Abstract

Modifications of the long trace profiler at the Advanced Photon Source at Argonne National Laboratory have significantly improved its accuracy and repeatability for measuring the figure of large flat and long-radius mirrors. Use of a Dove prism in the reference beam path corrects phasing problems between mechanical errors and thermally induced system errors. A single reference correction now completely removes both of these error signals from the measured surface profile. The addition of a precision air conditioner keeps the temperature in the metrology enclosure constant to within ±0.1 °C over a 24-h period and has significantly improved the stability and the repeatability of the measurements. Long-radius surface curvatures can now be measured absolutely with a high degree of confidence. These improved capabilities are illustrated with a series of measurements of a 500-mm-long mirror with a 5-km radius of curvature. The standard deviation in the average of ten slope profile scans is 0.3 µrad, and the corresponding standard deviation in the height error is 4.6 nm.

© 1999 Optical Society of America

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References

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  1. P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. A. Parks, eds., Proc. SPIE966, 354–364 (1989).
    [CrossRef]
  2. P. Z. Takacs, K. Furenlid, R. DeBiasse, E. L. Church, “Surface topography measurements over the 1 meter to 10 micrometer spatial period bandwidth,” in Surface Characterization and Testing II, J. E. Grievenkamp, M. Young, eds., Proc. SPIE1164, 203–211 (1989).
    [CrossRef]
  3. W. B. Emerson, “Determination of planeness and bending of optical flats,” J. Res. Natl. Bur. Stand. 49(4) , 241–247 (1952).
    [CrossRef]
  4. G. D. Dew, “The measurement of optical flatness,” J. Sci. Instrum. 43, 409–415 (1966).
    [CrossRef] [PubMed]
  5. W. Primak, “The determination of the absolute contours of optical flats,” Appl. Opt. 6, 1917–1923 (1967).
    [CrossRef] [PubMed]
  6. G. Schulz, J. Schwider, “Precise measurement of planeness,” Appl. Opt. 6, 1077–1084 (1967).
    [CrossRef] [PubMed]
  7. W. Primak, “Optical flatness standard,” Opt. Eng. 23 (6) , 806–815 (1984).
  8. W. Primak, “Optical flatness standard: comment,” Opt. Eng. 28 (8) , 934 (1989).
  9. Lord Rayleigh, “Interference bands and their applications,” Nature (London) 48, 212–214 (1893).
    [CrossRef]
  10. H. Barrell, R. Marriner, “Liquid surface interferometry,” Nature (London) 162, 529–530 (1948).
    [CrossRef]
  11. R. Bünnagel, “Untersuchungen über die Eignung eines Flüssigkeitsspiegels als Ebenheitsnormal,” Z. Angew. Phys. 8(7) , 342–350 (1956).
  12. I. Powell, E. Goulet, “Absolute figure measurements with a liquid-flat reference,” Appl. Opt. 37, 2579–2588 (1998).
    [CrossRef]
  13. G. Schulz, J. Grzanna, “Absolute flatness testing by the rotation method with optimal measuring-error compensation,” Appl. Opt. 31, 3767–3780 (1992).
    [CrossRef] [PubMed]
  14. P. Hariharan, “Interferometric testing of optical surfaces: absolute measurements of flatness,” Opt. Eng. 36, 2478–2481 (1997).
    [CrossRef]
  15. S. C. Irick, W. R. McKinney, D. L. T. Lunt, P. Z. Takacs, “Using a straightness reference in obtaining more accurate surface profiles,” Rev. Sci. Instrum. 63, 1436–1438 (1992).
    [CrossRef]
  16. S. C. Irick, “Improved measurement accuracy in a long trace profiler: compensation for laser pointing instability,” Nucl. Instrum. Methods Phys. Res. A 347, 226–230 (1994).
    [CrossRef]
  17. S. C. Irick, “Determining surface profile from sequential interference patterns from a long trace profiler,” Rev. Sci. Instrum. 63, 1432–1435 (1992).
    [CrossRef]
  18. S. C. Irick, “Advancements in one-dimensional profiling with a long trace profiler,” in International Symposium on Optical Fabrication, Testing, and Surface Evaluation, J. Tsujiuchi, ed., Proc. SPIE1720, 162–168 (1992).
    [CrossRef]
  19. S. Qian, W. Jark, P. Z. Takacs, “The Penta-Prism LTP: a long-trace-profiler with stationary optical head and moving penta-prism,” Rev. Sci. Instrum. 66, 2562–2569 (1995).
    [CrossRef]
  20. W. McKinney, S. C. Irick, D. J. Lunt, “XUV synchrotron optical components for the Advanced Light Source: summary of the requirements and the developmental program,” in Optics for High-Brightness Synchrotron Radiation Beamlines, J. Arthur, ed., Proc. SPIE1740, 154–160 (1993).
    [CrossRef]
  21. P. Z. Takacs, K. Furenlid, E. L. Church, “In search of the elusive true surface,” in Advanced Optical Manufacturing and Testing, G. M. Sanger, P. B. Reid, L. Baker, eds., Proc. SPIE1333, 205–219 (1990).
    [CrossRef]
  22. P. Z. Takacs, C. J. Bresloff, “Significant improvements in long trace profiler measurement performance,” in Optics for High-Brightness Synchrotron Radiation Beamlines II, L. E. Berman, J. Arthur, eds., Proc. SPIE2856, 236–245 (1996).
    [CrossRef]
  23. K. von Bieren, “Pencil beam interferometer for aspherical optical surfaces,” in Laser Diagnostics, S. Holly, ed., Proc. SPIE343, 101–108 (1982).
    [CrossRef]
  24. K. von Bieren, “Interferometry of wavefronts reflected off conical surfaces,” Appl. Opt. 22, 2109–2114 (1983).
    [CrossRef]
  25. J. Susini, R. Baker, A. Vivo, “Optical metrology facility at the ESRF,” Rev. Sci. Instrum. 66, 2232–2234 (1995).
    [CrossRef]
  26. U.S. Department of Defense, Optical Design, Military Standardization Handbook, MIL-HDBK-141 (Defense Supply Agency, Washington, D.C., 1962).
  27. D. J. Whitehouse, Handbook of Surface Metrology (Institute of Physics, Philadelphia, Pa., 1994).
  28. E. L. Church, P. Z. Takacs are preparing a manuscript to be called “Signal and noise analysis of LTP measurements.”
  29. J. Strong, Concepts of Classical Optics (Freeman, San Francisco, Calif., 1958), pp. 281–282.

