Abstract

In a previous paper, the University of Arizona (UA) has developed a measurement technique called: Software Configurable Optical Test System (SCOTS) based on the principle of reflection deflectometry. In this paper, we present results of this very efficient optical metrology method applied to the metrology of X-ray mirrors. We used this technique to measure surface slope errors with precision and accuracy better than 100 nrad (rms) and ~200 nrad (rms), respectively, with a lateral resolution of few mm or less. We present results of the calibration of the metrology systems, discuss their accuracy and address the precision in measuring a spherical mirror.

© 2012 OSA

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    [CrossRef]
  26. M. Vo, Z. Wang, L. Luu, and J. Ma, “Advanced geometric camera calibration for machine vision,” Opt. Eng. 50(11), 110503 (2011).
    [CrossRef]
  27. M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
    [CrossRef]

2012 (2)

2011 (1)

M. Vo, Z. Wang, L. Luu, and J. Ma, “Advanced geometric camera calibration for machine vision,” Opt. Eng. 50(11), 110503 (2011).
[CrossRef]

2010 (5)

2009 (2)

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, “Demonstration of 12 nm resolution Fresnel zone plate lens based soft x-ray microscopy,” Opt. Express 17(20), 17669–17677 (2009).
[CrossRef] [PubMed]

P. Su, J. H. Burge, B. Cuerden, R. Allen, and H. M. Martin, “Scanning pentaprism measurements of off-axis aspherics II,” Proc. SPIE 7426, 74260Y, 74260Y-9 (2009).
[CrossRef]

2008 (1)

P. Su, J. H. Burge, B. Cuerden, J. Sasian, and H. M. Martin, “Scanning pentaprism measurements of off-axis aspherics,” Proc. SPIE 7018, 70183T, 70183T-10 (2008).
[CrossRef]

2007 (1)

J. H. Burge, P. Su, C. Zhao, and T. Zobrist, “Use of a commercial laser tracker for optical alignment,” Proc. SPIE 6676, 66760E, 66760E-12 (2007).
[CrossRef]

2004 (2)

T. Bothe, W. Li, C. von Kopylow, and W. Jueptner, “High resolution 3D shape measurement on specular surfaces by fringe reflection,” Proc. SPIE 5457, 411–422 (2004).
[CrossRef]

M. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[CrossRef]

2003 (1)

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subapeture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
[CrossRef]

2000 (1)

R. Höfling, P. Aswendt, and R. Neugebauer, “Phase reflection—a new solution for the detection of shape defects on car body sheets,” Opt. Eng. 39(1), 175 (2000).
[CrossRef]

1998 (1)

1997 (1)

D. Perard and J. Beyerer, “Three-dimensional measurement of specular free-form surfaces with a structured-lighting reflection technique,” Proc. SPIE 3204, 74–80 (1997).
[CrossRef]

1995 (1)

S. N. Qian, W. Jark, and P. Z. Takacs, “The penta-prism LTP: A long-trace-profiler with stationary optical head and moving penta prism,” Rev. Sci. Instrum. 66(3), 2562–2569 (1995).
[CrossRef]

1987 (1)

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

1983 (1)

R. Ritter and R. Hahn, “Contribution to analysis of the reflection grating method,” Opt. Lasers Eng. 4(1), 13–24 (1983).
[CrossRef]

1954 (1)

F. Ligtenberg, “The moire method, a new experimental method for the determination of moments in small slab models,” Proc. Soc. Exp. Stress Anal. 12, 83–98 (1954).

Allen, R.

P. Su, J. H. Burge, B. Cuerden, R. Allen, and H. M. Martin, “Scanning pentaprism measurements of off-axis aspherics II,” Proc. SPIE 7426, 74260Y, 74260Y-9 (2009).
[CrossRef]

Anderson, E. H.

Angel, R. P.

Aswendt, P.

R. Höfling, P. Aswendt, and R. Neugebauer, “Phase reflection—a new solution for the detection of shape defects on car body sheets,” Opt. Eng. 39(1), 175 (2000).
[CrossRef]

Bergmann, R. B.

Beyerer, J.

D. Perard and J. Beyerer, “Three-dimensional measurement of specular free-form surfaces with a structured-lighting reflection technique,” Proc. SPIE 3204, 74–80 (1997).
[CrossRef]

Bothe, T.

