Abstract

A software configurable optical test system (SCOTS) based on the geometry of the fringe reflection or phase measuring deflectometry method was developed for rapidly, robustly, and accurately measuring large, highly aspherical shapes such as solar collectors and primary mirrors for astronomical telescopes. In addition to using phase shifting methods for data collection and reduction, we explore the test from the point view of performing traditional optical testing methods, such as Hartmann or Hartmann–Shack tests, in a reverse way. Using this concept, the slope data calculation and unwrapping in the test can also be done with centroiding and line-scanning methods. These concepts expand the test to work in more general situations where fringe illumination is not practical. Experimental results show that the test can be implemented without complex calibration for many applications by taking the geometric advantage of working near the center curvature of the test part. The results also show that the test has a large dynamic range, can achieve measurement accuracy comparable with interferometric methods, and can provide a good complement to interferometric tests in certain circumstances. A variation of this method is also useful for measuring refractive optics and optical systems. As such, SCOTS provides optical manufacturers with a new tool for performing quantitative full field system evaluation.

© 2010 Optical Society of America

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References

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  1. J. Ojeda-Castañeda, “Foucault, wire, and phase modulation tests,” in Optical Shop Testing, 3rd ed., D.Malacara, ed., Wiley Series in Pure and Applied Optics (Wiley, 2007), pp. 275–316.
  2. A. Cornejo-Rodriguez, “Ronchi test,” in Optical Shop Testing, 3rd ed., D.Malacara, ed., Wiley Series in Pure and Applied Optics (Wiley, 2007), pp. 317–360.
  3. D. Malacara-Doblado and I. Ghozeil, “Hartmann, Hartmann-Shack, and other screen tests,” in Optical Shop Testing, 3rd ed., D.Malacara, ed., Wiley Series in Pure and Applied Optics (Wiley, 2007), pp. 361–397.
  4. 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).
  5. R. Ritter and R. Hahn, “Contribution to analysis of the reflection grating method,” Opt. Lasers Eng. 4, 13–24 (1983).
    [CrossRef]
  6. 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]
  7. R. Diaz-Uribe and M. Campos-García, “Null screen testing of fast convex aspheric surfaces,” Appl. Opt. 39, 2670–2677(2000).
    [CrossRef]
  8. J. Burke, T. Bothe, W. Osten, and C. Hess, “Reverse engineering by fringe projection,” Proc. SPIE 4778, 312–324 (2002).
    [CrossRef]
  9. 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]
  10. 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]
  11. Y. Surrel, “Absolute flatness measurement with 10 nm resolution over a 400 mm field,” Proc. SPIE 6341, 634136 (2006).
    [CrossRef]
  12. W. Jüptner and T. Bothe, “Sub-nanometer resolution for the inspection of reflective surfaces using white light,” Proc. SPIE 7405, 740502 (2009).
    [CrossRef]
  13. For example, G. HaeuslerM. Knauer, , and R. Lampalzer, “Method and apparatus for determining the shape and the local surface normals of specular surfaces,” U.S. patent 7,532,333 (12 May 2009).
  14. Ondulo from VISUOL Technologies, Metz, France, www.visuol.com.
  15. CSP Services GmbH, QDec, www.cspservices.eu/files/downloads/CSPServices_OptimizingSolarPower.pdf.
  16. www.rehnu.com.
  17. J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
    [CrossRef]
  18. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980).
    [CrossRef]
  19. D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779, 148–160 (2002).
    [CrossRef]
  20. K. A. Winick, “Cramer–Rao lower bounds on the performance of charge-coupled-device optical position estimators,” J. Opt. Soc. Am. A 3, 1809–1815 (1986).
    [CrossRef]
  21. W. Osten, W. Nadeborn, and P. Andrä, “General hierarchical approach in absolute phase measurement,” Proc. SPIE 2860, 2–13 (1996).
    [CrossRef]
  22. J. M. Huntley and H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
    [CrossRef]
  23. M. Petz and R. Tutsch, “Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces,” Proc. SPIE 5869, 58691D (2005).
    [CrossRef]
  24. www.keyence.com.
  25. R. P. Angel and W. B. Davison, “Solar concentrator apparatus with large, multiple, co-axis dish reflectors,” U.S. patent application number 20090277440 (12 November 2009).
  26. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  27. L. Wang, P. Su, R. E. Parks, Y. Wang, R. P. Angel, J. M. Sasian, and J. H. Burge, “A low-cost, flexible, high dynamic range test for free-form illumination optics, ” presented at the International Optical Design Conference Jackson Hole, Wyoming, USA, 13–17 June 2010.
  28. J. H. Burge, L. B. Kot, H. M. Martin, R. Zehnder, and C. Zhao, “Design and analysis for interferometric measurements of the GMT primary mirror segments,” Proc. SPIE 6273, 62730M (2006).
    [CrossRef]
  29. J. H. Burge, C. Zhao, and M. Dubin, “Use of the Abbe sine condition to quantify alignment aberrations in optical imaging systems,” presented at the International Optical Design Conference Jackson Hole, Wyoming, USA, 13–17 June 2010.
  30. www.emargin.com.
  31. www.kopin.com.