1998 (1)

1997 (1)

P. Hariharan, “Interferometric testing of optical surfaces: absolute measurements of flatness,” Opt. Eng. 36, 2478–2481 (1997).
[CrossRef]

1995 (2)

S. Qian, W. Jark, P. Z. Takacs, “The Penta-Prism LTP: a long-trace-profiler with stationary optical head and moving penta-prism,” Rev. Sci. Instrum. 66, 2562–2569 (1995).
[CrossRef]

J. Susini, R. Baker, A. Vivo, “Optical metrology facility at the ESRF,” Rev. Sci. Instrum. 66, 2232–2234 (1995).
[CrossRef]

1994 (1)

S. C. Irick, “Improved measurement accuracy in a long trace profiler: compensation for laser pointing instability,” Nucl. Instrum. Methods Phys. Res. A 347, 226–230 (1994).
[CrossRef]

1992 (3)

S. C. Irick, “Determining surface profile from sequential interference patterns from a long trace profiler,” Rev. Sci. Instrum. 63, 1432–1435 (1992).
[CrossRef]

S. C. Irick, W. R. McKinney, D. L. T. Lunt, P. Z. Takacs, “Using a straightness reference in obtaining more accurate surface profiles,” Rev. Sci. Instrum. 63, 1436–1438 (1992).
[CrossRef]

G. Schulz, J. Grzanna, “Absolute flatness testing by the rotation method with optimal measuring-error compensation,” Appl. Opt. 31, 3767–3780 (1992).
[CrossRef] [PubMed]

1989 (1)

