Abstract

We experimentally demonstrate a nonimaging approach to displacement measurement for complex scattering materials. By spatially controlling the wavefront of the light that incidents on the material, we concentrate the scattered light in a focus on a designated position. This wavefront acts as a unique optical fingerprint that enables precise position detection of the illuminated material by simply measuring the intensity in the focus. By combining two fingerprints we demonstrate position detection along one in-plane dimension with a displacement resolution of 2.1 nm. As our approach does not require an image of the scattered field, it is possible to employ fast nonimaging detectors to enable high-speed position detection of scattering materials.

© 2012 Optical Society of America

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References

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  1. K. J. Gåsvik, Optical Metrology (Wiley, 2002).
  2. N. Bobroff, Meas. Sci. Technol. 4, 907 (1993).
    [CrossRef]
  3. R. J. Dewhurst and Q. Shan, Meas. Sci. Technol. 10, R139 (1999).
    [CrossRef]
  4. J. M. Burch and J. M. J. Tokarski, Opt. Acta 15, 101 (1968).
  5. E. Archbold, J. M. Burch, and A. E. Ennos, Opt. Acta 17, 883 (1970).
    [CrossRef]
  6. J. A. Leendertz, J. Phys. E 3 (1970).
    [CrossRef]
  7. J. Butters and J. Leendertz, Opt. Laser Technol. 3, 26 (1971).
    [CrossRef]
  8. A. Macovski, S. D. Ramsey, and L. F. Schaefer, Appl. Opt. 10, 2722 (1971).
    [CrossRef]
  9. O. Lekberg, Phys. Technol. 11, 16 (1980).
    [CrossRef]
  10. J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2006).
  11. G. H. Kaufmann, ed., Advances in Speckle Metrology and Related Techniques (Wiley, 2011).
  12. I. M. Vellekoop and A. P. Mosk, Opt. Lett. 32, 2309 (2007).
    [CrossRef]
  13. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
    [CrossRef]
  14. T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photon. 4, 388 (2010).
    [CrossRef]
  15. Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
    [CrossRef]
  16. E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 56, 523 (1966).
    [CrossRef]
  17. Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
    [CrossRef]
  18. M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J.-L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
    [CrossRef]
  19. C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Laser Photon. Rev. 5, 81 (2011).
    [CrossRef]
  20. I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, Opt. Express 16, 67 (2008).
    [CrossRef]
  21. J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
    [CrossRef]
  22. O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, Nat. Photon. 5, 372 (2011).
    [CrossRef]
  23. D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
    [CrossRef]
  24. I. M. Vellekoop and A. P. Mosk, Opt. Commun. 281, 3071 (2008).
    [CrossRef]
  25. M. Cui, Opt. Express 19, 2989 (2011).
    [CrossRef]
  26. G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
    [CrossRef]
  27. J. W. Wagner and J. B. Spicer, J. Opt. Soc. Am. B 4, 1316 (1987).
    [CrossRef]

2011 (7)

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Laser Photon. Rev. 5, 81 (2011).
[CrossRef]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, Nat. Photon. 5, 372 (2011).
[CrossRef]

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

M. Cui, Opt. Express 19, 2989 (2011).
[CrossRef]

G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
[CrossRef]

2010 (2)

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photon. 4, 388 (2010).
[CrossRef]

2008 (3)

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, Opt. Express 16, 67 (2008).
[CrossRef]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

I. M. Vellekoop and A. P. Mosk, Opt. Commun. 281, 3071 (2008).
[CrossRef]

2007 (1)

2000 (1)

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J.-L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

1999 (1)

R. J. Dewhurst and Q. Shan, Meas. Sci. Technol. 10, R139 (1999).
[CrossRef]

1993 (1)

N. Bobroff, Meas. Sci. Technol. 4, 907 (1993).
[CrossRef]

1987 (1)

1980 (1)

O. Lekberg, Phys. Technol. 11, 16 (1980).
[CrossRef]

1971 (2)

J. Butters and J. Leendertz, Opt. Laser Technol. 3, 26 (1971).
[CrossRef]

A. Macovski, S. D. Ramsey, and L. F. Schaefer, Appl. Opt. 10, 2722 (1971).
[CrossRef]

1970 (2)

E. Archbold, J. M. Burch, and A. E. Ennos, Opt. Acta 17, 883 (1970).
[CrossRef]

J. A. Leendertz, J. Phys. E 3 (1970).
[CrossRef]

1968 (1)

J. M. Burch and J. M. J. Tokarski, Opt. Acta 15, 101 (1968).

1966 (1)

Alekseenko, I.

G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
[CrossRef]

Archbold, E.

E. Archbold, J. M. Burch, and A. E. Ennos, Opt. Acta 17, 883 (1970).
[CrossRef]

Aulbach, J.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

Austin, D. R.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

Bernet, S.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Laser Photon. Rev. 5, 81 (2011).
[CrossRef]

Bobroff, N.

N. Bobroff, Meas. Sci. Technol. 4, 907 (1993).
[CrossRef]

Boccara, A. C.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Bondareff, P.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

Bromberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, Nat. Photon. 5, 372 (2011).
[CrossRef]

Burch, J. M.

E. Archbold, J. M. Burch, and A. E. Ennos, Opt. Acta 17, 883 (1970).
[CrossRef]

J. M. Burch and J. M. J. Tokarski, Opt. Acta 15, 101 (1968).

Butters, J.

J. Butters and J. Leendertz, Opt. Laser Technol. 3, 26 (1971).
[CrossRef]

Carminati, R.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Cassereau, D.

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J.-L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

Chatel, B.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

Choi, W.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Choi, Y.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Cižmár, T.

T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photon. 4, 388 (2010).
[CrossRef]

Cui, M.

Dasari, R. R.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Derode, A.

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J.-L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

Dewhurst, R. J.

R. J. Dewhurst and Q. Shan, Meas. Sci. Technol. 10, R139 (1999).
[CrossRef]

Dholakia, K.

T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photon. 4, 388 (2010).
[CrossRef]

Ennos, A. E.

E. Archbold, J. M. Burch, and A. E. Ennos, Opt. Acta 17, 883 (1970).
[CrossRef]

Fang-Yen, C.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Feld, M. S.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

Fink, M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J.-L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

Gaspar, J.

G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
[CrossRef]

Gåsvik, K. J.

K. J. Gåsvik, Optical Metrology (Wiley, 2002).

Gigan, S.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Gjonaj, B.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2006).

Jesacher, A.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Laser Photon. Rev. 5, 81 (2011).
[CrossRef]

Johnson, P. M.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

Kang, P.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Katz, O.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, Nat. Photon. 5, 372 (2011).
[CrossRef]

Kaufmann, G. H.

G. H. Kaufmann, ed., Advances in Speckle Metrology and Related Techniques (Wiley, 2011).

Lagendijk, A.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, Opt. Express 16, 67 (2008).
[CrossRef]

Lee, K. J.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Leendertz, J.

J. Butters and J. Leendertz, Opt. Laser Technol. 3, 26 (1971).
[CrossRef]

Leendertz, J. A.

J. A. Leendertz, J. Phys. E 3 (1970).
[CrossRef]

Leith, E. N.

Lekberg, O.

O. Lekberg, Phys. Technol. 11, 16 (1980).
[CrossRef]

Lerosey, G.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Macovski, A.

Maurer, C.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Laser Photon. Rev. 5, 81 (2011).
[CrossRef]

Mazilu, M.

T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photon. 4, 388 (2010).
[CrossRef]

McCabe, D. J.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

Mosk, A. P.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, Opt. Express 16, 67 (2008).
[CrossRef]

I. M. Vellekoop and A. P. Mosk, Opt. Commun. 281, 3071 (2008).
[CrossRef]

I. M. Vellekoop and A. P. Mosk, Opt. Lett. 32, 2309 (2007).
[CrossRef]

Osten, W.

G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
[CrossRef]

Paul, O.

G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
[CrossRef]

Pedrini, G.

G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
[CrossRef]

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Prada, C.

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J.-L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

Psaltis, D.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

Ramsey, S. D.

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Laser Photon. Rev. 5, 81 (2011).
[CrossRef]

Roux, P.

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J.-L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

Schaefer, L. F.

Schmidt, M. E.

