Abstract

Interferograms of plane parallel optical flats are hard to interpret when acquired with coherent illumination because of the complex fringe pattern resulting from the superposition of three main contributions, namely from the reference surface and the front and back sample surfaces. We illuminate the sample by a field of high temporal and specially tailored partial spatial coherence. This limits the fringe contrast to sheets of adjustable position and thickness along the axis of the interferometer. We outline the technique and demonstrate its application together with phase shifting interferometry to extract the topography of front and back surfaces of transparent samples.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Malacara, Optical Shop Testing (Wiley, 1978).
  2. J. Heil, T. Bauer, S. Schmax, T. Sure, and J. Wesner, “Phase shifting Fizeau interferometry of front and back surfaces of optical flats,” Appl. Opt. 46, 5282–5292 (2007).
    [CrossRef]
  3. P. de Groot, “Measurement of transparent plates with wavelength-tuned phase-shifting interferometry,” Appl. Opt. 39, 2658–2663 (2000).
    [CrossRef]
  4. L. L. Deck, “Multiple surface phase shifting interferometry,” Proc. SPIE 4451, 424–431 (2001).
    [CrossRef]
  5. L. L. Deck, “Absolute distance measurements using FTPSI with a widely tunable IR laser,” Proc. SPIE 4778, 218–226 (2002).
    [CrossRef]
  6. ZYGO verifire, Zygo Corporation, Laurel Brook Road, Middlefield, CT 06455-0448 ( http://www.zygo.com ).
  7. P. de Groot, “Metrology of transparent flats,” in Optical Fabrication and Testing Workshop, Technical Digest (Optical Society of America, 1994), pp. 160–163.
  8. P. de Groot, “Methods and apparatus for profiling surfaces of transparent objects,” U.S. patent 5, 4888, 477 (30Jan.1996).
  9. FizCam 2000, 4D Technology Corporation, 3280 E. Hemisphere Loop, Suite 146, Tucson, AZ 85706 ( http://www.4dtechnology.com ).
  10. J. Seok Oh and S.-W. Kim, “Femtosecond laser pulses for surface profile metrology,” Opt. Lett. 30, 2650–2652 (2005).
    [CrossRef]
  11. J. Schwider, “Superposition fringes for profiling applications,” in Optical Measurement Systems for Industrial Inspection V, W. Osten, C. Gorecki, and E. L. Novak, eds. (2007), 661627.
  12. J. Schwider, “Coarse frequency comb interferometry,” Proc. SPIE 7063, 706304 (2008).
    [CrossRef]
  13. J. Schwider, “Multiple beam Fizeau interferometer with frequency comb illumination,” DGAO Proc. C15 (2009).
  14. J. Schwider, “Multiple beam Fizeau interferometer with filtered frequency comb illumination,” Opt. Commun. 282, 3308–3324 (2009).
    [CrossRef]
  15. J. Rosen and M. Takeda, “Longitudinal spatial coherence applied for surface profilometry,” Appl. Opt. 39, 4107–4111 (2000).
    [CrossRef]
  16. W. Wang, H. Kozaki, M. Takeda, and J. Rosen, “New principle for optical tomography and profilometry based on spatial coherence synthesis with a spatially modulated extended light source,” Proc. SPIE 4596, 54–65 (2001).
    [CrossRef]
  17. W. Wang, H. Kozaki, J. Rosen, and M. Takeda, “Synthesis of longitudinal coherence functions by spatial modulation of an extended light source: a new interpretation and experimental verifications,” Appl. Opt. 41, 1962–1971 (2002).
    [CrossRef]
  18. Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthetic spatial coherence function for optical tomography and profilometry, simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110–117 (2002).
    [CrossRef]
  19. Z. Duan, H. Kozaki, Y. Miyamoto, J. Rosen, and M. Takeda, “Synthetic spatial coherence function for optical tomography and profilometry: influence of the observation condition,” Proc. SPIE 5531, 236–243 (2004).
    [CrossRef]
  20. Z. Duan, Y. Miyamoto, and M. Takeda, “Dispersion-free absolute interferometry based on angular spectrum scanning,” Opt. Express 14, 655–663 (2006).
    [CrossRef]
  21. Z. Duan, Y. Miyamoto, and M. Takeda, “Dispersion-free optical coherence depth sensing with a spatial frequency comb generated by an angular spectrum modulator,” Opt. Express 14, 12109–12121 (2006).
    [CrossRef]
  22. Z. Liu, T. Gemma, J. Rosen, and M. Takeda, “Improved illumination system for spatial coherence control,” Appl. Opt. 49, D12–D16 (2010).
    [CrossRef]
  23. M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, “Coherence holography,” Opt. Express 13, 9629–9635 (2005).
    [CrossRef]
  24. SAPPHIRE-488 laser, COHERENT, 5100 Patrik Henry Drive, Santa Clara, CA 95054.
  25. Point-Source, Mitchel Point, Hamble, UK, 5031 4RF.
  26. M. Küchel, “Vorrichtung und Verfahren zur Verminderung der Wirkungen kohärenter Bildfehler in einem Interferometer,” Offenlegungsschrift DE 101, 21 516 A 1, Deutsches Patent- und Markenamt, Offenlegungstag (7Nov.2002).
  27. M. Küchel, “Reducing coherent artifacts in an interferometer,” in International Application published under the Patent Cooperation Treaty (PCT) International Publication Number: WO 02/090880 A1. (14Nov.2002).
  28. M. Küchel, “Spatial coherence in interferometry, Zygos’s new method to reduce intrinsic noise in interferometers,” http://www.zygo com/library/papers , and patents referenced therein.
  29. L L. Deck, D. Stevenson, J. E. Gratix, and C. A. Zanoni, “Apparatus and method(s) for reducing the effects of coherent artifacts in an interferometer,” U.S. patent 6,643,024(4Nov.2003).
  30. M. Born and E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light6th ed. (Pergamon, 1980).
  31. P. H. van Cittert, “Die wahrscheinliche Schwingungsverteilung in einer von einer Lichtquelle direkt oder mittels einer Linse beleuchteten Ebene,” Physica 1, 201–210 (1934).
    [CrossRef]
  32. F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica 5, 785–795 (1938).
    [CrossRef]
  33. H. Fujiwara, T. Asakura, and K. Murata, “On the van Cittert–Zernike theorem,” Opt. Quantum Electron. 4, 197–205 (1972).
    [CrossRef]
  34. A. M. Zarubin, “Three-dimensional generalization of the van Cittert–Zernike theorem to wave and particle scattering,” Opt. Commun. 100, 491–507 (1993).
    [CrossRef]
  35. F. L. Pedrotti, L. S. Pedrotti, and W. Bausch, Optik, eine Einführung (Prentice Hall, 1996).
  36. K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis, Digital Fringe Pattern Measurement Techniques, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, 1993), pp. 94–140 (and references therein).

