Modern polishing methods of ion-beam milling, and single atom removal techniques are beginning to allow the fabrication of arbitrary surface shapes for reflecting grazing incidence optics. Moreover, the total expense of fabrication, coating, measuring, mounting, aligning, cooling, and surrounding the optic with vacuum make the reduction of optical part count attractive for the latest generation x-ray sources, not even considering potential effects on the scattering and reflective losses of the radiation. These two developments converge to effectively suggest the question of what surface would be the optimally de-magnifying surface to replace a toroid illuminated by a wave cylindrical in the sagittal direction if the sag of the single surface were determined by a function, and not constrained to be a typical optical shape. To address this we derive a simplified case of the formalism of Chrisp, using the classical optical path function approach of Fermat to give a power series calculation of this best surface. This surface, the "diaboloid," would in principle earn its name by its, at least ab initio, consideration of being very difficult to manufacture. We show an example of improvement this surface would provide.
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