2009 (1)

W. Jüptner and T. Bothe, “Sub-nanometer resolution for the inspection of reflective surfaces using white light,” Proc. SPIE 7405, 740502 (2009).
[CrossRef]

2007 (3)

J. Ojeda-Castañeda, “Foucault, wire, and phase modulation tests,” in Optical Shop Testing, 3rd ed., D.Malacara, ed., Wiley Series in Pure and Applied Optics (Wiley, 2007), pp. 275–316.

A. Cornejo-Rodriguez, “Ronchi test,” in Optical Shop Testing, 3rd ed., D.Malacara, ed., Wiley Series in Pure and Applied Optics (Wiley, 2007), pp. 317–360.

D. Malacara-Doblado and I. Ghozeil, “Hartmann, Hartmann-Shack, and other screen tests,” in Optical Shop Testing, 3rd ed., D.Malacara, ed., Wiley Series in Pure and Applied Optics (Wiley, 2007), pp. 361–397.

2006 (2)

Y. Surrel, “Absolute flatness measurement with 10 nm resolution over a 400 mm field,” Proc. SPIE 6341, 634136 (2006).
[CrossRef]

J. H. Burge, L. B. Kot, H. M. Martin, R. Zehnder, and C. Zhao, “Design and analysis for interferometric measurements of the GMT primary mirror segments,” Proc. SPIE 6273, 62730M (2006).
[CrossRef]

2005 (1)

M. Petz and R. Tutsch, “Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces,” Proc. SPIE 5869, 58691D (2005).
[CrossRef]

2004 (2)

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]

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]

2002 (2)

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779, 148–160 (2002).
[CrossRef]

J. Burke, T. Bothe, W. Osten, and C. Hess, “Reverse engineering by fringe projection,” Proc. SPIE 4778, 312–324 (2002).
[CrossRef]

2000 (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]

1996 (1)

W. Osten, W. Nadeborn, and P. Andrä, “General hierarchical approach in absolute phase measurement,” Proc. SPIE 2860, 2–13 (1996).
[CrossRef]

1993 (1)

1992 (1)

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

1986 (1)

1983 (1)

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

1980 (1)

1976 (1)

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J Opt. Soc. Am. 66, 207–211 (1976).
[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).

Andrä, P.

W. Osten, W. Nadeborn, and P. Andrä, “General hierarchical approach in absolute phase measurement,” Proc. SPIE 2860, 2–13 (1996).
[CrossRef]

Angel, R. P.

L. Wang, P. Su, R. E. Parks, Y. Wang, R. P. Angel, J. M. Sasian, and J. H. Burge, “A low-cost, flexible, high dynamic range test for free-form illumination optics, ” presented at the International Optical Design Conference Jackson Hole, Wyoming, USA, 13–17 June 2010.

R. P. Angel and W. B. Davison, “Solar concentrator apparatus with large, multiple, co-axis dish reflectors,” U.S. patent application number 20090277440 (12 November 2009).

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.

