Aspheric double mirror systems

Two surface aspheric systems are designed using the principle that Snell´s laws of reflection are obeyed at the first surface and an eikonal function used to derive the second surface for completely general focusing conditions in the image and source spaces. In most cases the solution requires a computational optimisation procedure and the results are best approximations. However, some situations exist where exact solutions can be derived. These range from the original solution by Schwarzschild for a dual mirror system obeying the sine law, and an afocal distortionless magnifying reflecting system.