W. Primak, “Optical flatness standard: comment,” Opt. Eng. 28 (8) , 934 (1989).

1984 (1)

W. Primak, “Optical flatness standard,” Opt. Eng. 23 (6) , 806–815 (1984).

1983 (1)

1967 (2)

1966 (1)

G. D. Dew, “The measurement of optical flatness,” J. Sci. Instrum. 43, 409–415 (1966).
[CrossRef] [PubMed]

1956 (1)

R. Bünnagel, “Untersuchungen über die Eignung eines Flüssigkeitsspiegels als Ebenheitsnormal,” Z. Angew. Phys. 8(7) , 342–350 (1956).

1952 (1)

W. B. Emerson, “Determination of planeness and bending of optical flats,” J. Res. Natl. Bur. Stand. 49(4) , 241–247 (1952).
[CrossRef]

1948 (1)

H. Barrell, R. Marriner, “Liquid surface interferometry,” Nature (London) 162, 529–530 (1948).
[CrossRef]

1893 (1)

Lord Rayleigh, “Interference bands and their applications,” Nature (London) 48, 212–214 (1893).
[CrossRef]

Baker, R.

J. Susini, R. Baker, A. Vivo, “Optical metrology facility at the ESRF,” Rev. Sci. Instrum. 66, 2232–2234 (1995).
[CrossRef]

Barrell, H.

H. Barrell, R. Marriner, “Liquid surface interferometry,” Nature (London) 162, 529–530 (1948).
[CrossRef]

Bresloff, C. J.

P. Z. Takacs, C. J. Bresloff, “Significant improvements in long trace profiler measurement performance,” in Optics for High-Brightness Synchrotron Radiation Beamlines II, L. E. Berman, J. Arthur, eds., Proc. SPIE2856, 236–245 (1996).
[CrossRef]

Bünnagel, R.

R. Bünnagel, “Untersuchungen über die Eignung eines Flüssigkeitsspiegels als Ebenheitsnormal,” Z. Angew. Phys. 8(7) , 342–350 (1956).

Church, E. L.

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. A. Parks, eds., Proc. SPIE966, 354–364 (1989).
[CrossRef]

P. Z. Takacs, K. Furenlid, R. DeBiasse, E. L. Church, “Surface topography measurements over the 1 meter to 10 micrometer spatial period bandwidth,” in Surface Characterization and Testing II, J. E. Grievenkamp, M. Young, eds., Proc. SPIE1164, 203–211 (1989).
[CrossRef]

E. L. Church, P. Z. Takacs are preparing a manuscript to be called “Signal and noise analysis of LTP measurements.”

P. Z. Takacs, K. Furenlid, E. L. Church, “In search of the elusive true surface,” in Advanced Optical Manufacturing and Testing, G. M. Sanger, P. B. Reid, L. Baker, eds., Proc. SPIE1333, 205–219 (1990).
[CrossRef]

DeBiasse, R.

P. Z. Takacs, K. Furenlid, R. DeBiasse, E. L. Church, “Surface topography measurements over the 1 meter to 10 micrometer spatial period bandwidth,” in Surface Characterization and Testing II, J. E. Grievenkamp, M. Young, eds., Proc. SPIE1164, 203–211 (1989).
[CrossRef]

Dew, G. D.

G. D. Dew, “The measurement of optical flatness,” J. Sci. Instrum. 43, 409–415 (1966).
[CrossRef] [PubMed]

Emerson, W. B.

W. B. Emerson, “Determination of planeness and bending of optical flats,” J. Res. Natl. Bur. Stand. 49(4) , 241–247 (1952).
[CrossRef]

Feng, S. K.

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. A. Parks, eds., Proc. SPIE966, 354–364 (1989).
[CrossRef]

Furenlid, K.