2010 (1)

2009 (2)

J. Schwider, “Multiple beam Fizeau interferometer with frequency comb illumination,” DGAO Proc. C15 (2009).

J. Schwider, “Multiple beam Fizeau interferometer with filtered frequency comb illumination,” Opt. Commun. 282, 3308–3324 (2009).
[CrossRef]

2008 (1)

J. Schwider, “Coarse frequency comb interferometry,” Proc. SPIE 7063, 706304 (2008).
[CrossRef]

2007 (1)

2006 (2)

2005 (2)

2004 (1)

Z. Duan, H. Kozaki, Y. Miyamoto, J. Rosen, and M. Takeda, “Synthetic spatial coherence function for optical tomography and profilometry: influence of the observation condition,” Proc. SPIE 5531, 236–243 (2004).
[CrossRef]

2002 (3)

Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthetic spatial coherence function for optical tomography and profilometry, simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110–117 (2002).
[CrossRef]

L. L. Deck, “Absolute distance measurements using FTPSI with a widely tunable IR laser,” Proc. SPIE 4778, 218–226 (2002).
[CrossRef]

W. Wang, H. Kozaki, J. Rosen, and M. Takeda, “Synthesis of longitudinal coherence functions by spatial modulation of an extended light source: a new interpretation and experimental verifications,” Appl. Opt. 41, 1962–1971 (2002).
[CrossRef]

2001 (2)

L. L. Deck, “Multiple surface phase shifting interferometry,” Proc. SPIE 4451, 424–431 (2001).
[CrossRef]

W. Wang, H. Kozaki, M. Takeda, and J. Rosen, “New principle for optical tomography and profilometry based on spatial coherence synthesis with a spatially modulated extended light source,” Proc. SPIE 4596, 54–65 (2001).
[CrossRef]

