Open Access
Add to BibSonomy
Abstract
Collimated illumination using a light-emitting diode (LED) is widely used in the residential, commercial, and optical inspection fields. A typical collimator, namely, one that is a parabolic reflector, has a focal point on which a light source should be placed. The light source approximates a point source, which enables light rays reflected by the reflector to form a collimated beam with a narrow light distribution angle. However, it is difficult to place an LED at the focal point of the reflector because a heat dissipator attached thermally to the LED prevents the reflected light rays from emitting out. A curved light guide that can generate a secondary light source at a focal point of the reflector without disturbing reflected light, like a ghost, is proposed here. A spotlight consisting of the curved light guide and a parabolic reflector is fabricated and shows that a collimated beam with a half-intensity angle of less than 4.3 deg can be realized with the reflector opening diameter of 90.0 mm.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. INTRODUCTION
Replacement of traditional incandescent lamps by light-emitting diodes (LEDs) has been progressing owing to the many advantages of LEDs such as high efficiency, eco friendliness, and long lifetime [1–20]. The traditional incandescent lamp has a wire filament heated to such a high temperature that it glows with visible light. The filament is usually protected from oxidation with a glass or fused quartz bulb that is filled with inert gas or a vacuum. For example, a halogen lamp has a tungsten filament sealed into a compact transparent envelope that is filled with a mixture of an inert gas and a small amount of a halogen such as iodine or bromine. The combination of the halogen gas and the tungsten filament produces a halogen cycle chemical reaction that redeposits evaporated tungsten on the filament and increases its life. On the other hand, inert gas is unnecessary for operation of LEDs. However, effective thermal management of LEDs is necessary to realize their abovementioned advantages, because the LEDs’ operating temperature of about 100–150 deg Celsius greatly affects the lighting color and the overall lifetime [21,22]. In particular, for higher-brightness LEDs and higher-density LED arrays, more effective thermal management solutions are required to keep the LED at an appropriate operating temperature. Therefore, it is necessary to thermally attach a large metal heat dissipator to the LED.
LED collimated illumination is widely used in the residential, commercial, and optical inspection fields. In particular, optical inspection in several types of manufacturing processes often requires highly collimated light to detect defects that make the collimated light scattered. A typical collimator, namely, one that is a parabolic reflector, has a focal point on which a light source should be placed. The light source approximates a point source, which enables light rays reflected by the reflector to be a collimated beam with a narrow light distribution angle. For reflector lamps, the traditional wire filament as the light source has several favorable features such as a wide-angle light distribution toward the reflector and a point-like compact light source where the typical size of the filament is about a few tens of millimeters. The point-like light source is often favored for reflector lamps since it can be placed at the focal point of the reflector, thus making light rays highly collimated. However, it is often difficult to place the LED at the focal point of the reflector because the heat dissipator that is thermally attached to the LED prevents the reflected light rays from emitting out. One of the outstanding optical elements for addressing this problem is a spotlight with a refraction-reflexion-total internal reflection (RXI) lens [23,24] that is thin enough and able to produce a narrow light distribution angle in accordance with the etendue conservation theory [25,26]. An axisymmetric light guide can also produce a secondary light source at a focal point of a reflector [27].
Another optical element, namely, a curved light guide that can produce a secondary light source at a focal point of a reflector without disturbing reflected light, like a ghost, is proposed here. The remainder of this paper is organized as follows. Section 2 describes the basic structure and functions of the curved light guide. Section 3 describes a design of the curved light guide based on the etendue conservation theory. Section 4 describes a prototype of a spotlight using the curved light guide and reports on the measurement of illumination angle distribution. Experimental and theoretical results are both described in Section 5. Discussions are given in Section 6, and conclusions are given in Section 7.
2. CONCEPT OF GHOST SECONDARY LIGHT SOURCE USING A CURVED LIGHT GUIDE
A typical reflector, namely, a parabolic reflector, has a focal point where a point-like light source should be placed. With the reflector, a parallel (collimated) light beam can be produced. However, it is often difficult to place an LED at the focal point because the LED needs a relatively large heat dissipator that prevents reflection of light rays from the reflector. Thus, it is necessary to generate a secondary light source at the focal point without significantly disturbing the reflected light.