P. Z. Takacs, K. Furenlid, R. DeBiasse, E. L. Church, “Surface topography measurements over the 1 meter to 10 micrometer spatial period bandwidth,” in Surface Characterization and Testing II, J. E. Grievenkamp, M. Young, eds., Proc. SPIE1164, 203–211 (1989).
[CrossRef]

P. Z. Takacs, K. Furenlid, E. L. Church, “In search of the elusive true surface,” in Advanced Optical Manufacturing and Testing, G. M. Sanger, P. B. Reid, L. Baker, eds., Proc. SPIE1333, 205–219 (1990).
[CrossRef]

Goulet, E.

Grzanna, J.

Hariharan, P.

P. Hariharan, “Interferometric testing of optical surfaces: absolute measurements of flatness,” Opt. Eng. 36, 2478–2481 (1997).
[CrossRef]

Irick, S. C.

S. C. Irick, “Improved measurement accuracy in a long trace profiler: compensation for laser pointing instability,” Nucl. Instrum. Methods Phys. Res. A 347, 226–230 (1994).
[CrossRef]

S. C. Irick, “Determining surface profile from sequential interference patterns from a long trace profiler,” Rev. Sci. Instrum. 63, 1432–1435 (1992).
[CrossRef]

S. C. Irick, W. R. McKinney, D. L. T. Lunt, P. Z. Takacs, “Using a straightness reference in obtaining more accurate surface profiles,” Rev. Sci. Instrum. 63, 1436–1438 (1992).
[CrossRef]

S. C. Irick, “Advancements in one-dimensional profiling with a long trace profiler,” in International Symposium on Optical Fabrication, Testing, and Surface Evaluation, J. Tsujiuchi, ed., Proc. SPIE1720, 162–168 (1992).
[CrossRef]

W. McKinney, S. C. Irick, D. J. Lunt, “XUV synchrotron optical components for the Advanced Light Source: summary of the requirements and the developmental program,” in Optics for High-Brightness Synchrotron Radiation Beamlines, J. Arthur, ed., Proc. SPIE1740, 154–160 (1993).
[CrossRef]

Jark, W.

S. Qian, W. Jark, P. Z. Takacs, “The Penta-Prism LTP: a long-trace-profiler with stationary optical head and moving penta-prism,” Rev. Sci. Instrum. 66, 2562–2569 (1995).
[CrossRef]

Liu, W.

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. A. Parks, eds., Proc. SPIE966, 354–364 (1989).
[CrossRef]

Lunt, D. J.

W. McKinney, S. C. Irick, D. J. Lunt, “XUV synchrotron optical components for the Advanced Light Source: summary of the requirements and the developmental program,” in Optics for High-Brightness Synchrotron Radiation Beamlines, J. Arthur, ed., Proc. SPIE1740, 154–160 (1993).
[CrossRef]

Lunt, D. L. T.

S. C. Irick, W. R. McKinney, D. L. T. Lunt, P. Z. Takacs, “Using a straightness reference in obtaining more accurate surface profiles,” Rev. Sci. Instrum. 63, 1436–1438 (1992).
[CrossRef]

Marriner, R.

H. Barrell, R. Marriner, “Liquid surface interferometry,” Nature (London) 162, 529–530 (1948).
[CrossRef]

McKinney, W.

W. McKinney, S. C. Irick, D. J. Lunt, “XUV synchrotron optical components for the Advanced Light Source: summary of the requirements and the developmental program,” in Optics for High-Brightness Synchrotron Radiation Beamlines, J. Arthur, ed., Proc. SPIE1740, 154–160 (1993).
[CrossRef]

McKinney, W. R.

S. C. Irick, W. R. McKinney, D. L. T. Lunt, P. Z. Takacs, “Using a straightness reference in obtaining more accurate surface profiles,” Rev. Sci. Instrum. 63, 1436–1438 (1992).
[CrossRef]

Powell, I.

Primak, W.

W. Primak, “Optical flatness standard: comment,” Opt. Eng. 28 (8) , 934 (1989).

W. Primak, “Optical flatness standard,” Opt. Eng. 23 (6) , 806–815 (1984).

W. Primak, “The determination of the absolute contours of optical flats,” Appl. Opt. 6, 1917–1923 (1967).
[CrossRef] [PubMed]

Qian, S.

