Abstract

We describe a novel interferometric method, based on nested Fresnel zone lenses or photon sieves, for testing and measuring the radius of curvature of precision spherical surfaces that have radii in a range between several meters and a few hundred meters. We illustrate the measurement concept with radius measurements of a spherical mirror with a radius of about 10 m. The measured radius is 9877mm±10mm for a coverage factor k=2. Our measurements also demonstrate, for the first time to the best of our knowledge, the utility of photon sieves for precision surface metrology because they diffuse higher diffraction orders of computer generated holograms, which reduces coherent noise.

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Twyman, Prism and LensMaking: A Textbook for Optical Glassworkers, 2nd ed. (CRC Press, 1988).
  2. J. E. Greivenkamp and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed., 2nd ed. (Wiley, 1992), pp. 574–580.
  3. L. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1966 (1992).
    [CrossRef]
  4. U. Griesmann, J. Soons, and Q. Wang, “Measuring form and radius of spheres with interferometry,” CIRP Ann. 53, 451–454 (2004).
    [CrossRef]
  5. T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
    [CrossRef]
  6. T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement uncertainty in interferometric radius measurements,” CIRP Ann. 51, 451–454 (2002).
    [CrossRef]
  7. A. Davies and T. L. Schmitz, “Correction for stage error motions in radius measurements,” Appl. Opt. 44, 5884–5893 (2005).
    [CrossRef]
  8. T. L. Schmitz, N. Gardner, M. Vaughn, K. Medicus, and A. Davies, “Improving optical bench radius measurements using stage error motion data,” Appl. Opt. 47, 6692–6700 (2008).
    [CrossRef]
  9. M. C. Gerchman and G. C. Hunter, “Differential technique for accurately measuring the radius of long radius concave optical surfaces,” Opt. Eng. 19, 843–848 (1980).
  10. K. Freischlad, M. Küchel, W. Wiedmann, W. Kaiser, and M. Mayer, “High precision interferometric testing of spherical mirrors with long radius of curvature,” Proc. SPIE 1332, 8–17 (1990).
    [CrossRef]
  11. R. E. Parks, C. J. Evans, P. J. Sullivan, L.-Z. Shao, and B. Loucks, “Measurements of the LIGO pathfinder optics,” Proc. SPIE 3134, 95–111 (1997).
    [CrossRef]
  12. Q. Wang, G. Gao, and U. Griesmann, “Radius measurement of spherical surfaces with large radii-of-curvature using dual-focus zone plates,” in Optical Fabrication and Testing (OF&T) (Optical Society of America, 2008), paper OWB2.
  13. A. F. Fercher and M. Kriese, “Justierung synthetischer Hologramme mit kugelförmigen Referenzwellen (engl.: Alignment of synthetic holograms with spherical reference waves),” Optik 36, 547–551 (1972).
  14. B. Kress and P. Meyrueis, Digital Diffractive Optics (Wiley, 2000).
  15. L. Kipp, M. Skibowski, R. L. Johnson, R. Bernd, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
    [CrossRef]
  16. Q. Cao and J. Jahns, “Focusing analysis of the pinhole photon sieve: individual far-field model,” J. Opt. Soc. Am. A 19, 2387–2393 (2002).
    [CrossRef]
  17. J. Jahns, Q. Cao, and S. Sinziger, “Micro- and nanooptics—an overview,” Laser Photon. Rev. 2, 249–263 (2008).
    [CrossRef]
  18. T. D. Beynon, I. Kirk, and T. R. Mathews, “Gabor zone plate with binary transmittance values,” Opt. Lett. 17, 544–546 (1992).
    [CrossRef]
  19. A. Engel and G. Herziger, “Computer-drawn modulated zone plates,” Appl. Opt. 12, 471–479 (1973).
    [CrossRef]
  20. Q. Wang and U. Griesmann, “A versatile bilayer resist for laser lithography at 405  nm on glass substrates,” Opt. Eng. 52, 105104 (2013).
    [CrossRef]
  21. H. I. Smith, M. E. Walsh, F. Zhang, J. Ferrera, G. Hourihan, D. Smith, R. Light, and M. Jaspan, “An innovative tool for fabricating computer-generated holograms,” J. Phys. Conf. Ser. 415, 012037 (2013).
    [CrossRef]
  22. R. Menon, A. Patel, D. Chao, M. Walsh, and H. I. Smith, “Zone-plate-array lithography (ZPAL): optical maskless lithography for cost-effective patterning,” Proc. SPIE 5751, 330–339 (2005).
    [CrossRef]
  23. D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).
  24. W. J. Smith, Modern Optical Engineering, 2nd ed. (McGraw-Hill, 1990), pp. 328–329.
  25. P. de Groot, “Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window,” Appl. Opt. 34, 4723–4730 (1995).
    [CrossRef]
  26. H. H. Ku, “Notes on the use of propagation of error formulas,” J. Res. Natl. Bur. Stand. 70C, 263–273 (1966).
    [CrossRef]
  27. Q. Wang, J. A. Soons, and U. Griesmann, “Holographic radius test plates,” Proc. SPIE 8838, 88380I (2013).
    [CrossRef]

