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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 4 — Feb. 13, 2012
  • pp: 4525–4536
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Ultra-precise characterization of LCLS hard X-ray focusing mirrors by high resolution slope measuring deflectometry

Frank Siewert, Jana Buchheim, Sébastien Boutet, Garth J. Williams, Paul A. Montanez, Jacek Krzywinski, and Riccardo Signorato  »View Author Affiliations


Optics Express, Vol. 20, Issue 4, pp. 4525-4536 (2012)
http://dx.doi.org/10.1364/OE.20.004525


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Abstract

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.

© 2012 OSA

1. Introduction

Transport and focusing of photons from a hard X-ray Free Electron Laser (FEL) to an experimental station on a length scale of a few hundred meters is a challenging task as it can result in a significant loss of brilliance and coherence. It requires X-ray optics with optical elements of utmost accuracy. The challenge is extreme for reflective focusing optics as such mirrors should be as long as possible and yet meet the minimum residual figure error requirement. This pushes both optics fabrication (polishing) and associated metrology verification to the very limits of currently available technology. Equally important to mirror polishing quality is manufacturing of a stress-free mount capable of integrating such optics with their high stability positioning system working in UHV environment. The mounting of such ultra-precise optical elements in their holders and in their working geometry is critical as it limits the beamline performance. Thus, the characterization of the optical elements in both the free and the mounted state and in their nominal configuration is of uttermost importance to enable a shape-preserving installation.

2. Measurement of slope deviation by use of the BESSY-NOM-autocollimator

S(x)=tanθ=dy/dx
(1)

h(xk)=h(x0)+m=1kdx2[S(xm)+S(xm1)]
(2)

The residual figure error is obtained after the subtraction of an ideal profile, given by an elliptical fit [26

26. A. Rommeveaux, L. Assoufid, H. Ohashi, H. Mimura, K. Yamauchi, J. Qian, T. Ishikawa, C. Morawe, A. T. Macrander, A. Khounsary, and S. Goto, “Second metrology round-robin of APS, ESRF and SPring-8 laboratories of elliptical and spherical hard-x-ray mirrors,” Proc. SPIE 6704(67040B), 1–12 (2007).

] based on the geometrical parameters as defined by the experimental setup. When using an aperture size of 2mm at the diaphragm the spatial period range covered by NOM is from 2mm to the full mirror length. Virtually any curved, reflective optical shape can be measured by the NOM as long as the slope change is within a ± 5mrad acceptance angle.

A larger slope change along a line of inspection can be measured by use of stitching techniques as long as the local curvature of the surface under test is not stronger than about 5m.

The double CCD array setup of the autocollimator provides a two-axis angle coordinate system (horizontal and vertical) which allows a measurement of a surface under test in face to the side or face up condition by use of the second CCD-array at the same optics head; only a simple change in the beam guiding mirror based penta prism (MBPP) setup is required. This option is realized at the NOM by a dedicated horizontal MBPP which must be aligned at the scanning carriage in order to change the scanning beam path from a vertical to a horizontal reflection, thus allowing to characterize the two mirrors used in a classic KB setup (herafter named Horizontally and Vertically Focusing mirror, HFM and VFM, respectively) in their real operating conditions concerning the relative orientation of the optical surface versus gravity.

3. Ultra-precise diffraction-limited elliptical focusing mirrors – requirements and characterization

A further approach to describe the influence of shape imperfections is given by the Strehl ratio, as it is universally accepted as a measure of the quality of an optical system [28

28. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge 1999).

]. For small wavefront distortions the Strehl ratio can be approximated as [29

29. J. C. Wyant and K. Creath, Basic Wavefront Aberration Theory for Optical Metrology, Applied Optics and Optical Engineering, Vol. XI, Chap. 1,R. Shannon and J. C. Wyant, eds. (Academic Press, Boston, MA, 1992).

