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

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2010 (10)

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, T. Noll, and H. Lammert, “The Diamond-NOM: A non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 224–228 (2010).
[CrossRef]

V. V. Yashchuk, S. Barber, E. E. Domning, J. L. Kirschman, G. Y. Morrison, B. V. Smith, F. Siewert, T. Zeschke, R. Geckler, and A. Just, “Sub-microradian surface slope metrology with the ALS Developmental Long Trace Profiler,” Nucl. Instrum. Meth. A 616(2-3), 212–223 (2010).
[CrossRef]

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).

F. Siewert, J. Buchheim, and T. Zeschke, “Characterization and calibration of 2nd generation slope measuring profiler,” Nucl. Instrum. Methods Phys. Rev. A 616, 119–127 (2010).
[CrossRef]

R. D. Geckeler, A. Just, M. Krause, and V. V. Yashchuk, “Autocollimators for deflectometry: Current status and future progress,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 140–146 (2010).
[CrossRef]

F. Siewert, R. Reininger, M. Rübhausen, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A KB-Focusing Mirror Pair for a VUV-Raman Spectrometer at FLASH-Mirror Metrology and Ray Tracing Results,” AIP Conf. Proc. 1234, 752–755 (2010).
[CrossRef]

S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krüger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, T. Salditt, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “The holography endstation of beamline P10 at PETRA III,” AIP Conf. Proc. 1234, 433–436 (2010).
[CrossRef]

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]

D. Cocco, G. Bartoletto, R. Sergo, G. Sostero, and I. Cudin, “A hybride active optical system for wave front preservation and available focal distance,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 128–133 (2010).
[CrossRef]

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]

2009 (3)

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

L. Samoylova, H. Sinn, F. Siewert, H. Mimura, K. Yamauchi, and T. Tschentscher, “Requirements on hard x-ray grazing incidence optics for European XFEL: analysis and simulation of wavefront transformations,” Proc. SPIE 7360, 1–9 (2009).

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 1457, 1–4 (2009).

2007 (2)

V. Yashchuk, W. McKinney, T. Warwick, T. Noll, F. Siewert, T. Zeschke, and R. Geckeler, “Proposal for a Universal Test Mirror for Characterization of Slope Measuring Instruments,” Advances in Metrology for X-Ray and EUV Optics II, Proc. of SPIE 6704, 4–16 (2007).

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).

2006 (1)

2004 (1)

F. Siewert, T. Noll, T. Schlegel, T. Zeschke, and H. Lammert, “The Nanometer Optical Component Measuring machine: a new Sub-nm Topography Measuring Device for X-ray Optics at BESSY,” AIP Conf. Proc. 705, 847–850 (2004).
[CrossRef]

2003 (1)

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]

2002 (3)

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

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]

R. D. Geckeler and I. Weingärtner, “Sub-nm topography measurement by deflectometry: flatness standard and wafer nanotopography,” Proc. SPIE 4779, 1–12 (2002).
[CrossRef]

1999 (1)

I. Weingärtner, M. Schulz, and C. Elster, “Novel scanning technique for ultra-precise measurement of topography”, in “Optical Manufacturing and Testing III,” Proc. SPIE 3782, 306–317 (1999).

1997 (1)

R. Signorato and M. Sanchez del Rio, “Structured slope errors on real x-ray mirrors: Ray tracing versus Experiment,” Proc. SPIE 3152, 136–147 (1997).
[CrossRef]

1995 (1)

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

1993 (1)

1992 (1)

S. C. Irick, “Determining surface profile from sequential interference patterns from a long tracer profiler,” Rev. Sci. Instrum. 63(1), 1432–1435 (1992).
[CrossRef]

1987 (1)

P. Takacs, S. N. Qian, and J. Colbert, “Design of a long trace surface profiler,” Proc. SPIE 749, 59–64 (1987).

1982 (1)

K. von Bieren, “Pencil beam interferometer for aspheric optical surfaces,” Proc. SPIE 343, 101–108 (1982).

1979 (1)

E. Debler and K. Zander, “Ebenheitsmessung an optischen Planflächen mit Autokollimationsfernrohr und Pentagonprisma“, PTB Mitteilungen Forschen + Prüfen,” Amts und Mitteilungsblatt der Physikalisch Technischen Bundesanstalt, Braunschweig und Berlin 89, 339–349 (1979).

