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When developing an LED illumination system, the designer is often restricted to a constrained working volume. This can lead to efficiency loss, thermal issues, and performance restriction. It becomes important to understand the etendue of the source and optics. Also, the optics should be designed so as to maximize the efficiency of the system. Along with discussion of these issues, a case example will be presented where incandescent position lights on the F-15 fighter are replaced with LED systems that have both visible and near infra-red functions.
Keywords: light emitting diode, LED, illumination, efficient, efficiency, design, etendue, position light
Light emitting diodes (LEDs) are being used in many illumination applications as a replacement for incandescent type sources. The driving factors for this change are long life, efficiency, and lower power usage. Although the cost of using LEDs is greater initially when compared to using incandescent sources, it usually turns out to be more cost effective over the life of the system after source replacement and maintenance costs are considered. However, to replace a single incandescent source often requires multiple LEDs to achieve desired light levels. If the system has a volume constraint, then this challenges the illumination designer. This article will discuss these challenges and show how first-order calculations can shed light on the limitations of the system. Understanding the limitations will aid the designer in choosing a design approach that will yield the best results. A real design case of F-15 fighter position lights will be used as an example throughout the article.
The Air Force Research Laboratory at Mesa, AZ tasked Breault Research Organization (BRO) to design an LED system to replace the current position lights on an F-15 fighter. As shown in Figure 1, the current wingtip position light uses a single incandescent source with a built in reflector. The cover lens has only one optic on the inside surface. The outer surface of the lens is sloped for aerodynamics. In addition to replacing the current visible light function (overt) with
LEDs, BRO also needed to add a near-IR function for use with night vision goggles. The latter will not be discussed in this article other than the fact that the near-IR function uses approximately half of the available volume.
Figure 1: Current F-15 right wingtip position light with and without outer lens cover.

Figure 2 shows the intensity versus angle distribution patterns of the desired target (left) and the prototype design
(right). A minimum of 4 candela is required through the range of 90 degrees up and down in the vertical direction, and from the forward direction to 110 degrees rearward. This is the low-intensity zone. In the forward direction, the required intensity is 60 candela 10 degrees up and down and 20 degrees rearward. In between, there are decreased contour levels out to about 40 degrees up/down and 70 degrees rearward. This is the high intensity zone. With the high and low intensity zone requirements defined, the designer can use first-order calculations to determine how many LEDs are required for the overt wingtip function. After determining the number of LEDs needed, the feasibility of fitting the required optics into the allowed volume can be decided.
Figure 2. Iso-candela plots of desired pattern and prototype design.
A prototype of the optical assembly is shown in Figure 3. The near-IR function source and optic fills the rearward half of the available space. The overt function consists of three Lumileds Luxeon 1-watt
LEDs. One LED is encapsulated by an optic to redirect the light into the high intensity zone. The remaining LEDs illuminate the low intensity zone.
Figure 3: Prototype wingtip position lamp.

First-order calculations can be used to estimate the number of LEDs required for an application as well as the aperture size of the optics required. From this, along with and understanding of efficiency losses, it can be determined early on whether it is feasible to continue with a detailed design.
3.1. Determine efficiency losses
Nearly every illumination system has at least one refractive optic, even if it’s just of a cover lens. Figure 4 shows the percent transmission through a lens made of polycarbonate with respect to angle of incidence. If all light is passing through the lens at an angle of incidence less than 40 degrees, we can expect a transmission loss due to Fresnel reflections of 10%. The loss increases as the incident angle increases with severe losses past 60 degrees. The Fresnel losses are significant in the case of the wingtip position lamp. Figure 5 shows a horizontal section through the cover lens. As shown in Figure 2, peak intensity is required in the forward direction. However, the shape of the lens is such that the angle of incidence is large for light passing in this direction. We see that passing the light through the lower part of the lens is best since efficiency loss will be on the order of 15%. A transmission loss of 50% occurs through the upper part of the lens.
Figure 4: Transmission loss through a clear lens with respect to angle of incidence.
Figure 5: Horizontal section through cover lens.