W. Jüptner and T. Bothe, “Sub-nanometer resolution for the inspection of reflective surfaces using white light,” Proc. SPIE 7405, 740502 (2009).
[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]

J. Burke, T. Bothe, W. Osten, and C. Hess, “Reverse engineering by fringe projection,” Proc. SPIE 4778, 312–324 (2002).
[CrossRef]

Burge, J. H.

J. H. Burge, L. B. Kot, H. M. Martin, R. Zehnder, and C. Zhao, “Design and analysis for interferometric measurements of the GMT primary mirror segments,” Proc. SPIE 6273, 62730M (2006).
[CrossRef]

J. H. Burge, C. Zhao, and M. Dubin, “Use of the Abbe sine condition to quantify alignment aberrations in optical imaging systems,” presented at the International Optical Design Conference Jackson Hole, Wyoming, USA, 13–17 June 2010.

L. Wang, P. Su, R. E. Parks, Y. Wang, R. P. Angel, J. M. Sasian, and J. H. Burge, “A low-cost, flexible, high dynamic range test for free-form illumination optics, ” presented at the International Optical Design Conference Jackson Hole, Wyoming, USA, 13–17 June 2010.

Burke, J.

J. Burke, T. Bothe, W. Osten, and C. Hess, “Reverse engineering by fringe projection,” Proc. SPIE 4778, 312–324 (2002).
[CrossRef]

Campos-García, M.

Cohen, P.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

Copland, J.

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779, 148–160 (2002).
[CrossRef]

Cornejo-Rodriguez, A.

A. Cornejo-Rodriguez, “Ronchi test,” in Optical Shop Testing, 3rd ed., D.Malacara, ed., Wiley Series in Pure and Applied Optics (Wiley, 2007), pp. 317–360.

Davison, W. B.

R. P. Angel and W. B. Davison, “Solar concentrator apparatus with large, multiple, co-axis dish reflectors,” U.S. patent application number 20090277440 (12 November 2009).

Diaz-Uribe, R.

Dubin, M.

J. H. Burge, C. Zhao, and M. Dubin, “Use of the Abbe sine condition to quantify alignment aberrations in optical imaging systems,” presented at the International Optical Design Conference Jackson Hole, Wyoming, USA, 13–17 June 2010.

Ghozeil, I.

D. Malacara-Doblado and I. Ghozeil, “Hartmann, Hartmann-Shack, and other screen tests,” in Optical Shop Testing, 3rd ed., D.Malacara, ed., Wiley Series in Pure and Applied Optics (Wiley, 2007), pp. 361–397.

Haeusler, G.

For example, G. HaeuslerM. Knauer, , and R. Lampalzer, “Method and apparatus for determining the shape and the local surface normals of specular surfaces,” U.S. patent 7,532,333 (12 May 2009).

Hahn, R.

R. Ritter and R. Hahn, “Contribution to analysis of the reflection grating method,” Opt. Lasers Eng. 4, 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]

Herniou, M.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

Hess, C.

J. Burke, T. Bothe, W. Osten, and C. Hess, “Reverse engineering by fringe projection,” Proc. SPIE 4778, 312–324 (2002).
[CrossRef]

Huntley, J. M.

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.

W. Jüptner and T. Bothe, “Sub-nanometer resolution for the inspection of reflective surfaces using white light,” Proc. SPIE 7405, 740502 (2009).
[CrossRef]

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]

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]

For example, G. HaeuslerM. Knauer, , and R. Lampalzer, “Method and apparatus for determining the shape and the local surface normals of specular surfaces,” U.S. patent 7,532,333 (12 May 2009).

Kot, L. B.

J. H. Burge, L. B. Kot, H. M. Martin, R. Zehnder, and C. Zhao, “Design and analysis for interferometric measurements of the GMT primary mirror segments,” Proc. SPIE 6273, 62730M (2006).
[CrossRef]

Lampalzer, R.

For example, G. HaeuslerM. Knauer, , and R. Lampalzer, “Method and apparatus for determining the shape and the local surface normals of specular surfaces,” U.S. patent 7,532,333 (12 May 2009).

Li, 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]

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).

Malacara-Doblado, D.