1947 (1)

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).

Alcock, S. G.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, T. Noll, and H. Lammert, “The Diamond-NOM: A non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 224–228 (2010).
[CrossRef]

Assoufid, L.

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).

Baez, A.V.

P. Kirkpatrick and A.V. Baez, “Formation of optical images by X-rays”, J. Opt.Soc. Am.38(9), 766–773 (1948).

Barber, S.

V. V. Yashchuk, S. Barber, E. E. Domning, J. L. Kirschman, G. Y. Morrison, B. V. Smith, F. Siewert, T. Zeschke, R. Geckler, and A. Just, “Sub-microradian surface slope metrology with the ALS Developmental Long Trace Profiler,” Nucl. Instrum. Meth. A 616(2-3), 212–223 (2010).
[CrossRef]

Bartels, M.

S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krüger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, T. Salditt, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “The holography endstation of beamline P10 at PETRA III,” AIP Conf. Proc. 1234, 433–436 (2010).
[CrossRef]

Bartoletto, G.

D. Cocco, G. Bartoletto, R. Sergo, G. Sostero, and I. Cudin, “A hybride active optical system for wave front preservation and available focal distance,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 128–133 (2010).
[CrossRef]

Boutet, S.

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]

Brenner, G.

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).

Buchheim, J.

F. Siewert, J. Buchheim, and T. Zeschke, “Characterization and calibration of 2nd generation slope measuring profiler,” Nucl. Instrum. Methods Phys. Rev. A 616, 119–127 (2010).
[CrossRef]

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).

Church, E. L.

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

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]

Cocco, D.

D. Cocco, G. Bartoletto, R. Sergo, G. Sostero, and I. Cudin, “A hybride active optical system for wave front preservation and available focal distance,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 128–133 (2010).
[CrossRef]

Colbert, J.

P. Takacs, S. N. Qian, and J. Colbert, “Design of a long trace surface profiler,” Proc. SPIE 749, 59–64 (1987).

Cudin, I.

D. Cocco, G. Bartoletto, R. Sergo, G. Sostero, and I. Cudin, “A hybride active optical system for wave front preservation and available focal distance,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 128–133 (2010).
[CrossRef]

Debler, E.

E. Debler and K. Zander, “Ebenheitsmessung an optischen Planflächen mit Autokollimationsfernrohr und Pentagonprisma“, PTB Mitteilungen Forschen + Prüfen,” Amts und Mitteilungsblatt der Physikalisch Technischen Bundesanstalt, Braunschweig und Berlin 89, 339–349 (1979).

Domning, E. E.

V. V. Yashchuk, S. Barber, E. E. Domning, J. L. Kirschman, G. Y. Morrison, B. V. Smith, F. Siewert, T. Zeschke, R. Geckler, and A. Just, “Sub-microradian surface slope metrology with the ALS Developmental Long Trace Profiler,” Nucl. Instrum. Meth. A 616(2-3), 212–223 (2010).
[CrossRef]

Elster, C.

I. Weingärtner, M. Schulz, and C. Elster, “Novel scanning technique for ultra-precise measurement of topography”, in “Optical Manufacturing and Testing III,” Proc. SPIE 3782, 306–317 (1999).

Endo, K.

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]

Garrett, R.

S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krüger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, T. Salditt, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “The holography endstation of beamline P10 at PETRA III,” AIP Conf. Proc. 1234, 433–436 (2010).
[CrossRef]

F. Siewert, R. Reininger, M. Rübhausen, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A KB-Focusing Mirror Pair for a VUV-Raman Spectrometer at FLASH-Mirror Metrology and Ray Tracing Results,” AIP Conf. Proc. 1234, 752–755 (2010).
[CrossRef]

Geckeler, R.

V. Yashchuk, W. McKinney, T. Warwick, T. Noll, F. Siewert, T. Zeschke, and R. Geckeler, “Proposal for a Universal Test Mirror for Characterization of Slope Measuring Instruments,” Advances in Metrology for X-Ray and EUV Optics II, Proc. of SPIE 6704, 4–16 (2007).

Geckeler, R. D.

