Abstract

Grazing incidence mirrors are a standard optic for focusing X-rays. Active mirrors, whose surface profile can be finely adjusted, allow control of beam shape and size at the sample. However, progress towards their routine use for beam shaping has been hampered by the strong striations in reflected beams away from the focal plane. Re-entrant (partly concave and partly convex) surface modifications are proposed for shaping X-ray beams to a top-hat in the focal plane while reducing the striations caused by unavoidable polishing errors. A method for constructing such surfaces with continuous height and slope (but only piecewise continuous curvature) will be provided. Ray tracing and wave propagation calculations confirm its effectiveness. A mirror system is proposed allowing vertical beam sizes in the range 0.5 to 10μm. A prototype will be fabricated and is expected to have applications on many synchrotron X-ray beamlines.

© 2015 Optical Society of America

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  1. J. Susini, D. Labergerie, and L. Zhang, “Compact active/adaptive x-ray mirror: Bimorph piezoelectric flexible mirror,” Rev. Sci. Instrum.66(2), 2229–2231 (1995).
    [Crossref]
  2. R. Signorato, O. Hignette, and J. Goulon, “Multi-segmented piezoelectric mirrors as active/adaptive optics components,” J. Synchrotron Radiat.5(3), 797–800 (1998).
    [Crossref] [PubMed]
  3. R. Signorato and T. Ishikawa, “R&D on third generation multi-segmented piezoelectric bimorph mirror substrates at Spring-8,” Nucl. Instrum. Methods Phys. Res. A467–468, 271–274 (2001).
    [Crossref]
  4. D. Spiga, L. Raimondi, C. Svetina, and M. Zangrando, “X-ray beam shaping via deformable mirrors: Analytical computation of the required mirror profile,” Nucl. Instrum. Methods Phys. Res. A710, 125–130 (2013).
    [Crossref]
  5. J. Nicolas and G. García, “Modulation of intensity in defocused beams,” Proc. SPIE8848, 884810 (2013).
    [Crossref]
  6. J. P. Sutter, S. G. Alcock, F. Rust, H. Wang, and K. Sawhney, “Structure in defocused beams of x-ray mirrors: causes and possible solutions,” Proc. SPIE9208, 920815 (2014).
  7. The MathWorks, Inc., [Matlab Version 7.0.1.24704 (R14) Service Pack 1] (2004).
  8. M. S. del Rio, N. Canestrari, F. Jiang, and F. Cerrina, “SHADOW3: a new version of the synchrotron X-ray optics modelling package,” J. Synchrotron Radiat.18(5), 708–716 (2011).
    [Crossref] [PubMed]
  9. S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, 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. Res. A616(2-3), 224–228 (2010).
    [Crossref]
  10. D. Spiga and L. Raimondi, “X-ray optical systems: from metrology to Point Spread Function,” Proc. SPIE9209, 92090E (2014).
  11. M. Born and E. Wolf, Principles of Optics, 10th ed, Cambridge University (1999)

2014 (2)

J. P. Sutter, S. G. Alcock, F. Rust, H. Wang, and K. Sawhney, “Structure in defocused beams of x-ray mirrors: causes and possible solutions,” Proc. SPIE9208, 920815 (2014).

D. Spiga and L. Raimondi, “X-ray optical systems: from metrology to Point Spread Function,” Proc. SPIE9209, 92090E (2014).

2013 (2)

D. Spiga, L. Raimondi, C. Svetina, and M. Zangrando, “X-ray beam shaping via deformable mirrors: Analytical computation of the required mirror profile,” Nucl. Instrum. Methods Phys. Res. A710, 125–130 (2013).
[Crossref]

J. Nicolas and G. García, “Modulation of intensity in defocused beams,” Proc. SPIE8848, 884810 (2013).
[Crossref]

2011 (1)

M. S. del Rio, N. Canestrari, F. Jiang, and F. Cerrina, “SHADOW3: a new version of the synchrotron X-ray optics modelling package,” J. Synchrotron Radiat.18(5), 708–716 (2011).
[Crossref] [PubMed]

2010 (1)

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, 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. Res. A616(2-3), 224–228 (2010).
[Crossref]

2001 (1)

R. Signorato and T. Ishikawa, “R&D on third generation multi-segmented piezoelectric bimorph mirror substrates at Spring-8,” Nucl. Instrum. Methods Phys. Res. A467–468, 271–274 (2001).
[Crossref]

1998 (1)

R. Signorato, O. Hignette, and J. Goulon, “Multi-segmented piezoelectric mirrors as active/adaptive optics components,” J. Synchrotron Radiat.5(3), 797–800 (1998).
[Crossref] [PubMed]

1995 (1)

J. Susini, D. Labergerie, and L. Zhang, “Compact active/adaptive x-ray mirror: Bimorph piezoelectric flexible mirror,” Rev. Sci. Instrum.66(2), 2229–2231 (1995).
[Crossref]

Alcock, S. G.

