Abstract

A complete absolute interferometric test of axially symmetric aspheres is presented. The method is based on a specially designed computer-generated hologram (CGH) that reconstructs an aspherical wave as well as a spherical auxiliary wave. Since both phase functions have the same symmetry and their pattern is simultaneously encoded, we call this type of multiplex hologram a Twin-CGH. The spherical wave is used for calibration. The aberrations of the spherical auxiliary wave are measured absolutely with either a spherical mirror or an absolute test for Fresnel zone plates. Thus the two types of aberration inherent in the CGH can be identified and separated from each other. The errors of the spherical wave can be transferred to those of the aspherical wave. Two different methods that use Twin-CGHs for absolute testing of aspheric surfaces are described. Test procedures are explained, equations are derived, and experimental results are presented. A mutual comparison of the two results and a comparison with the established N-position rotation test are given.

© 2003 Optical Society of America

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References

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  1. A. E. Jensen, “Absolute calibration method for laser Twyman‐Green wave-front testing interferometers,” J. Opt. Soc. Am. 63, p. 1313A (1973)(abstract only).
  2. G. Schulz, “Interferentielle Absolutprüfung zweier Flächen,” Opt. Acta 20, 699–706 (1973).
    [CrossRef]
  3. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
    [CrossRef] [PubMed]
  4. K.-E. Elssner, J. Grzanna, G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563–580 (1980).
    [CrossRef]
  5. B. E. Truax, “Absolute interferometric testing of spherical surfaces,” in Optical Fabrication and Testing, D. R. Campbell, C. W. Johnson, M. Lorenzen, eds., Proc. SPIE966, 130–137 (1988).
  6. K.-E. Elssner, R. Burow, J. Grzanna, R. Spolaczyk, “Absolute sphericity measurement,” Appl. Opt. 28, 4649–4661 (1989).
    [CrossRef] [PubMed]
  7. K. Creath, J. C. Wyant, “Testing spherical surfaces: a fast, quasi-absolute technique,” Appl. Opt. 31, 4350–4354 (1992).
    [CrossRef] [PubMed]
  8. L. A. Selberg, “Absolute testing of spherical surfaces,” in Optical Fabrication and Testing, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 181–184.
  9. P. E. Murphy, T. G. Brown, D. T. Moore, “Interference imaging for aspheric surface testing,” Appl. Opt. 39, 2122–2129 (2000).
    [CrossRef]
  10. P. E. Murphy, T. G. Brown, D. T. Moore, “Measurement and calibration of interferometric imaging aberrations,” Appl. Opt. 39, 6421–6429 (2000).
    [CrossRef]
  11. A. Davies, C. Tarrio, C. Evans, “Advanced optics characterization,” Opt. Photon. News 12, 34–37 (2001), http://www.opticsexpress.org .
    [CrossRef]
  12. S. Reichelt, C. Pruss, H. J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” in Interferometry XI: Applications, W. Osten, ed., Proc. SPIE4778, 158–168 (2002).
    [CrossRef]
  13. R. Freimann, B. Dörband, F. Höller, “Absolute measurement of non-comatic aspheric surface errors,” Opt. Commun. 161, 106–114 (1999).
    [CrossRef]
  14. R. E. Parks, “Removal of test optics errors,” in Advances in Optical Metrology I, N. Balasubramanian, J. C. Wyant, eds., Proc. SPIE153, 56–63 (1978).
    [CrossRef]
  15. C. J. Evans, R. N. Kestner, “Test optics error removal,” Appl. Opt. 35, 1015–1021 (1996).
    [CrossRef] [PubMed]
  16. D. S. Anderson, J. H. Burge, “Swing-arm profilometry of aspherics,” in Optical Manufacturing and Testing, V. J. Doherty, H. P. Stahl, eds., Proc. SPIE2536, 169–179 (1995).
    [CrossRef]
  17. F. Schillke, “Critical aspects of testing aspheres in interferometric setups,” in Optical Fabrication and Testing, R. Geyl, J. Maxwell, eds., Proc. SPIE3739, 317–324 (1999).
    [CrossRef]
  18. A. F. Fercher, “Computer-generated holograms for testing optical elements: error analysis and error compensation,” Opt. Acta 23, 347–365 (1976).
    [CrossRef]
  19. T. Yatagai, H. Saito, “Dual computer-generated holograms for testing aspherical surfaces,” Opt. Acta 26, 985–993 (1979).
    [CrossRef]
  20. M. Beyerlein, N. Lindlein, J. Schwider, “Dual-wave-front computer-generated holograms for quasi-absolute testing of aspherics,” Appl. Opt. 41, 2440–2447 (2002).
    [CrossRef] [PubMed]
  21. A. G. Poleshchuk, E. G. Churin, V. P. Koronkevich, V. P. Korolkov, A. A. Kharissov, V. V. Cherkashin, V. P. Kiryanov, A. V. Kiryanov, S. A. Kokarev, A. G. Verhoglyad, “Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure,” Appl. Opt. 38, 1295–1301 (1999).
    [CrossRef]
  22. S. Reichelt, H. J. Tiziani, “Twin-CGHs for absolute calibration in wavefront testing interferometry,” Opt. Commun. 220, 23–32 (2003).
    [CrossRef]
  23. J. C. Wyant, P. K. O’Neill, A. J. MacGovern, “Interferometric method of measuring plotter distortion,” Appl. Opt. 13, 1549–1551 (1974).
    [CrossRef] [PubMed]
  24. S. Reichelt, R. Freimann, H. J. Tiziani, “Absolute interferometric test of Fresnel zone plates,” Opt. Commun. 200, 107–117 (2001).
    [CrossRef]
  25. C. J. Evans, R. E. Parks, P. J. Sullivan, J. S. Taylor, “Visualization of surface figure by the use of Zernike polynomials,” Appl. Opt. 34, 7815–7819 (1995).
    [CrossRef] [PubMed]
  26. E. B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, L. Wittig, “Investigation of large null-CGH realization,” in Lithographic and Micromachining Techniques for Optical Component Fabrication, E.-B. Kley, H.-P. Herzig, eds., Proc. SPIE4440, 135–144 (2001).
    [CrossRef]
  27. J. Schwider, R. Burow, “Wave aberrations caused by misalignments of aspherics, and their elimination,” Opt. Appl. 9, 33–38 (1979).
  28. B. Dörband, H. J. Tiziani, “Testing aspheric surfaces with computer-generated holograms: analysis of adjustment and shape errors,” Appl. Opt. 24, 2604–2611 (1985).
    [CrossRef] [PubMed]
  29. L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1966 (1992).
    [CrossRef]