R. D. Geckeler, A. Just, M. Krause, and V. V. Yashchuk, “Autocollimators for deflectometry: Current status and future progress,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 140–146 (2010).
[CrossRef]

R. D. Geckeler and I. Weingärtner, “Sub-nm topography measurement by deflectometry: flatness standard and wafer nanotopography,” Proc. SPIE 4779, 1–12 (2002).
[CrossRef]

Geckler, R.

V. V. Yashchuk, S. Barber, E. E. Domning, J. L. Kirschman, G. Y. Morrison, B. V. Smith, F. Siewert, T. Zeschke, R. Geckler, and A. Just, “Sub-microradian surface slope metrology with the ALS Developmental Long Trace Profiler,” Nucl. Instrum. Meth. A 616(2-3), 212–223 (2010).
[CrossRef]

Gentle, I.

F. Siewert, R. Reininger, M. Rübhausen, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A KB-Focusing Mirror Pair for a VUV-Raman Spectrometer at FLASH-Mirror Metrology and Ray Tracing Results,” AIP Conf. Proc. 1234, 752–755 (2010).
[CrossRef]

S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krüger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, T. Salditt, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “The holography endstation of beamline P10 at PETRA III,” AIP Conf. Proc. 1234, 433–436 (2010).
[CrossRef]

Giewekemeyer, K.

S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krüger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, T. Salditt, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “The holography endstation of beamline P10 at PETRA III,” AIP Conf. Proc. 1234, 433–436 (2010).
[CrossRef]

Goto, S.

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. 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).

Gullikson, E. M.

Handa, S.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 1457, 1–4 (2009).

Hartmann, B.

S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krüger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, T. Salditt, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “The holography endstation of beamline P10 at PETRA III,” AIP Conf. Proc. 1234, 433–436 (2010).
[CrossRef]

Howells, M. R.

Inagaki, K.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 1457, 1–4 (2009).

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]

Irick, S. C.

Ishikawa, T.

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]

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 1457, 1–4 (2009).

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).

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).
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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).
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Just, A.

R. D. Geckeler, A. Just, M. Krause, and V. V. Yashchuk, “Autocollimators for deflectometry: Current status and future progress,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 140–146 (2010).
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V. V. Yashchuk, S. Barber, E. E. Domning, J. L. Kirschman, G. Y. Morrison, B. V. Smith, F. Siewert, T. Zeschke, R. Geckler, and A. Just, “Sub-microradian surface slope metrology with the ALS Developmental Long Trace Profiler,” Nucl. Instrum. Meth. A 616(2-3), 212–223 (2010).
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Kalbfleisch, S.

S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krüger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, T. Salditt, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “The holography endstation of beamline P10 at PETRA III,” AIP Conf. Proc. 1234, 433–436 (2010).
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Kapitzki, S.

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).

Khounsary, A.

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).

Kimura, T.

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]

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 1457, 1–4 (2009).

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P. Kirkpatrick and A.V. Baez, “Formation of optical images by X-rays”, J. Opt.Soc. Am.38(9), 766–773 (1948).

Kirschman, J. L.

V. V. Yashchuk, S. Barber, E. E. Domning, J. L. Kirschman, G. Y. Morrison, B. V. Smith, F. Siewert, T. Zeschke, R. Geckler, and A. Just, “Sub-microradian surface slope metrology with the ALS Developmental Long Trace Profiler,” Nucl. Instrum. Meth. A 616(2-3), 212–223 (2010).
[CrossRef]

Krause, M.

R. D. Geckeler, A. Just, M. Krause, and V. V. Yashchuk, “Autocollimators for deflectometry: Current status and future progress,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 140–146 (2010).
[CrossRef]

Krüger, S. P.

S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krüger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, T. Salditt, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “The holography endstation of beamline P10 at PETRA III,” AIP Conf. Proc. 1234, 433–436 (2010).
[CrossRef]

Lammert, H.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, T. Noll, and H. Lammert, “The Diamond-NOM: A non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 224–228 (2010).
[CrossRef]

F. Siewert, T. Noll, T. Schlegel, T. Zeschke, and H. Lammert, “The Nanometer Optical Component Measuring machine: a new Sub-nm Topography Measuring Device for X-ray Optics at BESSY,” AIP Conf. Proc. 705, 847–850 (2004).
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Leupold, O.

S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krüger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, T. Salditt, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “The holography endstation of beamline P10 at PETRA III,” AIP Conf. Proc. 1234, 433–436 (2010).
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MacDowell, A. A.

Macrander, A. T.