Fig. 1. Schematic cross-sectional view of the curved light guide producing a secondary light source without significantly disturbing the reflected light. The curved light guide has one flat end surface that faces an LED and the other flat end surface placed at a focal point of the reflector. A light ray emitted from the LED is incident on one end surface of the light guide, and it is internally totally reflected by the curved surface toward the other end surface. The flat end surfaces of the light guide are circles with radii of ${\rho _{{\rm{in}}}}$ and ${\rho _{{\rm{out}}}}$. The reflected light from the reflector might be refracted or reflected by the curved light guide, which can be negligible when the cross-sectional area of the curved light guide is sufficiently small. Thus, the reflected collimated light will not be significantly disturbed by the curved light guide. This means that the secondary light source appears like a ghost at the focal point of the reflector without significantly disturbing the reflected light.
Therefore, a curved light guide is used to produce the secondary light source at the focal point. A schematic cross-sectional view of the curved light guide with a reflector is shown in Fig. 1. The curved light guide has one flat end surface that faces an LED and the other flat end surface placed at the focal point of the reflector. A light ray emitted from the LED is incident on one end surface of the light guide, and it is internally reflected by the curved surface owing to the total internal reflection (TIR) toward the other end surface. The flat end surfaces of the light guide are circles with radii of ${\rho _{{\rm{in}}}}$ and ${\rho _{{\rm{out}}}}$. The reflected light from the reflector might be refracted or reflected by the curved light guide, which can be negligible when the cross-sectional area of the light guide is sufficiently small. Thus, the reflected collimated light will not be significantly disturbed by the curved light guide. This means that the secondary light source appears like a ghost at the focal point of the reflector without significantly disturbing the reflected light.
3. DESIGN OF THE CURVED LIGHT GUIDE
A. Flat End Surface Size Based on the Etendue Conservation Theory
A light ray emitted from the LED is incident on the flat end surface of a curved light guide, and it is refracted by the light guide of a refractive index of $n$. A maximum incident angle that corresponds to a critical angle ${\theta _{\rm{c}}}$ of the light guide can be written with the refractive index $n$ as
In an optical system, there is a conserved quantity, namely, an etendue. The etendue can be written as a product of an area of a cross section where light rays pass through and a maximum solid angle of the light rays on the cross section. When an infinitesimal surface element ${\rm{d}}S$, which is immersed in a medium of refractive index $n$, is crossed by the light rays confined to a solid angle ${\rm{d}}\Omega$ with an incident angle $\theta$, the infinitesimal etendue ${\rm{d}}G$ can be written [26,27] as
Thus, the following relationship can be derived using the etendue for the two flat surfaces with the radii of ${\rho _{{\rm{in}}}}$ and ${\rho _{{\rm{out}}}}$, respectively, as
In order to make the light rays emit from the flat end surface, it is necessary for the angle ${\theta _{{\rm{out}}}}$ to be less than the critical angle ${\theta _{\rm{c}}}$. Thus, the following condition is derived from Eq. (4) as
To make highly collimated illumination using a reflector, it is necessary that the end surface placed at the focal point should be sufficiently small. Thus, the radius of ${\rho _{{\rm{out}}}}$ is set to ${\rho _{{\rm{in}}}}$ and represented by ${\rho _0}$ as
B. Curvature of Curved Light Guide
The curved light guide is assumed to consist of a straight cylinder with a constant diameter and a curved cylinder with the same constant diameter and a constant curvature, which means that the two end surfaces of the light guide have the same diameter.
A cross-sectional view of the curved light in the $x - z$ plane of a global Cartesian coordinate system with the coordinate origin of $O$ is shown in Fig. 2. The $x$ direction is horizontal, and the $y$ direction is vertical. A local cylindrical coordinate system of ($r$, $\theta$) is taken with the coordinate origin of ${O^\prime}$. The angle $\theta$ is defined as an angle from the ${O^\prime} - {\rm{A}}$ line, where a point A is on the inner surface of the light guide. A light ray reflected internally at point A travels toward the outer surface of the light guide with an angle $\alpha$ between its path and the ${O^\prime} - {\rm{A}}$ line. The radius of the inner surface is ${r_0}$ and that of the outer surface is ${r_1}$. An angle $\Theta$ is defined as an angle between the light ray path and the radial direction.
