrical similarities between many ellipses, we use the ratio of focal distances $m$ to analyze the optical properties of elliptical reflectors, as proposed by Rehn [31]. This is defined by
B. Boundary of the Main Analysis Parameter (m)
A ray departing from ${{{F}}_1}$ with an emitting angle (${{\theta}}$) is focused to ${{{F}}_2}$ on the intermediate image plane with the incident angle (${{\gamma}}$). We can solve the incident angle (${{\gamma}}$) as a function of the emitting angle (${{\theta}}$) using the geometrical relationship below:
As the maximum emitting angle $({{\theta _{\rm{max}}}})$ can be assumed to be about 45° or $\pi /{{4}}$ under practical considerations [31], we can express the maximum incident angle (${{{\gamma}}_{\rm{max}}}$) as a function of the ratio of focal distances ($m$) as below:
Then the numerical aperture (NA) of the projection lens can be similarly approximated, also as a function of $m$, as below:
Considering lens aberration and fabrication issues, there is a practical maximum limit of the NA value, which is about 0.6–0.7. After an additional investigation of previously reported elliptical reflector models [15,27,28,32], we set the boundary of the main variable ($m$) from 0.14 to 0.18 in our analysis.
C. Geometrical Relationship
Figure 6 shows the geometrical parameters of an elliptical reflector with an LED source. We can express several magnifications as functions of the ray-emitting angle (${{\theta}}$) and the incident angle (${{\gamma}}$): a height magnification ${{{M}}_h}$, a width magnification ${{{M}}_w}$, an area magnification ${{{M}}_{{A}}}$, and a solid angle magnification ${{{M}}_{{\Omega}}}$. $d{{\Omega}}$ is the solid angle of a small ray bundle emitting from the source and $d{\rm{\Omega ^\prime}}$ is the solid angle of the bundle converging to ${{{F}}_2}$:
D. Photometric Relationship: Analytical Approach
It is quite challenging to analytically predict illuminance profiles on the intermediate plane due to strong image distortion and aberrations [33,34], especially for high-NA cases as in our study. However, Rehn approximated the $y^\prime$-axis illuminance for an arc-lamp source through the geometrical relationships described in Section 3.C and the luminance conservation via an elliptical reflector [31]. We similarly derived the $y^\prime$-axis illuminance in lux for a mostly available single-chip LED source with an area $A$ ${\rm{mm}}^2$, briefly expressed as below.
In the first approximation, we can consider the LED source as Lambertian. A Lambertian source is defined as one in which the luminance ($L$) is constant, given as ${L_0}$, independent of the emitting angle ($\theta$). Conventional surface-emitting LEDs approximate a Lambertian source obeying Lambert’s cosine law: the luminous intensity $(I)$ in candela is directly proportional to the cosine of the angle $\theta$ between the direction of the emitting light and the surface normal, as given below:
where $\Phi$ is the total luminous flux in lumen. $A$ is the emitting area of the LED, which is ${{s}} \times {{s}}\;{\rm{mm}}^2$ for a square LED with size $s$ mm. For a small Lambertian source, it can be shown that the luminance is conserved through reflection via elliptical reflectors, as expressed below:This can be integrated to yield the illuminance at the intermediate image plane:
Fig. 7. Analytically estimated $y^\prime$-axis illuminance profiles at the intermediate image plane formed by a ${{1}} \times {{1}}\;{\rm{mm}}^2$ LED.