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).

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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).

Masunga, T.

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).
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Matsuyama, S.

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).
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H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 1457, 1–4 (2009).

McKinney, W.

V. Yashchuk, W. McKinney, T. Warwick, T. Noll, F. Siewert, T. Zeschke, and R. Geckeler, “Proposal for a Universal Test Mirror for Characterization of Slope Measuring Instruments,” Advances in Metrology for X-Ray and EUV Optics II, Proc. of SPIE 6704, 4–16 (2007).

McKinney, W. R.

Metz, J. P.

Mimura, H.

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]

L. Samoylova, H. Sinn, F. Siewert, H. Mimura, K. Yamauchi, and T. Tschentscher, “Requirements on hard x-ray grazing incidence optics for European XFEL: analysis and simulation of wavefront transformations,” Proc. SPIE 7360, 1–9 (2009).

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 1457, 1–4 (2009).

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).

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]

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]

Morawe, C.

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).

Mori, Y.

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]

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]

Morrison, G. Y.

V. V. Yashchuk, S. Barber, E. E. Domning, J. L. Kirschman, G. Y. Morrison, B. V. Smith, F. Siewert, T. Zeschke, R. Geckler, and A. Just, “Sub-microradian surface slope metrology with the ALS Developmental Long Trace Profiler,” Nucl. Instrum. Meth. A 616(2-3), 212–223 (2010).
[CrossRef]

Neubauer, H.

S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krüger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, T. Salditt, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “The holography endstation of beamline P10 at PETRA III,” AIP Conf. Proc. 1234, 433–436 (2010).
[CrossRef]

Nishino, Y.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 1457, 1–4 (2009).

Noll, T.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, T. Noll, and H. Lammert, “The Diamond-NOM: A non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 224–228 (2010).
[CrossRef]

V. Yashchuk, W. McKinney, T. Warwick, T. Noll, F. Siewert, T. Zeschke, and R. Geckeler, “Proposal for a Universal Test Mirror for Characterization of Slope Measuring Instruments,” Advances in Metrology for X-Ray and EUV Optics II, Proc. of SPIE 6704, 4–16 (2007).

F. Siewert, T. Noll, T. Schlegel, T. Zeschke, and H. Lammert, “The Nanometer Optical Component Measuring machine: a new Sub-nm Topography Measuring Device for X-ray Optics at BESSY,” AIP Conf. Proc. 705, 847–850 (2004).
[CrossRef]

Nugent, K.

F. Siewert, R. Reininger, M. Rübhausen, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A KB-Focusing Mirror Pair for a VUV-Raman Spectrometer at FLASH-Mirror Metrology and Ray Tracing Results,” AIP Conf. Proc. 1234, 752–755 (2010).
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S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krüger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, T. Salditt, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “The holography endstation of beamline P10 at PETRA III,” AIP Conf. Proc. 1234, 433–436 (2010).
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Ohashi, H.

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. 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).

Okada, H.

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).
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S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krüger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, T. Salditt, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “The holography endstation of beamline P10 at PETRA III,” AIP Conf. Proc. 1234, 433–436 (2010).
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Pedersen, U.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, T. Noll, and H. Lammert, “The Diamond-NOM: A non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 224–228 (2010).
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Qian, J.

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).

Qian, S. N.

P. Takacs, S. N. Qian, and J. Colbert, “Design of a long trace surface profiler,” Proc. SPIE 749, 59–64 (1987).

Reininger, R.

F. Siewert, R. Reininger, M. Rübhausen, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A KB-Focusing Mirror Pair for a VUV-Raman Spectrometer at FLASH-Mirror Metrology and Ray Tracing Results,” AIP Conf. Proc. 1234, 752–755 (2010).
[CrossRef]

Rommeveaux, A.

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).

Rübhausen, M.

F. Siewert, R. Reininger, M. Rübhausen, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A KB-Focusing Mirror Pair for a VUV-Raman Spectrometer at FLASH-Mirror Metrology and Ray Tracing Results,” AIP Conf. Proc. 1234, 752–755 (2010).
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Saito, A.

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]

Salditt, T.

S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krüger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, T. Salditt, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “The holography endstation of beamline P10 at PETRA III,” AIP Conf. Proc. 1234, 433–436 (2010).
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Salmassi, F.

Samoylova, L.

