Abstract

We show that it is possible to perform electronic speckle pattern interferometry (ESPI) using, for the first time to our knowledge, vortex beams as the reference beam. The technique we propose is easy to implement, and the advantages obtained are, among others, environmental stability, lower processing time, and the possibility to switch between traditional ESPI and spiral ESPI. The experimental results clearly show the advantages of using the proposed technique for deformation studies of complex structures.

© 2011 Optical Society of America

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  1. N. Uribe-Patarroyo, A. Alvarez-Herrero, and T. Belenguer, Phys. Rev. A. 81, 053822 (2010).
    [CrossRef]
  2. Y.-D. Liu, C. Gao, M. Gao, X. Qi, and H. Weber, Opt. Commun. 281, 3636 (2008).
    [CrossRef]
  3. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
    [CrossRef] [PubMed]
  4. G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, Astron. Astrophys. 488, 1159 (2008).
    [CrossRef]
  5. A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, Phys. Rev. Lett. 94, 233902 (2005).
    [CrossRef] [PubMed]
  6. S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Lett. 30, 1953 (2005).
    [CrossRef] [PubMed]
  7. X.-C Yuan, N. Zhang, S. H. Tao, J. Bu, and J. Lin, Appl. Phys. Lett. 91, 171116 (2007).
    [CrossRef]
  8. K. G. Larkin, D. J. Bone, and M. A. Oldfield, J. Opt. Soc. Am. A. 18, 1862 (2001).
    [CrossRef]
  9. J. Villa, I. De la Rosa, G. Miramontes, and J. A. Quiroga, J. Opt. Soc. Am. A. 22, 2766 (2005).
    [CrossRef]
  10. J. W. Goodman, Speckle Phenomena in Optics, 1st ed.(Roberts & Co., 2006).
  11. M. Lehmann, in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley & Sons, 2001), Chap. 1.
  12. A. W. Koch, in Speckle Photography and Speckle Interferometry and Their Applications to Mechanic Solid Problems, F.Salazar-Bloise, ed. (Research Signpost, 2008), Chap. 4.
    [PubMed]
  13. T. Belenguer and G. Ramos, in Speckle Photography and Speckle Interferometry and Their Applications to Mechanic Solid Problems, F.Salazar-Bloise, ed. (Research Signpost, 2008), Chap. 5.
    [PubMed]
  14. R. Restrepo, N. Uribe-Patarroyo, D. Garranzo, J. Pintado, M. Frovel, and T. Belenguer, Proc. SPIE 7387, 73871B(2010).
    [CrossRef]
  15. A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, J. Opt. Soc. Am. A. 23, 1400 (2006).
    [CrossRef]
  16. J. A. Quiroga and M. Servin, Opt. Commun. 224, 221 (2003).
    [CrossRef]
  17. K. G. Larkin, Opt. Express 13, 8097 (2005).
    [CrossRef] [PubMed]
  18. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping, 1st ed. (Wiley & Sons, 1998).

2010 (2)

N. Uribe-Patarroyo, A. Alvarez-Herrero, and T. Belenguer, Phys. Rev. A. 81, 053822 (2010).
[CrossRef]

R. Restrepo, N. Uribe-Patarroyo, D. Garranzo, J. Pintado, M. Frovel, and T. Belenguer, Proc. SPIE 7387, 73871B(2010).
[CrossRef]

2008 (2)

Y.-D. Liu, C. Gao, M. Gao, X. Qi, and H. Weber, Opt. Commun. 281, 3636 (2008).
[CrossRef]

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, Astron. Astrophys. 488, 1159 (2008).
[CrossRef]

2007 (1)

X.-C Yuan, N. Zhang, S. H. Tao, J. Bu, and J. Lin, Appl. Phys. Lett. 91, 171116 (2007).
[CrossRef]

2006 (1)

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, J. Opt. Soc. Am. A. 23, 1400 (2006).
[CrossRef]

2005 (4)

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef] [PubMed]

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Lett. 30, 1953 (2005).
[CrossRef] [PubMed]

J. Villa, I. De la Rosa, G. Miramontes, and J. A. Quiroga, J. Opt. Soc. Am. A. 22, 2766 (2005).
[CrossRef]

K. G. Larkin, Opt. Express 13, 8097 (2005).
[CrossRef] [PubMed]

2003 (1)

J. A. Quiroga and M. Servin, Opt. Commun. 224, 221 (2003).
[CrossRef]

2001 (2)

K. G. Larkin, D. J. Bone, and M. A. Oldfield, J. Opt. Soc. Am. A. 18, 1862 (2001).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Alvarez-Herrero, A.