2003 (1)

S. Reichelt, H. J. Tiziani, “Twin-CGHs for absolute calibration in wavefront testing interferometry,” Opt. Commun. 220, 23–32 (2003).
[CrossRef]

2002 (1)

2001 (2)

S. Reichelt, R. Freimann, H. J. Tiziani, “Absolute interferometric test of Fresnel zone plates,” Opt. Commun. 200, 107–117 (2001).
[CrossRef]

A. Davies, C. Tarrio, C. Evans, “Advanced optics characterization,” Opt. Photon. News 12, 34–37 (2001), http://www.opticsexpress.org .
[CrossRef]

2000 (2)

1999 (2)

1996 (1)

1995 (1)

1992 (2)

1989 (1)

1985 (1)

1980 (1)

K.-E. Elssner, J. Grzanna, G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563–580 (1980).
[CrossRef]

1979 (2)

J. Schwider, R. Burow, “Wave aberrations caused by misalignments of aspherics, and their elimination,” Opt. Appl. 9, 33–38 (1979).

T. Yatagai, H. Saito, “Dual computer-generated holograms for testing aspherical surfaces,” Opt. Acta 26, 985–993 (1979).
[CrossRef]

1976 (1)

A. F. Fercher, “Computer-generated holograms for testing optical elements: error analysis and error compensation,” Opt. Acta 23, 347–365 (1976).
[CrossRef]

1974 (2)

1973 (2)

A. E. Jensen, “Absolute calibration method for laser Twyman‐Green wave-front testing interferometers,” J. Opt. Soc. Am. 63, p. 1313A (1973)(abstract only).