L. Samoylova, H. Sinn, F. Siewert, H. Mimura, K. Yamauchi, and T. Tschentscher, “Requirements on hard x-ray grazing incidence optics for European XFEL: analysis and simulation of wavefront transformations,” Proc. SPIE 7360, 1–9 (2009).

Sanchez del Rio, M.

R. Signorato and M. Sanchez del Rio, “Structured slope errors on real x-ray mirrors: Ray tracing versus Experiment,” Proc. SPIE 3152, 136–147 (1997).
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H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 1457, 1–4 (2009).

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).
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Sawhney, K. J. S.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, T. Noll, and H. Lammert, “The Diamond-NOM: A non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 224–228 (2010).
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Schlegel, T.

F. Siewert, T. Noll, T. Schlegel, T. Zeschke, and H. Lammert, “The Nanometer Optical Component Measuring machine: a new Sub-nm Topography Measuring Device for X-ray Optics at BESSY,” AIP Conf. Proc. 705, 847–850 (2004).
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I. Weingärtner, M. Schulz, and C. Elster, “Novel scanning technique for ultra-precise measurement of topography”, in “Optical Manufacturing and Testing III,” Proc. SPIE 3782, 306–317 (1999).

Scott, S.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, T. Noll, and H. Lammert, “The Diamond-NOM: A non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 224–228 (2010).
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Senba, Y.

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).
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D. Cocco, G. Bartoletto, R. Sergo, G. Sostero, and I. Cudin, “A hybride active optical system for wave front preservation and available focal distance,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 128–133 (2010).
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S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krüger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, T. Salditt, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “The holography endstation of beamline P10 at PETRA III,” AIP Conf. Proc. 1234, 433–436 (2010).
[CrossRef]

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, T. Noll, and H. Lammert, “The Diamond-NOM: A non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 224–228 (2010).
[CrossRef]

V. V. Yashchuk, S. Barber, E. E. Domning, J. L. Kirschman, G. Y. Morrison, B. V. Smith, F. Siewert, T. Zeschke, R. Geckler, and A. Just, “Sub-microradian surface slope metrology with the ALS Developmental Long Trace Profiler,” Nucl. Instrum. Meth. A 616(2-3), 212–223 (2010).
[CrossRef]

F. Siewert, R. Reininger, M. Rübhausen, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A KB-Focusing Mirror Pair for a VUV-Raman Spectrometer at FLASH-Mirror Metrology and Ray Tracing Results,” AIP Conf. Proc. 1234, 752–755 (2010).
[CrossRef]

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).

F. Siewert, J. Buchheim, and T. Zeschke, “Characterization and calibration of 2nd generation slope measuring profiler,” Nucl. Instrum. Methods Phys. Rev. A 616, 119–127 (2010).
[CrossRef]

L. Samoylova, H. Sinn, F. Siewert, H. Mimura, K. Yamauchi, and T. Tschentscher, “Requirements on hard x-ray grazing incidence optics for European XFEL: analysis and simulation of wavefront transformations,” Proc. SPIE 7360, 1–9 (2009).

V. Yashchuk, W. McKinney, T. Warwick, T. Noll, F. Siewert, T. Zeschke, and R. Geckeler, “Proposal for a Universal Test Mirror for Characterization of Slope Measuring Instruments,” Advances in Metrology for X-Ray and EUV Optics II, Proc. of SPIE 6704, 4–16 (2007).

F. Siewert, T. Noll, T. Schlegel, T. Zeschke, and H. Lammert, “The Nanometer Optical Component Measuring machine: a new Sub-nm Topography Measuring Device for X-ray Optics at BESSY,” AIP Conf. Proc. 705, 847–850 (2004).
[CrossRef]

Signorato, R.

R. Signorato and M. Sanchez del Rio, “Structured slope errors on real x-ray mirrors: Ray tracing versus Experiment,” Proc. SPIE 3152, 136–147 (1997).
[CrossRef]

Sinn, H.

L. Samoylova, H. Sinn, F. Siewert, H. Mimura, K. Yamauchi, and T. Tschentscher, “Requirements on hard x-ray grazing incidence optics for European XFEL: analysis and simulation of wavefront transformations,” Proc. SPIE 7360, 1–9 (2009).

Smith, B. V.

