Abstract

The principle and the alignment aberration functions are described for an axicon-type test interferometer for measuring cylindrical mantle surfaces. Additionally, we show that the derived systematic alignment functions fulfill for reasonably small misalignments the requirements for measurements in the range of approximately 1/100 of a fringe. We verify this with optical path-length calculations, using ray tracing.

© 1997 Optical Society of America

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References

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  1. J. Schwider, “Verfahren und Anordnung zur Prüfung beliebiger Mantelflächen rotations symmetrischer Festkörper mittels synthetischer Hologramme,” GDR-Wirtschafts-Patent106,769 (5July1974).
  2. U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
    [CrossRef]
  3. T. Dresel, J. Schwider, A. Wehrhahn, S. Babin, “Grazing incidence interferometry applied to the measurement of cylindrical surfaces,” Opt. Eng. 34, 3531–3535 (1995).
    [CrossRef]
  4. S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces,” Optik 102, 106–110 (1996).
  5. D. J. Whitehouse, Handbook of Surface Metrology (Institute of Physics Publishing, London, 1994).
  6. N. Lindlein, raytrace vers. 5.0, MIKOS, D-91058 Erlangen, Am Weichselgarten7 (1996).
  7. J. Schwider, “Advanced evaluation techniques in interferometry,” Prog. Opt. 28, 271–359 (1990).
    [CrossRef]

1996 (1)

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces,” Optik 102, 106–110 (1996).

1995 (1)

T. Dresel, J. Schwider, A. Wehrhahn, S. Babin, “Grazing incidence interferometry applied to the measurement of cylindrical surfaces,” Opt. Eng. 34, 3531–3535 (1995).
[CrossRef]

1993 (1)

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

1990 (1)

J. Schwider, “Advanced evaluation techniques in interferometry,” Prog. Opt. 28, 271–359 (1990).
[CrossRef]

Babin, S.

T. Dresel, J. Schwider, A. Wehrhahn, S. Babin, “Grazing incidence interferometry applied to the measurement of cylindrical surfaces,” Opt. Eng. 34, 3531–3535 (1995).
[CrossRef]

Brinkmann, S.

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces,” Optik 102, 106–110 (1996).

Dresel, T.

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces,” Optik 102, 106–110 (1996).

T. Dresel, J. Schwider, A. Wehrhahn, S. Babin, “Grazing incidence interferometry applied to the measurement of cylindrical surfaces,” Opt. Eng. 34, 3531–3535 (1995).
[CrossRef]

Krackhardt, U.

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

Lindlein, N.

N. Lindlein, raytrace vers. 5.0, MIKOS, D-91058 Erlangen, Am Weichselgarten7 (1996).

Schrader, M.

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

Schreiner, R.

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces,” Optik 102, 106–110 (1996).

Schwider, J.

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces,” Optik 102, 106–110 (1996).

T. Dresel, J. Schwider, A. Wehrhahn, S. Babin, “Grazing incidence interferometry applied to the measurement of cylindrical surfaces,” Opt. Eng. 34, 3531–3535 (1995).
[CrossRef]

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

J. Schwider, “Advanced evaluation techniques in interferometry,” Prog. Opt. 28, 271–359 (1990).
[CrossRef]

J. Schwider, “Verfahren und Anordnung zur Prüfung beliebiger Mantelflächen rotations symmetrischer Festkörper mittels synthetischer Hologramme,” GDR-Wirtschafts-Patent106,769 (5July1974).

Streibl, N.

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

Wehrhahn, A.

T. Dresel, J. Schwider, A. Wehrhahn, S. Babin, “Grazing incidence interferometry applied to the measurement of cylindrical surfaces,” Opt. Eng. 34, 3531–3535 (1995).
[CrossRef]

Whitehouse, D. J.

D. J. Whitehouse, Handbook of Surface Metrology (Institute of Physics Publishing, London, 1994).

Opt. Eng. (2)

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

T. Dresel, J. Schwider, A. Wehrhahn, S. Babin, “Grazing incidence interferometry applied to the measurement of cylindrical surfaces,” Opt. Eng. 34, 3531–3535 (1995).
[CrossRef]

Optik (1)

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces,” Optik 102, 106–110 (1996).

Prog. Opt. (1)

J. Schwider, “Advanced evaluation techniques in interferometry,” Prog. Opt. 28, 271–359 (1990).
[CrossRef]

Other (3)

J. Schwider, “Verfahren und Anordnung zur Prüfung beliebiger Mantelflächen rotations symmetrischer Festkörper mittels synthetischer Hologramme,” GDR-Wirtschafts-Patent106,769 (5July1974).

D. J. Whitehouse, Handbook of Surface Metrology (Institute of Physics Publishing, London, 1994).

N. Lindlein, raytrace vers. 5.0, MIKOS, D-91058 Erlangen, Am Weichselgarten7 (1996).

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Figures (7)

Fig. 1
Fig. 1

Interferometric setup of the axicon-type test interferometer.

Fig. 2
Fig. 2

Lateral shift of the test cylinder and corresponding notations.

Fig. 3
Fig. 3

Notations for the derivation of misalignment aberrations belonging to tilts of the cylinder under test.

Fig. 4
Fig. 4

a, Measured interferogram of a precise reference cylinder with some misalignment aberrations. b, Simulated interferogram of an ideal cylinder with the same misalignment aberrations as in a.

Fig. 5
Fig. 5

a, Simulated interferogram for the lateral shift of the test cylinder by 100 µm in the x direction. b, Corresponding deviations between the ray-tracing data and the aberration-function data for the lateral shift by 100 µm. P/V, 0.064 wavelengths. c, Simulated interferogram for a cylinder tilt of 0.025° in the xz plane. d, Corresponding deviations for a 0.025° tilt. P/V, 0.051 wavelengths.

Fig. 6
Fig. 6

P/V for the deviations between the ray-tracing data and the aberration-function data for lateral shifts of the cylinder to as high as 200 µm. Five values (markers) were calculated, and a parabolic function was fitted to the values.

Fig. 7
Fig. 7

P/V for the deviations between the ray-tracing data and the aberration-function data for cylinder tilts to 0.1°. Again five values (markers) were calculated, and a parabolic function was fitted to the values.

Equations (17)

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

Φx, y=kWx, y=kax2+y21/2=2πpx2+y21/2,
ΔΦx, y=Φx+2sx, y+2sy-Φx, y=2sxΦxx, y+2syΦyx, y+Os2,
ΔΦx, y=2sxka xx2+y21/2+2syka×yx2+y21/2+Os2.
ΔΦx, y=2sz·Φx, y,
sz=cot α x2+y21/2-z0×tan Ωex cos χ+ey sin χ,
V=i,jΦmeasij-ΔΦijsx, sy, χ, Ω2
M:=tan Ω cos χ,
N:=tan Ω sin χ,
sx:=sx-z0M,
sy:=sy-z0N.
ΔΦx, y=2kax2+y21/2xsx+ysy+cot α×x2+y21/2xM+yN.
i,jii2+j21/2Φmeasij-2kai2+j21/2sxi+syj+Δx cot αi2+j21/2Mi+Nj=!0,
i,jji2+j21/2Φmeasij-2kai2+j21/2sxi+syj+Δx cot αi2+j21/2Mi+Nj=!0,
i,j iΦmeasij-2kai2+j21/2sxi+syj+Δx cot αi2+j21/2Mi+Nj=!0,
 i,j jΦmeasij-2kai2+j21/2sxi+syj+Δx cot αi2+j21/2Mi+Nj=!0,
Ψij:=Φmeasij-ΔΦij.
i=0Dj=0D-iai,jxiyj

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