Nanofocused x rays are indispensable because they can provide high spatial resolution and high sensitivity for x-ray nanoscopy/spectroscopy. A focusing system using total reflection mirrors is one of the most promising methods for producing nanofocused x rays due to its high efficiency and energy-tunable focusing. The authors have developed a fabrication system for hard x-ray mirrors by developing elastic emission machining, microstitching interferometry, and relative angle determinable stitching interferometry. By using an ultraprecisely figured mirror, they realized hard x-ray line focusing with a beam width of 25nm at 15keV. The focusing test was performed at the 1-km-long beamline of SPring-8.

Efficient focusing of hard x rays to 25 nm by a total reflection mirror

Surface scatter effects from residual optical fabrication errors can severely degrade optical performance. The total integrated scatter (TIS) from a given mirror surface is determined by the ratio of the spatial frequency band-limited "relevant" root-mean-square surface roughness to the wavelength of light. For short-wavelength (extreme-ultraviolet/x-ray) applications, even state-of-the-art optical surfaces can scatter a significant fraction of the total reflected light. In this paper we first discuss how to calculate the band-limited relevant roughness from surface metrology data, then present parametric plots of the TIS for optical surfaces with arbitrary roughness, surface correlation widths, and incident angles. Surfaces with both Gaussian and ABC or K-correlation power spectral density functions have been modeled. These parametric TIS predictions provide insight that is useful in determining realistic optical fabrication tolerances necessary to satisfy specific optical performance requirements.

Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles

We present a rigorous theoretical treatment of nonspecular x-ray scattering in a distributed imaging system consisting of multilayer-coated reflective optics. The scattering from each optical surface is obtained using a vector scattering theory that incorporates a thin film growth model to provide a realistic description of the interfacial roughness of the multilayer coatings. The theory is validated by comparing calculations based on measured roughness to experimental measurements of nonspecular scattering from a Mo–Si multilayer coating. The propagation of the scattered radiation through the optical system is described in the context of transfer function theory. We find that the effect of nonspecular scattering is to convolve the image with a point spread function that is independent of the coherence of the object illumination. For a typical soft x-ray imaging system, the scattering within the image field from the multilayer coatings is expected to be slightly greater than for single surfaces (as normal...

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Nonspecular x-ray scattering in a multilayer-coated imaging system

The light scattering of rough metallic surfaces with roughness levels ranging from a few to several hundred nanometers is modeled and compared to experimental data. Different modeling approaches such as the classical Rayleigh-Rice vector perturbation theory and the new Generalized Harvey-Shack theory are used and critically assessed with respect to ranges of validity, accuracy, and practicability. Based on theoretical calculations and comparisons with Rigorous Coupled Wave Analysis for sinusoidal phase gratings, it is demonstrated that the approximate scatter models yield surprisingly accurate results and at the same time provide insight into light scattering phenomena. For stochastically rough metal surfaces, the predicted angles resolved scattering is compared to experimental results at 325 nm, 532 nm, and 1064 nm. In addition, the possibilities of retrieving roughness information from measured scattering data for different roughness regimes are discussed.

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Modeling of light scattering in different regimes of surface roughness

We present recent results on the inspection of a first diffraction-limited hard X-ray Kirkpatrick-Baez (KB) mirror pair for the Coherent X-ray Imaging (CXI) instrument at the Linac Coherent Light Source (LCLS). The full KB system – mirrors and holders - was under inspection by use of high resolution slope measuring deflectometry. The tests confirmed that KB mirrors of 350mm aperture length characterized by an outstanding residual figure error of <1 nm rms has been realized. This corresponds to the residual figure slope error of about 0.05µrad rms, unprecedented on such long elliptical mirrors. Additional measurements show the clamping of the mirrors to be a critical step for the final – shape preserving installation of such outstanding optics.

Ultra-precise characterization of LCLS hard X-ray focusing mirrors by high resolution slope measuring deflectometry.