Figure 7 plots the illuminance ${{E^\prime}}$ per the source flux, i.e., ${{E^\prime}}/{{\Phi}}$ and also the illuminance normalized by its maximum, of an LED of ${{1}} \times {{1}}\;{\rm{mm}}^2$. Looking at Fig. 7, we find that the illuminance stays at its peak value ($E_{\rm{peak}}^\prime$) for small image height (${{y^\prime}}$) which we call the peak illuminance region (H). Since the ${\rm NA}= {\rm{\sin\;}}\gamma _{\rm{max}}$ is a function of $m$ as in Eq. (4), the peak illuminance ($E_{\rm{peak}}^\prime$) in lux and the size of the peak illuminance region (H) in millimeters (mm) can also be approximated by functions of m, as below:
E. Photometric Relationship: Numerical Approach
To confirm the above analytic predictions a numerical analysis was performed using the illumination design software LightTools [35], using 15 (${{5}} \times {{3}}$) verification models. The first five geometrical models were constructed with five focal length ratios (${{m}}$) from 0.14 to 0.18 with increments of 0.01, as tabulated in Table 2. The geometrical parameters were selected based on previously reported elliptical reflector models [15,27,28]. Then, each geometrical model was simulated for three different LED configurations (${{1}} \times {{1}}$, ${{1}} \times {{3}}$, and ${{1}} \times {{5}}$) [36]. The ${{1}} \times {{5}}$ configuration was modeled with five emitting cells, each of which has an emitting area of ${{1}} \times {{1}}\;{\rm{mm}}^2$ with 0.1 mm space and a luminous flux of 250 lm. The ${{1}} \times {{3}}$ and ${{1}} \times {{1}}$ configurations were similarly constructed.
Table 2. Geometrical Parameters of the Elliptical Reflectors Used in the Numerical Analysis
Figure 8 plots the simulated illuminances at ${{{F}}_2}$ for three LED configurations (${{1}} \times {{1}}$, ${{1}} \times {{3}}$, and ${{1}} \times {{5}}$) (${{m}} = {0.16}$). The first three were simulated with ideal Lambertian sources and the latter three [(d)–(f)] were simulated with source data provided by a commercial supplier [36]. First, it is noticeable that the peak illuminances of three LED configurations (${{1}} \times {{1}}$, ${{1}} \times {{3}}$, and ${{1}} \times {{5}}$) do not vary, as estimated by Eq. (14). Table 3 lists the analytically predicted and simulated peak illuminances at the intermediate in ${{10}^6}\;{\rm{lux}}$. The simulations with ideal Lambertian sources are in good accordance (${\lt}\;{{2}}\%$ error) with the analytically predicted values with Eq. (15).
Fig. 8. Simulated illuminances at ${{{F}}_2}$ with three LED configurations (${{1}} \times {{1}}$, ${{1}} \times {{3}}$, and ${{1}} \times {{5}}$) (${{m}} = {0.16}$): (a)–(c) with ideal Lambertian sources and (d)–(f) with source data provided by a commercial supplier [36]. Each image is of ${{16}} \times {{8}}\;{\rm{mm}}^2$.
The simulations with real LED ray data had values 10% lower than the analytically predicted values, because the light intensity profiles of real LEDs are slightly offset from Lambertian. The peak illuminance ($E_{\rm{peak}}^\prime$) with source data can be approximated using the following equation:
Figure 9 plots the normalized ${{y^\prime}}$- and ${{x^\prime}}$- illuminance profiles simulated using the source LED data. Overall, the beam profiles are similar to those analytically predicted in Fig. 7. However, the estimated flattops near the center are smoothed and the beam edges are widened, due to the less-Lambertian sources and high-NA induced aberrations. The size of the flattop (H) in Eq. (16) is found to be the beam height of the 90% peak in the simulation. In addition, we note that only the ${{1}} \times {{5}}$ LED configuration satisfies the required profile.
Table 3. Peak Illuminances at the Intermediate in ${{10}^6}\;{\rm{lu}}$x
4. FAR-FIELD FORMATION
A. Modifying Illuminance by Focus Offset and Baffle
A projection lens conjugates the illuminance (${E_{\rm{focus}}}$) at its focus ($F_L$) to a target plane (or far field) 25 m away. Since the lens focus ($F_L$) is very close to the second focus of the elliptical reflector (${F_2}$), the focus illuminance (${E_{\rm{focus}}}$) is very similar to the intermediate illuminance (${\rm{E^\prime}}$). However, it is slightly modified by the focus offset and a baffle in the lens focus (${F_L}$), as shown in Figs. 4 and 10.
Fig. 9. Normalized illuminance profiles at the intermediate image plane: (a)–(c) and (d)–(f) are the $y^\prime$-axis and $x^\prime$-axis profiles of three LED (${{1}} \times {{1}}$, ${{1}} \times {{3}}$, and ${{1}} \times {{5}}$) configurations, respectively.
