[an error occurred while processing this directive]

[an error occurred while processing this directive]

LED Modeling: Pros and Cons of Common Methods

Light Emitting Diodes (LEDs) offer several advantages over incandescent, fluorescent, and discharge light sources, including longer lifetime, smaller size, and greater mechanical ruggedness. Continuing developments in LED technology are producing sources with increased output power and electrical efficiency as well as a wider range of colors, including so-called "white light" LEDs. Consequently, LEDs are replacing traditional light sources in numerous illumination applications, from traffic signals to instrumentation. As with any light source, effectively utilizing LEDs in an optical system requires the ability to accurately model their output characteristics with software.

There are three key opto-mechanical elements of most LEDs. The first is the LED die itself. The second is a metal cup in which the die sits. This cup provides one of the electrical contacts to the die, acts as a heatsink, and also works as a reflector to redirect light existing at the sides of the LED die. The final part is any integral lens or encapsulation. LEDs range from bare, cuboid emitters, to more complex designs that may include multiple emitters, integral lenses, and phosphor layers to alter their spectral output (color).

Modeling Tradeoffs
In designing optical systems containing LEDs, the goal at nay stage is to use the simplest model that adequately predicts the behavior of the system. a simple model is desirable because LEDs present considerable optical complexity and it is not uncommon to trace millions of rays in each iteration of an illumination system design and analysis. Of course, what constitutes an "adequate prediction" of performance can vary. A simpler model might suffice for a feasibility study, while a more rigorous approach may be needed for the actual design and optimization of the final optical system.

The most elementary way to effectively model an LED is as a point source whose output is apodized (varied in a systematic way) as a function of angle. The apodization is usually derived from manufacturer-supplied data. This simple model is straightforward to construct and ray trace in most optical or illumination design programs.

The point source model is most useful for doing first-order system design. This includes roughly determining values fro the focal lengths, f-numbers, element sizes, and components locations. The point source model also enables first-order calculation of the optical system's collection efficiency. However, the point source model is inadequate for performing any analysis in the near field of the LED, where effects due to the finite source size are most pronounced.

A significant increase in accuracy can be obtained by modeling and LED as an extended source, where the angular output distribution and any spatial nonuniformities are independently specified. At Optical Research Associates (ORA), a model of this type, in which the angular distribution is constrained to be the same from every point on the surface, is called an "apodized emitter."

The apodized emitter model is easy to construct and still simple enough to enable rapid ray tracing. For example, it can be specified in several different ways in ORA's illumination design and analysis software package, LightTools. These include applying apodization files directly to a source, creating a superposition of several sources, or even illuminating a scattering surface with collimated rays.

While still generic, the apodized emitter approach is sufficiently accurate for many uses, and is probably the most popular LED software model. Typical systems applications include light pipes, mixing rods, large core, plastic optical fibers, instrumentation lighting, tail lamps, and pillow optics.

The angular distribution of an apodized emitter model can be matched to manufacturer's data, and thus usually specified with good accuracy. However, determining source size, spatial variation, and position within the package is not always so straightforward; this makes it difficult to know the precise accuracy of the model. Errors in specifying these parameters have the most pronounced impact when analyzing systems with limiting apertures.

The next step in model complexity is to explicitly include representations of the LED's various components parts (e.g. die, cup, and lens). ORA terms a model composed of angularly and spatially apodized point sources, surface sources, and volume sources — together with optomechanical constructs —a "geometry + emitters" model.

This approach enables several source-specific characteristics to be examined in some detail. Examples include the reflective characteristics of the cup, and the refractive, reflective, and scattering properties of the lens and/or encapsulation. Incorporating "second order" effects, such as spurious reflections from parts of the LED package, is important because these can sometimes determine the real-world success or failure of a system.

Modeling the source as a series of discrete elements also facilitates answering "what if" questions about the system. For example, the reflection from a specific surface might be turned on or off to determine its significance, or the position of a particular LED components might be altered to assess the impact of part-to-part dimensional variations on system performance.

Unfortunately, the "geometry + emitters" model is time-consuming to create, and may require numerous iterations to get the model output to closely match the real LED output at all angles. This time can be mitigated through the use of optimization, but the level of detail adequate for one application may be insufficiently accurate for another, so the time investment to develop the model may not be preserved.

Measurement-Based Models
An accurate empirical approach to source modeling has been developed by Radiant Imaging. Their system utilizes a CCD camera, mounted on a computer-controlled, two-axis goniometer. This system scans an emitting source from all angles, and records the actual luminance distribution of each source view. The files created by the Radiant Imaging system can then be used in most illumination design programs to generate random ray sets that precisely match the angular and spatial output distributions of the source.

Radiant Imaging Source Models provide two primary advantages. First, they require very little or no time to create (if they are purchased directly from Radiant Imaging, which has a library of many different sources on file). Second, they are completely accurate, automatically taking into account all source characteristics, such as the effects of defects in the plastic lens.

The drawbacks of the Radiant Imaging Approach is that each model is of only one source sample. If the scanned source is not a "typical" representative of that source type, then neither is the model. Also, these source models cannot be altered, so there is no capability for adjusting source parameters or isolating the impact of specific source characteristics (e.g. scattering by the cup). Furthermore, the Radiant Imaging approach provides just a ray source to the program, not an optomechanical construct with which a program can interact. Thus, there is no ability to analyze rays that re-enter the source after hitting other parts of the optical system.

In conclusion, developments in LED and other source technologies, together with the rapid proliferation of displays, have created an increasing market for more complex and sophisticated illumination systems. A new generation of more powerful illumination system design programs has been created to meet this demand. However, using these programs successfully and cost effectively still requires an ability to identify and accurately model the most significant source characteristics.

This article was written by William Casarly, Ph.D., Optical Research Associates, 3601 Green Road, Suite 104, Beachwood, OH 441122-5719. Contact the author at: 216-831-0780; Fax 216-831-0790; or email: billc@opticalres.com. Visit ORA at www.opticalres.com.