Abstract

Aspheric optical surfaces are often tested using diffractive optics as null elements. For precise measurements, the errors caused by the diffractive optical element must be calibrated. Recently, we reported first experimental results of a three position quasi-absolute test for rotationally invariant aspherics by using combined-diffractive optical elements (combo-DOEs). Here we investigate the effects of the DOE substrate errors on the proposed calibration procedure and present a set of criteria for designing an optimized combo-DOE. It is demonstrated that this optimized design enhances the overall consistency of the procedure. Furthermore, the rotationally varying part of the surface deviations is compared with the rotationally varying deviations obtained by an N-position averaging procedure and is found to be in good agreement.

© 2007 Optical Society of America

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  1. J. C. Wyant, "Null tests using compensators," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1978), pp. 381-406.
  2. J. C. Wyant and P. K. O'Neill, "Computer generated hologram; null lens test of aspheric wave fronts," Appl. Opt. 13, 2762-2765 (1974).
    [CrossRef] [PubMed]
  3. A. F. Fercher, "Computer-generated holograms for testing optical elements: error analysis and error compensation," Opt. Acta 23, 347-365 (1976).
    [CrossRef]
  4. B. Dörband and H. J. Tiziani, "Testing aspheric surfaces with computer-generated holograms: analysis of adjustment and shape errors," Appl. Opt. 24, 2604-2611 (1985).
    [CrossRef] [PubMed]
  5. J. Schwider, "Interferometric tests for apsherics," in Fabrication and Testing of Aspheres, A. Lindquist, M. Piscotty, and J. S. Taylor, eds. Vol. 24 of 1999 OSA Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 103-114.
  6. S. M. Arnold and A. K. Jain, "How to test an asphere with a computer generated hologram," Proc. SPIE 1052, 191-197 (1989).
  7. J. Schwider, "Absolutprüfung von asphärischen Flächen unter Zuhilfenahme von diffraktiven Normalelementen und planen sowie sphärischen Referenzflächen," German patent 19822453.2 (20 June 1998).
  8. A. E. Jensen, "Absolute calibration method for laser Twyman-Green wave-front testing interferometers," J. Opt. Soc. Am. 63, 1313 (1973).
  9. M. Beyerlein, N. Lindlein, and J. Schwider, "Dual-wave-front computer generated holograms for quasi-absolute testing of aspherics," Appl. Opt. 41, 2440-2447 (2002).
    [CrossRef] [PubMed]
  10. S. Reichelt, C. Pruss, and H. J. Tiziani, "Absolute interferometric test of aspheres by use of twin computer-generated holograms," Appl. Opt. 42, 4468-4479 (2003).
    [CrossRef] [PubMed]
  11. C. J. Evans and R. N. Kestner, "Test optics error removal," Appl. Opt. 35, 1015-1021 (1996).
    [CrossRef] [PubMed]
  12. R. Freimann, B. Dörband, and F. Höller, "Absolute measurement of non-comatic aspheric surface errors," Opt. Commun. 161, 106-114 (1999).
    [CrossRef]
  13. F. Simon, G. Khan, K. Mantel, N. Lindlein, and J. Schwider, "Quasi-absolute measurement of aspheres with a combined diffractive optical element as reference," Appl. Opt. 45, 8606-8612 (2006).
    [CrossRef] [PubMed]
  14. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  15. N. Lindlein, "Analysis of the disturbing diffraction orders of computer-generated holograms used for testing optical aspherics," Appl. Opt. 40, 2698-2708 (2001).
    [CrossRef]
  16. http://www.optik.uni-erlangen.de/odem/research/work/index.php?lang=d&what=ray., and N. Lindlein, F. Simon, and J. Schwider, "Simulation of micro-optical array systems with RAYTRACE," Opt. Eng. 37, 1809-1816 (1998).
    [CrossRef]
  17. E. C. Young, "Optimal removal of all mislocation effects in interferometric tests," Proc. SPIE 661, 116-124 (1986).
  18. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, "Digital wave-front measuring interferometry: some systematic error sources," Appl. Opt. 22, 3421-3432 (1983).
    [CrossRef] [PubMed]

2006 (1)

2003 (1)

2002 (1)

2001 (1)

1999 (3)

J. Schwider, "Interferometric tests for apsherics," in Fabrication and Testing of Aspheres, A. Lindquist, M. Piscotty, and J. S. Taylor, eds. Vol. 24 of 1999 OSA Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 103-114.