The focus offset is the offset ($\Delta {\rm{Y}}$, $\Delta {\rm{Z}}$) of the projection lens focus (${{{F}}_L}$) from the elliptical reflector secondary focus (${{{F}}_2}$). The focus offset slightly moves in the hot zone (or peak) forward of the ${+}y^\prime$-axis and widens the spread zone. $\Delta {\rm{Z}}$ and $\Delta {\rm{Y}}$ are typically known as defocus and offset, respectively. The defocus ($\Delta {\rm{Z}}$) is the focus distance along the $Z$-axis, and the offset $\Delta {\rm{Y}}$ is the height difference between the optical axis of the elliptical reflector and the projection lens.
We investigated the variation in focus illuminances (${E_{\rm{focus}}}$) with defocus ($\Delta {\rm{Z}})$ from ${-}{0.6}$ to ${-}{1.5}\;{\rm{mm}}$ with ${-}{0.1}\;{\rm{mm}}$ step. The peak values are tabulated in Table 4. From the simulation, we found that only limited sets of ($\Delta {\rm{Z}}$, ${\rm{\;\Delta Y}}$), such as $({{\rm{\Delta Z}},{\rm{\Delta Y}}}) = ({- 0.9{L_0},0.6{L_0}}),$ could satisfy the ${\rm{V}} - {{\rm{V}}^\prime}$ regulation, as in Fig. 3 where ${L_0}$ is a geometrical parameter given by ${L_0} = H/{\rm NA}$ in mm as given by
With the sets, we could also approximate the peak illuminance of the focus illuminances ($E_{\rm focus,peak}$) in lux as a function of the focal length ratio (${{m}}$):
From the graphical investigation of the illuminance profiles, we can also approximate the image height (${H_{90}},\;{H_{36}},\;{H_{02}}$) in mm from the lens optical axis at three relative illuminances (90%, 36%, and 1.8%) with respect to the peak value as functions of the ratio of focal distance (${{m}}$), as below:
B. Projection Lens Focal Length (${{\rm{f}}_L}$) and Lens Diameter (D)
The far-field pattern or illuminance (${E_{25m}}$) at the 25 m target screen is a projected image of the focus illuminance (${E_{\rm{focus}}}$). The illuminance at the target screen (${E_{25m}}$) in lux can be estimated from the focus illuminance (${E_{\rm{focus}}}$), as given by the following:
where ${{{f}}_L}$ is the effective focal length of the projection lens in millimeters. The far-field light intensity (${I_F}$) in cd is then estimated from the target-screen illuminance (${E_{25m}}$) as below: where $h$ is the image height from the lens optical axis, and $V$ is the vertical beam angle in the far-field plane along the ${\rm{V}} - {{\rm{V}}^\prime}$ axis.Table 4. Relative Peak Reduction Ratio Due to Defocus ($\Delta Z$)
Fig. 11. Normalized focus illuminance (${E_{\rm{focus}}}$) with focus offset $({\Delta {\rm{Z}},{\rm{\Delta Y}}}) = ({- 0.9{L_0},0.6{L_0}})$ and beam cutting at the focus.
Then, we can rewrite the simpler ${\rm{V}} - {{\rm{V}}^\prime}$ regulation in Table 1 with the conditions below:
By combining all the equations into the four conditions, we can find valid focal lengths of the projection lens as a function of the focal length ratio (${{m}}$) in Fig. 12. During the calculation, we limited the maximum NA of the lens to 0.7 in order to consider practical limitations. Figure 13 plots the corresponding lens diameter (${\rm{D}}$), as given below:
5. CONCLUSION
Optical designers in the automotive lighting industry routinely design LED low-beam headlamps consisting of an elliptical reflector, a single LED source, a baffle, and a projection lens. However, even though so many LED headlamps have been released in the market, a simple question still challenges the optical designers: “Has the minimum lens diameter (or opening) been achieved?” In order to answer the question, we investigated LED headlamps via an analytical approach rather than using currently applied design trials or parametric studies. This was done by formulating all optical properties as functions of a geometrical parameter, which is the ratio of the focal distances ($m$) of an elliptical reflector. This was first based on an analytical analysis and then on a subsequent numerical analysis of ray-tracing results. By combining all the equations with the low-beam ${\rm{V}} - {{\rm{V}}^\prime}$ regulations, we finally found a suitable range of $m$ to satisfy the ${\rm{V}} - {{\rm{V}}^\prime}$ regulations. This was 0.15–0.17 in our study, and indicates the achievable height of a single module when ${{m}}\;\sim\;{0.15}$ is 46 mm.