Boutet, S.

Boye, P.

C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, D. Samberg, A. Schropp, A. Schwab, S. Stephan, G. Falkenberg, G. Wellenreuther, and N. Reimers, “Hard X-ray nanoprobe at beamline P06 at PETRA III,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 93–97 (2010).
[CrossRef]

Buchheim, J.

Bucourt, S.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[CrossRef]

Burge, J. H.

P. Su, R. E. Parks, Y. Wang, C. J. Oh, and J. H. Burge, “Swing arm optical coordinate-measuring machine: modal estimation of systematic errors from dual probe shear measurements,” Opt. Eng. 51(4), 043604 (2012).
[CrossRef]

P. Su, R. E. Parks, L. Wang, R. P. Angel, and J. H. Burge, “Software configurable optical test system: a computerized reverse Hartmann test,” Appl. Opt. 49(23), 4404–4412 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=ao-49-23-4404 .
[CrossRef] [PubMed]

P. Su, J. H. Burge, B. Cuerden, R. Allen, and H. M. Martin, “Scanning pentaprism measurements of off-axis aspherics II,” Proc. SPIE 7426, 74260Y, 74260Y-9 (2009).
[CrossRef]

P. Su, J. H. Burge, B. Cuerden, J. Sasian, and H. M. Martin, “Scanning pentaprism measurements of off-axis aspherics,” Proc. SPIE 7018, 70183T, 70183T-10 (2008).
[CrossRef]

J. H. Burge, P. Su, C. Zhao, and T. Zobrist, “Use of a commercial laser tracker for optical alignment,” Proc. SPIE 6676, 66760E, 66760E-12 (2007).
[CrossRef]

Chao, W.

Colbert, J.

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

Cuerden, B.

P. Su, J. H. Burge, B. Cuerden, R. Allen, and H. M. Martin, “Scanning pentaprism measurements of off-axis aspherics II,” Proc. SPIE 7426, 74260Y, 74260Y-9 (2009).
[CrossRef]

P. Su, J. H. Burge, B. Cuerden, J. Sasian, and H. M. Martin, “Scanning pentaprism measurements of off-axis aspherics,” Proc. SPIE 7018, 70183T, 70183T-10 (2008).
[CrossRef]

Dovillaire, G.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[CrossRef]

Dumas, P.

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subapeture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
[CrossRef]

Escolano, L.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[CrossRef]

Falkenberg, G.

C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, D. Samberg, A. Schropp, A. Schwab, S. Stephan, G. Falkenberg, G. Wellenreuther, and N. Reimers, “Hard X-ray nanoprobe at beamline P06 at PETRA III,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 93–97 (2010).
[CrossRef]

Feldkamp, J. M.

C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, D. Samberg, A. Schropp, A. Schwab, S. Stephan, G. Falkenberg, G. Wellenreuther, and N. Reimers, “Hard X-ray nanoprobe at beamline P06 at PETRA III,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 93–97 (2010).
[CrossRef]

Fischer, P.

Fleig, J.

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subapeture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
[CrossRef]

Forbes, G. W.

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subapeture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
[CrossRef]

Hahn, R.

R. Ritter and R. Hahn, “Contribution to analysis of the reflection grating method,” Opt. Lasers Eng. 4(1), 13–24 (1983).
[CrossRef]

Hausler, G.

M. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[CrossRef]

Höfling, R.

R. Höfling, P. Aswendt, and R. Neugebauer, “Phase reflection—a new solution for the detection of shape defects on car body sheets,” Opt. Eng. 39(1), 175 (2000).
[CrossRef]

Idir, M.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[CrossRef]

Ishikawa, T.

Jark, W.

S. N. Qian, W. Jark, and P. Z. Takacs, “The penta-prism LTP: A long-trace-profiler with stationary optical head and moving penta prism,” Rev. Sci. Instrum. 66(3), 2562–2569 (1995).
[CrossRef]

Jueptner, W.

T. Bothe, W. Li, C. von Kopylow, and W. Jueptner, “High resolution 3D shape measurement on specular surfaces by fringe reflection,” Proc. SPIE 5457, 411–422 (2004).
[CrossRef]

Jüptner, W. P. O.

Kaminski, J.

M. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[CrossRef]

Kidani, N.

Kim, J.

Kimura, T.

Knauer, M.

M. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[CrossRef]

Kohn, V.

Krzywinski, J.

Lengeler, B.

Levecq, X.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[CrossRef]

Li, W.

Ligtenberg, F.

F. Ligtenberg, “The moire method, a new experimental method for the determination of moments in small slab models,” Proc. Soc. Exp. Stress Anal. 12, 83–98 (1954).

Luu, L.

M. Vo, Z. Wang, L. Luu, and J. Ma, “Advanced geometric camera calibration for machine vision,” Opt. Eng. 50(11), 110503 (2011).
[CrossRef]

Ma, J.

M. Vo, Z. Wang, L. Luu, and J. Ma, “Advanced geometric camera calibration for machine vision,” Opt. Eng. 50(11), 110503 (2011).
[CrossRef]

Martin, H. M.

P. Su, J. H. Burge, B. Cuerden, R. Allen, and H. M. Martin, “Scanning pentaprism measurements of off-axis aspherics II,” Proc. SPIE 7426, 74260Y, 74260Y-9 (2009).
[CrossRef]

P. Su, J. H. Burge, B. Cuerden, J. Sasian, and H. M. Martin, “Scanning pentaprism measurements of off-axis aspherics,” Proc. SPIE 7018, 70183T, 70183T-10 (2008).
[CrossRef]

Matsuyama, S.

Mercere, P.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[CrossRef]

Mimura, H.

Modi, M. H.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[CrossRef]

Montanez, P. A.

Murphy, P. E.

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subapeture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
[CrossRef]

Neugebauer, R.

R. Höfling, P. Aswendt, and R. Neugebauer, “Phase reflection—a new solution for the detection of shape defects on car body sheets,” Opt. Eng. 39(1), 175 (2000).
[CrossRef]

Nishino, Y.

Oh, C. J.

P. Su, R. E. Parks, Y. Wang, C. J. Oh, and J. H. Burge, “Swing arm optical coordinate-measuring machine: modal estimation of systematic errors from dual probe shear measurements,” Opt. Eng. 51(4), 043604 (2012).
[CrossRef]

Parks, R. E.

P. Su, R. E. Parks, Y. Wang, C. J. Oh, and J. H. Burge, “Swing arm optical coordinate-measuring machine: modal estimation of systematic errors from dual probe shear measurements,” Opt. Eng. 51(4), 043604 (2012).
[CrossRef]

P. Su, R. E. Parks, L. Wang, R. P. Angel, and J. H. Burge, “Software configurable optical test system: a computerized reverse Hartmann test,” Appl. Opt. 49(23), 4404–4412 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=ao-49-23-4404 .
[CrossRef] [PubMed]

Patommel, J.

C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, D. Samberg, A. Schropp, A. Schwab, S. Stephan, G. Falkenberg, G. Wellenreuther, and N. Reimers, “Hard X-ray nanoprobe at beamline P06 at PETRA III,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 93–97 (2010).
[CrossRef]

Perard, D.

D. Perard and J. Beyerer, “Three-dimensional measurement of specular free-form surfaces with a structured-lighting reflection technique,” Proc. SPIE 3204, 74–80 (1997).
[CrossRef]

Qian, S. N.

S. N. Qian, W. Jark, and P. Z. Takacs, “The penta-prism LTP: A long-trace-profiler with stationary optical head and moving penta prism,” Rev. Sci. Instrum. 66(3), 2562–2569 (1995).
[CrossRef]

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

Reimers, N.

C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, D. Samberg, A. Schropp, A. Schwab, S. Stephan, G. Falkenberg, G. Wellenreuther, and N. Reimers, “Hard X-ray nanoprobe at beamline P06 at PETRA III,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 93–97 (2010).
[CrossRef]

Rekawa, S.

Ritter, R.

R. Ritter and R. Hahn, “Contribution to analysis of the reflection grating method,” Opt. Lasers Eng. 4(1), 13–24 (1983).
[CrossRef]

Samberg, D.

C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, D. Samberg, A. Schropp, A. Schwab, S. Stephan, G. Falkenberg, G. Wellenreuther, and N. Reimers, “Hard X-ray nanoprobe at beamline P06 at PETRA III,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 93–97 (2010).
[CrossRef]

Sano, Y.

Sasian, J.