J. P. Sutter, S. G. Alcock, F. Rust, H. Wang, and K. Sawhney, “Structure in defocused beams of x-ray mirrors: causes and possible solutions,” Proc. SPIE9208, 920815 (2014).

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, 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. Res. A616(2-3), 224–228 (2010).
[Crossref]

Canestrari, N.

M. S. del Rio, N. Canestrari, F. Jiang, and F. Cerrina, “SHADOW3: a new version of the synchrotron X-ray optics modelling package,” J. Synchrotron Radiat.18(5), 708–716 (2011).
[Crossref] [PubMed]

Cerrina, F.

M. S. del Rio, N. Canestrari, F. Jiang, and F. Cerrina, “SHADOW3: a new version of the synchrotron X-ray optics modelling package,” J. Synchrotron Radiat.18(5), 708–716 (2011).
[Crossref] [PubMed]

del Rio, M. S.

M. S. del Rio, N. Canestrari, F. Jiang, and F. Cerrina, “SHADOW3: a new version of the synchrotron X-ray optics modelling package,” J. Synchrotron Radiat.18(5), 708–716 (2011).
[Crossref] [PubMed]

GarcĂ­a, G.

J. Nicolas and G. García, “Modulation of intensity in defocused beams,” Proc. SPIE8848, 884810 (2013).
[Crossref]

Goulon, J.

R. Signorato, O. Hignette, and J. Goulon, “Multi-segmented piezoelectric mirrors as active/adaptive optics components,” J. Synchrotron Radiat.5(3), 797–800 (1998).
[Crossref] [PubMed]

Hignette, O.

R. Signorato, O. Hignette, and J. Goulon, “Multi-segmented piezoelectric mirrors as active/adaptive optics components,” J. Synchrotron Radiat.5(3), 797–800 (1998).
[Crossref] [PubMed]

Ishikawa, T.

R. Signorato and T. Ishikawa, “R&D on third generation multi-segmented piezoelectric bimorph mirror substrates at Spring-8,” Nucl. Instrum. Methods Phys. Res. A467–468, 271–274 (2001).
[Crossref]

Jiang, F.

M. S. del Rio, N. Canestrari, F. Jiang, and F. Cerrina, “SHADOW3: a new version of the synchrotron X-ray optics modelling package,” J. Synchrotron Radiat.18(5), 708–716 (2011).
[Crossref] [PubMed]

Labergerie, D.

J. Susini, D. Labergerie, and L. Zhang, “Compact active/adaptive x-ray mirror: Bimorph piezoelectric flexible mirror,” Rev. Sci. Instrum.66(2), 2229–2231 (1995).
[Crossref]

Lammert, H.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, 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. Res. A616(2-3), 224–228 (2010).
[Crossref]

Nicolas, J.

J. Nicolas and G. García, “Modulation of intensity in defocused beams,” Proc. SPIE8848, 884810 (2013).
[Crossref]

Noll, T.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, 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. Res. A616(2-3), 224–228 (2010).
[Crossref]

Pedersen, U.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, 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. Res. A616(2-3), 224–228 (2010).
[Crossref]

Raimondi, L.

D. Spiga and L. Raimondi, “X-ray optical systems: from metrology to Point Spread Function,” Proc. SPIE9209, 92090E (2014).

D. Spiga, L. Raimondi, C. Svetina, and M. Zangrando, “X-ray beam shaping via deformable mirrors: Analytical computation of the required mirror profile,” Nucl. Instrum. Methods Phys. Res. A710, 125–130 (2013).
[Crossref]

Rust, F.

J. P. Sutter, S. G. Alcock, F. Rust, H. Wang, and K. Sawhney, “Structure in defocused beams of x-ray mirrors: causes and possible solutions,” Proc. SPIE9208, 920815 (2014).

Sawhney, K.

J. P. Sutter, S. G. Alcock, F. Rust, H. Wang, and K. Sawhney, “Structure in defocused beams of x-ray mirrors: causes and possible solutions,” Proc. SPIE9208, 920815 (2014).

Sawhney, K. J. S.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, 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. Res. A616(2-3), 224–228 (2010).
[Crossref]

Scott, S.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, 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. Res. A616(2-3), 224–228 (2010).
[Crossref]

Senf, F.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, 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. Res. A616(2-3), 224–228 (2010).
[Crossref]

Siewert, F.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, 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. Res. A616(2-3), 224–228 (2010).
[Crossref]

Signorato, R.