D. Malacara-Doblado and I. Ghozeil, “Hartmann, Hartmann-Shack, and other screen tests,” in Optical Shop Testing, 3rd ed., D.Malacara, ed., Wiley Series in Pure and Applied Optics (Wiley, 2007), pp. 361–397.

Martin, H. M.

J. H. Burge, L. B. Kot, H. M. Martin, R. Zehnder, and C. Zhao, “Design and analysis for interferometric measurements of the GMT primary mirror segments,” Proc. SPIE 6273, 62730M (2006).
[CrossRef]

Nadeborn, W.

W. Osten, W. Nadeborn, and P. Andrä, “General hierarchical approach in absolute phase measurement,” Proc. SPIE 2860, 2–13 (1996).
[CrossRef]

Neal, D.

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779, 148–160 (2002).
[CrossRef]

Neal, D. R.

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779, 148–160 (2002).
[CrossRef]

Noll, R. J.

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J Opt. Soc. Am. 66, 207–211 (1976).
[CrossRef]

Ojeda-Castañeda, J.

J. Ojeda-Castañeda, “Foucault, wire, and phase modulation tests,” in Optical Shop Testing, 3rd ed., D.Malacara, ed., Wiley Series in Pure and Applied Optics (Wiley, 2007), pp. 275–316.

Osten, W.

J. Burke, T. Bothe, W. Osten, and C. Hess, “Reverse engineering by fringe projection,” Proc. SPIE 4778, 312–324 (2002).
[CrossRef]

W. Osten, W. Nadeborn, and P. Andrä, “General hierarchical approach in absolute phase measurement,” Proc. SPIE 2860, 2–13 (1996).
[CrossRef]

Parks, R. E.

L. Wang, P. Su, R. E. Parks, Y. Wang, R. P. Angel, J. M. Sasian, and J. H. Burge, “A low-cost, flexible, high dynamic range test for free-form illumination optics, ” presented at the International Optical Design Conference Jackson Hole, Wyoming, USA, 13–17 June 2010.

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]

Petz, M.

M. Petz and R. Tutsch, “Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces,” Proc. SPIE 5869, 58691D (2005).
[CrossRef]

Ritter, R.

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

Saldner, H.

Sasian, J. M.

L. Wang, P. Su, R. E. Parks, Y. Wang, R. P. Angel, J. M. Sasian, and J. H. Burge, “A low-cost, flexible, high dynamic range test for free-form illumination optics, ” presented at the International Optical Design Conference Jackson Hole, Wyoming, USA, 13–17 June 2010.

Southwell, W. H.

Su, P.

L. Wang, P. Su, R. E. Parks, Y. Wang, R. P. Angel, J. M. Sasian, and J. H. Burge, “A low-cost, flexible, high dynamic range test for free-form illumination optics, ” presented at the International Optical Design Conference Jackson Hole, Wyoming, USA, 13–17 June 2010.

Surrel, Y.

Y. Surrel, “Absolute flatness measurement with 10 nm resolution over a 400 mm field,” Proc. SPIE 6341, 634136 (2006).
[CrossRef]

Tutsch, R.

M. Petz and R. Tutsch, “Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces,” Proc. SPIE 5869, 58691D (2005).
[CrossRef]

von Kopylow, C.

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]

Wang, L.

L. Wang, P. Su, R. E. Parks, Y. Wang, R. P. Angel, J. M. Sasian, and J. H. Burge, “A low-cost, flexible, high dynamic range test for free-form illumination optics, ” presented at the International Optical Design Conference Jackson Hole, Wyoming, USA, 13–17 June 2010.

Wang, Y.

L. Wang, P. Su, R. E. Parks, Y. Wang, R. P. Angel, J. M. Sasian, and J. H. Burge, “A low-cost, flexible, high dynamic range test for free-form illumination optics, ” presented at the International Optical Design Conference Jackson Hole, Wyoming, USA, 13–17 June 2010.

Weng, J.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

Winick, K. A.

Zehnder, R.

J. H. Burge, L. B. Kot, H. M. Martin, R. Zehnder, and C. Zhao, “Design and analysis for interferometric measurements of the GMT primary mirror segments,” Proc. SPIE 6273, 62730M (2006).
[CrossRef]

Zhao, C.

