Abstract

We propose an optical correlation algorithm illustrating a new general method for reconstructing the phase skeleton of complex optical fields from the measured two-dimensional intensity distribution. The core of the algorithm consists in locating the saddle points of the intensity distribution and connecting such points into nets by the lines of intensity gradient that are closely associated with the equi-phase lines of the field. This algorithm provides a new partial solution to the inverse problem in optics commonly referred to as the phase problem.

© 2014 Optical Society of America

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References

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  1. R. H. T. Bates and M. J. McDonnell, Image Restoration and Reconstruction (Caledon Oxford, 1986).
  2. T. Acharya and A. K. Ray, Image Processing – Principles and Applications (Wiley InterScience, 2006).
  3. E. Abramochkin, V. Volostnikov, “Two-dimensional phase problem: differential approach,” Opt. Commun. 74(3–4), 139–143 (1989).
    [CrossRef]
  4. E. Abramochkin, V. Volostnikov, “Relationship between two-dimensional intensity and phase in a Fresnel diffraction zone,” Opt. Commun. 74(3–4), 144–148 (1989).
    [CrossRef]
  5. V. Volostnikov, “Phase problem in optics,” J. Sov. Laser Research 11(6), 601–626 (1990).
    [CrossRef]
  6. M. Loktev, V. Volostnikov, “Singular wavefields and phase retrieval problem,” Proc. SPIE 3487, 141–147 (1998).
    [CrossRef]
  7. K. G. Larkin, D. J. Bone, M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18(8), 1862–1870 (2001).
    [CrossRef] [PubMed]
  8. K. G. Larkin, “Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transforms,” J. Opt. Soc. Am. A 18(8), 1871–1881 (2001).
    [CrossRef]
  9. F. Yu. Kanev, V. P. Lukin, L. N. Lavrinova, “Correction of turbulent distortions based on the phase conjugation in the presence of phase dislocations in a reference beam,” Atmos. Oceanic Opt. 14, 1132–1169 (2001).
  10. V. P. Lukin, B. V. Fortes, “Phase-correction of turbulent distortions of an optical wave propagating under conditions of strong intensity fluctuations,” Appl. Opt. 41(27), 5616–5624 (2002).
    [CrossRef] [PubMed]
  11. V. A. Tartakovsky, V. A. Sennikov, P. A. Konyaev, V. P. Lukin, “Wave reversal under strong scintillation conditions and sequential phasing in adaptive optics,” Atmos. Oceanic Opt. 15, 1104–1113 (2002).
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  17. M. S. Soskin, M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
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  19. N. B. Baranova, A. V. Mamaev, H. F. Pilipetsky, V. V. Shkunov, B. Y. Zel’dovich, “Wavefront dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. 73(5), 525–528 (1983).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. V. I. Vasil’ev, M. S. Soskin, “Analysis of dynamics of topological peculiarities of varying random vector fields,” Ukr. J. Phys. 52, 1123–1129 (2007).

2013 (1)

2012 (2)

2011 (1)

2009 (1)

Y. Galushko, I. Mokhun, “Characteristics of scalar random field and its vortex networks. Recovery of the optical phase,” J. Opt. A: Pure Appl. Opt. 11094017 (2009).

2007 (1)

V. I. Vasil’ev, M. S. Soskin, “Analysis of dynamics of topological peculiarities of varying random vector fields,” Ukr. J. Phys. 52, 1123–1129 (2007).

2006 (1)

2002 (2)

V. P. Lukin, B. V. Fortes, “Phase-correction of turbulent distortions of an optical wave propagating under conditions of strong intensity fluctuations,” Appl. Opt. 41(27), 5616–5624 (2002).
[CrossRef] [PubMed]

V. A. Tartakovsky, V. A. Sennikov, P. A. Konyaev, V. P. Lukin, “Wave reversal under strong scintillation conditions and sequential phasing in adaptive optics,” Atmos. Oceanic Opt. 15, 1104–1113 (2002).

2001 (4)

K. G. Larkin, D. J. Bone, M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18(8), 1862–1870 (2001).
[CrossRef] [PubMed]

K. G. Larkin, “Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transforms,” J. Opt. Soc. Am. A 18(8), 1871–1881 (2001).
[CrossRef]

F. Yu. Kanev, V. P. Lukin, L. N. Lavrinova, “Correction of turbulent distortions based on the phase conjugation in the presence of phase dislocations in a reference beam,” Atmos. Oceanic Opt. 14, 1132–1169 (2001).

M. S. Soskin, M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).

1998 (1)

M. Loktev, V. Volostnikov, “Singular wavefields and phase retrieval problem,” Proc. SPIE 3487, 141–147 (1998).
[CrossRef]

1993 (1)

N. Freund, Shvartsman, V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101(3–4), 247–264 (1993).
[CrossRef]

1990 (1)

V. Volostnikov, “Phase problem in optics,” J. Sov. Laser Research 11(6), 601–626 (1990).
[CrossRef]

1989 (2)

E. Abramochkin, V. Volostnikov, “Two-dimensional phase problem: differential approach,” Opt. Commun. 74(3–4), 139–143 (1989).
[CrossRef]

E. Abramochkin, V. Volostnikov, “Relationship between two-dimensional intensity and phase in a Fresnel diffraction zone,” Opt. Commun. 74(3–4), 144–148 (1989).
[CrossRef]

1983 (1)

1981 (1)

R. Keys, “Cubic convolution interpolation for digital image processing,” IEEE Trans. Signal Processing Acoust. Speech Signal Processing 29(6), 1153–1160 (1981).
[CrossRef]

Abramochkin, E.

E. Abramochkin, V. Volostnikov, “Two-dimensional phase problem: differential approach,” Opt. Commun. 74(3–4), 139–143 (1989).
[CrossRef]

E. Abramochkin, V. Volostnikov, “Relationship between two-dimensional intensity and phase in a Fresnel diffraction zone,” Opt. Commun. 74(3–4), 144–148 (1989).
[CrossRef]

Baranova, N. B.

Barchiesi, D.

Bone, D. J.

Fienup, J. R.

Fortes, B. V.

Freilikher, V.

N. Freund, Shvartsman, V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101(3–4), 247–264 (1993).
[CrossRef]

Freund, N.

N. Freund, Shvartsman, V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101(3–4), 247–264 (1993).
[CrossRef]

Galushko, Y.

Y. Galushko, I. Mokhun, “Characteristics of scalar random field and its vortex networks. Recovery of the optical phase,” J. Opt. A: Pure Appl. Opt. 11094017 (2009).

Kanev, F. Yu.

F. Yu. Kanev, V. P. Lukin, L. N. Lavrinova, “Correction of turbulent distortions based on the phase conjugation in the presence of phase dislocations in a reference beam,” Atmos. Oceanic Opt. 14, 1132–1169 (2001).

Keys, R.

R. Keys, “Cubic convolution interpolation for digital image processing,” IEEE Trans. Signal Processing Acoust. Speech Signal Processing 29(6), 1153–1160 (1981).
[CrossRef]

Konyaev, P. A.

V. A. Tartakovsky, V. A. Sennikov, P. A. Konyaev, V. P. Lukin, “Wave reversal under strong scintillation conditions and sequential phasing in adaptive optics,” Atmos. Oceanic Opt. 15, 1104–1113 (2002).

Larkin, K. G.

Lavrinova, L. N.

F. Yu. Kanev, V. P. Lukin, L. N. Lavrinova, “Correction of turbulent distortions based on the phase conjugation in the presence of phase dislocations in a reference beam,” Atmos. Oceanic Opt. 14, 1132–1169 (2001).

Loktev, M.

M. