Abstract

A grazing-incidence interferometer for the testing of technical surfaces for macroscopic surface deviations is described. Computer-generated holograms serve as beam splitters and references for the workpieces tested. The sensitivity of the interferometer depends on the period of the computer-generated holograms. The method is demonstrated at a rod object of convex profile. Using phase-stepping techniques, the grazing-incidence interferometer provides fast measurements of the entire mantle surface of the test sample with submicrometer precision.

© 1999 Optical Society of America

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References

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  1. N. Abramson, “The Interferoscope, a new type of interferometer with variable fringe separation,” Optik 30, 56–71 (1969).
  2. K. G. Birch, F. J. Green, “Oblique incidence interferometry applied to non-optical surfaces,” J. Phys. E 6, 1045–1048 (1973).
    [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. J. Schwider, “Verfahren zur Prüfung technischer Oberflächen mit Hilfe von computer-erzeugten Hologrammen,” Germany patentWP 106769 (4January1972).
  5. S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces,” Optik 102, 106–110 (1996).
  6. S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Grazing incidence interferometer for plane and cylindrical surfaces,” Opt. Eng. 37, 2506–2511 (1998).
    [CrossRef]
  7. N. Lindlein, R. Schreiner, S. Brinkmann, T. Dresel, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces: systematic error assessment,” Appl. Opt. 36, 2791–2795 (1997).
    [CrossRef] [PubMed]
  8. T. Dresel, S. Brinkmann, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: theory,” J. Opt. Soc. Am. A 15, 2921–2928 (1998).
    [CrossRef]
  9. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital wave-front measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421–3432 (1983).
    [CrossRef] [PubMed]
  10. N. H. Ching, D. Rosenfeld, M. Braun, “Two-dimensional phase unwrapping using a minimum spanning tree algorithm,” IEEE Trans. Image Process. 1, 355–365 (1992).
    [CrossRef] [PubMed]

1998 (2)

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Grazing incidence interferometer for plane and cylindrical surfaces,” Opt. Eng. 37, 2506–2511 (1998).
[CrossRef]

T. Dresel, S. Brinkmann, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: theory,” J. Opt. Soc. Am. A 15, 2921–2928 (1998).
[CrossRef]

1997 (1)

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]

1992 (1)

N. H. Ching, D. Rosenfeld, M. Braun, “Two-dimensional phase unwrapping using a minimum spanning tree algorithm,” IEEE Trans. Image Process. 1, 355–365 (1992).
[CrossRef] [PubMed]

1983 (1)

1973 (1)

K. G. Birch, F. J. Green, “Oblique incidence interferometry applied to non-optical surfaces,” J. Phys. E 6, 1045–1048 (1973).
[CrossRef]

1969 (1)

N. Abramson, “The Interferoscope, a new type of interferometer with variable fringe separation,” Optik 30, 56–71 (1969).

Abramson, N.

N. Abramson, “The Interferoscope, a new type of interferometer with variable fringe separation,” Optik 30, 56–71 (1969).

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]

Birch, K. G.

K. G. Birch, F. J. Green, “Oblique incidence interferometry applied to non-optical surfaces,” J. Phys. E 6, 1045–1048 (1973).
[CrossRef]

Braun, M.

N. H. Ching, D. Rosenfeld, M. Braun, “Two-dimensional phase unwrapping using a minimum spanning tree algorithm,” IEEE Trans. Image Process. 1, 355–365 (1992).
[CrossRef] [PubMed]

Brinkmann, S.

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Grazing incidence interferometer for plane and cylindrical surfaces,” Opt. Eng. 37, 2506–2511 (1998).
[CrossRef]

T. Dresel, S. Brinkmann, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: theory,” J. Opt. Soc. Am. A 15, 2921–2928 (1998).
[CrossRef]

N. Lindlein, R. Schreiner, S. Brinkmann, T. Dresel, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces: systematic error assessment,” Appl. Opt. 36, 2791–2795 (1997).
[CrossRef] [PubMed]

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

Burow, R.

Ching, N. H.

N. H. Ching, D. Rosenfeld, M. Braun, “Two-dimensional phase unwrapping using a minimum spanning tree algorithm,” IEEE Trans. Image Process. 1, 355–365 (1992).
[CrossRef] [PubMed]

Dresel, T.

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Grazing incidence interferometer for plane and cylindrical surfaces,” Opt. Eng. 37, 2506–2511 (1998).
[CrossRef]

T. Dresel, S. Brinkmann, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: theory,” J. Opt. Soc. Am. A 15, 2921–2928 (1998).
[CrossRef]

N. Lindlein, R. Schreiner, S. Brinkmann, T. Dresel, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces: systematic error assessment,” Appl. Opt. 36, 2791–2795 (1997).
[CrossRef] [PubMed]

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]

Elssner, K.-E.

Green, F. J.

K. G. Birch, F. J. Green, “Oblique incidence interferometry applied to non-optical surfaces,” J. Phys. E 6, 1045–1048 (1973).
[CrossRef]

Grzanna, J.