G. Schulz, “Interferentielle Absolutprüfung zweier Flächen,” Opt. Acta 20, 699–706 (1973).
[CrossRef]

Anderson, D. S.

D. S. Anderson, J. H. Burge, “Swing-arm profilometry of aspherics,” in Optical Manufacturing and Testing, V. J. Doherty, H. P. Stahl, eds., Proc. SPIE2536, 169–179 (1995).
[CrossRef]

Beyerlein, M.

Brangaccio, D. J.

Brown, T. G.

Bruning, J. H.

Burge, J. H.

D. S. Anderson, J. H. Burge, “Swing-arm profilometry of aspherics,” in Optical Manufacturing and Testing, V. J. Doherty, H. P. Stahl, eds., Proc. SPIE2536, 169–179 (1995).
[CrossRef]

Burow, R.

K.-E. Elssner, R. Burow, J. Grzanna, R. Spolaczyk, “Absolute sphericity measurement,” Appl. Opt. 28, 4649–4661 (1989).
[CrossRef] [PubMed]

J. Schwider, R. Burow, “Wave aberrations caused by misalignments of aspherics, and their elimination,” Opt. Appl. 9, 33–38 (1979).

Cherkashin, V. V.

Churin, E. G.

Creath, K.

Davies, A.

A. Davies, C. Tarrio, C. Evans, “Advanced optics characterization,” Opt. Photon. News 12, 34–37 (2001), http://www.opticsexpress.org .
[CrossRef]

Dörband, B.

R. Freimann, B. Dörband, F. Höller, “Absolute measurement of non-comatic aspheric surface errors,” Opt. Commun. 161, 106–114 (1999).
[CrossRef]

B. Dörband, H. J. Tiziani, “Testing aspheric surfaces with computer-generated holograms: analysis of adjustment and shape errors,” Appl. Opt. 24, 2604–2611 (1985).
[CrossRef] [PubMed]

Drauschke, A.

E. B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, L. Wittig, “Investigation of large null-CGH realization,” in Lithographic and Micromachining Techniques for Optical Component Fabrication, E.-B. Kley, H.-P. Herzig, eds., Proc. SPIE4440, 135–144 (2001).
[CrossRef]

Elssner, K.-E.

K.-E. Elssner, R. Burow, J. Grzanna, R. Spolaczyk, “Absolute sphericity measurement,” Appl. Opt. 28, 4649–4661 (1989).
[CrossRef] [PubMed]

K.-E. Elssner, J. Grzanna, G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563–580 (1980).
[CrossRef]

Evans, C.

A. Davies, C. Tarrio, C. Evans, “Advanced optics characterization,” Opt. Photon. News 12, 34–37 (2001), http://www.opticsexpress.org .
[CrossRef]

Evans, C. J.

Fercher, A. F.

A. F. Fercher, “Computer-generated holograms for testing optical elements: error analysis and error compensation,” Opt. Acta 23, 347–365 (1976).
[CrossRef]

Freimann, R.

S. Reichelt, R. Freimann, H. J. Tiziani, “Absolute interferometric test of Fresnel zone plates,” Opt. Commun. 200, 107–117 (2001).
[CrossRef]

R. Freimann, B. Dörband, F. Höller, “Absolute measurement of non-comatic aspheric surface errors,” Opt. Commun. 161, 106–114 (1999).
[CrossRef]

Gallagher, J. E.

Grzanna, J.

K.-E. Elssner, R. Burow, J. Grzanna, R. Spolaczyk, “Absolute sphericity measurement,” Appl. Opt. 28, 4649–4661 (1989).
[CrossRef] [PubMed]

K.-E. Elssner, J. Grzanna, G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563–580 (1980).
[CrossRef]

Herriott, D. R.

Höller, F.

R. Freimann, B. Dörband, F. Höller, “Absolute measurement of non-comatic aspheric surface errors,” Opt. Commun. 161, 106–114 (1999).
[CrossRef]

Jensen, A. E.

A. E. Jensen, “Absolute calibration method for laser Twyman‐Green wave-front testing interferometers,” J. Opt. Soc. Am. 63, p. 1313A (1973)(abstract only).

Kestner, R. N.