2000 (2)

1993 (1)

A. M. Zarubin, “Three-dimensional generalization of the van Cittert–Zernike theorem to wave and particle scattering,” Opt. Commun. 100, 491–507 (1993).
[CrossRef]

1972 (1)

H. Fujiwara, T. Asakura, and K. Murata, “On the van Cittert–Zernike theorem,” Opt. Quantum Electron. 4, 197–205 (1972).
[CrossRef]

1938 (1)

F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica 5, 785–795 (1938).
[CrossRef]

1934 (1)

P. H. van Cittert, “Die wahrscheinliche Schwingungsverteilung in einer von einer Lichtquelle direkt oder mittels einer Linse beleuchteten Ebene,” Physica 1, 201–210 (1934).
[CrossRef]

Asakura, T.

H. Fujiwara, T. Asakura, and K. Murata, “On the van Cittert–Zernike theorem,” Opt. Quantum Electron. 4, 197–205 (1972).
[CrossRef]

Bauer, T.

Bausch, W.

F. L. Pedrotti, L. S. Pedrotti, and W. Bausch, Optik, eine Einführung (Prentice Hall, 1996).

Born, M.

M. Born and E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light6th ed. (Pergamon, 1980).

Creath, K.

K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis, Digital Fringe Pattern Measurement Techniques, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, 1993), pp. 94–140 (and references therein).

de Groot, P.

P. de Groot, “Measurement of transparent plates with wavelength-tuned phase-shifting interferometry,” Appl. Opt. 39, 2658–2663 (2000).
[CrossRef]

P. de Groot, “Metrology of transparent flats,” in Optical Fabrication and Testing Workshop, Technical Digest (Optical Society of America, 1994), pp. 160–163.

P. de Groot, “Methods and apparatus for profiling surfaces of transparent objects,” U.S. patent 5, 4888, 477 (30Jan.1996).

Deck, L L.

L L. Deck, D. Stevenson, J. E. Gratix, and C. A. Zanoni, “Apparatus and method(s) for reducing the effects of coherent artifacts in an interferometer,” U.S. patent 6,643,024(4Nov.2003).

Deck, L. L.

L. L. Deck, “Absolute distance measurements using FTPSI with a widely tunable IR laser,” Proc. SPIE 4778, 218–226 (2002).
[CrossRef]

L. L. Deck, “Multiple surface phase shifting interferometry,” Proc. SPIE 4451, 424–431 (2001).
[CrossRef]

Duan, Z.

Z. Duan, Y. Miyamoto, and M. Takeda, “Dispersion-free absolute interferometry based on angular spectrum scanning,” Opt. Express 14, 655–663 (2006).
[CrossRef]

Z. Duan, Y. Miyamoto, and M. Takeda, “Dispersion-free optical coherence depth sensing with a spatial frequency comb generated by an angular spectrum modulator,” Opt. Express 14, 12109–12121 (2006).
[CrossRef]

M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, “Coherence holography,” Opt. Express 13, 9629–9635 (2005).
[CrossRef]

Z. Duan, H. Kozaki, Y. Miyamoto, J. Rosen, and M. Takeda, “Synthetic spatial coherence function for optical tomography and profilometry: influence of the observation condition,” Proc. SPIE 5531, 236–243 (2004).
[CrossRef]

Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthetic spatial coherence function for optical tomography and profilometry, simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110–117 (2002).
[CrossRef]

Fujiwara, H.

H. Fujiwara, T. Asakura, and K. Murata, “On the van Cittert–Zernike theorem,” Opt. Quantum Electron. 4, 197–205 (1972).
[CrossRef]

Gemma, T.

Gokhler, M.

Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthetic spatial coherence function for optical tomography and profilometry, simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110–117 (2002).
[CrossRef]

Gratix, J. E.

L L. Deck, D. Stevenson, J. E. Gratix, and C. A. Zanoni, “Apparatus and method(s) for reducing the effects of coherent artifacts in an interferometer,” U.S. patent 6,643,024(4Nov.2003).

Heil, J.

Ishii, N.

Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthetic spatial coherence function for optical tomography and profilometry, simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110–117 (2002).
[CrossRef]

Kim, S.-W.

Kozaki, H.

