HPWA-DX00

application brief AB20 5 replaces AN1149 5 Secondary Optics Design Considerations for SuperFlux LEDs Secondary optics are those optics which exist outside of the LED package, such as reflector cavities, Fresnel lenses, and pillow lenses. Secondary optics are used to create the desired appearance and beam pattern of the LED signal lamp. The following section details the optical characteristics and optical model creation for Lumileds SuperFlux LEDs. In addition, simple techniques to aid in the design of collimating reflectors, collimating lenses, and pillow lenses are discussed. Table of Contents Optical Characteristics of SuperFlux LEDs LED Light Output SuperFlux LED Radiation Patterns Optical Modeling of SuperFlux LEDs Point Source Optical Model Detailed Optical Models Secondary Optics Pillow Lens Design Design Case—Pillow Design for an LED CHMSL Non symmetric Pillow Lenses Selecting the Size of the Pillow Optic Recommended Pillow Lens Prescriptions Other Diverging Optics Reflector Design Design Case—Reflector for a CHMSL Application Reflector Cavities with Linear Profiles Reflector Cavities with Square and Rectangular Exit Apertures Other Reflector Design Techniques Collimating Lens Design Fresnel Lens Design Design Case—Collimator Lens Other Lens Design Options Appendix 5A 2 2 2 3 3 4 5 9 9 11 11 12 13 14 14 15 15 16 17 18 19 19 21 Optical Characteristics of SuperFlux LEDs LED Light Output The light output of an LED is typically described by two photometric measurements, flux and intensity. In simple terms, flux describes the rate at which light energy is emitted from the LED. Total flux from an LED is the sum of the flux radiated in all directions. If the LED is placed at the center of a sphere, the total flux can be described as the sum of the light incident over the entire inside surface of the sphere. The symbol for photometric for flux is Φv, and the unit of measurement is the lumen (lm). In simple terms, intensity describes the flux density at a position in space. Intensity is the flux per unit solid angle radiating from the LED source. The symbol for photometric intensity is Iv, and the unit of measurement is the candela (cd). To put some of these concepts into perspective, consider the simple example of a candle. A candle has an intensity of approximately one candela. A candle placed in the center of a sphere radiates light in a fairly uniform manner over the entire inner surface (ω = A/ r2 = 4π r2/ r2 = 4π steradians). With this information, the flux from a candle can be calculated as shown below: Solid angle is used to describe the amount of angular space subtended. Angular space is described in terms of area on a sphere. If a solid angle ω, with its apex at the center of a sphere of radius r, subtends an area A on the surface of that sphere, then ω = A/r2. The units for solid angle are steradians (sr). SuperFlux LED Radiation Patterns The radiation pattern of an LED describes how the flux is distributed in space. This is accomplished by defining the intensity of the LED as a function of angle from the optical axis. Since the radiation pattern of most LEDs is rotationally symmetric about the optical axis, it can be described by a simple, two axis graph of intensity versus angle from the optical axis. Intensity is normalized in order to describe the relative intensity at any angle. By normalizing An attribute of the radiation pattern that is of common interest is known as the full width, half max, or 2θ1/2. This attribute describes the full angular width of the radiation pattern at the half power, or half maximum intensity point. Looking intensity, the radiation pattern becomes a description of how the flux is distributed, independent of the amount of flux produced. Figure 5.1 shows a graph of the radiation pattern for an HPWA Mx00 LED. at Figure 5.1, the 2θ1/2 of the HPWA Mx00 LED is approximately 90°. Another attribute that is of common interest is the total included angle, or θv 0.9. This attribute describes the cone angle within which 90% of the total flux is radiated. Using Figure 5.1, the percent of total flux versus included angle can be calculated and graphed. (The derivation of this graph is shown in Appendix 5A.) This graph is included in the data sheet of SuperFlux LEDs and is shown in Figure 5.2 for the HPWA Mx00 LED. Looking at Figure 5.2, the total included angle is approximately 95°. This implies that 90% of the flux produced by an HPWA Mx00 LED is emitted within a 95° cone centered on the optical axis. Figure 5.1 Graph of the radiation pattern for an HPWA-MxOO LED. Optical Modeling of SuperFlux LEDs An optical model of the LED is useful when designing secondary optic elements such as reflector cavities and pillow lenses. The optical output of an LED can be approximated as a point source of light passing through an aperture, but modeling errors may be unacceptable when lenses or reflectors are placed within 25 mm of the SuperFlux LED. A more accurate technique involves using an optical model, which takes into account the extended source size of the LED. Point Source Optical Model The internal structure of a SuperFlux LED is shown in Figure 5.3. Light is produced in the LED chip. A portion of this light goes directly from the chip and is refracted by the epoxy dome (refracted only light). The remainder of the light is reflected by the reflector cup and then refracted by the epoxy dome (reflected refracted light). The light that is refracted appears to come from a certain location within the LED, while the light which is reflected and refracted appears to come from a different location. In addition, because the LED chip itself has physical size Figure 5.2 Percent total flux vs. included angle for an HPWA-MxOO LED. and is not a point source, the refracted only light does not appear to come from a single location, but a range of locations or a focal smear. This is true for the reflected refracted light as well. 3 These focal smears overlap, creating an elongated focal smear as shown in Figure 5.4. To create the best approximation using a point source model, the center point of the focal smears should be chosen as the location of the points source; and the aperture size should be equal to that of the epoxy dome at its base as shown in Figure 5.5. The optimal position of the point source for each SuperFlux LED is shown in Table 5.1. Figure 5.3 Internal structure of a SuperFlux LED. Figure 5.4 Focal smear produced by reflected and reflected-refracted light. Detailed Optical Models Detailed optical models of LEDs include all the internal optical structures within the LED including the chip, the reflector, and the dome. In order to accurately construct such a model, detailed information about the chip, the reflector surface, and the epoxy encapsulant must be known. The process usually involves a tedious trial and error technique of changing parameters in the model until empirical measurements are matched. Table 5.1 Position of Point Source for SuperFlux LEDs SuperFlux LED Position of Point Source Part Number “Z” (mm) HPWA-MxOO HPWA-Dx00 HPWT-Mx00 HPWT-DxOO Due to the complexity of this process, Lumileds Lighting provides customers with rayset files for SuperFlux LEDs. The raysets contain spacial and angular information on a set of rays exiting the device at the dome surface. These raysets 1.03 1.13 0.99 1.17 can be used by many optical modeling software packages. Contact your local Lumileds Applications Engineer for more information and copies of the raysets. 4 Secondary Optics This section contains practical design tools for secondary optic design. More accurate and sophisticated techniques exist which are beyond the scope of this application note. The design methods discussed here are proven, but no analytical technique can completely replace empirical testing. Designs should always be prototyped and tested as early in the design process as possible. Secondary optics are used to modify the output beam of the LED such that the output beam of the finished signal lamp will efficiently meet the desired photometric specification. In addition, secondary optics serve an aesthetic purpose by determining the lit and unlit appearance of the signal lamp. The primary optic is included in the LED package, and the secondary optics are part of the finished signal lamp. There are two primary categories of secondary optics used, those that spread the incoming light (diverging Figure 5.5 Point source model of a SuperFlux LED. optics), and those that gather the incoming light into a collimated beam (collimating optics). The most common type of diverging optic used in automotive signal lamp applications is the pillow lens. The pillow lens spreads the incoming light into a more divergent beam pattern, and it breaks up the appearance of the source resulting in a more uniform appearance. A cross section of an LED signal lamp with a pillow lens is shown in Figure 5.6. Figure 5.6 Cross section of an LED signal lamp with a pillow lens. Figure 5.7 Cross section of an LED signal lamp with a reflector cavity and pillow lens. 5 Figure 5.8 Cross section of an LED signal lamp with Fresnel and pillow lenses. As the spacing between the pillow and the LEDs is increased, each LED will illuminate a larger area of the pillow lens. As the spot illuminated by each LED grows and as the adjacent spots begin to overlap, the lens will appear more evenly illuminated. The trade off between lamp depth and lit uniformity is a common consideration in LED design, where both unique appearance and space saving packages are desired. Collimating optics come in two main varieties: reflecting and refracting. Reflecting elements are typically metalized cavities with a straight or parabolic profile. A cross section of an LED signal lamp with a reflector cavity and a pillow lens is shown in Figure 5.7. Refracting, collimating optics typically used in LED signal lamp applications include plano convex, dualconvex, and collapsed plano convex (Fresnel) lenses. A cross section of an LED signal lamp with a Fresnel lens and a pillow lens is shown in Figure 5.8. In general, designs that use collimating secondary optics are more efficient, and produce a more uniform lit appearance than designs utilizing only pillow or other non collimating optics. Fresnel lenses are a good choice for thin lamp designs and produce a very uniform lit appearance. Reflectors are a good choice for thicker lamp designs and are more efficient than Fresnel lenses at illuminating non circular areas. This is because reflectors gather all of the light, which is emitted as a circular pattern for most SuperFlux LEDs, and redirect it into the desired shape. In addition, reflectors can be used to create a unique, “jeweled” appearance in both the on and off states. The dependency of reflector height on reflector efficiency will be covered later in this section. Figure 5.9 Half-angle subtended by an individual pillow (A) for convex (upper) and concave (lower) pillow lenses. 6 Figure 5.10 Half-angle divergence of the input beam (B). Figure 5.11 Ideal radiation pattern produced by a pillow optic where A(n-1) > B. Figure 5.12 Ideal radiation pattern produced by a pillow optic where A(n-1) < B. Figure 5.13 Ideal input beam with halfangle divergence B. 7 Figure 5.14 Common form of the input beam with half-angle divergence B. Figure 5.15 Ideal vs. actual radiation patterns from a pillow lens. Table 5.2 CHMSL INTENSITY SPECIFICATION Vertical Test Points (degrees) 10 U 5U H 5D Horizontal Test Points (degrees) Minimum Luminous Intensity (cd) 8 16 8 16 25 25 25 16 16 25 25 25 16 16 25 25 25 16 10 L 5L V 5R 10 R 8 Pillow Lens Design Consider a pillow lens where the half angle subtended by and individual pillow is A as shown in Figure 5.9, and the input beam has a half angle divergence B as shown in Figure 5.10. However, in actual cases the input beam will The ideal radiation pattern generated would be as shown in Figure 5.11, where n is the index of refraction of the pillow lens material. It should be noted that Figure 5.11 is applicable when B is smaller than A(n-1). This assumption is true for most LED applications using a collimating secondary optic. In cases where B is larger than A(n-1), which is often the case when the LED is used without a collimating optic, the ideal radiation pattern would be as shown in Figure 5.12. The differences between the ideal, box like input beam, and the more common Lambertian input beam result in changes to the final radiation pattern as shown in Figure 5.15. The magnitude of this deviation in the radiation pattern can be estimated by evaluating the magnitude of the input beam’s deviation from the ideal. This deviation from the ideal should be considered in the design of the pillow lens. have the characteristics of the Cosine form of the Lambertian as shown in Figure 5.14. The ideal radiation patterns shown in Figures 5.11 and 5.12 assume that the input beam has a box like radiation pattern as shown in Figure 5.13. Design Case—Pillow Design for an LED CHMSL Using a Center High Mounted Stop Lamp (CHMSL) as an example, we can see how the design techniques discussed previously can be used to determine an optimum value of A. The minimum intensity values for a CHMSL are shown in Table 5.2. As a conservative estimate, we can treat this pattern as symmetric about the most extreme points. The extreme points are those with the highest specified intensity values at the largest angular displacements from the center of the pattern. These points are shown in italics in Table 5.2. The angular displacement of a point from the center is found by taking the square root of the sum of the squares of the angular displacements in the vertical and horizontal directions. A point at 10R and 5U would have an angular displacement from the center of: Consider the case where a collimating secondary optic is used producing a beam divergence of B = 5° (B < A(n 1)) and similar to that shown in Figure 5.14. The pillow lens material is Polycarbonate which has an index of refraction of 1.59 (n = 1.59). The ideal CHMSL radiation pattern is shown in Figure 5.17 such that all the extreme points of the specification are satisfied. Figure 5.17 shows the predicted actual radiation pattern. From Figure 5.17, we can see that A(n 1) B = 8°? and A(n 1)+B = 18°; therefore, A = 22°. The value of A selected will determine how much spread the pillow optic adds to the input beam. These points are charted on an intensity versus angle plot in Figure 5.16. 