Concerted rotations of a self-focused varied line-space diffraction grating about its groove axis and surface normal define a new geometric class of monochromator. Defocusing is canceled, while the scanned wavelength is reinforced at fixed conjugate distances and horizontal deviation angle. This enables high spectral resolution over a wide band, and is of particular advantage at grazing reflection angles. A new, rigorous light-path formulation employs non-paraxial reference points to isolate the lateral ray aberrations, with those of power-sum ≤ 3 explicitly expanded for a plane grating. Each of these 14 Fermat equations agrees precisely with the value extracted from numerical raytrace simulations. An example soft X-ray design (6° deviation angle and 2 × 4 mrad aperture) attains a resolving power 25 , 000 over a three octave scan range. The proposed rotation scheme is not limited to plane surfaces or monochromators, providing a new degree of freedom in optical design.
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