Z. Duan, H. Kozaki, Y. Miyamoto, J. Rosen, and M. Takeda, “Synthetic spatial coherence function for optical tomography and profilometry: influence of the observation condition,” Proc. SPIE 5531, 236–243 (2004).
[CrossRef]

Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthetic spatial coherence function for optical tomography and profilometry, simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110–117 (2002).
[CrossRef]

W. Wang, H. Kozaki, J. Rosen, and M. Takeda, “Synthesis of longitudinal coherence functions by spatial modulation of an extended light source: a new interpretation and experimental verifications,” Appl. Opt. 41, 1962–1971 (2002).
[CrossRef]

W. Wang, H. Kozaki, M. Takeda, and J. Rosen, “New principle for optical tomography and profilometry based on spatial coherence synthesis with a spatially modulated extended light source,” Proc. SPIE 4596, 54–65 (2001).
[CrossRef]

Küchel, M.

M. Küchel, “Vorrichtung und Verfahren zur Verminderung der Wirkungen kohärenter Bildfehler in einem Interferometer,” Offenlegungsschrift DE 101, 21 516 A 1, Deutsches Patent- und Markenamt, Offenlegungstag (7Nov.2002).

M. Küchel, “Reducing coherent artifacts in an interferometer,” in International Application published under the Patent Cooperation Treaty (PCT) International Publication Number: WO 02/090880 A1. (14Nov.2002).

Liu, Z.

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, 1978).

Miyamoto, Y.

Murata, K.

H. Fujiwara, T. Asakura, and K. Murata, “On the van Cittert–Zernike theorem,” Opt. Quantum Electron. 4, 197–205 (1972).
[CrossRef]

Pedrotti, F. L.

F. L. Pedrotti, L. S. Pedrotti, and W. Bausch, Optik, eine Einführung (Prentice Hall, 1996).

Pedrotti, L. S.

F. L. Pedrotti, L. S. Pedrotti, and W. Bausch, Optik, eine Einführung (Prentice Hall, 1996).

Rosen, J.

Z. Liu, T. Gemma, J. Rosen, and M. Takeda, “Improved illumination system for spatial coherence control,” Appl. Opt. 49, D12–D16 (2010).
[CrossRef]

Z. Duan, H. Kozaki, Y. Miyamoto, J. Rosen, and M. Takeda, “Synthetic spatial coherence function for optical tomography and profilometry: influence of the observation condition,” Proc. SPIE 5531, 236–243 (2004).
[CrossRef]

Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthetic spatial coherence function for optical tomography and profilometry, simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110–117 (2002).
[CrossRef]

W. Wang, H. Kozaki, J. Rosen, and M. Takeda, “Synthesis of longitudinal coherence functions by spatial modulation of an extended light source: a new interpretation and experimental verifications,” Appl. Opt. 41, 1962–1971 (2002).
[CrossRef]

W. Wang, H. Kozaki, M. Takeda, and J. Rosen, “New principle for optical tomography and profilometry based on spatial coherence synthesis with a spatially modulated extended light source,” Proc. SPIE 4596, 54–65 (2001).
[CrossRef]

J. Rosen and M. Takeda, “Longitudinal spatial coherence applied for surface profilometry,” Appl. Opt. 39, 4107–4111 (2000).
[CrossRef]

Schmax, S.

Schwider, J.

J. Schwider, “Multiple beam Fizeau interferometer with frequency comb illumination,” DGAO Proc. C15 (2009).

J. Schwider, “Multiple beam Fizeau interferometer with filtered frequency comb illumination,” Opt. Commun. 282, 3308–3324 (2009).
[CrossRef]

J. Schwider, “Coarse frequency comb interferometry,” Proc. SPIE 7063, 706304 (2008).
[CrossRef]

J. Schwider, “Superposition fringes for profiling applications,” in Optical Measurement Systems for Industrial Inspection V, W. Osten, C. Gorecki, and E. L. Novak, eds. (2007), 661627.

Seok Oh, J.

Stevenson, D.

L L. Deck, D. Stevenson, J. E. Gratix, and C. A. Zanoni, “Apparatus and method(s) for reducing the effects of coherent artifacts in an interferometer,” U.S. patent 6,643,024(4Nov.2003).

Sure, T.

Takeda, M.