9 Figure 5.16 Extreme points on the CHMSL specification. Figure 5.17 Ideal and actual radiation patterns satisfying the extreme points of the CHMSL specifications. Figure 5.18 Toroidal pillow geometry. 10 Figure 5.19 Radiation pattern produced by a toroidal pillow (determine AV < Ah) Non symmetric Pillow Lenses In our previous example, the CHMSL radiation pattern was treated as if it were symmetric about its center. In this case, the radii of the pillow were the same along the horizontal and vertical axes, resulting in a spherical pillow. In some signal lamps, the desired output beam is much wider along the horizontal axis than along the vertical axis. In these cases, the optimum value of A will be larger for the horizontal axis (Ah) than the vertical axis (Av). The resulting geometry would be that of a circular toroid, which can be visualized as a rectangular piece cut from a doughnut as shown in Figure 5.18. For non symmetric pillow designs, an exercise similar to that performed for the CHMSL example must be performed for both the vertical and horizontal axes in order to determine Av and Ah. The resulting isocandela plot of the radiation pattern will appear as shown in Figure 5.19. Selecting the Size of the Pillow Optic After determining A for both axes, the next step is to determine the size, or pitch of the pillows. The pitch of the pillow typically does not effect performance, provided the individual pillows are small relative to the area illuminated by the light source. For incandescent designs, this is not an issue and aesthetic considerations dictate the pillow size. However, for LED designs, the light source is an array of individual LEDs. The pillow lens pitch must be small relative to the area illuminated by a single LED or the pillow will not behave as designed. For this reason, pillows designed for LED applications typically have a pitch of 1 to 5 mm; where those designed for incandescents can be as large as 10 mm. Figure 5.20 shows a top view of a single pillow with the pitches along both the horizontal, Ph , and vertical, Pv, axes. In addition, the cross section geometry through the center of the primary axes is shown. After Ah and Av have been calculated, and the pitch has been chosen along one axis; the radii, R, and pitch along the other axis can be determined by using the following equations: (Note: Ph was chosen as a known value for this example.) 11 Recommended Pillow Lens Prescriptions Table 5.3 lists recommended pillow prescriptions (Ah & Av) for different signal lamp applications. The pitch can be changed to suit by varying R as described in the previous section. Examining Table 5.3, we observe that for CHMSL designs, a symmetric pillow prescription was chosen (Ah = Av). However, for the rear combination lamp/front turn signal (RCL/FTS) application utilizing a collimating optic, a non symmetric pillow prescription was used (Ah > Av). The desired output beam pattern for the RCL/FTS applications is twice as wide in the horizontal than in the vertical; whereas in the case of the CHMSL, the desired output beam is the same in the vertical and horizontal. In addition, for applications where no collimating secondary optic is used, the function of the pillow is to break up the appearance of the sources rather than spread the output beam. In these cases, a weak, symmetric prescription pillow was chosen. The technique described above provides some practical tools for designing pillow lenses. If optical modeling software is available, along with an accurate model of the LED source, these tools should be utilized to aid in the design process and provide more accurate models of the final output beam. Table 5.3 RECOMMENDED PILLOW LENS PRESCRIPTIONS Application CHMSL CHMSL RCL/FTS RCL/FTS LED Type HPWA MHOO HPWT DHOO HPWT MxOO HPWT MxOO Collimating Optic Fresnel Lens (B = 5°) None (B = 20°) Fresnel Lens (B = 7°) Reflector Cavity (B = 20°) Ah (deg) 22 5 30 5 Av (deg) 22 5 20 5 Rh (mm) 5.3 17 4.0 17 Ph (mm) 4 3 4 3 Rv (mm) 5.3 17 8.9 17 Pv (mm) 4 3 5.7 3 Figure 5.20 Geometry of a single pillow. 