V. V. Yashchuk, S. Barber, E. E. Domning, J. L. Kirschman, G. Y. Morrison, B. V. Smith, F. Siewert, T. Zeschke, R. Geckler, and A. Just, “Sub-microradian surface slope metrology with the ALS Developmental Long Trace Profiler,” Nucl. Instrum. Meth. A 616(2-3), 212–223 (2010).
[CrossRef]

Sostero, G.

D. Cocco, G. Bartoletto, R. Sergo, G. Sostero, and I. Cudin, “A hybride active optical system for wave front preservation and available focal distance,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 128–133 (2010).
[CrossRef]

Souvurov, A.

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]

Sprung, M.

S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krüger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, T. Salditt, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “The holography endstation of beamline P10 at PETRA III,” AIP Conf. Proc. 1234, 433–436 (2010).
[CrossRef]

Takacs, P.

P. Takacs, S. N. Qian, and J. Colbert, “Design of a long trace surface profiler,” Proc. SPIE 749, 59–64 (1987).

Takacs, P. Z.

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

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]

Tamasaku, K.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 1457, 1–4 (2009).

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]

Tiedtke, K.

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).

Tonnessen, T. W.

Tschentscher, T.

L. Samoylova, H. Sinn, F. Siewert, H. Mimura, K. Yamauchi, and T. Tschentscher, “Requirements on hard x-ray grazing incidence optics for European XFEL: analysis and simulation of wavefront transformations,” Proc. SPIE 7360, 1–9 (2009).

Tsumura, T.

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]

Ueno, K.

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]

von Bieren, K.

K. von Bieren, “Pencil beam interferometer for aspheric optical surfaces,” Proc. SPIE 343, 101–108 (1982).

Walton, R.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, T. Noll, and H. Lammert, “The Diamond-NOM: A non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 224–228 (2010).
[CrossRef]

Warwick, T.

V. Yashchuk, W. McKinney, T. Warwick, T. Noll, F. Siewert, T. Zeschke, and R. Geckeler, “Proposal for a Universal Test Mirror for Characterization of Slope Measuring Instruments,” Advances in Metrology for X-Ray and EUV Optics II, Proc. of SPIE 6704, 4–16 (2007).

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]

Weingärtner, I.

R. D. Geckeler and I. Weingärtner, “Sub-nm topography measurement by deflectometry: flatness standard and wafer nanotopography,” Proc. SPIE 4779, 1–12 (2002).
[CrossRef]

I. Weingärtner, M. Schulz, and C. Elster, “Novel scanning technique for ultra-precise measurement of topography”, in “Optical Manufacturing and Testing III,” Proc. SPIE 3782, 306–317 (1999).

Wilkins, S.

S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krüger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, T. Salditt, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “The holography endstation of beamline P10 at PETRA III,” AIP Conf. Proc. 1234, 433–436 (2010).
[CrossRef]

F. Siewert, R. Reininger, M. Rübhausen, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A KB-Focusing Mirror Pair for a VUV-Raman Spectrometer at FLASH-Mirror Metrology and Ray Tracing Results,” AIP Conf. Proc. 1234, 752–755 (2010).
[CrossRef]

Wyant, J. C.

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

Yabashi, M.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 1457, 1–4 (2009).

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]

Yamakawa, D.

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]

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 1457, 1–4 (2009).

Yamamura, K.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 1457, 1–4 (2009).

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]

Yamauchi, K.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 1457, 1–4 (2009).

L. Samoylova, H. Sinn, F. Siewert, H. Mimura, K. Yamauchi, and T. Tschentscher, “Requirements on hard x-ray grazing incidence optics for European XFEL: analysis and simulation of wavefront transformations,” Proc. SPIE 7360, 1–9 (2009).

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).

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]

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]

Yamauchi, N. K.

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]

Yashchuk, V.

V. Yashchuk, W. McKinney, T. Warwick, T. Noll, F. Siewert, T. Zeschke, and R. Geckeler, “Proposal for a Universal Test Mirror for Characterization of Slope Measuring Instruments,” Advances in Metrology for X-Ray and EUV Optics II, Proc. of SPIE 6704, 4–16 (2007).

Yashchuk, V. V.