Z. Liu, T. Gemma, J. Rosen, and M. Takeda, “Improved illumination system for spatial coherence control,” Appl. Opt. 49, D12–D16 (2010).
[CrossRef]

Z. Duan, Y. Miyamoto, and M. Takeda, “Dispersion-free absolute interferometry based on angular spectrum scanning,” Opt. Express 14, 655–663 (2006).
[CrossRef]

Z. Duan, Y. Miyamoto, and M. Takeda, “Dispersion-free optical coherence depth sensing with a spatial frequency comb generated by an angular spectrum modulator,” Opt. Express 14, 12109–12121 (2006).
[CrossRef]

M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, “Coherence holography,” Opt. Express 13, 9629–9635 (2005).
[CrossRef]

Z. Duan, H. Kozaki, Y. Miyamoto, J. Rosen, and M. Takeda, “Synthetic spatial coherence function for optical tomography and profilometry: influence of the observation condition,” Proc. SPIE 5531, 236–243 (2004).
[CrossRef]

Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthetic spatial coherence function for optical tomography and profilometry, simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110–117 (2002).
[CrossRef]

W. Wang, H. Kozaki, J. Rosen, and M. Takeda, “Synthesis of longitudinal coherence functions by spatial modulation of an extended light source: a new interpretation and experimental verifications,” Appl. Opt. 41, 1962–1971 (2002).
[CrossRef]

W. Wang, H. Kozaki, M. Takeda, and J. Rosen, “New principle for optical tomography and profilometry based on spatial coherence synthesis with a spatially modulated extended light source,” Proc. SPIE 4596, 54–65 (2001).
[CrossRef]

J. Rosen and M. Takeda, “Longitudinal spatial coherence applied for surface profilometry,” Appl. Opt. 39, 4107–4111 (2000).
[CrossRef]

van Cittert, P. H.

P. H. van Cittert, “Die wahrscheinliche Schwingungsverteilung in einer von einer Lichtquelle direkt oder mittels einer Linse beleuchteten Ebene,” Physica 1, 201–210 (1934).
[CrossRef]

Wang, W.

Wesner, J.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light6th ed. (Pergamon, 1980).

Zanoni, C. A.

L L. Deck, D. Stevenson, J. E. Gratix, and C. A. Zanoni, “Apparatus and method(s) for reducing the effects of coherent artifacts in an interferometer,” U.S. patent 6,643,024(4Nov.2003).

Zarubin, A. M.

A. M. Zarubin, “Three-dimensional generalization of the van Cittert–Zernike theorem to wave and particle scattering,” Opt. Commun. 100, 491–507 (1993).
[CrossRef]

Zernike, F.

F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica 5, 785–795 (1938).
[CrossRef]

Appl. Opt. (5)

DGAO Proc. (1)

J. Schwider, “Multiple beam Fizeau interferometer with frequency comb illumination,” DGAO Proc. C15 (2009).

Opt. Commun. (2)

J. Schwider, “Multiple beam Fizeau interferometer with filtered frequency comb illumination,” Opt. Commun. 282, 3308–3324 (2009).
[CrossRef]

A. M. Zarubin, “Three-dimensional generalization of the van Cittert–Zernike theorem to wave and particle scattering,” Opt. Commun. 100, 491–507 (1993).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

H. Fujiwara, T. Asakura, and K. Murata, “On the van Cittert–Zernike theorem,” Opt. Quantum Electron. 4, 197–205 (1972).
[CrossRef]

Physica (2)

P. H. van Cittert, “Die wahrscheinliche Schwingungsverteilung in einer von einer Lichtquelle direkt oder mittels einer Linse beleuchteten Ebene,” Physica 1, 201–210 (1934).
[CrossRef]

F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica 5, 785–795 (1938).
[CrossRef]

Proc. SPIE (6)

L. L. Deck, “Multiple surface phase shifting interferometry,” Proc. SPIE 4451, 424–431 (2001).
[CrossRef]

L. L. Deck, “Absolute distance measurements using FTPSI with a widely tunable IR laser,” Proc. SPIE 4778, 218–226 (2002).
[CrossRef]

W. Wang, H. Kozaki, M. Takeda, and J. Rosen, “New principle for optical tomography and profilometry based on spatial coherence synthesis with a spatially modulated extended light source,” Proc. SPIE 4596, 54–65 (2001).
[CrossRef]

Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthetic spatial coherence function for optical tomography and profilometry, simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110–117 (2002).
[CrossRef]

Z. Duan, H. Kozaki, Y. Miyamoto, J. Rosen, and M. Takeda, “Synthetic spatial coherence function for optical tomography and profilometry: influence of the observation condition,” Proc. SPIE 5531, 236–243 (2004).
[CrossRef]

J. Schwider, “Coarse frequency comb interferometry,” Proc. SPIE 7063, 706304 (2008).
[CrossRef]

Other (15)

F. L. Pedrotti, L. S. Pedrotti, and W. Bausch, Optik, eine Einführung (Prentice Hall, 1996).

K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis, Digital Fringe Pattern Measurement Techniques, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, 1993), pp. 94–140 (and references therein).