Kharissov, A. A.

Kiryanov, A. V.

Kiryanov, V. P.

Kley, E. B.

E. B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, L. Wittig, “Investigation of large null-CGH realization,” in Lithographic and Micromachining Techniques for Optical Component Fabrication, E.-B. Kley, H.-P. Herzig, eds., Proc. SPIE4440, 135–144 (2001).
[CrossRef]

Kokarev, S. A.

Korolkov, V. P.

Koronkevich, V. P.

Lindlein, N.

MacGovern, A. J.

Moore, D. T.

Murphy, P. E.

O’Neill, P. K.

Parks, R. E.

C. J. Evans, R. E. Parks, P. J. Sullivan, J. S. Taylor, “Visualization of surface figure by the use of Zernike polynomials,” Appl. Opt. 34, 7815–7819 (1995).
[CrossRef] [PubMed]

R. E. Parks, “Removal of test optics errors,” in Advances in Optical Metrology I, N. Balasubramanian, J. C. Wyant, eds., Proc. SPIE153, 56–63 (1978).
[CrossRef]

Poleshchuk, A. G.

Pruss, C.

S. Reichelt, C. Pruss, H. J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” in Interferometry XI: Applications, W. Osten, ed., Proc. SPIE4778, 158–168 (2002).
[CrossRef]

Reichelt, S.

S. Reichelt, H. J. Tiziani, “Twin-CGHs for absolute calibration in wavefront testing interferometry,” Opt. Commun. 220, 23–32 (2003).
[CrossRef]

S. Reichelt, R. Freimann, H. J. Tiziani, “Absolute interferometric test of Fresnel zone plates,” Opt. Commun. 200, 107–117 (2001).
[CrossRef]

S. Reichelt, C. Pruss, H. J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” in Interferometry XI: Applications, W. Osten, ed., Proc. SPIE4778, 158–168 (2002).
[CrossRef]

Rockstroh, W.

E. B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, L. Wittig, “Investigation of large null-CGH realization,” in Lithographic and Micromachining Techniques for Optical Component Fabrication, E.-B. Kley, H.-P. Herzig, eds., Proc. SPIE4440, 135–144 (2001).
[CrossRef]

Rosenfeld, D. P.

Saito, H.

T. Yatagai, H. Saito, “Dual computer-generated holograms for testing aspherical surfaces,” Opt. Acta 26, 985–993 (1979).
[CrossRef]

Schillke, F.

F. Schillke, “Critical aspects of testing aspheres in interferometric setups,” in Optical Fabrication and Testing, R. Geyl, J. Maxwell, eds., Proc. SPIE3739, 317–324 (1999).
[CrossRef]

Schmidt, H.

E. B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, L. Wittig, “Investigation of large null-CGH realization,” in Lithographic and Micromachining Techniques for Optical Component Fabrication, E.-B. Kley, H.-P. Herzig, eds., Proc. SPIE4440, 135–144 (2001).
[CrossRef]

Schulz, G.

K.-E. Elssner, J. Grzanna, G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563–580 (1980).
[CrossRef]

G. Schulz, “Interferentielle Absolutprüfung zweier Flächen,” Opt. Acta 20, 699–706 (1973).
[CrossRef]

Schwider, J.

M. Beyerlein, N. Lindlein, J. Schwider, “Dual-wave-front computer-generated holograms for quasi-absolute testing of aspherics,” Appl. Opt. 41, 2440–2447 (2002).
[CrossRef] [PubMed]

J. Schwider, R. Burow, “Wave aberrations caused by misalignments of aspherics, and their elimination,” Opt. Appl. 9, 33–38 (1979).

Selberg, L. A.

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1966 (1992).
[CrossRef]

L. A. Selberg, “Absolute testing of spherical surfaces,” in Optical Fabrication and Testing, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 181–184.

Spolaczyk, R.

Sullivan, P. J.

Tarrio, C.

A. Davies, C. Tarrio, C. Evans, “Advanced optics characterization,” Opt. Photon. News 12, 34–37 (2001), http://www.opticsexpress.org .
[CrossRef]

Taylor, J. S.

Tiziani, H. J.