]:
II0exp[(2πσrmsλ)2]
(4)
with II0 for the ratio between the achieved peak intensity of the real optic and the ideal peak intensity of a perfect optical system. σrms is the root mean square wavefront distortion in units of length. A Strehl ratio of 0.8 or larger is generally accepted within the X-ray community as the measure of a high quality condensing optical system as it is associated with systems where 80% of the incoming light is found within the central intensity maximum at the focal plane. Using the calculated phase shift of the reflected light by an imperfect optical surface allows one to calculate the surface quality required in order to meet the Strehl ratio criterion of 0.8 which represents an rms wavefront distortion σrms <λ/14. This leads to a condition known as the Maréchal criterion [30

30. A. Maréchal, “Study of the combined effects of diffraction and geometrical aberrations on the image of a luminous point” Rev. Opt. Theor. Instrum. 26, 257 (1947).

] where the root mean square height error over all spatial frequencies present within the residual surface errors is given by hrms.
Δhrmsλ14N2θ
(5)
where N is the number of reflecting surfaces in the system and θ is once again the angle of incidence of the beam being reflected off this surface. Clearly, the requirements on surface quality become linearly more difficult to achieve with decreasing X-ray wavelength, hence the difficult challenge of making hard X-ray reflective optics of the necessary quality. In the case of the CXI instrument, this condition lead to a hrms <1.1 nm figure error requirement at a photon energy of 11 keV, if a single reflecting optic is present in each direction. However, as described in [21

21. S. Boutet and G. J Williams, “The Coherent X-ray Imaging (CXI) instrument at the Linac Coherent, Light Source (LCLS),” New J. Phys. 12(3), 035024 (2010). [CrossRef]

], a set of offset mirrors is always present in the front end of LCLS and there is a total of 3 reflective optics always present in the horizontal (2 offset mirrors and 1 KB mirror). Only one reflective optic is present in the vertical direction. With 3 optical elements in the beam path, the height error requirement becomes as stringent as hrms <0.7 nm on all the optical surfaces at 11 keV. This is an extreme specification for elliptical mirrors of 350 mm length. It is noted here that diffraction limited focussing mirrors manufactured in the past usually had a useful aperture length of less than 100mm. Only recent improvements in metrology and finishing technology made the finishing of the CXI mirrors possible [31

31. T. Kimura, H. Ohashi, H. Mimura, D. Yamakawa, H. Yumoto, S. Matsuyama, T. Tsumura, H. Okada, T. Masunga, Y. Senba, S. Goto, T. Ishikawa, and N. K. Yamauchi, “A stitching fugure profiler of large X-ray mirrors using RADSI for subaperture data acquisition,” Nucl. Instrum. Methods Phys. Rev. A 616, 229–232 (2010). [CrossRef]

]. A specification of hrms <1 nm was deemed achievable when the order for the CXI KB mirror substrates was placed and was thus requested to the optics manufacturer (JTEC Corporation, Osaka, Japan). Bruker ASC GmbH was responsible for the complete design, procurement, manufacturing, integration and testing of the KB system, including optics, UHV mirror holders and positioning mechanics, vacuum system and overall high-stabilizy support. The energy of 11 keV is used here to define the Maréchal criterion since it represents the high energy cutoff of the reflectivity of the CXI KB when coated with SiC, as specified with a 3.4 mrad incidence angle for these mirrors. The CXI instrument is expected to operate primarily in the 4 to 10 keV range when using these KB mirrors. The beam delivered by the LCLS undulators will range in size between 0.75 mm and 2 mm depending on the photon energy when it reaches the CXI mirrors. With the mirrors located 420 m away from the source, a demagnification of the source by a factor of 50 is expected to produce a ~1.5 micron focus at the sample. The collection efficiency of the mirrors is expected to be above 50%, with some losses coming from the overfilling of the 1.18 mm aperture by the larger beam at lower photon energies. The collection efficiency decreases for lower energy, due to a larger beam caused by larger divergence. Each pulse of the LCLS will have approximately 2 mJ of energy delivered in 50 fs or less.