SAPPHIRE-488 laser, COHERENT, 5100 Patrik Henry Drive, Santa Clara, CA 95054.

Point-Source, Mitchel Point, Hamble, UK, 5031 4RF.

M. Küchel, “Vorrichtung und Verfahren zur Verminderung der Wirkungen kohärenter Bildfehler in einem Interferometer,” Offenlegungsschrift DE 101, 21 516 A 1, Deutsches Patent- und Markenamt, Offenlegungstag (7Nov.2002).

M. Küchel, “Reducing coherent artifacts in an interferometer,” in International Application published under the Patent Cooperation Treaty (PCT) International Publication Number: WO 02/090880 A1. (14Nov.2002).

M. Küchel, “Spatial coherence in interferometry, Zygos’s new method to reduce intrinsic noise in interferometers,” http://www.zygo com/library/papers , and patents referenced therein.

L L. Deck, D. Stevenson, J. E. Gratix, and C. A. Zanoni, “Apparatus and method(s) for reducing the effects of coherent artifacts in an interferometer,” U.S. patent 6,643,024(4Nov.2003).

M. Born and E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light6th ed. (Pergamon, 1980).

ZYGO verifire, Zygo Corporation, Laurel Brook Road, Middlefield, CT 06455-0448 ( http://www.zygo.com ).

P. de Groot, “Metrology of transparent flats,” in Optical Fabrication and Testing Workshop, Technical Digest (Optical Society of America, 1994), pp. 160–163.

P. de Groot, “Methods and apparatus for profiling surfaces of transparent objects,” U.S. patent 5, 4888, 477 (30Jan.1996).

FizCam 2000, 4D Technology Corporation, 3280 E. Hemisphere Loop, Suite 146, Tucson, AZ 85706 ( http://www.4dtechnology.com ).

J. Schwider, “Superposition fringes for profiling applications,” in Optical Measurement Systems for Industrial Inspection V, W. Osten, C. Gorecki, and E. L. Novak, eds. (2007), 661627.

D. Malacara, Optical Shop Testing (Wiley, 1978).

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 (16)

Fig. 1.
Fig. 1.

Fizeau interferograms of two cylindrical plane parallel flats with either a plus and a minus sign polished into its opposing surfaces (top row) or a shallow dimple polished into one of its surfaces (bottom row); the labels (+), () indicate which sample side is oriented towards the interferometer, the label (u) indicates that the sample is oriented with the dimple towards the interferometer, the image labeled (_) shows the sample with the plane surface towards the interferometer.

Fig. 2.
Fig. 2.

Fizeau interferometer illuminated by an off-axis point source. (a) General scheme of the setup: P, point source; yP, lateral offset of P; θ=yP/fC, angular offset of P; C, collimator lens with focal length fC; R, reference surface; O, object surface; d, cavity length; U, V, W, see text. (b) Diffraction of the illuminating wave at a local defect D generates a spherical wave propagating along with the incoming wave, P and P, possible positions of the illuminating point source, BE and BE, corresponding bull’s-eye patterns at the object surface.

Fig. 3.
Fig. 3.

Interferogram of a plane mirror with diameter 10 mm obtained at λ=633nm; (.) illumination by a point source realized by the exit of a single mode optical fiber; (o) illumination by an incoherent RoF with a diameter of 1 mm realized by introducing a rotating optical wedge between the point source and the collimating lens of the illumination light path and averaging over the camera exposure time of 20 ms.

Fig. 4.
Fig. 4.

Michelson interferometer used to generate an incoherent sinusoidal Fresnel zone plate intensity pattern. P, point source formed by the exit of a single mode optical fiber; L1, collimator lens with focal length fL1; BS, beam splitter; L2, focusing lens with focal length fL2; F, cat’s-eye focus; M, plane mirror; MCE, plane mirror in cat’s-eye position; F, image of F produced by MCE; S, stop; D, rotating diffusor disk; U, V, W, see text.

