A Single-Element Plane Grating Monochromator
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
... oints to isolate the lateral ray aberrations, with those of power-sum ď 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 2ˆ4 mrad aperture) attains a resolving power ą 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. Grating rotation about its third (meridional) axis may be employed to cancel vertical deflection of the diffracted beam while maintaining the above aberration correction. This enables a simpler (pure rotary) motion for the exit slit and a fixed beam direction both horizontally and vertically. Photonics 2016, 3, 3 2 of 44 plane mirror ; and (V) a CLS grating rotating about its surface normal plus a fixed (ideally elliptical) concave mirror . The cited references are the original disclosures, with the defining (minimum) optical geometries and characteristic imaging properties being unchanged in numerous reformulations, optimizations, augmentations, rebranding and other derivatives. Presented here is a new monochromator geometry, in which a self-focusing VLS grating scans wavelength between slits at fixed distances and horizontal deviation angle, without the need for other optics. This paper reports the detailed imaging characteristics of the basic (astigmatic, single-element, plane grating) configuration, particularly the spectral resolution as a function of aperture and scan range. In Section 2, an approximate light-path formulation provides a cogent algebraic and geometric understanding of the new focusing principle (first degree correction) and derives an advantageous conjugate distance ratio to correct the spectral aberration of second degree. Section 3 introduces a rigorous general light-path formulation and Section 4 applies this to obtain the expansion equations for the present dual-rotation plane VLS grating. As analyzed in Section 5, these equations provide to an exacting degree the focusing condition, the required tilts of the object (or entrance slit) and image (or exit slit) and the lateral ray aberrations in both directions. In Section 6, these spatial aberrations are converted to the geometrical spectral resolution and are exemplified using the dimensional parameters of an ultra-high resolution soft X-ray monochromator. In Section 7, independent simulations (numerical raytracings) are performed and quantitatively compared to the light-path calculations. As the present introductory work lays the theoretical foundation on which subsidiary performance characteristics may be added, Section 8 briefly indicates some prospects for future practical enhancements. The new results disclosed in this paper, including the proposed geometry and two precise methods of deriving the component geometrical aberrations, are summarized in Section 9. Photonics 2016, 3, 3 3 of 44 results in a strong defocusing of the spectral width which, as will be shown, may be canceled by the defocusing of opposite sign resulting from then-axis rotation.