Spherical Focusing Mirror for the VUV-FEL

Based on analysis and ray-tracing that he did, Jacek Krzywinski has suggested that it should be possible to focus the 32 nmVUV-FEL beam down below 0.2 {micro}m spot size with a normal-incidence multilayer-coated spherical mirror. There are advantages to a spherical mirror over an ellipsoid (or near-paraboloid) which are ease of manufacture and alignment. Off-axis aberrations are generally small, since for a beam that underfills the sphere's aperture, the beam itself defines the axis (rather than the optic). The dominant aberration for a sphere is spherical aberration, which decreases with increasing sphere radius of curvature. However, as the radius of curvature increases, so too does the focal length and f-number, and the diffraction-limited spot increases. Hence, as Jacek has pointed out, there is an optimum radius of curvature, to achieve the smallest possible spot, given a beam diameter. This optimum is determined by balancing the spread of the beam due to spherical aberration and the spread due to diffraction