N. Uribe-Patarroyo, A. Alvarez-Herrero, and T. Belenguer, Phys. Rev. A. 81, 053822 (2010).
[CrossRef]

Anzolin, G.

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, Astron. Astrophys. 488, 1159 (2008).
[CrossRef]

Barbieri, C.

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, Astron. Astrophys. 488, 1159 (2008).
[CrossRef]

Belenguer, T.

N. Uribe-Patarroyo, A. Alvarez-Herrero, and T. Belenguer, Phys. Rev. A. 81, 053822 (2010).
[CrossRef]

R. Restrepo, N. Uribe-Patarroyo, D. Garranzo, J. Pintado, M. Frovel, and T. Belenguer, Proc. SPIE 7387, 73871B(2010).
[CrossRef]

T. Belenguer and G. Ramos, in Speckle Photography and Speckle Interferometry and Their Applications to Mechanic Solid Problems, F.Salazar-Bloise, ed. (Research Signpost, 2008), Chap. 5.
[PubMed]

Bernet, S.

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, J. Opt. Soc. Am. A. 23, 1400 (2006).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef] [PubMed]

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Lett. 30, 1953 (2005).
[CrossRef] [PubMed]

Bianchini, A.

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, Astron. Astrophys. 488, 1159 (2008).
[CrossRef]

Bone, D. J.

K. G. Larkin, D. J. Bone, and M. A. Oldfield, J. Opt. Soc. Am. A. 18, 1862 (2001).
[CrossRef]

Bu, J.

X.-C Yuan, N. Zhang, S. H. Tao, J. Bu, and J. Lin, Appl. Phys. Lett. 91, 171116 (2007).
[CrossRef]

De la Rosa, I.

J. Villa, I. De la Rosa, G. Miramontes, and J. A. Quiroga, J. Opt. Soc. Am. A. 22, 2766 (2005).
[CrossRef]

Frovel, M.

R. Restrepo, N. Uribe-Patarroyo, D. Garranzo, J. Pintado, M. Frovel, and T. Belenguer, Proc. SPIE 7387, 73871B(2010).
[CrossRef]

Fürhapter, S.

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, J. Opt. Soc. Am. A. 23, 1400 (2006).
[CrossRef]

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Lett. 30, 1953 (2005).
[CrossRef] [PubMed]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef] [PubMed]

Gao, C.

Y.-D. Liu, C. Gao, M. Gao, X. Qi, and H. Weber, Opt. Commun. 281, 3636 (2008).
[CrossRef]

Gao, M.

Y.-D. Liu, C. Gao, M. Gao, X. Qi, and H. Weber, Opt. Commun. 281, 3636 (2008).
[CrossRef]

Garranzo, D.

R. Restrepo, N. Uribe-Patarroyo, D. Garranzo, J. Pintado, M. Frovel, and T. Belenguer, Proc. SPIE 7387, 73871B(2010).
[CrossRef]

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping, 1st ed. (Wiley & Sons, 1998).

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics, 1st ed.(Roberts & Co., 2006).

Jesacher, A.

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, J. Opt. Soc. Am. A. 23, 1400 (2006).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef] [PubMed]

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Lett. 30, 1953 (2005).
[CrossRef] [PubMed]

Koch, A. W.

A. W. Koch, in Speckle Photography and Speckle Interferometry and Their Applications to Mechanic Solid Problems, F.Salazar-Bloise, ed. (Research Signpost, 2008), Chap. 4.
[PubMed]

Larkin, K. G.

