Computational Illumination Optics
When it gets dark and we turn on the lights, we want the light to feel nice and comfy. Usually, the light source is an LED, and we use special tools like reflectors and lenses to direct the light where we need it. The big question is: What kind of reflector or lens should we use to make the light go where we want it? This area of study is called freeform design, and it’s used for things like car headlights, street lights, and indoor lamps.
The figure shows a 2D reflector system that converts a point light source with a Gaussian energy distribution into a parallel light beam with a uniform distribution.
Effective method for calculating shapes
Traditionally, figuring out the right optical components has been done through a direct method. In this method, designers use a computer program to create the optical component and then simulate how the light will spread. They track many light rays from the source to the target using rules of optics (like how light reflects and refracts). If the light does not spread as desired, they tweak the design and try again. This process is based on trial-and-error and can be very slow and time-consuming.
However, Computational Science enables a more effective, inverse approach. This method calculates the perfect shape of the lens or reflector by solving a complex mathematical problem directly. Specifically, the optimal shapes can be obtained by solving a special kind of partial differential equation (PDE) known as the Monge-Ampère equation. The resulting method is faster as it reduces the design iterations and avoids cumbersome trial-and-error.
