Abstract

A novel technique for biological kinematic analysis is proposed that makes use of the pseudophase singularities in a complex signal generated from a speckle-like pattern. In addition to the information about the locations and the anisotropic core structures of the pseudophase singularities, we also detect the spatial structures of a cluster of phase singularities, which serves as a unique constellation characterizing the mutual position relation between the individual pseudophase singularities. Experimental results of in vivo measurements for a swimming fish along with its kinematic analysis are presented, which demonstrate the validity of the proposed technique.

© 2008 Optical Society of America

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References

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  1. J. M. Benyus, Biomimicry: Innovation inspired by nature (William Morrow and Co, 1998), Chap. 1.
  2. R. S. Sirohi, Speckle Metrology (Marcel Dekker Inc., New York, 1993).
  3. S. J. Kirkpatrick and D. D. Duncan, "Optical assessment of tissue mechanics," in Handbook of Optical Biological Diagnostics, V. V. Tuchin, ed., (SPIE Press, Bellingham, 2002).
  4. J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. Lond. A 336, 165-190 (1974).
  5. M. S. Soskin and M. V. Vasnetsov, "Singular Optics," in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2001).
  6. M. Takeda, "Recent progress in phase unwrapping techniques," Proc. SPIE 2782, 334-343 (1996).
    [CrossRef]
  7. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (John Wiley and Sons, New York, 1998).
  8. W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248, 59-68 (2005).
    [CrossRef]
  9. W. Wang, T. Yokozeki, R. Ishijima, A. Wada, S. G. Hanson, Y. Miyamoto, and M. Takeda, "Optical vortex metrology for nanometric speckle displacement measurement," Opt. Express 14, 120-127 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-1-120.
    [CrossRef] [PubMed]
  10. W. Wang, T. Yokozeki, R. Ishijima, S. G. Hanson, and M. Takeda, "Optical vortex metrology based on the core structures of phase singularities in Laguerre-Gauss transform of a speckle pattern," Opt. Express 14, 10195-10206 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-22-10195.
    [CrossRef] [PubMed]
  11. W. Wang, M. R. Dennis, Reika Ishijima, T. Yokozeki, A. Matsuda, S. G. Hanson, and M. Takeda, "Poincaré sphere representation for the anisotropy of phase singularities and its applications to optical vortex metrology for fluid mechanical analysis," Opt. Express 15, 11008-11019 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-17-11008.
    [CrossRef] [PubMed]
  12. K. G. Larkin, D. J. Bone, and M. A. Oldfield, "Natural demodulation of two-dimensional fringe pattern. I. General background of the spiral phase quadrature transform," J. Opt. Soc. Am. A 18, 1862-1870 (2001).
    [CrossRef]
  13. C. -S. Guo, Y. -Y. Han, J. -B. Xu, and J. Ding, "Radial Hilbert transform with Laguerre-Gaussian spatial filters," Opt. Lett. 31, 1394-1396 (2006).
    [CrossRef] [PubMed]
  14. M. V. Berry and M. R. Dennis, "Phase singularities in isotropic random waves," Proc. R. Soc. Lond. A,  456, 2059-2079 (2000).
    [CrossRef]
  15. M. R. Dennis, "Local structure of wave dislocation lines: twist and twirl," J. Opt. A: Pure Appl. Opt. 6, S202-S208 (2004).
    [CrossRef]
  16. Y. A. Egorov, T. A. Fadeyeva, and A. V. Volyar, "The fine structure of singular beams in crystals: colours and polarization," J. Opt. A: Pure Appl. Opt. 6, S217-S228 (2004).
    [CrossRef]
  17. M. R. Dennis, "Polarization singularities in paraxial vector fields: morphology and statistics," Opt. Commun. 213, 201-221 (2002).
    [CrossRef]
  18. L. D. Landau and E. M. Lifshits, Theory of Elasticity, (Butterworth-Heinemann, 1984).
  19. J. F. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations, (Institute of Physics Publishing, 1999).
  20. M. S. Soskin, V. Denisenko, and R. Egorov, "Topological networks of paraxial ellipse speckle-fields," J. Opt. A: Pure Appl. Opt. 6, S281-287 (2004).
    [CrossRef]
  21. W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, "Pseudophase information from the complex analytic signal of speckle fields and its applications. Part II: statistical properties of the analytic signal of a white-light speckle pattern applied to the micro displacement measurement," Appl. Opt. 44, 4916-4921 (2005).
    [CrossRef] [PubMed]

2007 (1)

2006 (1)

2005 (2)

2004 (3)

M. R. Dennis, "Local structure of wave dislocation lines: twist and twirl," J. Opt. A: Pure Appl. Opt. 6, S202-S208 (2004).
[CrossRef]