P. Su, J. H. Burge, B. Cuerden, J. Sasian, and H. M. Martin, “Scanning pentaprism measurements of off-axis aspherics,” Proc. SPIE 7018, 70183T, 70183T-10 (2008).
[CrossRef]

Sauvageot, P.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[CrossRef]

Schroer, C. G.

C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, D. Samberg, A. Schropp, A. Schwab, S. Stephan, G. Falkenberg, G. Wellenreuther, and N. Reimers, “Hard X-ray nanoprobe at beamline P06 at PETRA III,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 93–97 (2010).
[CrossRef]

Schropp, A.

C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, D. Samberg, A. Schropp, A. Schwab, S. Stephan, G. Falkenberg, G. Wellenreuther, and N. Reimers, “Hard X-ray nanoprobe at beamline P06 at PETRA III,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 93–97 (2010).
[CrossRef]

Schulte, M.

Schwab, A.

C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, D. Samberg, A. Schropp, A. Schwab, S. Stephan, G. Falkenberg, G. Wellenreuther, and N. Reimers, “Hard X-ray nanoprobe at beamline P06 at PETRA III,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 93–97 (2010).
[CrossRef]

Siewert, F.

Signorato, R.

Snigirev, A.

Snigireva, I.

Souvorov, A.

Stephan, S.

C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, D. Samberg, A. Schropp, A. Schwab, S. Stephan, G. Falkenberg, G. Wellenreuther, and N. Reimers, “Hard X-ray nanoprobe at beamline P06 at PETRA III,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 93–97 (2010).
[CrossRef]

Su, P.

P. Su, R. E. Parks, Y. Wang, C. J. Oh, and J. H. Burge, “Swing arm optical coordinate-measuring machine: modal estimation of systematic errors from dual probe shear measurements,” Opt. Eng. 51(4), 043604 (2012).
[CrossRef]

P. Su, R. E. Parks, L. Wang, R. P. Angel, and J. H. Burge, “Software configurable optical test system: a computerized reverse Hartmann test,” Appl. Opt. 49(23), 4404–4412 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=ao-49-23-4404 .
[CrossRef] [PubMed]

P. Su, J. H. Burge, B. Cuerden, R. Allen, and H. M. Martin, “Scanning pentaprism measurements of off-axis aspherics II,” Proc. SPIE 7426, 74260Y, 74260Y-9 (2009).
[CrossRef]

P. Su, J. H. Burge, B. Cuerden, J. Sasian, and H. M. Martin, “Scanning pentaprism measurements of off-axis aspherics,” Proc. SPIE 7018, 70183T, 70183T-10 (2008).
[CrossRef]

J. H. Burge, P. Su, C. Zhao, and T. Zobrist, “Use of a commercial laser tracker for optical alignment,” Proc. SPIE 6676, 66760E, 66760E-12 (2007).
[CrossRef]

Takacs, P. Z.

S. N. Qian, W. Jark, and P. Z. Takacs, “The penta-prism LTP: A long-trace-profiler with stationary optical head and moving penta prism,” Rev. Sci. Instrum. 66(3), 2562–2569 (1995).
[CrossRef]

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

Tamasaku, K.

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M. Vo, Z. Wang, L. Luu, and J. Ma, “Advanced geometric camera calibration for machine vision,” Opt. Eng. 50(11), 110503 (2011).
[CrossRef]

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Wakioka, T.

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Wang, Y.

P. Su, R. E. Parks, Y. Wang, C. J. Oh, and J. H. Burge, “Swing arm optical coordinate-measuring machine: modal estimation of systematic errors from dual probe shear measurements,” Opt. Eng. 51(4), 043604 (2012).
[CrossRef]

Wang, Z.

M. Vo, Z. Wang, L. Luu, and J. Ma, “Advanced geometric camera calibration for machine vision,” Opt. Eng. 50(11), 110503 (2011).
[CrossRef]

Wellenreuther, G.

C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, D. Samberg, A. Schropp, A. Schwab, S. Stephan, G. Falkenberg, G. Wellenreuther, and N. Reimers, “Hard X-ray nanoprobe at beamline P06 at PETRA III,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 93–97 (2010).
[CrossRef]

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Yabashi, M.

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Zhao, C.