S. Qian, W. Jark, P. Z. Takacs, “The Penta-Prism LTP: a long-trace-profiler with stationary optical head and moving penta-prism,” Rev. Sci. Instrum. 66, 2562–2569 (1995).
[CrossRef]

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. A. Parks, eds., Proc. SPIE966, 354–364 (1989).
[CrossRef]

Rayleigh, Lord

Lord Rayleigh, “Interference bands and their applications,” Nature (London) 48, 212–214 (1893).
[CrossRef]

Schulz, G.

Schwider, J.

Strong, J.

J. Strong, Concepts of Classical Optics (Freeman, San Francisco, Calif., 1958), pp. 281–282.

Susini, J.

J. Susini, R. Baker, A. Vivo, “Optical metrology facility at the ESRF,” Rev. Sci. Instrum. 66, 2232–2234 (1995).
[CrossRef]

Takacs, P. Z.

S. Qian, W. Jark, P. Z. Takacs, “The Penta-Prism LTP: a long-trace-profiler with stationary optical head and moving penta-prism,” Rev. Sci. Instrum. 66, 2562–2569 (1995).
[CrossRef]

S. C. Irick, W. R. McKinney, D. L. T. Lunt, P. Z. Takacs, “Using a straightness reference in obtaining more accurate surface profiles,” Rev. Sci. Instrum. 63, 1436–1438 (1992).
[CrossRef]

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. A. Parks, eds., Proc. SPIE966, 354–364 (1989).
[CrossRef]

P. Z. Takacs, K. Furenlid, R. DeBiasse, E. L. Church, “Surface topography measurements over the 1 meter to 10 micrometer spatial period bandwidth,” in Surface Characterization and Testing II, J. E. Grievenkamp, M. Young, eds., Proc. SPIE1164, 203–211 (1989).
[CrossRef]

P. Z. Takacs, K. Furenlid, E. L. Church, “In search of the elusive true surface,” in Advanced Optical Manufacturing and Testing, G. M. Sanger, P. B. Reid, L. Baker, eds., Proc. SPIE1333, 205–219 (1990).
[CrossRef]

P. Z. Takacs, C. J. Bresloff, “Significant improvements in long trace profiler measurement performance,” in Optics for High-Brightness Synchrotron Radiation Beamlines II, L. E. Berman, J. Arthur, eds., Proc. SPIE2856, 236–245 (1996).
[CrossRef]

E. L. Church, P. Z. Takacs are preparing a manuscript to be called “Signal and noise analysis of LTP measurements.”

Vivo, A.

J. Susini, R. Baker, A. Vivo, “Optical metrology facility at the ESRF,” Rev. Sci. Instrum. 66, 2232–2234 (1995).
[CrossRef]

von Bieren, K.

K. von Bieren, “Interferometry of wavefronts reflected off conical surfaces,” Appl. Opt. 22, 2109–2114 (1983).
[CrossRef]

K. von Bieren, “Pencil beam interferometer for aspherical optical surfaces,” in Laser Diagnostics, S. Holly, ed., Proc. SPIE343, 101–108 (1982).
[CrossRef]

Whitehouse, D. J.

D. J. Whitehouse, Handbook of Surface Metrology (Institute of Physics, Philadelphia, Pa., 1994).

Appl. Opt. (5)

J. Res. Natl. Bur. Stand. (1)

W. B. Emerson, “Determination of planeness and bending of optical flats,” J. Res. Natl. Bur. Stand. 49(4) , 241–247 (1952).
[CrossRef]

J. Sci. Instrum. (1)

G. D. Dew, “The measurement of optical flatness,” J. Sci. Instrum. 43, 409–415 (1966).
[CrossRef] [PubMed]

Nature (London) (2)

Lord Rayleigh, “Interference bands and their applications,” Nature (London) 48, 212–214 (1893).
[CrossRef]

H. Barrell, R. Marriner, “Liquid surface interferometry,” Nature (London) 162, 529–530 (1948).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A (1)

S. C. Irick, “Improved measurement accuracy in a long trace profiler: compensation for laser pointing instability,” Nucl. Instrum. Methods Phys. Res. A 347, 226–230 (1994).
[CrossRef]