The two elliptical cylinder shaped focusing mirrors under discussion here were manufactured by use of elastic emission machining (EEM) – a deterministic surface finishing technology [32

32. K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, “Figuring with subnanometer-level accuracy by numerically controlled elastic emission machining,” Rev. Sci. Instrum. 73(11), 4028 (2002). [CrossRef]

], developed at Osaka University, Japan. Interferometric sub-aperture stitching metrology [33

33. K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, K. Ueno, K. Endo, A. Souvurov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, “Microstitching interferometry for x-ray reflective optics,” Rev. Sci. Instrum. 74(5), 2894–2898 (2003). [CrossRef]

] was applied by the manufacturer to control the level of figure accuracy achieved during the different steps of deterministic polishing and for the final acceptance tests. The task of the verification in Berlin was to give an independent third-party cross-check of the mirrors shape by use of a different measuring method. Slope measuring deflectometry was used to investigate the shape of the mirrors as delivered by the manufacturer and subsequently to assess the influence of the mirror mount (holder) on the final shape. The aperture for these grazing incidence KB mirrors is 350mm long in meridional direction, while in the sagittal direction only 1-2 mm of the aperture width is used. Thus, a line-scan along the long axis of the mirror allows one to obtain adequate information on the mirror state for the LSFE. The radius of curvature of the two mirrors is ranging from about 4 to 5 km, thus the used angular range on the autocollimator detector is small, about ± 35 µrad only and the impact of inherent systematic error sources coming from the instrument itself is very limited [11

11. F. Siewert, J. Buchheim, T. Zeschke, G. Brenner, S. Kapitzki, and K. Tiedtke, “Sub-nm accuracy metrology for ultra-precise reflective X-ray optics,” Nucl. Instrum. Methods Phys. Rev. A 635, 552–557 (2010).

]. The higher spatial frequency error part was measured in another set of measurements, by use of a White Light Interferometer (WLI), with magnification 2.5x and 20x applied. WLI measurements are a well known standard technique to inspect this part of the figure error budget and thus will not further be discussed here [34

34. J. C. Wyant, “White light interferometry,” Proc. SPIE 4737, 98–107 (2002). [CrossRef]

] (for the measured values see Table 1

Table 1. Shape parameter of the HFM elliptical cylinder mirror, as measured by use of NOM and WLIa.

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and 2

Table 2. Shape parameter of the VFM elliptical cylinder mirror, as measured by use of NOM and WLIb.

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).

Due to the extremely challenging requirements for the residual figure error of 1nm rms for the optics in the mounted state, the mirrors were measured under three different conditions (see also Table 1 and 2 for the detailed mirror specification). First both mirrors were supported by a cloth on a flat surface, providing full contact to the underside of the optic with evenly distributed loads. Then the mirrors were placed in their respective mechanical holders and measured in the free (mirrors simply resting on three spherical support points located at the Bessel points) and clamped (with all contact point between the mirror and the holder fully locked) state, in face up condition for the vertically focusing mirror (VFM) and face to the side for the horizontally focusing mirror (HFM), see Fig. 3
Fig. 3 left: - the VFM in the mounted state in face up position during measurement; right: - the HFM in the mounted state during measurement in face to the side condition.
.

4. Measurement results

The measurement results show that both mirrors are fully compliant with the specifications in the mounted state, see Table 1 and 2. In case of the HFM no significant change of the mirror shape occurred comparing the face up (on a cloth) and the face to the side state, see Fig. 4
Fig. 4 HFM profiles of residual slope error after subtraction of a best fit ellipse for free state face up and face to side state free and clamped in the mechanics. The measurement in the face up state was performed with dx = 0.5 mm increments, averaging 20 scans forward and backward. The measurements in face to side condition were performed with dx = 0.2 mm increments, averaging 12 scans in the free state and 39 scans forward and backward in clamped state. For better visualization a shift was added to the profiles of the face to side measurements.
and 5
Fig. 5 Mirror HFM profiles of residual height corresponding to the profiles of residual slope shown in Fig. 4.
. The residual figure error is 0.57 nm rms / 2.5 nm pv for the free standing (cloth-supported) and face up state. While the mounted state in face to the side condition shows 0.68 nm rms / 2.8 nm pv.

These values correspond to a residual slope error of 0.056 µrad rms (free) and 0.047 µrad rms (in the mounted state). To achieve a residual figure error of < 1nm rms the VFM got a dedicated pre-figuring to compensate the deformation of the mirror blank caused by gravitation under the designed mechanical support scheme. For the VFM a change in the order of a factor of 2 for the residual figure error can be considered due to gravity alone. The free state (cloth-supported) of the VFM in the face up measurement shows a residual figure error of 1.8 nm rms, see Fig. 6
Fig. 6 VFM - profiles of residual height for the free state on a cloth and the free and clamped state in the mechanics at the centre line of the useful aperture.
. Then a figure error of 0.9 nm rms was found in the mounted state (mirror supported at the Bessel points), face up in the mechanical holder. The corresponding values for the residual slope error are 0.066 µrad rms (free) and at 0.061 µrad rms in the mounted state, see Fig. 7
Fig. 7 VFM profiles of residual slope in the clamped state in the mechanic (face up condition). The measurements were taken in upstream – downstream and downstream – upstream direction at the centre line of the aperture. The agreement of both measurements is 0.04 μrad rms For better visualization a shift was added to the downstream – upstream measurement and the plot of the difference.
. A more sophisticated option to evaluate the quality of the surface finishing is to transform the obtained height profiles into a one dimensional PSD [35

35. E. L. Church and P. Z. Takacs, “Specification of surface figure and finish in terms of system performance,” Appl. Opt. 32(19), 3344–3353 (1993). [CrossRef] [PubMed]

37

37. V. V. Yashchuk, E. M. Gullikson, M. R. Howells, S. C. Irick, A. A. MacDowell, W. R. McKinney, F. Salmassi, T. Warwick, J. P. Metz, and T. W. Tonnessen, “Surface roughness of stainless-steel mirrors for focusing soft x rays,” Appl. Opt. 45(20), 4833–4842 (2006). [CrossRef] [PubMed]

]. Figure 8
Fig. 8 Comparison of 1-dimensional PSD curves for the HFM and VFM made by EEM finishing technology (measurements for the state on the mechanic) with an ellipsoidal focussing mirror made by classical polishing technology.
shows the PSD-curves for the HFM and the VFM (in the mounted state) in comparison with the PSD-curve of an ellipsoidal focussing mirror manufactured by classical polishing technology. This mirror is characterized by a residual slope error of about 1.5 µrad rms on a length of 490 mm [38

38. M. Bowler, F. Siewert, B. Faatz, and K. Tiedtke, “Investigating the effect of mirror imperfections in photon transport systems for FEL`s”, Proceedings of the FEL2009, Liverpool, UK (2009).

] – for the PSD comparison a reduced section of 350mm in length was chosen. The classical polishing causes a characteristic fingerprint of certain spatial frequencies like in the range of 3-5 mm and of further longer spatial frequency too (e.g. some 10 mm - see Fig. 8). The curves for the HFM and the VFM demonstrate that these specific shape deviations do not appear due to the deterministic surface finishing applied. In the case of the VFM a further cross check along the line of inspection was carried out to validate the reproducibility of the measurement as well as the achieved accuracy of the residual slope. The mirror was measured face up in the clamped state along the centre line in upstream – downstream and after a 180° horizontal flipping in downstream – upstream direction. Comparing the achieved results an agreement of 0.04 μrad rms was found. This value can be assumed as the estimated accuracy for the measured residual slope deviation. The contribution of random noise in both measurements is at approximately the same level. Thus, both measurements can be averaged, which allows to suppress parts of the systematic error on the measurement [39

39. V. V. Yashchuk, “Optimal measurement strategies for effective suppression of drift errors,” Rev. Sci. Instrum. 80(11), 115101 (2009). [CrossRef] [PubMed]

], and a residual slope error of 0.056 μrad rms can then be achieved for the VFM in the clamped state (see also Table 2).

5. Shape preservation and mechanical mounting of optical elements – a critical issue

In the case of ultra precise optical elements their mechanical holder and clamping could easily cause system performance limiting shape deformations. Our measurements have shown that even a minor change in the mirror shape can be detected after fastening the clamping screws (see Fig. 5 and 6). This important issue needs to be to considered and kept strictly under control for a shape preserving installation of such high performance optical elements at a beamline in general.

