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A high-resolution laboratory reflectometer designed for operation in the soft x-ray (SXR) and extreme ultraviolet (EUV) ranges is described. High spectral resolution, up to 0.028 nm, in a wide spectral range is achieved due to the Czerny–Turner monochromator. A laser plasma generated by irradiating a solid-state target with a focused laser beam (wavelength 1.06 µm, pulse energy 0.5 J, duration 4 ns, and pulse repetition rate 10 Hz) is used as a source of SXR and EUV radiation. The goniometer allows the study of curved optical elements with an aperture up to NA = 0.5 and a diameter of up to 500 mm. The methods providing high efficiency of the optical system and spectral resolution in a wide range of wavelengths are described in detail. The problem of taking into account high orders in the recorded spectra of a laser plasma is discussed. A comparison of the measurement results with the described reflectometer and the optics beamline at the BESSY-II synchrotron is given.

Problems in the application of a null lens for surface shape measurements of aspherical mirrors are discussed using the example of manufacturing an aspherical concave mirror for the beyond extreme ultraviolet nanolithographer. A method for allowing measurement of the surface shape of a sample under study and the aberration of a null lens simultaneously, and for evaluating measurement accuracy, is described. Using this method, we made a mirror with an aspheric surface of the 6th order (i.e., the maximum deviation from the best-fit sphere is 6.6 μm) with the parameters of the deviations from the designed surface PV=5.3  nm and RMS=0.8  nm. An approximation of the surface shape was carried out using Zernike polynomials {Z(n)(m)(r,φ),m+n≤36}. The physical limitations of this technique are analyzed. It is shown that for aspheric measurements to an Angstrom accuracy, one needs to have a null lens with errors of less than 1 nm. For accurate measurements, it is necessary to establish compliance with the coordinates on the sample and on the interferogram.

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