Abstract

Increasing accuracy requirements in aspheric metrology make the development of absolute testing procedures for aspheric surfaces important. One strategy is transferring the standard practice three-position test for spheres to aspherics. The three-position test, however, involves a cat’s eye position and therefore has certain drawbacks. We propose an absolute testing method for rotationally symmetric aspherics where the cat’s eye position is replaced with a radially sheared position. Together with rotational movements of the specimen, the surface deviations can be obtained in an absolute manner. To demonstrate the validity of the procedure, we present a measurement result for a sphere and compare it with a result obtained by the standard three-position test.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Schulz and J. Schwider, in Progress in Optics, E.Wolf, ed. (Elsevier, 1976), Vol. XIII, pp. 93-167.
    [CrossRef]
  2. J. Schwider, OSA Trends Opt. Photonics Ser. 24, 103 (1999).
  3. A. E. Jensen, J. Opt. Soc. Am. 63, 1313A (1973).
  4. J. Schwider, “Absolutprüfung von asphärischen Flächen unter Zuhilfenahme von diffraktiven Normalelementen und planen sowie sphärischen Referenzflächen,” German patent 19822453.2 (June 20, 1998).
  5. M. Beyerlein, N. Lindlein, and J. Schwider, Appl. Opt. 41, 2440 (2002).
    [CrossRef] [PubMed]
  6. S. Reichelt, C. Pruss, and H. J. Tiziani, Appl. Opt. 42, 4468 (2003).
    [CrossRef] [PubMed]
  7. F. Simon, G. Khan, K. Mantel, N. Lindlein, and J. Schwider, Appl. Opt. 45, 8606 (2006).
    [CrossRef] [PubMed]
  8. G. Khan, K. Mantel, I. Harder, N. Lindlein, and J. Schwider, Appl. Opt. 46, 7040 (2007).
    [CrossRef] [PubMed]
  9. M. F. Küchel, “Apparatus and method(s) for reducing the effects of coherent artifacts in an interferometer,” U.S. patent 6,804,011 (October 12, 2004).
  10. B. Dörband and G. Seitz, Optik (Stuttgart) 112, 392 (2001).
    [CrossRef]
  11. G. Seitz, in DgaO Proceedings (2006).
  12. C. J. Evans and R. N. Kestner, Appl. Opt. 35, 1015 (1996).
    [CrossRef] [PubMed]
  13. A. F. Fercher, Opt. Acta 23, 347 (1976).
    [CrossRef]

2007 (1)

2006 (1)

2003 (1)

2002 (1)

2001 (1)

B. Dörband and G. Seitz, Optik (Stuttgart) 112, 392 (2001).
[CrossRef]

1999 (1)

J. Schwider, OSA Trends Opt. Photonics Ser. 24, 103 (1999).

1996 (1)

1976 (1)

A. F. Fercher, Opt. Acta 23, 347 (1976).
[CrossRef]

1973 (1)

A. E. Jensen, J. Opt. Soc. Am. 63, 1313A (1973).

Beyerlein, M.

Dörband, B.

B. Dörband and G. Seitz, Optik (Stuttgart) 112, 392 (2001).
[CrossRef]

Evans, C. J.

Fercher, A. F.

A. F. Fercher, Opt. Acta 23, 347 (1976).
[CrossRef]

Harder, I.

Jensen, A. E.

A. E. Jensen, J. Opt. Soc. Am. 63, 1313A (1973).

Kestner, R. N.

Khan, G.

Küchel, M. F.

M. F. Küchel, “Apparatus and method(s) for reducing the effects of coherent artifacts in an interferometer,” U.S. patent 6,804,011 (October 12, 2004).

Lindlein, N.

Mantel, K.

Pruss, C.

Reichelt, S.

Schulz, G.

G. Schulz and J. Schwider, in Progress in Optics, E.Wolf, ed. (Elsevier, 1976), Vol. XIII, pp. 93-167.
[CrossRef]

Schwider, J.

G. Khan, K. Mantel, I. Harder, N. Lindlein, and J. Schwider, Appl. Opt. 46, 7040 (2007).
[CrossRef] [PubMed]

F. Simon, G. Khan, K. Mantel, N. Lindlein, and J. Schwider, Appl. Opt. 45, 8606 (2006).
[CrossRef] [PubMed]

M. Beyerlein, N. Lindlein, and J. Schwider, Appl. Opt. 41, 2440 (2002).
[CrossRef] [PubMed]

J. Schwider, OSA Trends Opt. Photonics Ser. 24, 103 (1999).

G. Schulz and J. Schwider, in Progress in Optics, E.Wolf, ed. (Elsevier, 1976), Vol. XIII, pp. 93-167.
[CrossRef]

J. Schwider, “Absolutprüfung von asphärischen Flächen unter Zuhilfenahme von diffraktiven Normalelementen und planen sowie sphärischen Referenzflächen,” German patent 19822453.2 (June 20, 1998).

Seitz, G.

B. Dörband and G. Seitz, Optik (Stuttgart) 112, 392 (2001).
[CrossRef]

G. Seitz, in DgaO Proceedings (2006).

Simon, F.

Tiziani, H. J.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

A. E. Jensen, J. Opt. Soc. Am. 63, 1313A (1973).

Opt. Acta (1)

A. F. Fercher, Opt. Acta 23, 347 (1976).
[CrossRef]

Optik (Stuttgart) (1)

B. Dörband and G. Seitz, Optik (Stuttgart) 112, 392 (2001).
[CrossRef]

OSA Trends Opt. Photonics Ser. (1)

J. Schwider, OSA Trends Opt. Photonics Ser. 24, 103 (1999).

Other (4)

G. Schulz and J. Schwider, in Progress in Optics, E.Wolf, ed. (Elsevier, 1976), Vol. XIII, pp. 93-167.
[CrossRef]

J. Schwider, “Absolutprüfung von asphärischen Flächen unter Zuhilfenahme von diffraktiven Normalelementen und planen sowie sphärischen Referenzflächen,” German patent 19822453.2 (June 20, 1998).

M. F. Küchel, “Apparatus and method(s) for reducing the effects of coherent artifacts in an interferometer,” U.S. patent 6,804,011 (October 12, 2004).

G. Seitz, in DgaO Proceedings (2006).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Radial shear movement. Upper part, different points of the surface (represented by the circle and the square) are related to the same interferometer “point” (represented by the black dot). Lower part, the surface deviations at radial distance r are therefore sheared by an r-dependent amount δ r with respect to the systematic aberrations of the setup, depending on the vertex distances z 0 and z 1 .

Fig. 2
Fig. 2

Absolute test via measuring difference quotients.

Fig. 3
Fig. 3

Absolute test via rotational averaging.

Fig. 4
Fig. 4

Radial shear as a function of radial coordinate r for several ideal lens shapes and two parameter sets.

Fig. 5
Fig. 5

Absolute testing results of a concave sphere, with radius R = 49.35   mm . Left, absolute result obtained via measuring difference quotients, z 0 = 75.11   mm , z 1 = 80.11   mm , represented by Zernike polynomials of degree 12. The central part has been cut to avoid systematic errors owing to the low sensitivity in this region. Right, difference to an absolute result obtained via three-position test, after a polynomial fit of degree 12. All values are in λ = 633   nm .

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

δ r ( r ) = r z 1 + R z 0 + R r = r d z 0 + R ,

Metrics