The precise number will differ depending on the different geometrical and ray-emitting properties of the LED employed, but our study provides a valid general framework when designing an LED-based single-module low-beam headlamp, and it can be expanded for the design of non-conventional headlamps, such as multi-LEDs/multi-reflector designs.
Funding
Institute for Information and Communications Technology Promotion (1711117093); Hyundai Mobis; Kongju National University (2020).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
REFERENCES
1. A. Bielawny, T. Schupp, and C. Neumann, “Automotive lighting continues to evolve,” Opt. Photonics News 27, 36–43 (2016). [CrossRef]
2. J. Bhardwaj and B. Spinger, “What will mainstream adaptive driving beam look like by 2025?” Proc. SPIE 10940, 109400O (2019). [CrossRef]
3. S. Berlitz, M. Grimm, K. Eichhorn, M. Goetz, P. Meyrueis, T. P. Pearsall, J. Reill, P. Repetto, and L. Tupinier, “A technology roadmap for photonics in the automobile, part 1: innovative front lighting,” Proc. SPIE 6198, 619804 (2006). [CrossRef]
4. M. Hamm and W. Huhn, “Design claims and technical solution steps generating the world first full LED headlamp,” SAE Tech. Paper 2008-01-0337 (2008).
5. S. Grötsch, M. Brink, R. Fiederling, T. Liebetrau, I. Möllers, J. Moisel, H. Oppermann, and A. Pfeuffer, “μAFS high resolution ADB/AFS solution,” SAE Tech. Paper 2016-01-1410 (2016).
6. J. H. Yu, S. J. Ro, J. H. Lee, C. K. Hwang, and D. J. Go, “Smart headlamp optics design with multi-array LEDs,” Korean J. Opt. Photonics 24, 231–236 (2013). [CrossRef]
7. J. H. Lee, J. Byeon, D. J. Go, and J. R. Park, “Automotive adaptive front lighting requiring only on/off modulation of multi-array LEDs,” Curr. Opt. Photonics 1, 207–213 (2017). [CrossRef]
8. S. Weber, A. Buck, and C. Amann, “Laser light in the BMW i8 design, system integration and test,” ATZ Worldwide 116, 44–49 (2014). [CrossRef]
9. Y. H. Song, E. K. Ji, B. W. Jeong, M. K. Jung, E. Y. Kim, and D. H. Yoon, “High power laser-driven ceramic phosphor plate for outstanding efficient white light conversion in application of automotive lighting,” Sci. Rep. 6, 31206 (2016). [CrossRef]
10. United Nations Economic Commission for Europe vehicle regulations, Reg. 112-Rev. 3 (2013).
11. A. Timinger and B. Spinger, “Managing source luminance distribution in automotive front lighting systems,” in Optical Design and Fabrication (Freeform, IODC, OFT), OSA technical digest (online) (Optical Society of America, 2017), paper JW3C.1.
12. H. Wu, X. M. Zhang, P. Ge, and J. D. Yu, “A high-efficiency freeform reflector for a light-emitting diode low-beam headlamp,” Lighting Res. Technol. 48, 1005–1016 (2015). [CrossRef]
13. F. Chen, K. Wang, Z. Qin, D. Wu, X. Luo, and S. Liu, “Design method of high-efficient LED headlamp lens,” Opt. Express 18, 20926–20938 (2015). [CrossRef]
14. H. S. Lee, H. J. Park, and J. S. Kwak, “Improvement of disturbing color effects depending on the axial color of an automotive headlamp lens,” Appl. Opt. 56, 5106–5111 (2017). [CrossRef]
15. S. Ma, C. Lee, and C. Yang, “Achromatic LED-based projection lens design for automobile headlamp,” Optik 191, 89–99 (2019). [CrossRef]
16. B. Joo and J. Ko, “Optimization of cutoff shields in projection headlight systems to achieve high intensity gradient and low color separation at the cutoff line,” J. Opt. Soc. Korea 20, 118–124 (2016). [CrossRef]
17. M. Tsai, C. Sun, T. Yang, C. Wu, S. Lin, and X. Lee, “Robust optical design for high-contrast cut-off line in vehicle forward lighting,” OSA Continuum 2, 1080–1088 (2019). [CrossRef]
18. P. Albou, L. Boinet, and J. P. Ravier, “Very thin headlamps with laser beam,” in Proceedings of 13th International Symposium on Automotive Lighting (ISAL) (2013), pp. 128–139.