R. D. Geckeler, A. Just, M. Krause, and V. V. Yashchuk, “Autocollimators for deflectometry: Current status and future progress,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 140–146 (2010).
[CrossRef]

V. V. Yashchuk, S. Barber, E. E. Domning, J. L. Kirschman, G. Y. Morrison, B. V. Smith, F. Siewert, T. Zeschke, R. Geckler, and A. Just, “Sub-microradian surface slope metrology with the ALS Developmental Long Trace Profiler,” Nucl. Instrum. Meth. A 616(2-3), 212–223 (2010).
[CrossRef]

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

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]

Yokoyama, H.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 1457, 1–4 (2009).

Yumoto, H.

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]

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 1457, 1–4 (2009).

Zander, K.

E. Debler and K. Zander, “Ebenheitsmessung an optischen Planflächen mit Autokollimationsfernrohr und Pentagonprisma“, PTB Mitteilungen Forschen + Prüfen,” Amts und Mitteilungsblatt der Physikalisch Technischen Bundesanstalt, Braunschweig und Berlin 89, 339–349 (1979).

Zeschke, T.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, T. Noll, and H. Lammert, “The Diamond-NOM: A non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 224–228 (2010).
[CrossRef]

V. V. Yashchuk, S. Barber, E. E. Domning, J. L. Kirschman, G. Y. Morrison, B. V. Smith, F. Siewert, T. Zeschke, R. Geckler, and A. Just, “Sub-microradian surface slope metrology with the ALS Developmental Long Trace Profiler,” Nucl. Instrum. Meth. A 616(2-3), 212–223 (2010).
[CrossRef]

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).

F. Siewert, J. Buchheim, and T. Zeschke, “Characterization and calibration of 2nd generation slope measuring profiler,” Nucl. Instrum. Methods Phys. Rev. A 616, 119–127 (2010).
[CrossRef]

V. Yashchuk, W. McKinney, T. Warwick, T. Noll, F. Siewert, T. Zeschke, and R. Geckeler, “Proposal for a Universal Test Mirror for Characterization of Slope Measuring Instruments,” Advances in Metrology for X-Ray and EUV Optics II, Proc. of SPIE 6704, 4–16 (2007).

F. Siewert, T. Noll, T. Schlegel, T. Zeschke, and H. Lammert, “The Nanometer Optical Component Measuring machine: a new Sub-nm Topography Measuring Device for X-ray Optics at BESSY,” AIP Conf. Proc. 705, 847–850 (2004).
[CrossRef]

Advances in Metrology for X-Ray and EUV Optics II, Proc. of SPIE (1)

V. Yashchuk, W. McKinney, T. Warwick, T. Noll, F. Siewert, T. Zeschke, and R. Geckeler, “Proposal for a Universal Test Mirror for Characterization of Slope Measuring Instruments,” Advances in Metrology for X-Ray and EUV Optics II, Proc. of SPIE 6704, 4–16 (2007).

AIP Conf. Proc. (3)

F. Siewert, R. Reininger, M. Rübhausen, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A KB-Focusing Mirror Pair for a VUV-Raman Spectrometer at FLASH-Mirror Metrology and Ray Tracing Results,” AIP Conf. Proc. 1234, 752–755 (2010).
[CrossRef]

S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krüger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, T. Salditt, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “The holography endstation of beamline P10 at PETRA III,” AIP Conf. Proc. 1234, 433–436 (2010).
[CrossRef]

F. Siewert, T. Noll, T. Schlegel, T. Zeschke, and H. Lammert, “The Nanometer Optical Component Measuring machine: a new Sub-nm Topography Measuring Device for X-ray Optics at BESSY,” AIP Conf. Proc. 705, 847–850 (2004).
[CrossRef]

Amts und Mitteilungsblatt der Physikalisch Technischen Bundesanstalt, Braunschweig und Berlin (1)

E. Debler and K. Zander, “Ebenheitsmessung an optischen Planflächen mit Autokollimationsfernrohr und Pentagonprisma“, PTB Mitteilungen Forschen + Prüfen,” Amts und Mitteilungsblatt der Physikalisch Technischen Bundesanstalt, Braunschweig und Berlin 89, 339–349 (1979).

Appl. Opt. (2)

Nat. Phys. (1)

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 1457, 1–4 (2009).