Another important efficiency consideration is how much of the light from each source can be collected by the optic.
The collection efficiency for various design approaches is discussed in section 4 below.
Distribution pattern match efficiency accounts for how well the optic is expected to direct the light from the LED into the desired distribution shape. As shown in Figure 2, the actual distribution does not exactly replicate the desired pattern. The pattern match efficiency worsens when the design volume is constrained since the optic is relatively small and close to the LED. Light collected by any point on the optic will subtend a greater solid angle when compared to a larger optic (Fig. 6). Smaller optics have less control over how well light is redirected. Another factor that contributes to distribution pattern mismatch is tolerance error. If the quality of the optic is very high and the location of the LED with respect to the optic is held tight, there will be little contribution from tolerance error. However, in many cases, especially in high volume production, tolerances must be traded off with manufacturing costs. In this case, an understanding of how the tolerance errors will effect the distribution is required to make reasonable predictions.
Figure 6. Large optic versus small optic.
Reflectors and filters will have various losses due to absorption. Rough surfaces and diffuse materials will scatter light outside of the desired distribution pattern. These efficiency losses also need to be accounted for in the first-order calculations.
When using LEDs, thermal derating is almost always a factor. LEDs are now being developed that can be driven at high current. Increased current means that more heat needs to be pulled from the mounting junction. Figure 7 shows the effect of junction temperature on the relative lumens output for a Luxeon
LED. Junction temperature is affected by the ambient temperature, heat sinking, and by modulating the LEDs. In a volume constraint system, there may not be room to provide adequate heat sinking. In this case, additional thermal derating must be taken into account when calculating efficiency loss.
Figure 7: Junction temperature vs. relative lumens. (1)

3.2. Etendue
Within the small constraints of the wingtip housing, a large portion of the power needs to be directed forward in order to meet the higher intensity requirements in that direction (Fig 2.). If the optic is not big enough to overcome the etendue of the source, then there will be an additional efficiency loss. Etendue is defined as follows:
Note that etendue is conserved. The area of the source times the projected solid angle of emission defines the limit of etendue. If the product of the aperture area of the collection optic and the projected solid angle of the output light distribution is less than this limit, there will be an efficiency loss defined as follows:
If this is the case, then the etendue efficiency needs to be applied along with all other efficiency losses defined in 3.1.
Each source has a fixed etendue limit. In the case of the Luxeon 1W emitter, it is the area of the die times the projected solid angle of emission:
There is only room in the wingtip volume for one optic to interact with one LED. Figure 6 shows the optic used in the prototype. The idea is to capture most of the light from one LED and direct it into the high intensity zone.
Figure 8: Wingtip optic to direct light into high intensity zone.
The aperture of this optic is 16 mm diameter and cannot be larger. The high intensity zone can be approximated with a cone of light with a half angle of 30 degrees. The etendue of the optic is calculated as follows:
The etendue of the optic is much greater than the etendue of the source so there will not be any additional efficiency losses. It should be noted that etendue does not tell us anything about the distribution of the light within the solid angle of the optic. In some cases, etendue is conserved by imaging the source which can be a uniform distribution. In other cases, it will be conserved by a Gaussian type distribution.