K. G. Larkin, Opt. Express 13, 8097 (2005).
[CrossRef] [PubMed]

K. G. Larkin, D. J. Bone, and M. A. Oldfield, J. Opt. Soc. Am. A. 18, 1862 (2001).
[CrossRef]

Lehmann, M.

M. Lehmann, in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley & Sons, 2001), Chap. 1.

Lin, J.

X.-C Yuan, N. Zhang, S. H. Tao, J. Bu, and J. Lin, Appl. Phys. Lett. 91, 171116 (2007).
[CrossRef]

Liu, Y.-D.

Y.-D. Liu, C. Gao, M. Gao, X. Qi, and H. Weber, Opt. Commun. 281, 3636 (2008).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Miramontes, G.

J. Villa, I. De la Rosa, G. Miramontes, and J. A. Quiroga, J. Opt. Soc. Am. A. 22, 2766 (2005).
[CrossRef]

Oldfield, M. A.

K. G. Larkin, D. J. Bone, and M. A. Oldfield, J. Opt. Soc. Am. A. 18, 1862 (2001).
[CrossRef]

Pintado, J.

R. Restrepo, N. Uribe-Patarroyo, D. Garranzo, J. Pintado, M. Frovel, and T. Belenguer, Proc. SPIE 7387, 73871B(2010).
[CrossRef]

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping, 1st ed. (Wiley & Sons, 1998).

Qi, X.

Y.-D. Liu, C. Gao, M. Gao, X. Qi, and H. Weber, Opt. Commun. 281, 3636 (2008).
[CrossRef]

Quiroga, J. A.

J. Villa, I. De la Rosa, G. Miramontes, and J. A. Quiroga, J. Opt. Soc. Am. A. 22, 2766 (2005).
[CrossRef]

J. A. Quiroga and M. Servin, Opt. Commun. 224, 221 (2003).
[CrossRef]

Ramos, G.

T. Belenguer and G. Ramos, in Speckle Photography and Speckle Interferometry and Their Applications to Mechanic Solid Problems, F.Salazar-Bloise, ed. (Research Signpost, 2008), Chap. 5.
[PubMed]

Restrepo, R.

R. Restrepo, N. Uribe-Patarroyo, D. Garranzo, J. Pintado, M. Frovel, and T. Belenguer, Proc. SPIE 7387, 73871B(2010).
[CrossRef]

Ritsch-Marte, M.

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, J. Opt. Soc. Am. A. 23, 1400 (2006).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef] [PubMed]

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Lett. 30, 1953 (2005).
[CrossRef] [PubMed]

Servin, M.

J. A. Quiroga and M. Servin, Opt. Commun. 224, 221 (2003).
[CrossRef]

Tamburini, F.

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, Astron. Astrophys. 488, 1159 (2008).
[CrossRef]

Tao, S. H.

X.-C Yuan, N. Zhang, S. H. Tao, J. Bu, and J. Lin, Appl. Phys. Lett. 91, 171116 (2007).
[CrossRef]

Umbriaco, G.

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, Astron. Astrophys. 488, 1159 (2008).
[CrossRef]

Uribe-Patarroyo, N.

N. Uribe-Patarroyo, A. Alvarez-Herrero, and T. Belenguer, Phys. Rev. A. 81, 053822 (2010).
[CrossRef]

R. Restrepo, N. Uribe-Patarroyo, D. Garranzo, J. Pintado, M. Frovel, and T. Belenguer, Proc. SPIE 7387, 73871B(2010).
[CrossRef]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Villa, J.

J. Villa, I. De la Rosa, G. Miramontes, and J. A. Quiroga, J. Opt. Soc. Am. A. 22, 2766 (2005).
[CrossRef]

Weber, H.

Y.-D. Liu, C. Gao, M. Gao, X. Qi, and H. Weber, Opt. Commun. 281, 3636 (2008).
[CrossRef]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Yuan, X.-C

X.-C Yuan, N. Zhang, S. H. Tao, J. Bu, and J. Lin, Appl. Phys. Lett. 91, 171116 (2007).
[CrossRef]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Zhang, N.

