Development of Methods for the design of Microfocus Optical Systems

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A third-order aberration theory has been developed for a plane-symmetric double-element optical system that consists of an extended source, two ellipsoidal gratings, and an image plane. Analytic formulas were derived for spot diagrams and aberration curves similar to Seidel aberrations. The theory was shown to be extended to multi-element systems by means of a recurrence formula. Analytic aberration curves were also derived, on the basis of the theory, for Schwarzschild optics as a function of axis alignment error and the distance between the centers of curvature of the concave and convex spherical mirrors. The effects of various factors on the performance of a Schwarzschild objective was further investigated by means of ray tracing on condition that the objective had a magnification of 50, a numerical aperture of 0.25, and an object-to-image distance of 〜1 m. the result showed that a spatial resolution of 30 nm could be obtained on the optical axis by arranging the mirrors non-concentrically by an amount of 0.69 mm. A design method was established for a varied-line-spacing plane grating monochromator, whose wavelength scanning was made by simple grating rotation about the surface normal. The result showed that the designed monochromator was capable of providing a high throughput in an energy range of 1-2 keV. In addition, a scalar theory was developed to estimate the optimum land-to-groove ratio and groove depth of a laminar grating. A three-aspheric-mirror optics for extreme ultraviolet lithography (EUVL) was designed, constructed, and tested. The mirrors were aligned to a precision of 3 nm RMS by successively adjusting the mirrors by amounts computed from wavefront errors measured with a Fizeau-type interferometer. The EUVL system was then tested on a synchrotron radiation beamline and showed a diffraction-limited performance of 56 nm.