R. Signorato and T. Ishikawa, “R&D on third generation multi-segmented piezoelectric bimorph mirror substrates at Spring-8,” Nucl. Instrum. Methods Phys. Res. A467–468, 271–274 (2001).
[Crossref]

R. Signorato, O. Hignette, and J. Goulon, “Multi-segmented piezoelectric mirrors as active/adaptive optics components,” J. Synchrotron Radiat.5(3), 797–800 (1998).
[Crossref] [PubMed]

Spiga, D.

D. Spiga and L. Raimondi, “X-ray optical systems: from metrology to Point Spread Function,” Proc. SPIE9209, 92090E (2014).

D. Spiga, L. Raimondi, C. Svetina, and M. Zangrando, “X-ray beam shaping via deformable mirrors: Analytical computation of the required mirror profile,” Nucl. Instrum. Methods Phys. Res. A710, 125–130 (2013).
[Crossref]

Susini, J.

J. Susini, D. Labergerie, and L. Zhang, “Compact active/adaptive x-ray mirror: Bimorph piezoelectric flexible mirror,” Rev. Sci. Instrum.66(2), 2229–2231 (1995).
[Crossref]

Sutter, J. P.

J. P. Sutter, S. G. Alcock, F. Rust, H. Wang, and K. Sawhney, “Structure in defocused beams of x-ray mirrors: causes and possible solutions,” Proc. SPIE9208, 920815 (2014).

Svetina, C.

D. Spiga, L. Raimondi, C. Svetina, and M. Zangrando, “X-ray beam shaping via deformable mirrors: Analytical computation of the required mirror profile,” Nucl. Instrum. Methods Phys. Res. A710, 125–130 (2013).
[Crossref]

Walton, R.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, 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. Res. A616(2-3), 224–228 (2010).
[Crossref]

Wang, H.

J. P. Sutter, S. G. Alcock, F. Rust, H. Wang, and K. Sawhney, “Structure in defocused beams of x-ray mirrors: causes and possible solutions,” Proc. SPIE9208, 920815 (2014).

Zangrando, M.

D. Spiga, L. Raimondi, C. Svetina, and M. Zangrando, “X-ray beam shaping via deformable mirrors: Analytical computation of the required mirror profile,” Nucl. Instrum. Methods Phys. Res. A710, 125–130 (2013).
[Crossref]

Zeschke, T.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, 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. Res. A616(2-3), 224–228 (2010).
[Crossref]

Zhang, L.

J. Susini, D. Labergerie, and L. Zhang, “Compact active/adaptive x-ray mirror: Bimorph piezoelectric flexible mirror,” Rev. Sci. Instrum.66(2), 2229–2231 (1995).
[Crossref]

J. Synchrotron Radiat. (2)

R. Signorato, O. Hignette, and J. Goulon, “Multi-segmented piezoelectric mirrors as active/adaptive optics components,” J. Synchrotron Radiat.5(3), 797–800 (1998).
[Crossref] [PubMed]

M. S. del Rio, N. Canestrari, F. Jiang, and F. Cerrina, “SHADOW3: a new version of the synchrotron X-ray optics modelling package,” J. Synchrotron Radiat.18(5), 708–716 (2011).
[Crossref] [PubMed]

Nucl. Instrum. Methods Phys. Res. A (3)

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, 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. Res. A616(2-3), 224–228 (2010).
[Crossref]

R. Signorato and T. Ishikawa, “R&D on third generation multi-segmented piezoelectric bimorph mirror substrates at Spring-8,” Nucl. Instrum. Methods Phys. Res. A467–468, 271–274 (2001).
[Crossref]

D. Spiga, L. Raimondi, C. Svetina, and M. Zangrando, “X-ray beam shaping via deformable mirrors: Analytical computation of the required mirror profile,” Nucl. Instrum. Methods Phys. Res. A710, 125–130 (2013).
[Crossref]

Proc. SPIE (3)

J. Nicolas and G. García, “Modulation of intensity in defocused beams,” Proc. SPIE8848, 884810 (2013).
[Crossref]

J. P. Sutter, S. G. Alcock, F. Rust, H. Wang, and K. Sawhney, “Structure in defocused beams of x-ray mirrors: causes and possible solutions,” Proc. SPIE9208, 920815 (2014).

D. Spiga and L. Raimondi, “X-ray optical systems: from metrology to Point Spread Function,” Proc. SPIE9209, 92090E (2014).

Rev. Sci. Instrum. (1)

J. Susini, D. Labergerie, and L. Zhang, “Compact active/adaptive x-ray mirror: Bimorph piezoelectric flexible mirror,” Rev. Sci. Instrum.66(2), 2229–2231 (1995).
[Crossref]

Other (2)

M. Born and E. Wolf, Principles of Optics, 10th ed, Cambridge University (1999)

The MathWorks, Inc., [Matlab Version 7.0.1.24704 (R14) Service Pack 1] (2004).

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