Theoretical Approach to X-ray Imaging by Toroidal Mirrors

X-rays can be totally reflected when the incident ray makes a very acute angle with a reflecting surface. But the glancing angle becomes fairly large when a soft X-ray is used. A part of a quadratic surface or a toroidal surface can be used as the soft X-ray reflector to make images. Particularly, toroidal mirrors are promising from the practical point of view. The theory of the optical system, aberration, magnification and resolving power is discussed, and the possibility of making an X-ray microscope is proposed.