Fig. 2. Cross-sectional view of the curved light guide in the $x - z$ plane of a global Cartesian coordinate system with the coordinate origin of $O$. The $x$ direction is horizontal, and the $y$ direction is vertical. A local cylindrical coordinate system of ($r$, $\theta$) is taken with the coordinate origin of ${O^\prime}$. The angle $\theta$ is defined as an angle from the ${O^\prime} - {\rm{A}}$ line, where a point A is on the inner surface of the light guide. A light ray reflected internally at point A travels toward the outer surface of the light guide with an angle $\alpha$ between its path and the ${O^\prime} - {\rm{A}}$ line. The radius of the inner surface is ${r_0}$, and that of the outer surface is ${r_1}$. An angle $\Theta$ is defined as an angle between the light ray path and the radial direction.
The path of the light ray can be written as
which can be transformed in the form of the differential equation asBecause the angle $\alpha$ is constant before the light ray reaches the outer surface, Eq. (8) can be solved as
which can be transformed asEquation (10) can be further transformed at $r = {r_1}$ with the diameter of the curved light guide of ${{2}}{\rho _0}$ as
At the outer surface of the curved light guide with the radius of ${r_1}$, the angle $\Theta$ should be larger than the critical angle ${\theta _{\rm{c}}}$ in order to be reflected owing to TIR. Using Eq. (11), the following equation can thus be derived as
On the other hand, the light ray reflected by the outer surface toward the inner surface will be always internally reflected by the inner surface owing to TIR. Thus, the light rays that are incident on the light guide can always be internally reflected owing to TIR when the condition represented by Eq. (12) holds.
4. PROTOTYPE OF A SPOTLIGHT USING THE CURVED LIGHT GUIDE
A prototype of a spotlight using the abovementioned curved light guide is designed using Eq. (12). The perspective view of the prototype is shown in Fig. 3. The prototype is composed of a curved light guide and a reflector with an opening diameter of 90.0 mm and a focal length of 22.5 mm. An LED faces the one flat end surface where a mask with a hole of a diameter of 2.0 mm is placed between the LED and the end surface in order to lessen stray light rays. The other flat end surface of the light guide is placed at the focal point of the reflector.
Fig. 3. Perspective view of prototype of spotlight. The prototype is composed of a curved light guide and a reflector with an opening diameter of 90.0 mm and a focal length of 22.5 mm. An LED faces the one flat end surface where a mask with a hole of a diameter of 2.0 mm is placed between the LED and the end surface in order to lessen stray light rays. The other flat end surface of the light guide is placed at the focal point of the reflector.
The light guide is made of acrylic with its refractive index of 1.49, and its critical angle ${\theta _{\rm{c}}}$ is 42.2 deg. For a light ray that travels internally along the straight cylinder, a maximum incident angle at the side surface of the cylinder is 47.8 deg. The angle $\alpha$ in Eq. (12) is then set to 47.8 deg. The diameter of the curved light guide ${{2}}{\rho _0}$ is set to 2.5 mm. The radius of the curvature of the curved cylinder ${r_0}$ is set to 25.0 mm. These parameters satisfy Eq. (12), which means the light rays that are incident on the light guide can travel along it owing to TIR, assuming that leak of skew rays is negligible. The parameters of the curved light guide are summed up in Table 1.
The prototype fabricated with a surface mounted diode (SMD)-type LED and a heat dissipator attached to the LED is shown in Fig. 4. Parameters used for the prototype are as listed in Table 1. The reflector is made by aluminum deposition on acrylic. The heat dissipator can be sufficiently large without disturbing reflected light rays.
Table 1. Parameters of the Curved Light Guide
Fig. 4. Perspective view of fabricated prototype of a spotlight. Parameters for the curved light guide and the reflector are as listed in Table 1. The reflector is made by aluminum deposition on acrylic. The heat dissipator can be sufficiently large without disturbing reflected light rays.
Fig. 5. Light intensity angle distributions of both the simulation and experimental results with respect to angle from the $z$ direction on the right-hand side. The horizontal and vertical directions in the global Cartesian coordinate system are indicated on the left-hand side. The light intensity angle distributions are plotted with a solid line, a dotted line, a circle mark, and a diamond mark. These represent a simulation in the vertical direction, a simulation in the horizontal direction, an experiment in the vertical direction, and an experiment in the horizontal direction, respectively. The simulation results agree well with the experimental results.