19. O. Shchekin, B. Spinger, N. Lesch, D. Vanderhaeghen, and J. Tarne, “Frontiers in LED and Micro-LED technology,” in Proceedings of 13th International Symposium on Automotive Lighting (ISAL) (2019), pp. 453–462.
20. C. Yeh, P. Han, I. Wang, and E. Lin, “Using design of experiment for parameter optimization on smart headlamp optics design,” Appl. Opt. 58, 7661–7683 (2019). [CrossRef]
21. H. Wang, X. Wang, Y. Li, and P. Ge, “Design of a newly projected light-emitting diode low-beam headlamp based on microlenses,” Appl. Opt. 54, 1794–1801 (2015). [CrossRef]
22. Y. Chiang, S. Hwang, H. Lee, D. Hwang, and C. Liao, “Design with white light-emitting diodes for an automotive low-beam projector headlamp,” Sensors Mater. 28, 1035–1042 (2016). [CrossRef]
23. A. Whang, K. Jhan, S. Chao, G. Chen, C. Chou, C. Lin, C. Chang, K. Chen, and Y. Lai, “An innovative vehicle headlamp design based on a high-efficiency LED light pipe system,” Lighting Res. Technol. 47, 210–220 (2015). [CrossRef]
24. A. Perrotin, M. Hermitte, Y. Gromfeld, and M. Laminette, “Thin lens solutions for lighting,” in Proceedings of 13th International Symposium on Automotive Lighting (ISAL) (2017), pp. 155–164.
25. Mitsubishi electric, “Mitsubishi electric unveils compact, flexible and highly efficient optical module for LED headlights in smart mobility age,” 2020, http://www.mitsubishielectric.com/sites/news/2018/pdf/0607-a.pdf.
26. Hyundai Mobis, “Head lamps,” 2020, https://en.mobis.co.kr/products/P0020/index.do.
27. S.-P. Ying and J. Lyu, “Ellipsoidal reflector design of the LED vehicle projector type headlamp,” Proc. SPIE 9954, 99540P (2016). [CrossRef]
28. K. Park and J. Joo, “High efficiency headlamp for ECE regulation based on 5-chips LED,” in Proceedings of 13th International Symposium on Automotive Lighting (ISAL) (2017), pp. 425–434.
29. C. Hsieh, Y. Li, and C. Hung, “Modular design of the LED vehicle projector headlamp system,” Appl. Opt. 52, 5221–5229 (2013). [CrossRef]
30. J. Liu, M. Ai, H. Zhang, and J. Tan, “Focusing properties of elliptical mirror with an aperture angle greater than π,” Opt. Eng. 53, 061606 (2013). [CrossRef]
31. H. Rehn, “Optical properties of elliptical reflectors,” Opt. Eng. 43, 1480–1488 (2004). [CrossRef]
32. J. Zhang, L. Li, and W. Zeng, “Designing method of projector type vehicle headlamp reflector based on the variable ellipse profile,” in Symposium on Photonics and Optoelectronics (SOPO) (2011), pp. 1–6.
33. J. Liu, J. Tan, T. Wilson, and C. Zhong, “Rigorous theory on elliptical mirror focusing for point scanning microscopy,” Opt. Express 20, 6175–6184 (2012). [CrossRef]
34. M. R. Benson and M. A. Marciniak, “Design considerations regarding ellipsoidal mirror based reflectometers,” Opt. Express 21, 27519–27536 (2013). [CrossRef]
35. Synopsys, “Optical design solutions,” 2020, https://www.synopsys.com/optical-solutions/lighttools.html.
36. OSRAM, “OSRAM OSTAR headlamp pro, LE UW U1A5 01,” 2020, https://www.osram.com/.
