Abstract

The paper presents an algorithm able to retrieve the phase in speckle interferometry by a single intensity pattern acquired in a deformed state, provided that the integrated speckle field is resolved in the reference condition in terms of mean intensity, modulation amplitude and phase. The proposed approach, called throughout the paper “one-step”, can be applied for studying phenomena whose rapid evolution does not allow the application of a standard phase-shifting procedure, which, on the other hand, must be applied at the beginning of the experiment. The approach was proved by an experimental test reported at the end of the paper.

© 2008 Optical Society of America

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References

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  1. K. Creath, "Temporal phase measurement methods," in Interferogram Analysis, D. W. Robinson and G. T. Reid, eds., (Institute of Physics Publishing, Bristol, Philadelphia, 1993) Chap. 4, pp. 94-140.
  2. M. Kujawinska, "Spatial phase measurement methods," in Interferogram Analysis, D. W. Robinson and G. T. Reid, eds., (Institute of Physics Publishing, Bristol, Philadelphia, 1993) Chap. 5, pp. 141-193
  3. J. M. Huntley, "Automated fringe pattern analysis in experimental mechanics: a review," J. Strain Anal. Eng. Des. 33, 105-125 (1998).
    [CrossRef]
  4. P. A. A. M. Somers and N. Bhattacharya, "Maintaining sub-pixel alignment for a single-camera two-bucket shearing speckle interferometer," J. Opt. A: Pure and Appl. Opt. 7, S385-S391 (2005).
  5. L. Yang, W. Steinchen, G. Kupfer, P. Mackel, and F. Vossing, "Vibration analysis by means of digital shearography," Opt. Lasers Eng. 30, 199-212 (1998).
  6. F. J. Casillas, A. Davilla, S. J. Rothberg, and G. Garnica, "Small amplitude estimation of mechanical vibrations using electronic speckle shearing pattern interferometry," Opt. Eng. 43, 880-887 (2004).
    [CrossRef]
  7. S. Liu, D. Thomas, P. R. Samala and L. X. Yang, "Vibration measurement of MEMS by digital laser microinterferometer," Proc. SPIE 5878, 58780C1-9 (2005).
  8. M. Takeda, H. Ina, and S. Kobayashi, "Fourier-transorm method of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. 72, 156-160 (1982).
  9. G. H. Kaufmann and G. E. Galizzi, "Phase measurement in temporal speckle pattern interferometry: comparison between the phase-shifting and the Fourier transform methods," Appl. Opt. 41, 7254-7263 (2002).
    [CrossRef]
  10. B. Bhaduri, N. Krishna Mohan, M. P. Kothiyal, and R. S. Sirohi, "Use of spatial phase shifting technique in digital speckle pattern interferometry (DSPI) and digital shearography (DS)," Opt. Express 14, 11598-11607 (2006).
    [CrossRef]
  11. M. Kujawinska and D. W. Robinson, "Multichannel phase-stepped holographic interferometry," Appl. Opt. 27, 312-320 (1988).
  12. M. Adachi, Y. Ueyama, and K. Inabe, "Automatic deformation analysis in electronic speckle pattern interferometry using one speckle interferogram of deformed object," Opt. Rev. 4, 429-432 (1997).
    [CrossRef]
  13. C. C. Kao, G. B. Yeh, S. S. Lee, C. K. Lee, C. S. Yang, and K. C. Wu, "Phase-shifting algorithms for electronic speckle pattern interferometry," Appl. Opt. 41, 46-54 (2002).
    [CrossRef]
  14. W. An and T. E. Carlsson, "Speckle interferometry for measurement of continuous deformations," Opt. Lasers Eng. 40, 529-541 (2003).
    [CrossRef]
  15. M. Adachi, J. N. Petzing, and D. Kerr, "Deformation-phase measurement of diffuse objects that have started nonrepeatable dynamic deformation," Appl. Opt. 40, 6187-6192 (2001).
    [CrossRef]
  16. L. Bruno and A. Poggialini, "Phase retrieval in speckle interferometry: a one-step approach," in Proceedings of Interferometry in Speckle Light - Theory and Applications, P. Jacquot and J. M. Fournier, eds., (Springer, Heidelberg, Germany, 2000), pp. 461-472.
  17. A. E. Arthur, Regression and the Moore-Penrose Pseudoinverse (Academic Press, New York, 1972).
  18. A. Knight, Basics of Matlab and Beyond (Chapman & Hall/CRC, Natick, Massachusetts, 2000).
  19. S. Wolfram, The Mathematica Book, 5th edition (Wolfram Media, Champaign, Illinois, 2003).
  20. L. Bruno, G. Felice and A. Poggialini, "Design and calibration of a piezoelectric actuator for interferometric applications," Opt. Lasers Eng. 45, 1148-1156 (2007).
    [CrossRef]

2007 (1)

L. Bruno, G. Felice and A. Poggialini, "Design and calibration of a piezoelectric actuator for interferometric applications," Opt. Lasers Eng. 45, 1148-1156 (2007).
[CrossRef]

2006 (1)

2005 (1)

P. A. A. M. Somers and N. Bhattacharya, "Maintaining sub-pixel alignment for a single-camera two-bucket shearing speckle interferometer," J. Opt. A: Pure and Appl. Opt. 7, S385-S391 (2005).