S. Reichelt, H. J. Tiziani, “Twin-CGHs for absolute calibration in wavefront testing interferometry,” Opt. Commun. 220, 23–32 (2003).
[CrossRef]

S. Reichelt, R. Freimann, H. J. Tiziani, “Absolute interferometric test of Fresnel zone plates,” Opt. Commun. 200, 107–117 (2001).
[CrossRef]

B. Dörband, H. J. Tiziani, “Testing aspheric surfaces with computer-generated holograms: analysis of adjustment and shape errors,” Appl. Opt. 24, 2604–2611 (1985).
[CrossRef] [PubMed]

S. Reichelt, C. Pruss, H. J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” in Interferometry XI: Applications, W. Osten, ed., Proc. SPIE4778, 158–168 (2002).
[CrossRef]

Truax, B. E.

B. E. Truax, “Absolute interferometric testing of spherical surfaces,” in Optical Fabrication and Testing, D. R. Campbell, C. W. Johnson, M. Lorenzen, eds., Proc. SPIE966, 130–137 (1988).

Verhoglyad, A. G.

White, A. D.

Wittig, L.

E. B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, L. Wittig, “Investigation of large null-CGH realization,” in Lithographic and Micromachining Techniques for Optical Component Fabrication, E.-B. Kley, H.-P. Herzig, eds., Proc. SPIE4440, 135–144 (2001).
[CrossRef]

Wyant, J. C.

Wyrowski, F.

E. B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, L. Wittig, “Investigation of large null-CGH realization,” in Lithographic and Micromachining Techniques for Optical Component Fabrication, E.-B. Kley, H.-P. Herzig, eds., Proc. SPIE4440, 135–144 (2001).
[CrossRef]

Yatagai, T.

T. Yatagai, H. Saito, “Dual computer-generated holograms for testing aspherical surfaces,” Opt. Acta 26, 985–993 (1979).
[CrossRef]

Appl. Opt. (11)

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
[CrossRef] [PubMed]

K.-E. Elssner, R. Burow, J. Grzanna, R. Spolaczyk, “Absolute sphericity measurement,” Appl. Opt. 28, 4649–4661 (1989).
[CrossRef] [PubMed]

K. Creath, J. C. Wyant, “Testing spherical surfaces: a fast, quasi-absolute technique,” Appl. Opt. 31, 4350–4354 (1992).
[CrossRef] [PubMed]

P. E. Murphy, T. G. Brown, D. T. Moore, “Interference imaging for aspheric surface testing,” Appl. Opt. 39, 2122–2129 (2000).
[CrossRef]

C. J. Evans, R. E. Parks, P. J. Sullivan, J. S. Taylor, “Visualization of surface figure by the use of Zernike polynomials,” Appl. Opt. 34, 7815–7819 (1995).
[CrossRef] [PubMed]

C. J. Evans, R. N. Kestner, “Test optics error removal,” Appl. Opt. 35, 1015–1021 (1996).
[CrossRef] [PubMed]

A. G. Poleshchuk, E. G. Churin, V. P. Koronkevich, V. P. Korolkov, A. A. Kharissov, V. V. Cherkashin, V. P. Kiryanov, A. V. Kiryanov, S. A. Kokarev, A. G. Verhoglyad, “Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure,” Appl. Opt. 38, 1295–1301 (1999).
[CrossRef]

B. Dörband, H. J. Tiziani, “Testing aspheric surfaces with computer-generated holograms: analysis of adjustment and shape errors,” Appl. Opt. 24, 2604–2611 (1985).
[CrossRef] [PubMed]

P. E. Murphy, T. G. Brown, D. T. Moore, “Measurement and calibration of interferometric imaging aberrations,” Appl. Opt. 39, 6421–6429 (2000).
[CrossRef]

M. Beyerlein, N. Lindlein, J. Schwider, “Dual-wave-front computer-generated holograms for quasi-absolute testing of aspherics,” Appl. Opt. 41, 2440–2447 (2002).
[CrossRef] [PubMed]

J. C. Wyant, P. K. O’Neill, A. J. MacGovern, “Interferometric method of measuring plotter distortion,” Appl. Opt. 13, 1549–1551 (1974).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

A. E. Jensen, “Absolute calibration method for laser Twyman‐Green wave-front testing interferometers,” J. Opt. Soc. Am. 63, p. 1313A (1973)(abstract only).