Opt. Eng. (3)

P. Hariharan, “Interferometric testing of optical surfaces: absolute measurements of flatness,” Opt. Eng. 36, 2478–2481 (1997).
[CrossRef]

W. Primak, “Optical flatness standard,” Opt. Eng. 23 (6) , 806–815 (1984).

W. Primak, “Optical flatness standard: comment,” Opt. Eng. 28 (8) , 934 (1989).

Rev. Sci. Instrum. (4)

S. C. Irick, W. R. McKinney, D. L. T. Lunt, P. Z. Takacs, “Using a straightness reference in obtaining more accurate surface profiles,” Rev. Sci. Instrum. 63, 1436–1438 (1992).
[CrossRef]

S. C. Irick, “Determining surface profile from sequential interference patterns from a long trace profiler,” Rev. Sci. Instrum. 63, 1432–1435 (1992).
[CrossRef]

J. Susini, R. Baker, A. Vivo, “Optical metrology facility at the ESRF,” Rev. Sci. Instrum. 66, 2232–2234 (1995).
[CrossRef]

S. Qian, W. Jark, P. Z. Takacs, “The Penta-Prism LTP: a long-trace-profiler with stationary optical head and moving penta-prism,” Rev. Sci. Instrum. 66, 2562–2569 (1995).
[CrossRef]

Z. Angew. Phys. (1)

R. Bünnagel, “Untersuchungen über die Eignung eines Flüssigkeitsspiegels als Ebenheitsnormal,” Z. Angew. Phys. 8(7) , 342–350 (1956).

Other (11)

S. C. Irick, “Advancements in one-dimensional profiling with a long trace profiler,” in International Symposium on Optical Fabrication, Testing, and Surface Evaluation, J. Tsujiuchi, ed., Proc. SPIE1720, 162–168 (1992).
[CrossRef]

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. A. Parks, eds., Proc. SPIE966, 354–364 (1989).
[CrossRef]

P. Z. Takacs, K. Furenlid, R. DeBiasse, E. L. Church, “Surface topography measurements over the 1 meter to 10 micrometer spatial period bandwidth,” in Surface Characterization and Testing II, J. E. Grievenkamp, M. Young, eds., Proc. SPIE1164, 203–211 (1989).
[CrossRef]

W. McKinney, S. C. Irick, D. J. Lunt, “XUV synchrotron optical components for the Advanced Light Source: summary of the requirements and the developmental program,” in Optics for High-Brightness Synchrotron Radiation Beamlines, J. Arthur, ed., Proc. SPIE1740, 154–160 (1993).
[CrossRef]

P. Z. Takacs, K. Furenlid, E. L. Church, “In search of the elusive true surface,” in Advanced Optical Manufacturing and Testing, G. M. Sanger, P. B. Reid, L. Baker, eds., Proc. SPIE1333, 205–219 (1990).
[CrossRef]

P. Z. Takacs, C. J. Bresloff, “Significant improvements in long trace profiler measurement performance,” in Optics for High-Brightness Synchrotron Radiation Beamlines II, L. E. Berman, J. Arthur, eds., Proc. SPIE2856, 236–245 (1996).
[CrossRef]

K. von Bieren, “Pencil beam interferometer for aspherical optical surfaces,” in Laser Diagnostics, S. Holly, ed., Proc. SPIE343, 101–108 (1982).
[CrossRef]

U.S. Department of Defense, Optical Design, Military Standardization Handbook, MIL-HDBK-141 (Defense Supply Agency, Washington, D.C., 1962).

D. J. Whitehouse, Handbook of Surface Metrology (Institute of Physics, Philadelphia, Pa., 1994).

E. L. Church, P. Z. Takacs are preparing a manuscript to be called “Signal and noise analysis of LTP measurements.”

J. Strong, Concepts of Classical Optics (Freeman, San Francisco, Calif., 1958), pp. 281–282.

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Figures (13)

Fig. 1
Fig. 1

Schematic diagram of the standard LTP II optical system. The first beam splitter, BS1, and the right-angle Porro prisms separate the laser beam into two collinear beams. The polarizing beam splitter, PBS, separates them further into two pairs of beams that are directed to a test surface and to the reference mirror. The return beams pass through the Fourier transform (FT) lens and each form a separate interference pattern on the detector.