We describe methods of predicting the degradation of the performance of a simple imaging system in terms of the statistics of the shape errors of the focusing element and, conversely, of specifying those statistics in terms of requirements on image quality. Results are illustrated for normal-incidence, x-ray mirrors with figure errors plus conventional and/or fractal finish errors. It is emphasized that the imaging properties of a surface with fractal errors are well behaved even though fractal-power spectra diverge at low spatial frequencies.

Specification of surface figure and finish in terms of system performance

Modifications of the long trace profiler at the Advanced Photon
Source at Argonne National Laboratory have significantly improved its
accuracy and repeatability for measuring the figure of large flat and
long-radius mirrors. Use of a Dove prism in the reference beam path
corrects phasing problems between mechanical errors and thermally
induced system errors. A single reference correction now completely
removes both of these error signals from the measured surface
profile. The addition of a precision air conditioner keeps the
temperature in the metrology enclosure constant to within ±0.1 °C
over a 24-h period and has significantly improved the stability and the
repeatability of the measurements. Long-radius surface curvatures
can now be measured absolutely with a high degree of
confidence. These improved capabilities are illustrated with a
series of measurements of a 500-mm-long mirror with a 5-km radius of
curvature. The standard deviation in the average of ten slope
profile scans is 0.3 µrad, and the corresponding standard
deviation in the height error is 4.6 nm.

Improvements in the accuracy and the repeatability of long trace profiler measurements.

We discuss the specification of x-ray mirror surfaces in terms of their imaging perlormance and express the results in terms of quantities that are directly accessible from laboratory profile measurements. Procedures are illustrated by strawman examples in glancing- and normal-incidence geometries.

Specification of glancing- and normal-incidence x-ray mirrors [also Erratum 34(11)3348(Nov1995)]

In the smooth-surface limit, the angular distribution of the intensity of light reflected and scattered from a rough surface depends only on the root-mean-square value of its surface roughness and is independent of the details of the distribution of the surface height fluctuations. In the case of rougher surfaces, the effects of the shape of the height distribution function which do appear are usually evaluated using an assumed Gaussian height distribution, even though real surfaces can be, and frequently are, non-Gaussian. This paper describes the results of an analytic study of the effects of non-Gaussian height distributions on the reflection and scattering properties of moderately-rough surfaces. As an example we compare predictions based on a Gaussian distribution with those of a one-sided exponential distribution. Large differences are found in and near the specular core, which eventually disappear in the scattering tail. Suggestions for follow-on experimental and analytic studies are given.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Light scattering from non-Gaussian surfaces

The frequency footprint of ID and 2D profiling instruments needs to be carefully considered in comparing ID surface roughness spectrum measurements made by different instruments. Contributions from orthogonal direction frequency components can not be neglected. The use of optical profiling instruments is ubiquitous in the measurement of the roughness of optical surfaces. Their ease-of-use and non-contact measurement method found widespread use in the optics industry for measuring the quality of delicate optical surfaces. Computerized digital data acquisition with these instruments allowed for quick and easy calculation of surface roughness statistics, such as root-mean-square (RMS) roughness. The computing power of the desktop computer allowed for the rapid conversion of spatial domain data into the frequency domain, enabling the application of sophisticated signal processing techniques to be applied to the analysis of surface roughness, the most powerful of which is the power spectral density (PSP) function. Application of the PSD function to surface statistics introduced the concept of 'bandwidth-limited' roughness, where the value of the RMS roughness depends critically upon the spatial frequency response of the instrument. Different instruments with different spatial frequency response characteristics give different answers when measuring the same surface.

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Eugene L. Church

Papers

Specification of surface figure and finish in terms of system performance

Improvements in the accuracy and the repeatability of long trace profiler measurements.

Specification of glancing- and normal-incidence x-ray mirrors [also Erratum 34(11)3348(Nov1995)]

Light scattering from non-Gaussian surfaces

2D Spatial Frequency Considerations in Comparing 1D Power Spectral Density Measurements