3.3. Lumens required
We previously defined the desired angle versus intensity pattern (Fig. 2). The total lumens required to fill this distribution pattern is determined by integrating the intensity with respect to solid angle. For the F-15 position light, a total of 50 lumens are required. Of this, approximately 15 lumens are required to fill the high intensity zone. This zone will be the most challenging to meet since only one LED/optic can fit into the allowed space. Table 1 shows the results of the first order calculations for this zone.
Table 1: Predicted efficiency for high intensity zone.
Efficiency Lumens
Luxeon 1 watt red emitter
Thermal Derating
Collection Efficiency
Fresnel loss (optic)
Fresnel loss (cover)
Distribution Match
70%
95%
90%
70%
80%
44.0
30.8
29.3
26.3
18.4
14.7
Etendue Efficiency 100% 14.7
The largest loss comes from thermal derating (due to high ambient temperature), the Fresnel loss (due to the large angle of incidence through the cover lens) and distribution pattern mismatch (due to small optic and tolerance error). The predictions show that barely enough useable lumens are available to fulfill the required 15 lumens in the high intensity zone. This does not leave any safety factor in the design. The measured prototype results (Figure 2) show these predictions to be on par. Of course, going into a design, we would like to have a much larger safety factor since firstorder predictions are just estimates. In the case of the wingtip, adding another LED and optic is not an option due to the volume constraint. Further, there does not appear to be any practical way to increase any of the efficiencies. For example, adding an anti-reflection (AR) coating to the cover lens would have a significant impact on the Fresnel loss efficiency. However it is not feasible in this application because of its extreme shape (high coating cost) and operating environment. The best way to increase the intensity levels is through increased source power. The production design of this optic may use the new Luxeon K2 emitters which can be driven at higher currents and offer twice the lumens output.
The remaining 35 lumens are required for the low intensity zone. Table 2 shows the efficiency predictions in this zone for a single LED. There are 23.7 useable lumens from one LED; therefore two LEDs should be sufficient to fill this zone.
Table 2: Predicted efficiency for low intensity zone.
Luxeon 1 watt red emitter
Efficiency Lumens
44.0
Thermal Derating
Collection Efficiency
Fresnel loss (cover)
Distribution Match
70%
95%
90%
90%
30.8
29.3
26.3
23.7
Etendue Efficiency 100% 23.7
The above predictions are for the right wing position lamp only which uses AlInGaP LEDs that comply with aviation red chromaticity requirements. The left wing uses InGaN LEDs that comply with aviation green chromaticity requirements. The difference in efficiency will vary between the two based on the initial lumens available for each and the effect of thermal derating. The red LED is the worst case, so we used it to do first-order calculations.

When working with volume constraints, the choice of design approach is important. The goal is to use an optic that fits within the allowed volume and maximizes total efficiency as discussed in section 3. There are many innovative design approaches, and each has its pros and cons. The most common approaches will be discussed in this section. All can be manufactured in high volume with acceptable tolerance error. The trade-off for other efficiencies will be discussed for each design.
4.1. Encapsulated optic
An example of an encapsulated optic is shown in Figure 9. This type of optic has excellent collection efficiency since it wraps around the LED. Light going forward is refracted into the desired pattern. Light going out to the side is reflected by total internal reflection into the forward direction. There is usually a size restriction on this type of optic since a large aperture results in a part that is too thick to effectively produce in volume mainly because of molding issues (sinking, long cycle times). Having a smaller optic is often desirable in a volume constraint system. The downside is that a small aperture means smaller etendue. In the case of the wingtip optic, we found that etendue is not an issue. Therefore, this approach was selected to fill the high intensity zone.
Figure 9: Encapsulated optic
4.2. Flat Fresnel optics
Another design approach commonly used is flat Fresnel optics. The main advantage of this approach is that the aperture diameter can be large while part thickness is small. A large aperture may be required when etendue is an issue. The
Fresnel optics use refraction or total internal reflection to redirect the collected light. As show in Figure 10, the collection efficiency varies. The smaller the optic, the less light is collected. Further, if it is necessary to place the
Fresnel optics facing the LED, there will be additional collection loss through the draft walls that connect the optics.
When optics are placed on the outside of the lens, away from the LED, this additional loss can be avoided.
Figure 10: Fresnel optics on side facing away from LED are more efficient.

4.3. Reflector with side emitter
Use of the Luxeon side emitter with a reflector can be a good option when a low profile system is required. Most of the light from the die is redirected out the sides by the shape of the LED optic. The light can then be redirected by reflection. This system does not have good etendue since the LED optic that redirects the light is small. Figure 12 shows the intensity versus angle distribution from the Luxeon side emitter.
Figure 11: Reflector with side emitter.
Figure 12: Intensity vs. angle distribution from Luxeon side emitter. (1)
When designing an optical system that uses LEDs in a volume constraint environment, there are various factors to consider. This includes etendue, collection efficiency, thermal derating, Fresnel loss, and other loss due to material. By planning out the system and by performing first-order calculations before beginning detailed design work, it can be determined whether the volume constraints are reasonable given the required number of LED sources. Afterwards, the design approach that fits the volume with the best total efficiency should be chosen.
1.
Lumileds Technical Datasheet DS25; Luxeon Emitter; 4/05