J. H. Burge, L. B. Kot, H. M. Martin, R. Zehnder, and C. Zhao, “Design and analysis for interferometric measurements of the GMT primary mirror segments,” Proc. SPIE 6273, 62730M (2006).
[CrossRef]

J. H. Burge, C. Zhao, and M. Dubin, “Use of the Abbe sine condition to quantify alignment aberrations in optical imaging systems,” presented at the International Optical Design Conference Jackson Hole, Wyoming, USA, 13–17 June 2010.

Appl. Opt. (2)

IEEE Trans. Pattern Anal. Mach. Intell. (1)

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

J Opt. Soc. Am. (1)

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J Opt. Soc. Am. 66, 207–211 (1976).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Lasers Eng. (1)

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

Proc. Soc. Exp. Stress Anal. (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).

Proc. SPIE (10)

J. H. Burge, L. B. Kot, H. M. Martin, R. Zehnder, and C. Zhao, “Design and analysis for interferometric measurements of the GMT primary mirror segments,” Proc. SPIE 6273, 62730M (2006).
[CrossRef]

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]

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779, 148–160 (2002).
[CrossRef]

W. Osten, W. Nadeborn, and P. Andrä, “General hierarchical approach in absolute phase measurement,” Proc. SPIE 2860, 2–13 (1996).
[CrossRef]

M. Petz and R. Tutsch, “Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces,” Proc. SPIE 5869, 58691D (2005).
[CrossRef]

J. Burke, T. Bothe, W. Osten, and C. Hess, “Reverse engineering by fringe projection,” Proc. SPIE 4778, 312–324 (2002).
[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]

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]

Y. Surrel, “Absolute flatness measurement with 10 nm resolution over a 400 mm field,” Proc. SPIE 6341, 634136 (2006).
[CrossRef]

W. Jüptner and T. Bothe, “Sub-nanometer resolution for the inspection of reflective surfaces using white light,” Proc. SPIE 7405, 740502 (2009).
[CrossRef]

Other (13)

For example, G. HaeuslerM. Knauer, , and R. Lampalzer, “Method and apparatus for determining the shape and the local surface normals of specular surfaces,” U.S. patent 7,532,333 (12 May 2009).

Ondulo from VISUOL Technologies, Metz, France, www.visuol.com.

CSP Services GmbH, QDec, www.cspservices.eu/files/downloads/CSPServices_OptimizingSolarPower.pdf.

www.rehnu.com.

www.keyence.com.

R. P. Angel and W. B. Davison, “Solar concentrator apparatus with large, multiple, co-axis dish reflectors,” U.S. patent application number 20090277440 (12 November 2009).

J. Ojeda-Castañeda, “Foucault, wire, and phase modulation tests,” in Optical Shop Testing, 3rd ed., D.Malacara, ed., Wiley Series in Pure and Applied Optics (Wiley, 2007), pp. 275–316.

A. Cornejo-Rodriguez, “Ronchi test,” in Optical Shop Testing, 3rd ed., D.Malacara, ed., Wiley Series in Pure and Applied Optics (Wiley, 2007), pp. 317–360.

D. Malacara-Doblado and I. Ghozeil, “Hartmann, Hartmann-Shack, and other screen tests,” in Optical Shop Testing, 3rd ed., D.Malacara, ed., Wiley Series in Pure and Applied Optics (Wiley, 2007), pp. 361–397.

J. H. Burge, C. Zhao, and M. Dubin, “Use of the Abbe sine condition to quantify alignment aberrations in optical imaging systems,” presented at the International Optical Design Conference Jackson Hole, Wyoming, USA, 13–17 June 2010.

www.emargin.com.

www.kopin.com.

L. Wang, P. Su, R. E. Parks, Y. Wang, R. P. Angel, J. M. Sasian, and J. H. Burge, “A low-cost, flexible, high dynamic range test for free-form illumination optics, ” presented at the International Optical Design Conference Jackson Hole, Wyoming, USA, 13–17 June 2010.

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