2013 (3)

Q. Wang and U. Griesmann, “A versatile bilayer resist for laser lithography at 405  nm on glass substrates,” Opt. Eng. 52, 105104 (2013).
[CrossRef]

H. I. Smith, M. E. Walsh, F. Zhang, J. Ferrera, G. Hourihan, D. Smith, R. Light, and M. Jaspan, “An innovative tool for fabricating computer-generated holograms,” J. Phys. Conf. Ser. 415, 012037 (2013).
[CrossRef]

Q. Wang, J. A. Soons, and U. Griesmann, “Holographic radius test plates,” Proc. SPIE 8838, 88380I (2013).
[CrossRef]

2008 (2)

2005 (2)

A. Davies and T. L. Schmitz, “Correction for stage error motions in radius measurements,” Appl. Opt. 44, 5884–5893 (2005).
[CrossRef]

R. Menon, A. Patel, D. Chao, M. Walsh, and H. I. Smith, “Zone-plate-array lithography (ZPAL): optical maskless lithography for cost-effective patterning,” Proc. SPIE 5751, 330–339 (2005).
[CrossRef]

2004 (1)

U. Griesmann, J. Soons, and Q. Wang, “Measuring form and radius of spheres with interferometry,” CIRP Ann. 53, 451–454 (2004).
[CrossRef]

2002 (2)

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement uncertainty in interferometric radius measurements,” CIRP Ann. 51, 451–454 (2002).
[CrossRef]

Q. Cao and J. Jahns, “Focusing analysis of the pinhole photon sieve: individual far-field model,” J. Opt. Soc. Am. A 19, 2387–2393 (2002).
[CrossRef]

2001 (2)

L. Kipp, M. Skibowski, R. L. Johnson, R. Bernd, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef]

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[CrossRef]

1997 (1)

R. E. Parks, C. J. Evans, P. J. Sullivan, L.-Z. Shao, and B. Loucks, “Measurements of the LIGO pathfinder optics,” Proc. SPIE 3134, 95–111 (1997).
[CrossRef]

1995 (1)

1992 (2)

1990 (1)

K. Freischlad, M. Küchel, W. Wiedmann, W. Kaiser, and M. Mayer, “High precision interferometric testing of spherical mirrors with long radius of curvature,” Proc. SPIE 1332, 8–17 (1990).
[CrossRef]

1980 (1)

M. C. Gerchman and G. C. Hunter, “Differential technique for accurately measuring the radius of long radius concave optical surfaces,” Opt. Eng. 19, 843–848 (1980).

1973 (1)

1972 (1)

A. F. Fercher and M. Kriese, “Justierung synthetischer Hologramme mit kugelförmigen Referenzwellen (engl.: Alignment of synthetic holograms with spherical reference waves),” Optik 36, 547–551 (1972).