2004 (1)

F. J. Casillas, A. Davilla, S. J. Rothberg, and G. Garnica, "Small amplitude estimation of mechanical vibrations using electronic speckle shearing pattern interferometry," Opt. Eng. 43, 880-887 (2004).
[CrossRef]

2003 (1)

W. An and T. E. Carlsson, "Speckle interferometry for measurement of continuous deformations," Opt. Lasers Eng. 40, 529-541 (2003).
[CrossRef]

2002 (2)

2001 (1)

1998 (2)

J. M. Huntley, "Automated fringe pattern analysis in experimental mechanics: a review," J. Strain Anal. Eng. Des. 33, 105-125 (1998).
[CrossRef]

L. Yang, W. Steinchen, G. Kupfer, P. Mackel, and F. Vossing, "Vibration analysis by means of digital shearography," Opt. Lasers Eng. 30, 199-212 (1998).

1997 (1)

M. Adachi, Y. Ueyama, and K. Inabe, "Automatic deformation analysis in electronic speckle pattern interferometry using one speckle interferogram of deformed object," Opt. Rev. 4, 429-432 (1997).
[CrossRef]

1988 (1)

1982 (1)

Adachi, M.

M. Adachi, J. N. Petzing, and D. Kerr, "Deformation-phase measurement of diffuse objects that have started nonrepeatable dynamic deformation," Appl. Opt. 40, 6187-6192 (2001).
[CrossRef]

M. Adachi, Y. Ueyama, and K. Inabe, "Automatic deformation analysis in electronic speckle pattern interferometry using one speckle interferogram of deformed object," Opt. Rev. 4, 429-432 (1997).
[CrossRef]

An, W.

W. An and T. E. Carlsson, "Speckle interferometry for measurement of continuous deformations," Opt. Lasers Eng. 40, 529-541 (2003).
[CrossRef]

Bhaduri, B.

Bhattacharya, N.

P. A. A. M. Somers and N. Bhattacharya, "Maintaining sub-pixel alignment for a single-camera two-bucket shearing speckle interferometer," J. Opt. A: Pure and Appl. Opt. 7, S385-S391 (2005).

Bruno, L.

L. Bruno, G. Felice and A. Poggialini, "Design and calibration of a piezoelectric actuator for interferometric applications," Opt. Lasers Eng. 45, 1148-1156 (2007).
[CrossRef]

Carlsson, T. E.

W. An and T. E. Carlsson, "Speckle interferometry for measurement of continuous deformations," Opt. Lasers Eng. 40, 529-541 (2003).
[CrossRef]

Casillas, F. J.

F. J. Casillas, A. Davilla, S. J. Rothberg, and G. Garnica, "Small amplitude estimation of mechanical vibrations using electronic speckle shearing pattern interferometry," Opt. Eng. 43, 880-887 (2004).
[CrossRef]

Davilla, A.

F. J. Casillas, A. Davilla, S. J. Rothberg, and G. Garnica, "Small amplitude estimation of mechanical vibrations using electronic speckle shearing pattern interferometry," Opt. Eng. 43, 880-887 (2004).
[CrossRef]

Felice, G.

L. Bruno, G. Felice and A. Poggialini, "Design and calibration of a piezoelectric actuator for interferometric applications," Opt. Lasers Eng. 45, 1148-1156 (2007).
[CrossRef]

Galizzi, G. E.

Garnica, G.

F. J. Casillas, A. Davilla, S. J. Rothberg, and G. Garnica, "Small amplitude estimation of mechanical vibrations using electronic speckle shearing pattern interferometry," Opt. Eng. 43, 880-887 (2004).
[CrossRef]

Huntley, J. M.

J. M. Huntley, "Automated fringe pattern analysis in experimental mechanics: a review," J. Strain Anal. Eng. Des. 33, 105-125 (1998).
[CrossRef]

Ina, H.

Inabe, K.

M. Adachi, Y. Ueyama, and K. Inabe, "Automatic deformation analysis in electronic speckle pattern interferometry using one speckle interferogram of deformed object," Opt. Rev. 4, 429-432 (1997).
[CrossRef]

Kao, C. C.

Kaufmann, G. H.

Kerr, D.

Kobayashi, S.

Kothiyal, M. P.

Krishna Mohan, N.

Kujawinska, M.

Kupfer, G.

L. Yang, W. Steinchen, G. Kupfer, P. Mackel, and F. Vossing, "Vibration analysis by means of digital shearography," Opt. Lasers Eng. 30, 199-212 (1998).

Lee, C. K.

Lee, S. S.

Mackel, P.

L. Yang, W. Steinchen, G. Kupfer, P. Mackel, and F. Vossing, "Vibration analysis by means of digital shearography," Opt. Lasers Eng. 30, 199-212 (1998).

Petzing, J. N.

Poggialini, A.

L. Bruno, G. Felice and A. Poggialini, "Design and calibration of a piezoelectric actuator for interferometric applications," Opt. Lasers Eng. 45, 1148-1156 (2007).
[CrossRef]

Robinson, D. W.

Rothberg, S. J.

F. J. Casillas, A. Davilla, S. J. Rothberg, and G. Garnica, "Small amplitude estimation of mechanical vibrations using electronic speckle shearing pattern interferometry," Opt. Eng. 43, 880-887 (2004).
[CrossRef]

Sirohi, R. S.

Somers, P. A. A. M.

P. A. A. M. Somers and N. Bhattacharya, "Maintaining sub-pixel alignment for a single-camera two-bucket shearing speckle interferometer," J. Opt. A: Pure and Appl. Opt. 7, S385-S391 (2005).

Steinchen, W.

L. Yang, W. Steinchen, G. Kupfer, P. Mackel, and F. Vossing, "Vibration analysis by means of digital shearography," Opt. Lasers Eng. 30, 199-212 (1998).

Takeda, M.

Ueyama, Y.

M. Adachi, Y. Ueyama, and K. Inabe, "Automatic deformation analysis in electronic speckle pattern interferometry using one speckle interferogram of deformed object," Opt. Rev. 4, 429-432 (1997).
[CrossRef]

Vossing, F.

L. Yang, W. Steinchen, G. Kupfer, P. Mackel, and F. Vossing, "Vibration analysis by means of digital shearography," Opt. Lasers Eng. 30, 199-212 (1998).

Wu, K. C.

Yang, C. S.

Yang, L.

L. Yang, W. Steinchen, G. Kupfer, P. Mackel, and F. Vossing, "Vibration analysis by means of digital shearography," Opt. Lasers Eng. 30, 199-212 (1998).

Yeh, G. B.

Appl. Opt. (4)

J. Opt. A: Pure and Appl. Opt. (1)

P. A. A. M. Somers and N. Bhattacharya, "Maintaining sub-pixel alignment for a single-camera two-bucket shearing speckle interferometer," J. Opt. A: Pure and Appl. Opt. 7, S385-S391 (2005).

J. Opt. Soc. Am. (1)

J. Strain Anal. Eng. Des. (1)

J. M. Huntley, "Automated fringe pattern analysis in experimental mechanics: a review," J. Strain Anal. Eng. Des. 33, 105-125 (1998).
[CrossRef]

Opt. Eng. (1)

F. J. Casillas, A. Davilla, S. J. Rothberg, and G. Garnica, "Small amplitude estimation of mechanical vibrations using electronic speckle shearing pattern interferometry," Opt. Eng. 43, 880-887 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (3)

W. An and T. E. Carlsson, "Speckle interferometry for measurement of continuous deformations," Opt. Lasers Eng. 40, 529-541 (2003).
[CrossRef]

L. Yang, W. Steinchen, G. Kupfer, P. Mackel, and F. Vossing, "Vibration analysis by means of digital shearography," Opt. Lasers Eng. 30, 199-212 (1998).

L. Bruno, G. Felice and A. Poggialini, "Design and calibration of a piezoelectric actuator for interferometric applications," Opt. Lasers Eng. 45, 1148-1156 (2007).
[CrossRef]

Opt. Rev. (1)

M. Adachi, Y. Ueyama, and K. Inabe, "Automatic deformation analysis in electronic speckle pattern interferometry using one speckle interferogram of deformed object," Opt. Rev. 4, 429-432 (1997).
[CrossRef]

Other (7)

S. Liu, D. Thomas, P. R. Samala and L. X. Yang, "Vibration measurement of MEMS by digital laser microinterferometer," Proc. SPIE 5878, 58780C1-9 (2005).

K. Creath, "Temporal phase measurement methods," in Interferogram Analysis, D. W. Robinson and G. T. Reid, eds., (Institute of Physics Publishing, Bristol, Philadelphia, 1993) Chap. 4, pp. 94-140.

M. Kujawinska, "Spatial phase measurement methods," in Interferogram Analysis, D. W. Robinson and G. T. Reid, eds., (Institute of Physics Publishing, Bristol, Philadelphia, 1993) Chap. 5, pp. 141-193

L. Bruno and A. Poggialini, "Phase retrieval in speckle interferometry: a one-step approach," in Proceedings of Interferometry in Speckle Light - Theory and Applications, P. Jacquot and J. M. Fournier, eds., (Springer, Heidelberg, Germany, 2000), pp. 461-472.

A. E. Arthur, Regression and the Moore-Penrose Pseudoinverse (Academic Press, New York, 1972).

A. Knight, Basics of Matlab and Beyond (Chapman & Hall/CRC, Natick, Massachusetts, 2000).

S. Wolfram, The Mathematica Book, 5th edition (Wolfram Media, Champaign, Illinois, 2003).

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