Aspherical lens shapes for focusing synchrotron beams

Aspherical surfaces required for focusing collimated and divergent synchrotron beams using a single refractive element (lens) are reviewed. The Cartesian oval, a lens shape that produces perfect point‐to‐point focusing for monochromatic radiation, is studied in the context of X‐ray beamlines. Optical surfaces that approximate ideal shapes are compared. Results are supported by ray‐tracing simulations. Elliptical lenses, rather than parabolic, are preferred for nanofocusing X‐rays because of the higher peak and lower tails in the intensity distribution. Cartesian ovals will improve the gain when using high‐demagnification lenses of high numerical aperture.