Compact reflective system for ideal imaging concentration

We propose a new design principle for optimal concentration of light with small diffusivity based on the conservation of local brightness in passive optical transformations. A coordinate transformation is applied on the incoming rays to compensate for the variations in local brightness by the focusing stage. We apply this analytic design for a compact reflective configuration for ideal imaging concentration of diffuse light such as sunlight in one dimension on an elongated target with arbitrary cross-sectional shape at the thermodynamic limit. As illustrations, we present the design for two different target geometries and verify its validity using numerical ray-tracing simulations. The same configuration can be used in reverse as an ideal collimator of a finite diffuse source.