5. RESULTS
Ray-tracing simulation [28] is performed for the prototype of the spotlight. Light intensity angle distributions in the horizontal direction ($x$ direction) and the vertical direction ($y$ direction) are both calculated in the far field. Experiments are also performed in the far field with a distance from the prototype of about 2 m. Shown on the right-hand side of Fig. 5 are the light intensity angle distributions of both the simulation and experimental results with respect to angle from the $z$ direction. The horizontal and vertical directions in the global Cartesian coordinate system are indicated on the left-hand side. The light intensity angle distributions are plotted with a solid line, a dotted line, a circle mark, and a diamond mark. These represent a simulation in the vertical direction, a simulation in the horizontal direction, an experiment in the vertical direction, and an experiment in the horizontal direction, respectively. The simulation results agree well with the experimental results.
A half-intensity angle of the simulation in the vertical direction is about 3.6 deg, and that of the experiment in the same direction is about 4.3 deg. A half-intensity angle of the simulation in the horizontal direction is about 3.2 deg, and that of the experiment in the same direction is about 3.8 deg. These results show that the half-intensity angles of the simulation agree well with those of the experiments, with errors of less than 0.7 deg.
The light intensity angle distribution in the vertical direction is symmetric. On the other hand, the light intensity angle distribution in the horizontal direction has slight asymmetry. The shadowing effect due to the curved light guide to prevent the reflected light from emitting out is not found in either of the light intensity angle distributions.
The proposed curved light guide then shows that highly collimated illumination can be produced with the half-intensity angle of less than 4.3 deg.
Fig. 6. Illuminance distribution calculated using the ray-tracing simulation in the far field with a distance from the spotlight of 2 m. The $x$ and $y$ directions in the global Cartesian coordinate system correspond to horizontal and vertical directions, respectively. The illuminance distribution in the horizontal direction is asymmetric, whereas that in the vertical direction is symmetric.
Fig. 7. Illuminance distribution on the flat end surface parallel to the $x - y$ plane of the global Cartesian coordinate. The $x$ and $y$ directions in the global Cartesian coordinate system correspond to horizontal and vertical directions, respectively. The illuminance distribution in the horizontal direction is asymmetric, whereas that in the vertical direction is symmetric.
6. DISCUSSIONS
Although the light intensity angle distributions in both the vertical and horizontal directions seem to be unaffected by the shadowing effect due to the curved light guide, those in the horizontal direction have slight asymmetry. Indeed, an illuminance distribution calculated using the ray-tracing simulation in the far field with a distance from the spotlight of 2 m has slight asymmetry as shown in Fig. 6. The $x$ and $y$ directions in the global Cartesian coordinate system correspond to horizontal and vertical directions, respectively. The illuminance distribution is asymmetric in the horizontal direction, whereas it is symmetric in the vertical direction.
This asymmetric feature seems to be due to an illuminance distribution asymmetry at the flat end surface placed at the focal point. Figure 7 shows the illuminance distribution on the flat end surface parallel to the $x - y$ plane of the global Cartesian coordinate. The $x$ and $y$ directions in the global Cartesian coordinate system correspond to the horizontal and vertical directions, respectively. The illuminance distribution is asymmetric in the horizontal direction, whereas it is symmetric in the vertical direction. This asymmetry can describe the light intensity angle distribution asymmetry. Thus, the asymmetry of the light intensity angle distribution should be removable when the position of the flat end surface is adjusted.
A power loss at the connection between the LED and the light guide flat surface can be suppressed when the LED is set closer to the surface. To realize this, however, the heatproof temperature of the light guide should be above the LED temperature. In the proposed optical system, the LED temperature can be low enough with large heat dissipator.
7. CONCLUSIONS
An optical system with LEDs to produce collimated illumination without disturbing reflected light is proposed. A curved light guide can generate a secondary light source, like a ghost, at a focal point of a collimator. A spotlight consisting of the curved light guide and a parabolic reflector is fabricated and shows that a collimated beam with a half-intensity angle of less than 4.3 deg can be realized with the reflector opening diameter of 90.0 mm.
Disclosures
The author declares no conflicts of interest.