Fig. 2
Fig. 2

Effect of optical head pitch error on detector fringe position in the standard LTP II system. For simplicity the REF and the SUT surfaces are shown as rotated by the same angle. The rotation angle shown is highly exaggerated. Mechanical rotation errors move the fringe patterns in opposite directions while thermal drift errors in the Porro prism optical path move the fringe patterns in the same direction on the detector. The filled circles label the probe beam component generated by the upper Porro prism path.

Fig. 3
Fig. 3

Fringe pattern motion with a Dove prism mounted on the optics board. Both mechanical pitch errors and thermal optical path errors are now phased to move in the same direction.

Fig. 4
Fig. 4

Stability scans (a) without and (b) with the Dove prism installed. Data were taken at 1 s/point. Mechanical force is applied to the air-bearing carriage to induce large mechanical error signals. The reference correction removes the mechanical error completely in both scans. The standard deviation in the residual signal in (a) is 2.03 µrad without the Dove prism, whereas in (b) it is only 0.86 µrad with the Dove prism.

Fig. 5
Fig. 5

Stability scans during a deliberate temperature change of 2 °C (a) without and (b) with the Dove prism. Without the Dove prism, the large thermal and small mechanical errors in (a) can never be compensated simultaneously. Complete error correction occurs in (b) with both beams in phase.

Fig. 6
Fig. 6

Stability scan run overnight for 7.5 h at 30 s/point. The REF beam is displaced downward by 5 µrad from the test beam for clarity. Total drift in both beams is approximately 30 µrad, but the difference is only 0.75 µrad rms. The 6.5-min period is related to the ±0.1 °C air-conditioner cycle time.

Fig. 7
Fig. 7

Overnight stability scan started immediately after installing and aligning a test mirror. Here, to highlight the error at the start of the scan, we did not separate the two traces. Relaxation in the test mirror and its support structure is the probable cause of the differential error between the REF and the test surfaces. In this case it takes 75 min for the error to dissipate.

Fig. 8
Fig. 8

Forward-direction repeatability test slope profiles. (a) All ten detrend-0 (D0) profiles superimposed. (b) Detrend-1 (D1) on the average of the ten. The rms slope error for the detrend-1 profile is 4.88 µrad.

Fig. 9
Fig. 9

Forward scan residual slope profiles (a) after subtraction of the average from each detrend-0 profile and (b) after removing the first-order drift from each residual in (a).

Fig. 10
Fig. 10

Height profiles generated from the detrend-0 slope profiles in Fig. 8 by integration. For convenience, each height profile was centered around its mean value.

Fig. 11
Fig. 11

Residual height profiles obtained from the ten detrend-0 profiles shown in Fig. 10. (a) Average of the ten subtracted from each. (b) Detrend-2 on each residual removes tilt and curvature remnant. Standard deviation in the mean for the detrend-2 profiles is 4.6 nm.

Fig. 12
Fig. 12

Residual height after the removal of a second-order polynomial from the average of the Fig. 10 profiles with the ±13.3-nm error bars included. The least-squares fit radius of curvature removed is 4606 m. The significance of various error features can be estimated by eye relative to the error envelope.

Fig. 13
Fig. 13

Comparison of forward and reverse scans. The residual slope profiles of the detrend-1 forward and reverse scans are nearly identical. The difference between the two is shown as the fluctuations about zero. The difference rms of 0.51 µrad is at the noise level of the system with no indication of any significant systematic error.

Equations (8)

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L|Rmin|10 mrad.
T=S+P+D+Es,
R=R0-P+D+Er,
M=T+R=S+2D+Es+Er.
R=R0+P+D+Er.
M=T-R=S+Es-Er,
σ¯z=σmDNK,
K=9/35=0.507.

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