Y. A. Egorov, T. A. Fadeyeva, and A. V. Volyar, "The fine structure of singular beams in crystals: colours and polarization," J. Opt. A: Pure Appl. Opt. 6, S217-S228 (2004).
[CrossRef]

M. S. Soskin, V. Denisenko, and R. Egorov, "Topological networks of paraxial ellipse speckle-fields," J. Opt. A: Pure Appl. Opt. 6, S281-287 (2004).
[CrossRef]

2002 (1)

M. R. Dennis, "Polarization singularities in paraxial vector fields: morphology and statistics," Opt. Commun. 213, 201-221 (2002).
[CrossRef]

2001 (1)

2000 (1)

M. V. Berry and M. R. Dennis, "Phase singularities in isotropic random waves," Proc. R. Soc. Lond. A,  456, 2059-2079 (2000).
[CrossRef]

1996 (1)

M. Takeda, "Recent progress in phase unwrapping techniques," Proc. SPIE 2782, 334-343 (1996).
[CrossRef]

1974 (1)

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. Lond. A 336, 165-190 (1974).

Berry, M. V.

M. V. Berry and M. R. Dennis, "Phase singularities in isotropic random waves," Proc. R. Soc. Lond. A,  456, 2059-2079 (2000).
[CrossRef]

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. Lond. A 336, 165-190 (1974).

Bone, D. J.

Denisenko, V.

M. S. Soskin, V. Denisenko, and R. Egorov, "Topological networks of paraxial ellipse speckle-fields," J. Opt. A: Pure Appl. Opt. 6, S281-287 (2004).
[CrossRef]

Dennis, M. R.

W. Wang, M. R. Dennis, Reika Ishijima, T. Yokozeki, A. Matsuda, S. G. Hanson, and M. Takeda, "Poincaré sphere representation for the anisotropy of phase singularities and its applications to optical vortex metrology for fluid mechanical analysis," Opt. Express 15, 11008-11019 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-17-11008.
[CrossRef] [PubMed]

M. R. Dennis, "Local structure of wave dislocation lines: twist and twirl," J. Opt. A: Pure Appl. Opt. 6, S202-S208 (2004).
[CrossRef]

M. R. Dennis, "Polarization singularities in paraxial vector fields: morphology and statistics," Opt. Commun. 213, 201-221 (2002).
[CrossRef]

M. V. Berry and M. R. Dennis, "Phase singularities in isotropic random waves," Proc. R. Soc. Lond. A,  456, 2059-2079 (2000).
[CrossRef]

Ding, J.

Egorov, R.

M. S. Soskin, V. Denisenko, and R. Egorov, "Topological networks of paraxial ellipse speckle-fields," J. Opt. A: Pure Appl. Opt. 6, S281-287 (2004).
[CrossRef]

Egorov, Y. A.

Y. A. Egorov, T. A. Fadeyeva, and A. V. Volyar, "The fine structure of singular beams in crystals: colours and polarization," J. Opt. A: Pure Appl. Opt. 6, S217-S228 (2004).
[CrossRef]

Fadeyeva, T. A.

Y. A. Egorov, T. A. Fadeyeva, and A. V. Volyar, "The fine structure of singular beams in crystals: colours and polarization," J. Opt. A: Pure Appl. Opt. 6, S217-S228 (2004).
[CrossRef]

Guo, C. -S.

Han, Y. -Y.

Hanson, S. G.

Ishii, N.

Larkin, K. G.

Miyamoto, Y.

Nye, J. F.

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. Lond. A 336, 165-190 (1974).

Oldfield, M. A.

Reika Ishijima, M. R.

Soskin, M. S.

M. S. Soskin, V. Denisenko, and R. Egorov, "Topological networks of paraxial ellipse speckle-fields," J. Opt. A: Pure Appl. Opt. 6, S281-287 (2004).
[CrossRef]

Takeda, M.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248, 59-68 (2005).
[CrossRef]

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, "Pseudophase information from the complex analytic signal of speckle fields and its applications. Part II: statistical properties of the analytic signal of a white-light speckle pattern applied to the micro displacement measurement," Appl. Opt. 44, 4916-4921 (2005).
[CrossRef] [PubMed]

M. Takeda, "Recent progress in phase unwrapping techniques," Proc. SPIE 2782, 334-343 (1996).
[CrossRef]

Volyar, A. V.

Y. A. Egorov, T. A. Fadeyeva, and A. V. Volyar, "The fine structure of singular beams in crystals: colours and polarization," J. Opt. A: Pure Appl. Opt. 6, S217-S228 (2004).
[CrossRef]

Wang, W.

Xu, J. -B.