REFERENCES
1. H. Ohno, “Design of a coaxial light guide producing a wide-angle light distribution,” Appl. Opt. 56, 3977–3983 (2017). [CrossRef]
2. H. Ohno and M. Kato, “Total internal reflection shell for light-emitting diode bulbs,” Appl. Opt. 58, 87–93 (2019). [CrossRef]
3. T. Kelly, T. Yeo, and D. Morin, “Light bulb with omnidirectional output,” U.S. patent 8750671 B1 (10 June 2014).
4. C. Scianna and D. Plaines, “Omnidirectional lighting device,” U.S. patent 6568834 B1 (27 May 2003).
5. T. Chen, “Light bulb with light emitting elements for use in conventional incandescent light bulb sockets,” U.S. patent 7726836 B2 (1 June 2010).
6. P. Premysler, “Omnidirectional LED light bulb,” U.S. patent 8680754 B2 (25 March 2014).
7. S. Liu and J. An, “Omnidirectional LED light bulb,” U.S. patent 2014/0043823 A1 (13 February 2014).
8. N. Desilva, D. Nava, and R. Higley, “LED lamp with omnidirectional light distribution,” U.S. patent 2014/0218931 A1 (7 August 2014).
9. Y. C. Chou, “Omnidirectional LED lamp and complex unitary lens,” U.S. patent 8297799 B2 (30 October 2012).
10. N. Kanai, “Illuminating device,” U.S. patent 8118457 B2 (21 February 2012).
11. A. Rizkin and R. Beach, “LED light module for omnidirectional luminaire,” U.S. patent 8360615 B2 (29 January 2013).
12. J. P. M. Ansems and V. S. D. Gielen, “Single chamber lighting device,” U.S. patent 2013/0120965 A1 (16 May 2013).
13. C. M. Coushaine, “Replaceable LED bulb with interchangeable lens optic,” U.S. patent 6637921 (25 January 2005).
14. K. Harrity, C. J. Nelson, D. R. Carlson, M. E. Johnson, S. W. Demarest, M. B. Dubin, and K. W. Michaels, “Light apparatus,” U.S. patent 7726860 B2 (1 June 2010).
15. P. J. Wu and P. C. Wu, “Structure of light bulb,” U.S. patent 2010/0148650 A1 (17 June , 2010).
16. K. H. Liu, “Illuminated traffic wand,” U.S. patent 7261456 B2 (28 August 2007).
17. P. C. Chen, “Light guide tube and light emitting diode tube lamp incorporating the same,” U.S. patent 2015/0029742 A1 (29 January 2015).
18. E. J. Tersa and B. Thibeault, “High output radial dispersing lamp using a solid state light source,” U.S. patent 6350041 (26 February 2002).
19. E. Boonekamp and T. Duester, “Light source,” U.S. patent 8292471 B2 (23 October 2012).
20. H. Ohno, Y. Yamamoto, M. Kato, and K. Hisano, “Lighting apparatus and light guide,” U.S. patent 2014/0362599 A1 (11 December 2014).
21. Z. T. Ye, H. C. Kuo, and C. H. Chen, “Optical and thermal design of light emitting diodes omnidirectional bulb,” Appl. Opt. 54, E94–E101 (2015). [CrossRef]
22. S. C. Allen and A. J. Steckl, “A nearly ideal phosphor-converted white light-emitting diode,” Appl. Phys. Lett. 92, 143309 (2008). [CrossRef]
23. J. C. Minano, J. C. Gonzlez, and P. Benitez, “RXI: a high-gain, compact, nonimaging concentrator,” Appl. Opt. 34, 7850–7856 (1995). [CrossRef]
24. P. Benitez, J. C. Minano, and F. Munoz, “Compact folded-optics illumination lens,” U.S. Patent 7181378 (24 May 2005).
25. J. Chaves, Introduction to Nonimaging Optics (CRC Press, 2008).
26. R. Winston, J. Minano, and P. Benitez, Nonimaging Optics (Academic, 2005).
27. H. Ohno, K. Nakagawa, and T. Kamikawa, “Design of secondary light source for reflectors with axisymmetric light guide,” Appl. Opt. 58, 3848–3855 (2019). [CrossRef]
28. LightTools, https://optics.synopsys.com/lighttools/.