Opt. Acta (4)

G. Schulz, “Interferentielle Absolutprüfung zweier Flächen,” Opt. Acta 20, 699–706 (1973).
[CrossRef]

K.-E. Elssner, J. Grzanna, G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563–580 (1980).
[CrossRef]

A. F. Fercher, “Computer-generated holograms for testing optical elements: error analysis and error compensation,” Opt. Acta 23, 347–365 (1976).
[CrossRef]

T. Yatagai, H. Saito, “Dual computer-generated holograms for testing aspherical surfaces,” Opt. Acta 26, 985–993 (1979).
[CrossRef]

Opt. Appl. (1)

J. Schwider, R. Burow, “Wave aberrations caused by misalignments of aspherics, and their elimination,” Opt. Appl. 9, 33–38 (1979).

Opt. Commun. (3)

S. Reichelt, H. J. Tiziani, “Twin-CGHs for absolute calibration in wavefront testing interferometry,” Opt. Commun. 220, 23–32 (2003).
[CrossRef]

S. Reichelt, R. Freimann, H. J. Tiziani, “Absolute interferometric test of Fresnel zone plates,” Opt. Commun. 200, 107–117 (2001).
[CrossRef]

R. Freimann, B. Dörband, F. Höller, “Absolute measurement of non-comatic aspheric surface errors,” Opt. Commun. 161, 106–114 (1999).
[CrossRef]

Opt. Eng. (1)

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1966 (1992).
[CrossRef]

Opt. Photon. News (1)

A. Davies, C. Tarrio, C. Evans, “Advanced optics characterization,” Opt. Photon. News 12, 34–37 (2001), http://www.opticsexpress.org .
[CrossRef]

Other (7)

S. Reichelt, C. Pruss, H. J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” in Interferometry XI: Applications, W. Osten, ed., Proc. SPIE4778, 158–168 (2002).
[CrossRef]

E. B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, L. Wittig, “Investigation of large null-CGH realization,” in Lithographic and Micromachining Techniques for Optical Component Fabrication, E.-B. Kley, H.-P. Herzig, eds., Proc. SPIE4440, 135–144 (2001).
[CrossRef]

R. E. Parks, “Removal of test optics errors,” in Advances in Optical Metrology I, N. Balasubramanian, J. C. Wyant, eds., Proc. SPIE153, 56–63 (1978).
[CrossRef]

D. S. Anderson, J. H. Burge, “Swing-arm profilometry of aspherics,” in Optical Manufacturing and Testing, V. J. Doherty, H. P. Stahl, eds., Proc. SPIE2536, 169–179 (1995).
[CrossRef]

F. Schillke, “Critical aspects of testing aspheres in interferometric setups,” in Optical Fabrication and Testing, R. Geyl, J. Maxwell, eds., Proc. SPIE3739, 317–324 (1999).
[CrossRef]

B. E. Truax, “Absolute interferometric testing of spherical surfaces,” in Optical Fabrication and Testing, D. R. Campbell, C. W. Johnson, M. Lorenzen, eds., Proc. SPIE966, 130–137 (1988).

L. A. Selberg, “Absolute testing of spherical surfaces,” in Optical Fabrication and Testing, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 181–184.

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Figures (14)

Fig. 1
Fig. 1

Twyman‐Green interferometer setups for CGH null testing of aspheric surfaces. (a) Testing of an aspheric surface with a single diffractive null lens or (b) with a hybrid null system.

Fig. 2
Fig. 2

Sagitta of an asphere, its best-fit sphere, and difference. The maximum sag deviation from the best-fit sphere is 169 μm.

Fig. 3
Fig. 3

Method 1: Setup for absolute testing of aspheric surfaces with Twin-CGH used as a null lens. (a) Calibration with a Twin-CGH used as a zone plate (FZL mode in -1 order). (b) Calibration with a Twin-CGH used as a zone plate (FZL mode in +1 order). (c) Null test of the asphere with a Twin-CGH used in null mode.