Lindlein, N.

Merkel, K.

Rosenfeld, D.

N. H. Ching, D. Rosenfeld, M. Braun, “Two-dimensional phase unwrapping using a minimum spanning tree algorithm,” IEEE Trans. Image Process. 1, 355–365 (1992).
[CrossRef] [PubMed]

Schreiner, R.

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Grazing incidence interferometer for plane and cylindrical surfaces,” Opt. Eng. 37, 2506–2511 (1998).
[CrossRef]

T. Dresel, S. Brinkmann, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: theory,” J. Opt. Soc. Am. A 15, 2921–2928 (1998).
[CrossRef]

N. Lindlein, R. Schreiner, S. Brinkmann, T. Dresel, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces: systematic error assessment,” Appl. Opt. 36, 2791–2795 (1997).
[CrossRef] [PubMed]

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

Schwider, J.

T. Dresel, S. Brinkmann, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: theory,” J. Opt. Soc. Am. A 15, 2921–2928 (1998).
[CrossRef]

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Grazing incidence interferometer for plane and cylindrical surfaces,” Opt. Eng. 37, 2506–2511 (1998).
[CrossRef]

N. Lindlein, R. Schreiner, S. Brinkmann, T. Dresel, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces: systematic error assessment,” Appl. Opt. 36, 2791–2795 (1997).
[CrossRef] [PubMed]

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]

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

J. Schwider, “Verfahren zur Prüfung technischer Oberflächen mit Hilfe von computer-erzeugten Hologrammen,” Germany patentWP 106769 (4January1972).

Spolaczyk, R.

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]

Appl. Opt. (2)

IEEE Trans. Image Process. (1)

N. H. Ching, D. Rosenfeld, M. Braun, “Two-dimensional phase unwrapping using a minimum spanning tree algorithm,” IEEE Trans. Image Process. 1, 355–365 (1992).
[CrossRef] [PubMed]

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

J. Phys. E (1)

K. G. Birch, F. J. Green, “Oblique incidence interferometry applied to non-optical surfaces,” J. Phys. E 6, 1045–1048 (1973).
[CrossRef]

Opt. Eng. (2)

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]

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Grazing incidence interferometer for plane and cylindrical surfaces,” Opt. Eng. 37, 2506–2511 (1998).
[CrossRef]

Optik (2)

N. Abramson, “The Interferoscope, a new type of interferometer with variable fringe separation,” Optik 30, 56–71 (1969).

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

Other (1)

J. Schwider, “Verfahren zur Prüfung technischer Oberflächen mit Hilfe von computer-erzeugten Hologrammen,” Germany patentWP 106769 (4January1972).

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Figures (8)

Fig. 1
Fig. 1

Setup of the grazing-incidence interferometer.

Fig. 2
Fig. 2

Contour plot of the demo object and classification of the interference pattern into regions.

Fig. 3
Fig. 3

Simulated interferogram of the demo object according to a 0.02° rotation around the y axis.

Fig. 4
Fig. 4

Simulated interferogram of the demo object according to a 0.2° rotation around the z axis.

Fig. 5
Fig. 5

Experimental interferogram of the demo object, containing surface deviations and misalignment aberrations.

Fig. 6
Fig. 6

Simulated interferogram of the misalignment aberrations that best fit the experimental interferogram of Fig. 5. The misalignment parameters are t x = 5.4 µm, t y = 4.4 µm, ω x = -0.0053°, ω y = -0.0086°, and ω z = 0.0030°.

Fig. 7
Fig. 7

Genuine surface deviations of the demo object from an ideally shaped object. The unrolled mantle surface is shown. An ideally shaped object would result in a plane.

Fig. 8
Fig. 8

Profile of surface segment #5 along a line parallel to the optical axis.

Equations (8)

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Φmeasurement=2πpWdeviations+Wmisalignment.
Wmisalignmentx, y=txTxx, y+tyTyx, y+ωxΩxx, y+ωyΩyx, y+ωzΩzx, y.
region 1: x  x0, y0  y  y1,region 2: xx2, yy1, x2+y2ra2,region 3: x3xx2, yy2,region 4: xx3, yy4, x2+y2rb2,region 5: xx5, y5yy4.
Txx, y=2:region 1,2 x-xax-xa:region 2,0:region 3,2 x-xbx-xb:region 4,-2:region 5,
Tyx, y=0:region 1,2 y-yax-xa:region 2,2:region 3,2 y-ybx-xb:region 4,O:region 5,
Ωxx, y=0:region 1,2Cy-ya1-rax-xa:region 2,2Cy-y2:region 3,2Cy-yb1-rbx-xb:region 4,0:region 5,
Ωyx, y=2Cy-x-x0:region 1,2Cx-xa1-rax-xa:region 2,0:region 3,2Cx-xb1-rbx-xb:region 4,2Cx-x4:region 5,
Ωyx, y=2y:region 1,2yx-xa-xy-yax-xa:region 2,-2x:region 3,2yx-xb-xy-ybx-xb:region 4,-2y:region 5.

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