Nonimaging Optics - Kohler Integration

Kohler Integration

In some applications it is important to achieve a given irradiance (or illuminance) pattern on a target, while allowing for movements or inhomogeneities of the source. Figure "Kohler integrator" on the right illustrates this for the particular case of solar concentration. Here the light source is the sun moving in the sky. On the left this figure shows a lens L₁ L₂ capturing sunlight incident at an angle α to the optical axis and concentrating it onto a receiver L₃ L₄. As seen, this light is concentrated onto a hotspot on the receiver. This may be a problem in some applications. One way around this is to add a new lens extending from L₃ to L₄ that captures the light from L₁ L₂ and redirects it onto a receiver R₁ R₂, as shown in the middle of the figure.

The situation in the middle of the figure shows a nonimaging lens L₁ L₂ is designed in such a way that sunlight (here considered as a set of parallel rays) incident at an angle θ to the optical axis will be concentrated to point L₃. On the other hand, nonimaging lens L₃ L₄ is designed in such a way that light rays coming from L₁ are focused on R₂ and light rays coming from L₂ are focused on R₁. Therefore, ray r₁ incident on the first lens at an angle θ will be redirected towards L₃. When it hits the second lens, it is coming from point L₁ and it is redirected by the second lens to R₂. On the other hand, ray r₂ also incident on the first lens at an angle θ will also be redirected towards L₃. However, when it hits the second lens, it is coming from point L₂ and it is redirected by the second lens to R₁. Intermediate rays incident on the first lens at an angle θ will be redirected to points between R₁ and R₂, fully illuminating the receiver.

Something similar happens in the situation shown in the same figure, on the right. Ray r₃ incident on the first lens at an angle α<θ will be redirected towards a point between L₃ and L₄. When it hits the second lens, it is coming from point L₁ and it is redirected by the second lens to R₂. Also, Ray r₄ incident on the first lens at an angle α<θ will be redirected towards a point between L₃ and L₄. When it hits the second lens, it is coming from point L₂ and it is redirected by the second lens to R₁. Intermediate rays incident on the first lens at an angle α<θ will be redirected to points between R₁ and R₂, also fully illuminating the receiver.

This combination of optical elements is called Köhler illumination. Although the example given here was for solar energy concentration, the same principles apply for illumination in general. In practice, Köhler optics are typically not designed as a combination of nonimaging optics, but they are simplified versions with a lower number of active optical surfaces. This decreases the effectiveness of the method, but allows for simpler optics. Also, Köhler optics are often divided into several sectors, each one of them channeling light separately and then combining all the light on the target.

An example of one of these optics used for solar concentration is the Fresnel-R Köhler.