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

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

1998 (2)

http://www.optik.uni-erlangen.de/odem/research/work/index.php?lang=d&what=ray., and N. Lindlein, F. Simon, and J. Schwider, "Simulation of micro-optical array systems with RAYTRACE," Opt. Eng. 37, 1809-1816 (1998).
[CrossRef]

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

1996 (1)

1989 (1)

S. M. Arnold and A. K. Jain, "How to test an asphere with a computer generated hologram," Proc. SPIE 1052, 191-197 (1989).

1986 (1)

E. C. Young, "Optimal removal of all mislocation effects in interferometric tests," Proc. SPIE 661, 116-124 (1986).

1985 (1)

1983 (1)

1978 (1)

J. C. Wyant, "Null tests using compensators," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1978), pp. 381-406.

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 (1)

1973 (1)

A. E. Jensen, "Absolute calibration method for laser Twyman-Green wave-front testing interferometers," J. Opt. Soc. Am. 63, 1313 (1973).

Arnold, S. M.

S. M. Arnold and A. K. Jain, "How to test an asphere with a computer generated hologram," Proc. SPIE 1052, 191-197 (1989).

Beyerlein, M.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Burow, R.

Dörband, B.

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

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

Elssner, K.-E.

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.

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

Grzanna, J.

Höller, F.

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

Jain, A. K.

S. M. Arnold and A. K. Jain, "How to test an asphere with a computer generated hologram," Proc. SPIE 1052, 191-197 (1989).

Jensen, A. E.

A. E. Jensen, "Absolute calibration method for laser Twyman-Green wave-front testing interferometers," J. Opt. Soc. Am. 63, 1313 (1973).

Kestner, R. N.

Khan, G.

Lindlein, N.

Mantel, K.

Merkel, K.

O'Neill, P. K.

Pruss, C.

Reichelt, S.

Schwider, J.

F. Simon, G. Khan, K. Mantel, N. Lindlein, and J. Schwider, "Quasi-absolute measurement of aspheres with a combined diffractive optical element as reference," Appl. Opt. 45, 8606-8612 (2006).
[CrossRef] [PubMed]

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

J. Schwider, "Interferometric tests for apsherics," in Fabrication and Testing of Aspheres, A. Lindquist, M. Piscotty, and J. S. Taylor, eds. Vol. 24 of 1999 OSA Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 103-114.

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

http://www.optik.uni-erlangen.de/odem/research/work/index.php?lang=d&what=ray., and N. Lindlein, F. Simon, and J. Schwider, "Simulation of micro-optical array systems with RAYTRACE," Opt. Eng. 37, 1809-1816 (1998).
[CrossRef]

J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, "Digital wave-front measuring interferometry: some systematic error sources," Appl. Opt. 22, 3421-3432 (1983).
[CrossRef] [PubMed]

Simon, F.

F. Simon, G. Khan, K. Mantel, N. Lindlein, and J. Schwider, "Quasi-absolute measurement of aspheres with a combined diffractive optical element as reference," Appl. Opt. 45, 8606-8612 (2006).
[CrossRef] [PubMed]

http://www.optik.uni-erlangen.de/odem/research/work/index.php?lang=d&what=ray., and N. Lindlein, F. Simon, and J. Schwider, "Simulation of micro-optical array systems with RAYTRACE," Opt. Eng. 37, 1809-1816 (1998).
[CrossRef]

Spolaczyk, R.

Tiziani, H. J.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Wyant, J. C.

J. C. Wyant, "Null tests using compensators," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1978), pp. 381-406.

J. C. Wyant and P. K. O'Neill, "Computer generated hologram; null lens test of aspheric wave fronts," Appl. Opt. 13, 2762-2765 (1974).
[CrossRef] [PubMed]

Young, E. C.