1966 (1)

H. H. Ku, “Notes on the use of propagation of error formulas,” J. Res. Natl. Bur. Stand. 70C, 263–273 (1966).
[CrossRef]

Adelung, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Bernd, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef]

Bernd, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Bernd, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef]

Beynon, T. D.

Bruning, J. H.

J. E. Greivenkamp and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed., 2nd ed. (Wiley, 1992), pp. 574–580.

Cao, Q.

J. Jahns, Q. Cao, and S. Sinziger, “Micro- and nanooptics—an overview,” Laser Photon. Rev. 2, 249–263 (2008).
[CrossRef]

Q. Cao and J. Jahns, “Focusing analysis of the pinhole photon sieve: individual far-field model,” J. Opt. Soc. Am. A 19, 2387–2393 (2002).
[CrossRef]

Chao, D.

R. Menon, A. Patel, D. Chao, M. Walsh, and H. I. Smith, “Zone-plate-array lithography (ZPAL): optical maskless lithography for cost-effective patterning,” Proc. SPIE 5751, 330–339 (2005).
[CrossRef]

Davies, A.

Davies, A. D.

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[CrossRef]

de Groot, P.

Engel, A.

Estler, W. T.

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement uncertainty in interferometric radius measurements,” CIRP Ann. 51, 451–454 (2002).
[CrossRef]

Evans, C. J.

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement uncertainty in interferometric radius measurements,” CIRP Ann. 51, 451–454 (2002).
[CrossRef]

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[CrossRef]

R. E. Parks, C. J. Evans, P. J. Sullivan, L.-Z. Shao, and B. Loucks, “Measurements of the LIGO pathfinder optics,” Proc. SPIE 3134, 95–111 (1997).
[CrossRef]

Fercher, A. F.

A. F. Fercher and M. Kriese, “Justierung synthetischer Hologramme mit kugelförmigen Referenzwellen (engl.: Alignment of synthetic holograms with spherical reference waves),” Optik 36, 547–551 (1972).

Ferrera, J.

H. I. Smith, M. E. Walsh, F. Zhang, J. Ferrera, G. Hourihan, D. Smith, R. Light, and M. Jaspan, “An innovative tool for fabricating computer-generated holograms,” J. Phys. Conf. Ser. 415, 012037 (2013).
[CrossRef]

Freischlad, K.

K. Freischlad, M. Küchel, W. Wiedmann, W. Kaiser, and M. Mayer, “High precision interferometric testing of spherical mirrors with long radius of curvature,” Proc. SPIE 1332, 8–17 (1990).
[CrossRef]

Gao, G.

Q. Wang, G. Gao, and U. Griesmann, “Radius measurement of spherical surfaces with large radii-of-curvature using dual-focus zone plates,” in Optical Fabrication and Testing (OF&T) (Optical Society of America, 2008), paper OWB2.

Gardner, N.

Gerchman, M. C.

M. C. Gerchman and G. C. Hunter, “Differential technique for accurately measuring the radius of long radius concave optical surfaces,” Opt. Eng. 19, 843–848 (1980).

Greivenkamp, J. E.

J. E. Greivenkamp and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed., 2nd ed. (Wiley, 1992), pp. 574–580.

Griesmann, U.

Q. Wang and U. Griesmann, “A versatile bilayer resist for laser lithography at 405  nm on glass substrates,” Opt. Eng. 52, 105104 (2013).
[CrossRef]

Q. Wang, J. A. Soons, and U. Griesmann, “Holographic radius test plates,” Proc. SPIE 8838, 88380I (2013).
[CrossRef]

U. Griesmann, J. Soons, and Q. Wang, “Measuring form and radius of spheres with interferometry,” CIRP Ann. 53, 451–454 (2004).
[CrossRef]

Q. Wang, G. Gao, and U. Griesmann, “Radius measurement of spherical surfaces with large radii-of-curvature using dual-focus zone plates,” in Optical Fabrication and Testing (OF&T) (Optical Society of America, 2008), paper OWB2.