J. H. Burge, P. Su, C. Zhao, and T. Zobrist, “Use of a commercial laser tracker for optical alignment,” Proc. SPIE 6676, 66760E, 66760E-12 (2007).
[CrossRef]

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J. H. Burge, P. Su, C. Zhao, and T. Zobrist, “Use of a commercial laser tracker for optical alignment,” Proc. SPIE 6676, 66760E, 66760E-12 (2007).
[CrossRef]

Appl. Opt. (3)

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M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[CrossRef]

C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, D. Samberg, A. Schropp, A. Schwab, S. Stephan, G. Falkenberg, G. Wellenreuther, and N. Reimers, “Hard X-ray nanoprobe at beamline P06 at PETRA III,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 93–97 (2010).
[CrossRef]

Opt. Eng. (3)

P. Su, R. E. Parks, Y. Wang, C. J. Oh, and J. H. Burge, “Swing arm optical coordinate-measuring machine: modal estimation of systematic errors from dual probe shear measurements,” Opt. Eng. 51(4), 043604 (2012).
[CrossRef]

M. Vo, Z. Wang, L. Luu, and J. Ma, “Advanced geometric camera calibration for machine vision,” Opt. Eng. 50(11), 110503 (2011).
[CrossRef]

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[CrossRef]

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[CrossRef]

T. Bothe, W. Li, C. von Kopylow, and W. Jueptner, “High resolution 3D shape measurement on specular surfaces by fringe reflection,” Proc. SPIE 5457, 411–422 (2004).
[CrossRef]

M. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[CrossRef]

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

P. Su, J. H. Burge, B. Cuerden, J. Sasian, and H. M. Martin, “Scanning pentaprism measurements of off-axis aspherics,” Proc. SPIE 7018, 70183T, 70183T-10 (2008).
[CrossRef]

P. Su, J. H. Burge, B. Cuerden, R. Allen, and H. M. Martin, “Scanning pentaprism measurements of off-axis aspherics II,” Proc. SPIE 7426, 74260Y, 74260Y-9 (2009).
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[CrossRef]

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S. N. Qian, W. Jark, and P. Z. Takacs, “The penta-prism LTP: A long-trace-profiler with stationary optical head and moving penta prism,” Rev. Sci. Instrum. 66(3), 2562–2569 (1995).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Comparison of the test geometry for (a) a Hartmann test and (b) the SCOTS.

Fig. 2
Fig. 2

Geometric layout (a) and experiment setup(b) of the SCOTS test for the spherical mirror.

Fig. 3
Fig. 3

The fringe data of the SCOTS.

Fig. 4
Fig. 4

Unwrapped slope data in x and y directions (unit: radian).

Fig. 5
Fig. 5

Integrated surface data, rms = 8nm (unit: micron).

Fig. 6
Fig. 6

Slope residuals are ~0.1 µrad from the integration process.

Fig. 7
Fig. 7

An example of the measured fringe from the flat.

Fig. 8
Fig. 8

The integrated surface from the flat (left, unit: micron) interferometric data for the flat (right, unit:nm), both with power and astigmatism removed.

Fig. 9
Fig. 9

Sphere surface map with power rms = 6 micron, calculated radius R = 54.15m; surface map without power and astigmatism, rms = 4nm. Calibration from the flat is applied (unit: micron).

Fig. 10
Fig. 10

The center line profiles of the test sphere from the SCOTS and LTP measurement.

Fig. 11
Fig. 11

Layout of a Double Gauss type camera lens design, which illustrates the effect of the pupil aberration.

Fig. 12
Fig. 12

Pupil aberration effect: ray displacement at the pupil plane as a function of the lens field of view.

Fig. 13
Fig. 13

Test difference before and after rotating the illumination screen 180degs, rms = 0.6nm (unit: micron).

Tables (1)

Tables Icon

Table1 Experiment Uncertainties for Measuring the Test Sphere with the SCOTS

Equations (4)

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w x ( x m , y m )= x m x screen d m2screen + x m x camera d m2camera z m2screen w( x m , y m ) d m2screen + z m2camera w( x m , y m ) d m2camera w x ( x m , y m )= y m y screen d m2screen + y m y camera d m2camera z m2screen w( x m , y m ) d m2screen + z m2camera w( x m , y m ) d m2camera
x screen = iESP x i I i iESP I i , y screen = iESP y i I i iESP I i
W(x,y) x x screen d m2screen , W(x,y) y y screen d m2screen
tanδαδx= πλ Q

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