Fig. 4
Fig. 4

Spatial frequencies ν of the Twin-CGH versus the radius h.

Fig. 5
Fig. 5

Flow chart of the measurement and calibration procedure for absolute testing of an asphere with Twin-CGHs (method 1).

Fig. 6
Fig. 6

Result of the aspheric absolute test according to method 1. Wave-front error of the asphere W ASPH.

Fig. 7
Fig. 7

Bar chart diagram of the Zernike aberrations25 of the wave front W ASPH depicted in Fig. 6. The main parts of the aberrations are primary astigmatism (m = 2, n = 2) and spherical aberration (m = 0).

Fig. 8
Fig. 8

Method 2: Setup for absolute testing of aspheric surfaces with calibration of a hybrid null system. (a) Calibration of the diffractive master element with a Twin-CGH used as a zone plate (FZM mode). (b) Calibration of the hybrid null system with a Twin-CGH used as a diffractive aspheric master (CGH-null mode). (c) Null test of the asphere.

Fig. 9
Fig. 9

Spatial frequencies ν of the Twin-CGH versus the radius h.

Fig. 10
Fig. 10

Flow chart of the measurement and calibration procedure for absolute testing of an asphere with Twin-CGHs (method 2).

Fig. 11
Fig. 11

Result of the aspheric absolute test according to method 2. Wave-front error of the asphere W ASPH.

Fig. 12
Fig. 12

Bar chart diagram of the Zernike aberrations of the wave front W ASPH depicted in Fig. 11. The main parts of the aberrations are primary astigmatism and spherical aberration.

Fig. 13
Fig. 13

Comparison of the nonrotational wave-front error part of the asphere obtained by the proposed novel method 2 (nonrot part of Fig. 11).

Fig. 14
Fig. 14

Comparison of the nonrotational wave-front error part of the asphere obtained by the N-position test (after distortion correction). The smoother character results from averaging over N = 12 single measurements.

Tables (2)

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Table 1 Selected Zernike Aberrations Anm of the Wave Fronts Depicted in Figs. 13 and 14 a

Tables Icon

Table 2 Selected Zernike Aberrations Anm of the Wave Fronts Depicted in Figs. 6 and 11 a

Equations (23)

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WPDx, y=-mRλ0ζNx, yνNx, y,
WPD2x, y=mR2νN2x, ymR1νN1x, y WPD1x, y.
WPASS2x, y=WPASS1x, y×cosarcsin12 mR1λ0νN1x, ycosarcsin12 mR2λ0νN2x, y.
W1=WM0+WR0+WPASS0+WPD1|-10,
W2=WMπ+WR0+WPASS0+WPD1|-10,
W3=WR0+12WPASS0+WPD1|-10+WPASSπ+WPD1|-1π,
WM0=12W1+W¯2-W¯3-W3,
WINT10=WR0+WPASS0+WPD1|-10=14W1+W2-W¯1-W¯2+12W3+W¯3.
W4=WMπ+WR0+WPASS0+WPD1|+10.
WPD1|-1=-WPD1|+1.
WPD1|-10=18W1+3W2+W¯1-W¯2-12 W4.
W5=WR0+WPASS0+WPD2|-10+WASPH0.
WASPH0=W5-14W1+W2-W¯1-W¯2-12W3+W¯3+18W1+3W2+W¯1-W¯2-12 W41-mR2ν2mR1ν1.
W1=WFZMif0+WO0+WR0,
W2=WFZMifπ+WO0+WR0,
W3=WFZMef0+WO0+WR0,
W4=WFZMefπ+WO0+WR0,
W5=WR0+12WO0+WOπ,
WPD1|+10=14W1+W¯2-W¯3-W4,
WPASS10=14W1+W¯2+W¯3+W4-12W5+W¯5,
W6=WSYS0+WPD20+WPASS20=WSYS0+WNULL0.
W7=WSYS0+WASPH0.
WASPH0=W7-W6+14mR2ν2mR1ν1W1+W¯2-W¯3-W4+cosarcsin12 mR1λ0ν1cosarcsin12 mR2λ0ν214W1+W¯2+W¯3+W4-12W5+W¯5.

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