G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
[CrossRef]

Shan, Q.

R. J. Dewhurst and Q. Shan, Meas. Sci. Technol. 10, R139 (1999).
[CrossRef]

Silberberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, Nat. Photon. 5, 372 (2011).
[CrossRef]

Small, E.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, Nat. Photon. 5, 372 (2011).
[CrossRef]

Spicer, J. B.

Tajalli, A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

Tanter, M.

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J.-L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

Thomas, J.-L.

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J.-L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

Tokarski, J. M. J.

J. M. Burch and J. M. J. Tokarski, Opt. Acta 15, 101 (1968).

Upatnieks, J.

van Putten, E. G.

Vellekoop, I. M.

Wagner, J. W.

Walmsley, I. A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

Wu, F.

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J.-L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

Yang, C.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

Yang, T. D.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Yaqoob, Z.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

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

J. Phys. E (1)

J. A. Leendertz, J. Phys. E 3 (1970).
[CrossRef]

Laser Photon. Rev. (1)

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Laser Photon. Rev. 5, 81 (2011).
[CrossRef]

Meas. Sci. Technol. (2)

N. Bobroff, Meas. Sci. Technol. 4, 907 (1993).
[CrossRef]

R. J. Dewhurst and Q. Shan, Meas. Sci. Technol. 10, R139 (1999).
[CrossRef]

Nat. Commun. (1)

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

Nat. Photon. (3)

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, Nat. Photon. 5, 372 (2011).
[CrossRef]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photon. 4, 388 (2010).
[CrossRef]

Opt. Acta (2)

J. M. Burch and J. M. J. Tokarski, Opt. Acta 15, 101 (1968).

E. Archbold, J. M. Burch, and A. E. Ennos, Opt. Acta 17, 883 (1970).
[CrossRef]

Opt. Commun. (1)

I. M. Vellekoop and A. P. Mosk, Opt. Commun. 281, 3071 (2008).
[CrossRef]

Opt. Eng. (1)

G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
[CrossRef]

Opt. Express (2)

Opt. Laser Technol. (1)

J. Butters and J. Leendertz, Opt. Laser Technol. 3, 26 (1971).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (3)

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

Phys. Technol. (1)

O. Lekberg, Phys. Technol. 11, 16 (1980).
[CrossRef]

Rep. Prog. Phys. (1)

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J.-L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

Other (3)

J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2006).

G. H. Kaufmann, ed., Advances in Speckle Metrology and Related Techniques (Wiley, 2011).

K. J. Gåsvik, Optical Metrology (Wiley, 2002).

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Figures (3)

Fig. 1.
Fig. 1.

Method to detect sample displacements. Light modulated by a wavefront synthesizer is projected on a scattering sample by a microscope objective (not shown). At the back of the sample a microscope objective (not shown) captures the scattered light. A detector coupled to the wavefront synthesizer monitors the scattered light in the Fourier plane of the sample surface. Two optical fingerprints are generated for two sample positions. Each of the fingerprints redirects the scattered light onto one of the detectors. The sample position r is determined by illuminating the sample with a superposition of the fingerprints and monitoring the intensity difference ΔI between the two detectors. While this figure shows a horizontal displacement, the method is more generally valid and can be made to work in all directions.

Fig. 2.
Fig. 2.

Spot intensities as function of the sample displacement. (a)–(c) Camera images for different values of the sample displacement Δx. The scale bars denote 1 mm. (d) Measured spot intensities (circles IA, squares IB) as function of the sample displacement. The solid curves denote the theoretical expected behavior. One count on our detector is equal to an amount of photoelectrons of the order of 10.

Fig. 3.
Fig. 3.

Intensity difference IBIA as a function of the sample displacement Δx. The circles denote the measured intensity difference, while the solid curve represents the theoretical intensity difference. Within the gray area the function is bijective. The dotted line is a linear fit to the data points close to Δx=0. From the fit we find that the slope equals Sopt=0.66counts/ms/nm.

Equations (3)

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

I0(Δr)=ηIbg|γ(Δr)|2,
|γ(Δr)|2=[2J1(kmax|Δr|)kmax|Δr|]2,
Soptmax[(ΔI)]=5.8NAηλIbg.

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