X.-C Yuan, N. Zhang, S. H. Tao, J. Bu, and J. Lin, Appl. Phys. Lett. 91, 171116 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

X.-C Yuan, N. Zhang, S. H. Tao, J. Bu, and J. Lin, Appl. Phys. Lett. 91, 171116 (2007).
[CrossRef]

Astron. Astrophys. (1)

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, Astron. Astrophys. 488, 1159 (2008).
[CrossRef]

J. Opt. Soc. Am. A. (3)

K. G. Larkin, D. J. Bone, and M. A. Oldfield, J. Opt. Soc. Am. A. 18, 1862 (2001).
[CrossRef]

J. Villa, I. De la Rosa, G. Miramontes, and J. A. Quiroga, J. Opt. Soc. Am. A. 22, 2766 (2005).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, J. Opt. Soc. Am. A. 23, 1400 (2006).
[CrossRef]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Opt. Commun. (2)

J. A. Quiroga and M. Servin, Opt. Commun. 224, 221 (2003).
[CrossRef]

Y.-D. Liu, C. Gao, M. Gao, X. Qi, and H. Weber, Opt. Commun. 281, 3636 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A. (1)

N. Uribe-Patarroyo, A. Alvarez-Herrero, and T. Belenguer, Phys. Rev. A. 81, 053822 (2010).
[CrossRef]

Phys. Rev. Lett. (1)

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef] [PubMed]

Proc. SPIE (1)

R. Restrepo, N. Uribe-Patarroyo, D. Garranzo, J. Pintado, M. Frovel, and T. Belenguer, Proc. SPIE 7387, 73871B(2010).
[CrossRef]

Other (5)

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping, 1st ed. (Wiley & Sons, 1998).

J. W. Goodman, Speckle Phenomena in Optics, 1st ed.(Roberts & Co., 2006).

M. Lehmann, in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley & Sons, 2001), Chap. 1.

A. W. Koch, in Speckle Photography and Speckle Interferometry and Their Applications to Mechanic Solid Problems, F.Salazar-Bloise, ed. (Research Signpost, 2008), Chap. 4.
[PubMed]

T. Belenguer and G. Ramos, in Speckle Photography and Speckle Interferometry and Their Applications to Mechanic Solid Problems, F.Salazar-Bloise, ed. (Research Signpost, 2008), Chap. 5.
[PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) Simulation setup. (b) Experimental setup. Details are explained in the text.

Fig. 2
Fig. 2

Simulation of ESPI using an n z -OAM beam. (a) Mathematical deformation function. (b) Simulated fringes obtained.

Fig. 3
Fig. 3

(a) Classical ESPI interferogram. (b) ESPI spiral pattern interferogram.

Fig. 4
Fig. 4

(a) Traditional ESPI phase modulo 2 π using four phase shifts. (b) Traditional ESPI phase unwrap. (c) Spiral ESPI phase modulo 2 π using vortex operator. (d) Spiral ESPI phase unwrap.

Equations (9)

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

E o ( x , y ) = E o ^ ( x , y ) · e i ϕ o ( x , y ) ,
E r ( x , y ) = E r ^ ( x , y ) · e i ϕ r ( x , y ) ,
I 1 ( x , y ) = | E o | 2 + | E r | 2 + | E o | · | E r | · ( e i ( ϕ o ϕ r ) + e i ( ϕ r ϕ o ) ) .
I 2 ( x , y ) = | E o | 2 + | E r | 2 + | E o | · | E r | · ( e i ( ( ϕ o ϕ r ) + Δ ϕ ) + e i ( ( ϕ r ϕ o ) Δ ϕ ) ) .
Δ ϕ = F 1 { F { e i ( Δ ϕ D ) } · n z - OAM } .
n z - OAM = e i l ϕ ( ρ , θ ) ,
I = | I 2 I 1 | .
V { I } = i · e i ( β ( x , y ) ) · { F 1 { n z - OAM ( u , v ) · F { I ( x , y ) } } } .
ψ ( x , y ) = arctan ( Re ( V { I ( x , y ) } ) I ( x , y ) ) .

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