New J. Phys. (1)

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]

Nucl. Instrum. Meth. A (1)

V. V. Yashchuk, S. Barber, E. E. Domning, J. L. Kirschman, G. Y. Morrison, B. V. Smith, F. Siewert, T. Zeschke, R. Geckler, and A. Just, “Sub-microradian surface slope metrology with the ALS Developmental Long Trace Profiler,” Nucl. Instrum. Meth. A 616(2-3), 212–223 (2010).
[CrossRef]

Nucl. Instrum. Methods Phys. Rev. A (6)

R. D. Geckeler, A. Just, M. Krause, and V. V. Yashchuk, “Autocollimators for deflectometry: Current status and future progress,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 140–146 (2010).
[CrossRef]

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).

F. Siewert, J. Buchheim, and T. Zeschke, “Characterization and calibration of 2nd generation slope measuring profiler,” Nucl. Instrum. Methods Phys. Rev. A 616, 119–127 (2010).
[CrossRef]

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, T. Noll, and H. Lammert, “The Diamond-NOM: A non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 224–228 (2010).
[CrossRef]

D. Cocco, G. Bartoletto, R. Sergo, G. Sostero, and I. Cudin, “A hybride active optical system for wave front preservation and available focal distance,” Nucl. Instrum. Methods Phys. Rev. A 616(2-3), 128–133 (2010).
[CrossRef]

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]

Opt. Eng. (1)

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

Proc. SPIE (8)

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

R. Signorato and M. Sanchez del Rio, “Structured slope errors on real x-ray mirrors: Ray tracing versus Experiment,” Proc. SPIE 3152, 136–147 (1997).
[CrossRef]

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).

L. Samoylova, H. Sinn, F. Siewert, H. Mimura, K. Yamauchi, and T. Tschentscher, “Requirements on hard x-ray grazing incidence optics for European XFEL: analysis and simulation of wavefront transformations,” Proc. SPIE 7360, 1–9 (2009).

I. Weingärtner, M. Schulz, and C. Elster, “Novel scanning technique for ultra-precise measurement of topography”, in “Optical Manufacturing and Testing III,” Proc. SPIE 3782, 306–317 (1999).

R. D. Geckeler and I. Weingärtner, “Sub-nm topography measurement by deflectometry: flatness standard and wafer nanotopography,” Proc. SPIE 4779, 1–12 (2002).
[CrossRef]

K. von Bieren, “Pencil beam interferometer for aspheric optical surfaces,” Proc. SPIE 343, 101–108 (1982).

P. Takacs, S. N. Qian, and J. Colbert, “Design of a long trace surface profiler,” Proc. SPIE 749, 59–64 (1987).

Rev. Opt. Theor. Instrum. (1)

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).

Rev. Sci. Instrum. (4)

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]

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).
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Other (9)

F. Siewert, “Slope Error and Surface Roughness”, in: Modern Developments in X-ray and Neutron Optics (Springer, 2008) 175–179.

F. Siewert, H. Lammert, T. Noll, T. Schlegel, T. Zeschke, T. Hänsel, A. Nickel, A. Schindler, B. Grubert, and C. Schlewitt, “Advanced metrology, an essential support for the surface finishing of high performance x-ray optics”, in “Advances in Metrology for X-Ray and EUV Optics”, Ed. By Lahsen Assoufid, Peter Z. Takacs, John S. Taylor, Proc. of SPIE 5921, 1–14 (2005).

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H. Lammert, T. Noll, T. Schlegel, F. Siewert, and T. Zeschke, “Optisches Messverfahren und Präzisionsmessmaschine zur Ermittlung von Idealformabweichungen technisch polierter Oberflächen“, Patent No.: EP 1 585 938 B1 (07.26. 2006).

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Figures (9)

Fig. 1
Fig. 1

principle set-up of a mirror based moving penta prism slope measuring profiler as realized for the BESSY-NOM

Fig. 2
Fig. 2

Wave front distortion caused by shape deviations on an imperfect mirror

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.

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.

Fig. 5
Fig. 5

Mirror HFM profiles of residual height corresponding to the profiles of residual slope shown in Fig. 4.

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.

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.

Fig. 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.

Fig. 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

Tables (2)

Tables Icon

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

Tables Icon

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

Equations (5)

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S( x )=tanθ=dy/dx
h( x k )=h( x 0 )+ m=1 k dx 2 [ S( x m )+S( x m1 ) ]
φ= 2Δhsinθ λ
I I 0 exp[ ( 2π σ rms λ ) 2 ]
Δ h rms λ 14 N 2θ

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