Harm, S.

L. Kipp, M. Skibowski, R. L. Johnson, R. Bernd, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef]

Herziger, G.

Hourihan, G.

H. I. Smith, M. E. Walsh, F. Zhang, J. Ferrera, G. Hourihan, D. Smith, R. Light, and M. Jaspan, “An innovative tool for fabricating computer-generated holograms,” J. Phys. Conf. Ser. 415, 012037 (2013).
[CrossRef]

Hunter, G. C.

M. C. Gerchman and G. C. Hunter, “Differential technique for accurately measuring the radius of long radius concave optical surfaces,” Opt. Eng. 19, 843–848 (1980).

Jahns, J.

J. Jahns, Q. Cao, and S. Sinziger, “Micro- and nanooptics—an overview,” Laser Photon. Rev. 2, 249–263 (2008).
[CrossRef]

Q. Cao and J. Jahns, “Focusing analysis of the pinhole photon sieve: individual far-field model,” J. Opt. Soc. Am. A 19, 2387–2393 (2002).
[CrossRef]

Jaspan, M.

H. I. Smith, M. E. Walsh, F. Zhang, J. Ferrera, G. Hourihan, D. Smith, R. Light, and M. Jaspan, “An innovative tool for fabricating computer-generated holograms,” J. Phys. Conf. Ser. 415, 012037 (2013).
[CrossRef]

Johnson, R. L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Bernd, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef]

Kaiser, W.

K. Freischlad, M. Küchel, W. Wiedmann, W. Kaiser, and M. Mayer, “High precision interferometric testing of spherical mirrors with long radius of curvature,” Proc. SPIE 1332, 8–17 (1990).
[CrossRef]

Kathman, A. D.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).

Kipp, L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Bernd, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef]

Kirk, I.

Kress, B.

B. Kress and P. Meyrueis, Digital Diffractive Optics (Wiley, 2000).

Kriese, M.

A. F. Fercher and M. Kriese, “Justierung synthetischer Hologramme mit kugelförmigen Referenzwellen (engl.: Alignment of synthetic holograms with spherical reference waves),” Optik 36, 547–551 (1972).

Ku, H. H.

H. H. Ku, “Notes on the use of propagation of error formulas,” J. Res. Natl. Bur. Stand. 70C, 263–273 (1966).
[CrossRef]

Küchel, M.

K. Freischlad, M. Küchel, W. Wiedmann, W. Kaiser, and M. Mayer, “High precision interferometric testing of spherical mirrors with long radius of curvature,” Proc. SPIE 1332, 8–17 (1990).
[CrossRef]

Light, R.

H. I. Smith, M. E. Walsh, F. Zhang, J. Ferrera, G. Hourihan, D. Smith, R. Light, and M. Jaspan, “An innovative tool for fabricating computer-generated holograms,” J. Phys. Conf. Ser. 415, 012037 (2013).
[CrossRef]

Loucks, B.

R. E. Parks, C. J. Evans, P. J. Sullivan, L.-Z. Shao, and B. Loucks, “Measurements of the LIGO pathfinder optics,” Proc. SPIE 3134, 95–111 (1997).
[CrossRef]

Mathews, T. R.

Mayer, M.

K. Freischlad, M. Küchel, W. Wiedmann, W. Kaiser, and M. Mayer, “High precision interferometric testing of spherical mirrors with long radius of curvature,” Proc. SPIE 1332, 8–17 (1990).
[CrossRef]

Medicus, K.

Menon, R.

R. Menon, A. Patel, D. Chao, M. Walsh, and H. I. Smith, “Zone-plate-array lithography (ZPAL): optical maskless lithography for cost-effective patterning,” Proc. SPIE 5751, 330–339 (2005).
[CrossRef]

Meyrueis, P.