Appl. Opt. (1)

J. Opt. A: Pure Appl. Opt. (3)

M. S. Soskin, V. Denisenko, and R. Egorov, "Topological networks of paraxial ellipse speckle-fields," J. Opt. A: Pure Appl. Opt. 6, S281-287 (2004).
[CrossRef]

M. R. Dennis, "Local structure of wave dislocation lines: twist and twirl," J. Opt. A: Pure Appl. Opt. 6, S202-S208 (2004).
[CrossRef]

Y. A. Egorov, T. A. Fadeyeva, and A. V. Volyar, "The fine structure of singular beams in crystals: colours and polarization," J. Opt. A: Pure Appl. Opt. 6, S217-S228 (2004).
[CrossRef]

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

Opt. Commun. (2)

M. R. Dennis, "Polarization singularities in paraxial vector fields: morphology and statistics," Opt. Commun. 213, 201-221 (2002).
[CrossRef]

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248, 59-68 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. R. Soc. Lond. A (2)

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. Lond. A 336, 165-190 (1974).

M. V. Berry and M. R. Dennis, "Phase singularities in isotropic random waves," Proc. R. Soc. Lond. A,  456, 2059-2079 (2000).
[CrossRef]

Proc. SPIE (1)

M. Takeda, "Recent progress in phase unwrapping techniques," Proc. SPIE 2782, 334-343 (1996).
[CrossRef]

Other (9)

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (John Wiley and Sons, New York, 1998).

W. Wang, T. Yokozeki, R. Ishijima, A. Wada, S. G. Hanson, Y. Miyamoto, and M. Takeda, "Optical vortex metrology for nanometric speckle displacement measurement," Opt. Express 14, 120-127 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-1-120.
[CrossRef] [PubMed]

W. Wang, T. Yokozeki, R. Ishijima, S. G. Hanson, and M. Takeda, "Optical vortex metrology based on the core structures of phase singularities in Laguerre-Gauss transform of a speckle pattern," Opt. Express 14, 10195-10206 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-22-10195.
[CrossRef] [PubMed]

M. S. Soskin and M. V. Vasnetsov, "Singular Optics," in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2001).

J. M. Benyus, Biomimicry: Innovation inspired by nature (William Morrow and Co, 1998), Chap. 1.

R. S. Sirohi, Speckle Metrology (Marcel Dekker Inc., New York, 1993).

S. J. Kirkpatrick and D. D. Duncan, "Optical assessment of tissue mechanics," in Handbook of Optical Biological Diagnostics, V. V. Tuchin, ed., (SPIE Press, Bellingham, 2002).

L. D. Landau and E. M. Lifshits, Theory of Elasticity, (Butterworth-Heinemann, 1984).

J. F. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations, (Institute of Physics Publishing, 1999).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram for the constellation of pseudophase singularities. (a) Before movement; (b) After movement.

Fig. 2.
Fig. 2.

(Media 1) Recorded images for the swimming fugu at different instants of time and the generated Laguerre-Gauss signals with pseudophase singularities inserted.

Fig. 3.
Fig. 3.

(Media 2) The trajectory of the pseudophase singularities inside the fugu’s body at different instants of time (a) t=0.067s,(b) t=0.699s, (c) t=1.665s, (d) t=3.33s.

Fig. 4.
Fig. 4.

Movement decomposition based on the pseudophase singularities constellation

Fig. 5.
Fig. 5.

History of the sum force (a) and torque (b) applied to the fugu.

Equations (15)

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

g ( x , y ) = g ( x , y ) exp [ j θ ( x , y ) ] = g ( x , y ) * L G ( x , y ) ,
L G ( x , y ) = ( j π 2 ω 4 ) ( x + j y ) exp [ π 2 ω 2 ( x 2 + y 2 ) ]
= ( j π 2 ω 4 ) [ r exp ( π 2 r 2 ω 2 ) exp ( j α ) ] .
g ( x , y ) = 𝔽 1 { LG ( f x , f y ) · G ( f x , f y ) } .
LG ( f x , f y ) = ( f x + j f y ) exp [ ( f x 2 + f y 2 ) ω 2 ] = ρ exp ( ρ 2 ω 2 ) exp ( j β ) ,
( x i x y i y ) = β ( cos δ sin δ sin δ cos δ ) ( x i x y i y ) ,
x = Σ i x i N , and y = Σ i y i N ;
x = Σ i x i N , and y = Σ i y i N ;
E = Σ i { [ x i x C ( x i x ) S ( y i y ) ] 2 + [ y i y + S ( x i x ) C ( y i y ) ] 2 } ,
C = Σ i ( x i x i + y i y i ) Σ i ( x i 2 + y i 2 ) ,
S = Σ i ( x i y i x i y i ) Σ i ( x i 2 + y i 2 ) ,
β = S 2 + C 2 ,
δ = arctan ( S C ) ,
Δ x = x x ,
Δ y = y y .

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