To demonstrate this problem we report a test measurement of the VFM. Figure 9
Fig. 9 VFM – profiles of residual height for the free in the mechanic and clamped in the mechanic state – showing the impact of miss-clamping in meridional direction
shows a comparison of different states of the mirror as inspected by use of the NOM. Our measurements clearly show that at the extreme level of accuracy of these optics, inappropriate clamping forces can easily cause a significant shape deformation, see Fig. 9 (for this demonstration the same ellipse fit parameters were used as for the final mounted state). In this specific case the specified acceptable figure error of hrms < 1 nm would clearly not be met with excessive meridional clamping forces applied. This represents a simple but eplicit demonstration that optics and mechanics together have to be understood and tested as a unit. Thus the mounting supported by precise metrology instrumentation is mandatory.

6. Concluding remarks

The results presented here have shown that even extreme requirements for diffraction limited focusing optics such as < 1nm rms figure error are realistic to be manufactured and, very importantly, can also be obtained with the mounted optics. Deterministic surface finishing technology allows to provide sub-nanometer rms accuracy on the entire range from low to high spatial frequency for mirrors up to 350mm in length.

High resolution slope measuring deflectometry allows accurate inspection of ultra-precise optical elements in the free state as well as in the mounted state with sub nm accuracy. Optical elements can be inspected for both orientations, in the face up and face to the side condition if an autocollimator and an adaptive based penta prism (MBPP) are used to perform slope measurements.

It was shown that gravitational effects on the mirror shape can be compensated if advanced metrology and deterministic surface finishing technique is applied to figure the mirror shape. The clamping of optics was shown to be a critical step for the final installation of such optics. A mis-clamping could cause changes in the range of the long spatial figure error. This can be easily identified by NOM slope measurements and thus optimized.

Acknowledgments

This work was partly funded by the LCLS Ultrafast Science Instrument (LUSI) major item of equipment project, which provided funding from the U.S. Department of Energy – Basic Energy Science for the construction of three hard X-ray instruments at LCLS. Portions of this research were carried out at the Linac Coherent Light Source (LCLS) at the SLAC National Accelerator Laboratory. LCLS is an Office of Science User Facility operated for the U.S. Department of Energy Office of Science by Stanford University. Design, procurement, manufacturing, testing and installation of the CXI KB1 system has been fully performed by Bruker ASC GmbH, in the framework of subcontract 80060 issued by the Leland Stanford Jr. University, Menlo Park, CA. The authors would like to thank JTEC Corp., Kobe, Japan for excellent work on the mirror finishing.

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E. L. Church and P. Z. Takacs, “Specification of surface figure and finish in terms of system performance,” Appl. Opt. 32(19), 3344–3353 (1993). [CrossRef] [PubMed]

36.

E. L. Church and P. Z. Takacs, “Specification of glancing- and normal-incidence X-ray mirrors,” Opt. Eng. 34(2), 353–360 (1995). [CrossRef]

37.

V. V. Yashchuk, E. M. Gullikson, M. R. Howells, S. C. Irick, A. A. MacDowell, W. R. McKinney, F. Salmassi, T. Warwick, J. P. Metz, and T. W. Tonnessen, “Surface roughness of stainless-steel mirrors for focusing soft x rays,” Appl. Opt. 45(20), 4833–4842 (2006). [CrossRef] [PubMed]

38.

M. Bowler, F. Siewert, B. Faatz, and K. Tiedtke, “Investigating the effect of mirror imperfections in photon transport systems for FEL`s”, Proceedings of the FEL2009, Liverpool, UK (2009).

39.

V. V. Yashchuk, “Optimal measurement strategies for effective suppression of drift errors,” Rev. Sci. Instrum. 80(11), 115101 (2009). [CrossRef] [PubMed]

OCIS Codes
(120.3940) Instrumentation, measurement, and metrology : Metrology
(140.2600) Lasers and laser optics : Free-electron lasers (FELs)
(340.0340) X-ray optics : X-ray optics

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: September 6, 2011
Revised Manuscript: October 20, 2011
Manuscript Accepted: October 26, 2011
Published: February 9, 2012

Citation
Frank Siewert, Jana Buchheim, Sébastien Boutet, Garth J. Williams, Paul A. Montanez, Jacek Krzywinski, and Riccardo Signorato, "Ultra-precise characterization of LCLS hard X-ray focusing mirrors by high resolution slope measuring deflectometry," Opt. Express 20, 4525-4536 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-4525


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References

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