B. Kress and P. Meyrueis, Digital Diffractive Optics (Wiley, 2000).

O’Shea, D. C.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).

Parks, R. E.

R. E. Parks, C. J. Evans, P. J. Sullivan, L.-Z. Shao, and B. Loucks, “Measurements of the LIGO pathfinder optics,” Proc. SPIE 3134, 95–111 (1997).
[CrossRef]

Patel, A.

R. Menon, A. Patel, D. Chao, M. Walsh, and H. I. Smith, “Zone-plate-array lithography (ZPAL): optical maskless lithography for cost-effective patterning,” Proc. SPIE 5751, 330–339 (2005).
[CrossRef]

Prather, D. W.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).

Schmitz, T. L.

T. L. Schmitz, N. Gardner, M. Vaughn, K. Medicus, and A. Davies, “Improving optical bench radius measurements using stage error motion data,” Appl. Opt. 47, 6692–6700 (2008).
[CrossRef]

A. Davies and T. L. Schmitz, “Correction for stage error motions in radius measurements,” Appl. Opt. 44, 5884–5893 (2005).
[CrossRef]

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement uncertainty in interferometric radius measurements,” CIRP Ann. 51, 451–454 (2002).
[CrossRef]

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[CrossRef]

Seemann, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Bernd, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef]

Selberg, L.

L. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1966 (1992).
[CrossRef]

Shao, L.-Z.

R. E. Parks, C. J. Evans, P. J. Sullivan, L.-Z. Shao, and B. Loucks, “Measurements of the LIGO pathfinder optics,” Proc. SPIE 3134, 95–111 (1997).
[CrossRef]

Sinziger, S.

J. Jahns, Q. Cao, and S. Sinziger, “Micro- and nanooptics—an overview,” Laser Photon. Rev. 2, 249–263 (2008).
[CrossRef]

Skibowski, M.

L. Kipp, M. Skibowski, R. L. Johnson, R. Bernd, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef]

Smith, D.

H. I. Smith, M. E. Walsh, F. Zhang, J. Ferrera, G. Hourihan, D. Smith, R. Light, and M. Jaspan, “An innovative tool for fabricating computer-generated holograms,” J. Phys. Conf. Ser. 415, 012037 (2013).
[CrossRef]

Smith, H. I.

H. I. Smith, M. E. Walsh, F. Zhang, J. Ferrera, G. Hourihan, D. Smith, R. Light, and M. Jaspan, “An innovative tool for fabricating computer-generated holograms,” J. Phys. Conf. Ser. 415, 012037 (2013).
[CrossRef]

R. Menon, A. Patel, D. Chao, M. Walsh, and H. I. Smith, “Zone-plate-array lithography (ZPAL): optical maskless lithography for cost-effective patterning,” Proc. SPIE 5751, 330–339 (2005).
[CrossRef]

Smith, W. J.

W. J. Smith, Modern Optical Engineering, 2nd ed. (McGraw-Hill, 1990), pp. 328–329.

Soons, J.

U. Griesmann, J. Soons, and Q. Wang, “Measuring form and radius of spheres with interferometry,” CIRP Ann. 53, 451–454 (2004).
[CrossRef]

Soons, J. A.

Q. Wang, J. A. Soons, and U. Griesmann, “Holographic radius test plates,” Proc. SPIE 8838, 88380I (2013).
[CrossRef]

Suleski, T. J.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).

Sullivan, P. J.

R. E. Parks, C. J. Evans, P. J. Sullivan, L.-Z. Shao, and B. Loucks, “Measurements of the LIGO pathfinder optics,” Proc. SPIE 3134, 95–111 (1997).
[CrossRef]

Twyman, F.

F. Twyman, Prism and LensMaking: A Textbook for Optical Glassworkers, 2nd ed. (CRC Press, 1988).

Vaughn, M.

Walsh, M.

