This article is also available in Japanese.

Light-emitting diodes (LEDs) are important light sources in a wide range of applications. In areas like automotive illumination and display lighting, it is often required to improve on the brightness of an LED by adding auxiliary optics to modify the luminous intensity of such a source.

In this example, we will take measured data from a real LED source, and optimize a free-form mirror so that the brightness (power/unit solid angle) is increased. We will discuss some aspects of the optimization of non-sequential systems in general, and also discuss pitfalls in optimization and how to avoid them. This article should be of interest to anyone needing to optimize a pure non-sequential system, not just the designers of LED-based illumination systems!

Note that refractive and even diffractive correctors can be designed using the same technqiues.

We will start with the measured data from a real LED source. See this article for more details on how the LED is modeled: for now, all we need to know is that a source_radial is used to input the measured power as a function of angle. The source was measured to have a total output power of 27 Lumens, and is reasonably monochromatic with a peak wavelength of 627 nm. See the article How to Create a Simple Non-Sequential System if you are not familiar with how to enter this data. The source uses Sobol sampling for best signal/noise with fewest rays.

Under General...Units we set the system units as follows:

The luminous flux of the LED is measured in units of Lumens so we choose that unit for this simulation. Illuminance is therefore measured in terms of lm/m², or Lux. Luminous intensity ("brightness") is measured in lumens/steradian or Candela (Cd). Luminance is measured in lm/m²/sr, or Cd/m², which is sometimes referered to as a nit.
 
The starting system is set up as follows:

The LED source fires rays onto a flat mirror which then illuminates a detector surface. This file can be downloaded from the link at the end of this article. The detector sees the following spatial and angular distributions:

It can be seen that the mirror is slightly overfilled by the LED, and so the spatial and angular distributions are slightly asymmetric. This is done deliberately, just to add a little more complexity to the design.

Looking at the luminous intensity plot, it can be seen that peak brightness of about 46 Cd occurs at polar angles of around 27 degrees. Rays which are approximately normal to the detector surface have a luminous intensity of only 25 Cd (how this number is obtained is discussed on the next page). Such a profile is not good for a headlamp illumination system, or projector illumination system. It is generally desired to have as high a brightness for low-angle rays as possible, so the source can be projected over a distance.

We will now optimize the shape of the mirror to give the highest brightness on axis. To do this, we must perform the following steps:

• Define a merit function that describes what we want to achieve
• Define how the miror surface can change
• Run an optimization algorithm

If you are not familiar with optimization, this article is a useful primer.