E. C. Young, "Optimal removal of all mislocation effects in interferometric tests," Proc. SPIE 661, 116-124 (1986).

Appl. Opt. (8)

J. Opt. Soc. Am. (1)

A. E. Jensen, "Absolute calibration method for laser Twyman-Green wave-front testing interferometers," J. Opt. Soc. Am. 63, 1313 (1973).

Opt. Acta (1)

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

Opt. Commun. (1)

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

Opt. Eng. (1)

http://www.optik.uni-erlangen.de/odem/research/work/index.php?lang=d&what=ray., and N. Lindlein, F. Simon, and J. Schwider, "Simulation of micro-optical array systems with RAYTRACE," Opt. Eng. 37, 1809-1816 (1998).
[CrossRef]

Proc. SPIE (2)

E. C. Young, "Optimal removal of all mislocation effects in interferometric tests," Proc. SPIE 661, 116-124 (1986).

S. M. Arnold and A. K. Jain, "How to test an asphere with a computer generated hologram," Proc. SPIE 1052, 191-197 (1989).

Other (4)

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

J. Schwider, "Interferometric tests for apsherics," in Fabrication and Testing of Aspheres, A. Lindquist, M. Piscotty, and J. S. Taylor, eds. Vol. 24 of 1999 OSA Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 103-114.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

J. C. Wyant, "Null tests using compensators," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1978), pp. 381-406.

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Figures (10)

Fig. 1
Fig. 1

Measurement principle: three positions for the quasi-absolute measurement of aspheric surfaces.

Fig. 2
Fig. 2

(a) Systematic error of the empty interferometer in double pass configuration (b) DOE substrate error in double pass configuration. Contour line spacing is λ / 30 .

Fig. 3
Fig. 3

Four choices of the linear offset for the spherical wavefront with respect to the optical axis of the interferometer: (a) + X direction, (b) + Y direction, (c) X direction, and (d) −Y direction. DOE has been tilted around the Y axis.

Fig. 4
Fig. 4

Simulation results of the described consistency test in all the four possible cases of the linear offset for the spherical wavefront with respect to the optical axis of the interferometer (a) + X direction, (b) + Y direction, (c) X direction, and (d) Y direction. Contour line spacing is λ / 300 .

Fig. 5
Fig. 5

Simulation results of the consistency test for the varying amount of global tilt of the DOE from 0.25° to 2° with respect to the interferometer while following the symmetry condition discussed in the last section [see Fig. 3(a)] (a) 0.25° tilt, (b) 0.5° tilt, (c) 1.0° tilt, and (d) 2.0° tilt. Contour line spacing is λ / 1000 .

Fig. 6
Fig. 6

Consistency results when the calibrating spherical wavefront is chosen as (a) base fit to the aspheric and (b) best fit to the aspheric. Contour line spacing is λ / 1000 .

Fig. 7
Fig. 7

Specimen under test (a) rotationally invariant aspheric surface and best fit sphere of the chosen specimen and (b) departure of the aspheric surface from its best fit sphere.

Fig. 8
Fig. 8

Quasi-absolute three position test procedure. (a) Absolute deviations of the aspheric surface. Contour line spacing is λ / 5 . (b) Reproducibility of the three position test as a whole. (c) Interferometric errors extracted by subtracting the absolute measurement from a single measurement. Contour line spacing is λ / 50 .

Fig. 9
Fig. 9

Results of the consistency test when the combo-DOE (a) does not fulfill any of the design condition (b) follows only the symmetry condition (c) is optimized by having the offset angle of the spherical wavefront as 0.5°.

Fig. 10
Fig. 10

Comparison of the rotationally varying deviations of the aspheric surface extracted by using (a) quasi-absolute three position test procedure, (b) N-position averaging procedure, (c) difference of rotationally varying deviations obtained from both procedures (a) and (b).

Tables (3)

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Table 1 Drift Analysis for a Duration of 1 h

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Table 2 Residual Aberrations after Misalignment Elimination in Simulations

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Table 3 Residual Aberrations after Misalignment Elimination in Experiments

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