R. Menon, A. Patel, D. Chao, M. Walsh, and H. I. Smith, “Zone-plate-array lithography (ZPAL): optical maskless lithography for cost-effective patterning,” Proc. SPIE 5751, 330–339 (2005).
[CrossRef]

Walsh, M. E.

H. I. Smith, M. E. Walsh, F. Zhang, J. Ferrera, G. Hourihan, D. Smith, R. Light, and M. Jaspan, “An innovative tool for fabricating computer-generated holograms,” J. Phys. Conf. Ser. 415, 012037 (2013).
[CrossRef]

Wang, Q.

Q. Wang and U. Griesmann, “A versatile bilayer resist for laser lithography at 405  nm on glass substrates,” Opt. Eng. 52, 105104 (2013).
[CrossRef]

Q. Wang, J. A. Soons, and U. Griesmann, “Holographic radius test plates,” Proc. SPIE 8838, 88380I (2013).
[CrossRef]

U. Griesmann, J. Soons, and Q. Wang, “Measuring form and radius of spheres with interferometry,” CIRP Ann. 53, 451–454 (2004).
[CrossRef]

Q. Wang, G. Gao, and U. Griesmann, “Radius measurement of spherical surfaces with large radii-of-curvature using dual-focus zone plates,” in Optical Fabrication and Testing (OF&T) (Optical Society of America, 2008), paper OWB2.

Wiedmann, W.

K. Freischlad, M. Küchel, W. Wiedmann, W. Kaiser, and M. Mayer, “High precision interferometric testing of spherical mirrors with long radius of curvature,” Proc. SPIE 1332, 8–17 (1990).
[CrossRef]

Zhang, F.

H. I. Smith, M. E. Walsh, F. Zhang, J. Ferrera, G. Hourihan, D. Smith, R. Light, and M. Jaspan, “An innovative tool for fabricating computer-generated holograms,” J. Phys. Conf. Ser. 415, 012037 (2013).
[CrossRef]

Appl. Opt. (4)

CIRP Ann. (2)

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement uncertainty in interferometric radius measurements,” CIRP Ann. 51, 451–454 (2002).
[CrossRef]

U. Griesmann, J. Soons, and Q. Wang, “Measuring form and radius of spheres with interferometry,” CIRP Ann. 53, 451–454 (2004).
[CrossRef]

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

J. Phys. Conf. Ser. (1)

H. I. Smith, M. E. Walsh, F. Zhang, J. Ferrera, G. Hourihan, D. Smith, R. Light, and M. Jaspan, “An innovative tool for fabricating computer-generated holograms,” J. Phys. Conf. Ser. 415, 012037 (2013).
[CrossRef]

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

H. H. Ku, “Notes on the use of propagation of error formulas,” J. Res. Natl. Bur. Stand. 70C, 263–273 (1966).
[CrossRef]

Laser Photon. Rev. (1)

J. Jahns, Q. Cao, and S. Sinziger, “Micro- and nanooptics—an overview,” Laser Photon. Rev. 2, 249–263 (2008).
[CrossRef]

Nature (1)

L. Kipp, M. Skibowski, R. L. Johnson, R. Bernd, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef]

Opt. Eng. (3)

Q. Wang and U. Griesmann, “A versatile bilayer resist for laser lithography at 405  nm on glass substrates,” Opt. Eng. 52, 105104 (2013).
[CrossRef]

L. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1966 (1992).
[CrossRef]

M. C. Gerchman and G. C. Hunter, “Differential technique for accurately measuring the radius of long radius concave optical surfaces,” Opt. Eng. 19, 843–848 (1980).

Opt. Lett. (1)

Optik (1)

A. F. Fercher and M. Kriese, “Justierung synthetischer Hologramme mit kugelförmigen Referenzwellen (engl.: Alignment of synthetic holograms with spherical reference waves),” Optik 36, 547–551 (1972).