12 Figure 5.21 Cross-section geometry of a desired reflector cavity. Other Diverging Optics Pillow lenses are the most popular diverging optic used in automotive signal lamps, however, other types exist which produce similar effects but have different appearances. Alternate types of diverging optics include: diffuse lenses, faceted lenses, rod lenses, and many others including combinations of the above. For example, diffuse lenses produce a uniform lit appearance and a cloudy unlit appearance. Pillow lenses can be diffused by bead blasting the pillow lens surface on the mold tool resulting in a less efficient optic, but one that is more uniform in appearance when lit. Figure 5.22 Geometry of a parabola. Figure 5.23 LED position relative to the parabola. Figure 5.24 Design of parabolic reflector with f = 0.66 mm. 13 Reflector Design Reflector cavities serve two main purposes: to redirect the light from the LED into a useful beam pattern, and to provide a unique appearance for the finished lamp. Often the look sought after is not achievable by the most optically efficient design. As a result, there is a trade off required between optical efficiency and lit appearance to arrive at an acceptable design. As discussed in the previous section Point Source Optical Model, a parabola is designed to collimate the light from the point source. For the design technique discussed here, the LED is treated as a point source. This treatment is very accurate for larger parabolas where the size of the dome is small relative to the exit aperture of In order to accommodate the SuperFlux LED dome, the bottom aperture of the reflector must be greater than three millimeters in diameter. Considering the tolerances of the molded reflector, the LED, the LED alignment to the PCB, and the alignment of the reflector to the PCB, the bottom reflector aperture should be a minimum of 3.5 mm in diameter. The focal length of the reflector must be greater than 0.5 mm to produce a bottom aperture of greater than 3.5 mm. the reflector. Once the parabola has been designed, a cavity with a profile comprised of multiple linear sections that closely approximates the form of the parabola may be used depending on the look desired. Design Case—Reflector for a CHMSL Application Consider the case where a reflector cavity will be used to collimate the light from an HPWT MH00 source, and a pillow optic cover lens will be used to form the final radiation pattern. Vacuum metalized ABS plastic will be used as the reflector material. The reflector cavity can be a maximum of 20 mm in height and should have a minimum opening for the LED dome of diameter 3.75mm to accommodate piece part misalignment and tolerances. The LED spacing is 15 mm, and each cell must illuminate a 15 mm x 15 mm patch on the pillow lens. Figure 5.21 shows a cross section of the lamp described above. The geometry of a parabola, in polar coordinates, is described by the following equation: Table 5.4 describes the profiles of three different parabolas (f = 0.9 mm, 0.7 mm, 0.66 mm). An efficient, practical collimator design for a CHMSL application should collimate all the light beyond 20°? from on axis (φ ≤ 20°). More efficient reflectors can be designed which collimate more of the light, but they are typically too deep to be of practical value. The ideal reflector for this application will have the following characteristics: Height constraint: 0.99 ≤ z ≤ 20 mm Fit of LED dome into bottom aperture:x (z = 0.99 mm) ≥? 1.875 mm 15 mm pitch: x (Φ = 20°) ≅? mm 7.5 Looking at Table 5.4, we find that the parabola with f = 0.66 mm most closely meets these requirements. Figure 5.24 gives the geometry of the parabolic reflector chosen. Figure 5.22 shows how the terms in this equation are applied. From Table 5.1, we find that the optimum point source location for the HPWT MH00 LED is at Z = 0.99 mm. Placing the point source of the LED at the focus of the parabola will result in an LED position as shown in Figure 5.23. Since the base of the LED dome is above the location of the parabola’s focus, this implies that 2f < 1/2 base aperture = 3.75 mm/2 = 1.875 mm (f < 0.94 mm). This information will give us a starting point to begin searching for the optimum parabola. 14 Figure 5.25 shows the profiles of several practical reflector geometries (f = 0.5 to 1.0 mm). It should be noted that in order to produce a reflector with a cutoff angle less than 20°, the height must increase radically. For this reason, reflectors with a high degree of collimation (