Design of an elliptically bent refocus mirror for the MERLIN beamline at the advanced light source

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Abstract

There is an increasing demand for well-focused beam with high quality imaging of the full field to further explore the potential of novel instruments. For beamlines operating at focal point, mechanical benders have often been used to shape the refocusing mirror into an ideal elliptical cylinder. Unfortunately, the limited number of couplings for these mechanisms requires specific substrate side-shaping, often calculated using beam bending theory [J.H. Underwood, Space Sci. Instrum. 3 (1977) 259; M. Howells et al., Opt. Eng. 39 (2000) 2748; T. Warwick et al., Document available at OSTI website: http://www.osti.gov/energycitations/servlets/purl/842557-JYZCS3/native/], to meet demanding figure requirements. Here, we use finite element analysis (FEA) to validate the side-shaping algorithm and then couple the output with SHADOW to evaluate mirror performance when an ideal ellipse is not achieved.

Introduction

There are many techniques available to obtain a well-focused beam by creating an ideal elliptical shape with the source and image points at the foci [1], [2], [3], [4]. Differential polishing, differential deposition, and mechanical benders are three examples of available technologies. Cost, configuration, operation and figure requirements are generally balanced in determining which method is appropriate for a specific application. For beamlines operating at focal point, mechanical benders have been widely utilized due to their low cost and high reliability. These systems take advantage of the ability to fabricate high quality flat optics and relatively simple bender mechanisms to accurately form elliptical profiles. Unfortunately, the limited number of couplings for these mechanisms require specific substrate side shaping, often calculated using beam bending theory [1], [2], [3], to meet demanding figure requirements.

However, the current requirements for high quality, full field, focused beams have led to us to examine the validity of the basic kinematic assumptions of the Euler–Bernoulli hypothesis for large and highly varied curvatures. Additionally, the extremely demanding figure tolerances (∼1–5 μrad) of the MERLIN beamline optics necessitated the development of a methodology for rational design and performance evaluation of X-ray optics. Here we propose to use finite element analysis (FEA) to both confirm the validity of the beam theory based algorithm used for side shaping and then couple the output with the ray-tracing program SHADOW® [5] to provide a basis for establishing mirror tolerances and performance implications.

Section snippets

Mirror width design and finite element analysis

The refocus optics for the MERLIN beamline at the Advanced Light Source have a curvature ranging from ∼0.07 to ∼0.14 m−1 that severely limits substrate material options. Specifically, these small radii prohibit the use of polished Silicon and have necessitated the choice of a metal substrate. Based on discussions with optic vendors, a 4-mm thick 17-4PH stainless steel substrate was selected. However, this geometry is severely affected by gravity and therefore it is desirable to compensate for

Example: MERLIN mirror M323

As an example of this approach, we show the results from the RIXS endstation vertical refocus optic (M323) of the meV-resolution beamline (MERLIN) at the Advanced Light Source. Fig. 1 shows the geometric configuration of the refocus scheme (inset) as well the difference in surface profile along the centerline between the ideal ellipse and the FEA simulated results. Deviations on the order of 0.1 μm are visible at the ends and are likely due to the simplified constraints in the FEA model. This

Summary

In summary, FEA not only validates the proposed application of beam bending theory in the mirror width design, but when coupled with SHADOW also provides a dynamic tool for thorough investigation of beamline performance before the actual hardware is designed or fabricated. Additionally, this process enables deterministic design modifications to the assembly if the ideal elliptical profile is not achieved.

Acknowledgment

The Advanced Light Source is operated by the Office of Basic Energy Sciences (BES), U.S. Department of Energy (DOE) with contract no. DE-AC03-76SF00098 at LBNL.

References (11)

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    Space Sci. Instrum.

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    J. Synchrotron Rad.

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  • SHADOW ray-tracing code was developed by Center for Nanotechnology (CNTech), See...
There are more references available in the full text version of this article.

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