Fig. 5.
Fig. 5.

Close up photograph of the sinusoidal Fresnel zone plate-type intensity distribution generated with the setup shown in Fig. 4 for λ=488nm, with fL2=300mm, δ30mm, and w=10mm; the axis of the spinning diffusor disk can be seen in the upper right corner.

Fig. 6.
Fig. 6.

Normalized interferometric fringe contrast as a function of interferometer imbalance d measured in a Michelson interferometer illuminated by the setup shown in Figs. 2 and 4, with fC=fL2=300mm and w=10mm at λ=488nm for two different displacements δ of the cat’s-eye mirror MCE. The data are normalized to the contrast for perfect balance at d=0.

Fig. 7.
Fig. 7.

Experimental configurations: (a) Michelson interferometer, (b) Fizeau interferometer. ILL, illumination path (for details, see Figs. 2 and 4); IM, imaging path (not outlined); BS, beam splitter; W, glass wedge with reference surface R; S, glass sample of thickness t with front surface F and back surface B; d, interferometer imbalance; δ, displacement of the cats-eye mirror MCE in Fig. 4; M–M4, F1– F3, sample positions eligible for measurements; grayed areas, regions of thickness Δd=λ/u2 with finite fringe contrast.

Fig. 8.
Fig. 8.

Interferograms of the same sample as in Fig. 1 (+), () captured in the Michelson setup sketched in Fig. 7(a); the column labels (+) and () indicate which sample surface is oriented towards the interferometer, and the row labels M1– M4 correspond to the configurations outlined in Fig. 7(a).

Fig. 9.
Fig. 9.

Like Fig. 8 except for the Fizeau setup sketched in Fig. 7(b), the row labels F1–F3 correspond to the configurations outlined in Fig. 7(b).

Fig. 10.
Fig. 10.

The top row repeats the interferograms from the top row of Fig. 9 captured in configuration F1. The intensity I is represented with enhanced contrast to bring out the faint crosstalk from features on the back sample surface. The bottom row shows the corresponding real part of the amplitude of the wave field as registered by PSI, where no crosstalk is observed.

Fig. 11.
Fig. 11.

Real part of the amplitude distribution reflected from the same sample as shown in Fig. 1 (u), (_) as measured by PSI in the Michelson configuration shown in Fig. 7(a); the column labels (u) and (_) indicate which surface of the sample is oriented towards the interferometer, and the row labels M3 and M4 denote the corresponding sample positions.

Fig. 12.
Fig. 12.

Perspective representation of the phase of the wave fields belonging to the Michelson interferograms in Fig. 11; again (u), (_) denote sample orientation and M3, M4 denote sample positioning. The top row represents the topography of the front surface, the middle row represents the back surface topography as seen through the front surface, and the bottom row shows the pure contribution of the back sample surface, as computed with Eq. (15) from the M4-data but compensated for the refraction at the front surface given by the M3-data.

Fig. 13.
Fig. 13.

Horizontal linear cuts through the Michelson data shown in Fig. 12; again (u), (_) denote sample orientation.

Fig. 14.
Fig. 14.

Like Fig. 11 for the Fizeau configuration sketched in Fig. 7(b).

Fig. 15.
Fig. 15.

Like Fig. 12 for the Fizeau data in Fig. 14.

Fig. 16.
Fig. 16.

Horizontal linear cuts through the Fizeau data shown in Fig. 15.

Equations (15)

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

Δl=2d{cos(θ)1},dθ2=d(yP/fC)2.
I=I0+ΔIcos(Δϕ),
Im(x,y)cos[k{2zO(x,y)2zR(x,y)dθ2}]=cos[k{2zO(x,y)dθ2}],
ImScos[k{2zOdθ2}]ρ(θ,φ)θdθdφ.
Imcos{2kzO}·{sin(kdu2)/(kdu2)}.
Δd=λ/u2.
rn=fC(nλ/d)1/2
rn=(2fZPnλ)1/2,
fZP=fC2/(2d).
rL2=fL22/(2δ)+fL2fL22/(2δ),
fZPfL22/(2δ).
(fC/fL2)2d/δ.
ϕF=2k0zF,
ϕB=2k0zF+2k0n(zFzB)=(n1)ϕF2k0nzB.
ϕnetback=ϕB+(n1)ϕF.

Metrics