Distributed focusing reduces mirror error sensitivity on x-ray beamlines

The appearance of very low emittance, high-power synchrotron sources has resulted in ever longer beamlines, often requiring a very weak curvature on the mirrors that transport the beam to the experiment, where the radius of curvature is on the order of kilometers. Manufacturing weakly curved, low figure error grazing incidence mirrors is difficult as the mirrors must be manufactured to an accuracy comparable to the wavelength of the transmitted light. Often the delivered mirrors have figure errors at various length scales (general shape, slope errors, roughness), which compromise image quality. An error in general shape, like the radii of a toroidal mirror, results in long-sighted or short-sighted imaging that is not so simply corrected by changing the distances and incidence angles as the mirror controls the beam focus in both vertical and horizontal directions; for a toroidal mirror, the tangential and sagittal radii need to match correctly for the desired focusing effect. Adaptive downstream optics can compensate for this. In this paper, an alternative method to reduce the sensitivity to a large radius error outside the specified tolerance range in the first mirror of a plane grating monochromator beamline at MAX IV is presented. It is found that distributed focusing by two passive, fixed radius mirrors reduces greatly the sensitivity to the radius errors in both mirrors. The radius tolerance of a mirror initially found to be unacceptable for single stage focusing is easily accommodated on both mirrors in distributed focusing, without compromising the imaging capability.