Proc. SPIE (5)

K. Freischlad, M. Küchel, W. Wiedmann, W. Kaiser, and M. Mayer, “High precision interferometric testing of spherical mirrors with long radius of curvature,” Proc. SPIE 1332, 8–17 (1990).
[CrossRef]

R. E. Parks, C. J. Evans, P. J. Sullivan, L.-Z. Shao, and B. Loucks, “Measurements of the LIGO pathfinder optics,” Proc. SPIE 3134, 95–111 (1997).
[CrossRef]

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[CrossRef]

Q. Wang, J. A. Soons, and U. Griesmann, “Holographic radius test plates,” Proc. SPIE 8838, 88380I (2013).
[CrossRef]

R. Menon, A. Patel, D. Chao, M. Walsh, and H. I. Smith, “Zone-plate-array lithography (ZPAL): optical maskless lithography for cost-effective patterning,” Proc. SPIE 5751, 330–339 (2005).
[CrossRef]

Other (6)

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).

W. J. Smith, Modern Optical Engineering, 2nd ed. (McGraw-Hill, 1990), pp. 328–329.

F. Twyman, Prism and LensMaking: A Textbook for Optical Glassworkers, 2nd ed. (CRC Press, 1988).

J. E. Greivenkamp and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed., 2nd ed. (Wiley, 1992), pp. 574–580.

Q. Wang, G. Gao, and U. Griesmann, “Radius measurement of spherical surfaces with large radii-of-curvature using dual-focus zone plates,” in Optical Fabrication and Testing (OF&T) (Optical Society of America, 2008), paper OWB2.

B. Kress and P. Meyrueis, Digital Diffractive Optics (Wiley, 2000).

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 (7)

Fig. 1.
Fig. 1.

Radius bench method with a nested zone lens (see [12]). ZL denotes the nested zone lens, and TF denotes an interferometer transmission flat. The surfaces of the interferometer cavity are indicated with dotted (blue) lines.

Fig. 2.
Fig. 2.

Schematic of radius test setup with a holographic test plate. ZL denotes the nested zone lens, or photon sieve, and TS denotes an f/7 interferometer transmission sphere. The interferometer cavity is marked with dotted (blue) lines.

Fig. 3.
Fig. 3.

Layout of a radius test plate with a central zone lens and an annular photon sieve. The red area (outer ring) is a Fresnel zone mirror that retroreflects the spherical test wavefront, for alignment of the hologram in the test beam of the interferometer.

Fig. 4.
Fig. 4.

Interferometer fringes of the interferometer cavity in Fig. 2 with a Fresnel type zone lens (left) and a photon sieve (right). The dashed (yellow) lines indicate the boundaries between the central and annular zone lenses.

Fig. 5.
Fig. 5.

Difference of test mirror surface (blue, left, arc) with design radius, R, and radius error, ΔR, and reference wavefront with design radius, R, (black, right, arc) when the mirror is positioned near the primary focus of the central zone lens with a displacement, Δz.

Fig. 6.
Fig. 6.

Measured defocus Zernike coefficient in the outer zone lens (red circles, nonzero inner ZLs area) as functions of the defocus Zernike coefficient in the inner zone lens area.

Fig. 7.
Fig. 7.

Measured defocus Zernike coefficient in the outer photon sieve (red circles, nonzero inner ZLs area) as functions of the defocus Zernike coefficient in the inner zone lens area.

Tables (1)

Tables Icon

Table 1. Results of Two Radius Measurements of a Test Mirror With a Fresnel Type Nested Zone Lens (ZL) and a Nested Photon Sieve (PS)a

Equations (6)

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

R=f1+f2+δ,
d(θ)R+ΔR(ΔR+Δz)cosθ,
Δm(θ)=Rd(θ)=ΔR+(ΔR+Δz)cosθΔz(ΔR+Δz)·12θ2.
δm=2a20(yra)2,
ΔR+Δz=4a20(Rra)2.
u(ΔR)=4(Rra)2u(a20)2+4(a20ra)2u(ra)2.

Metrics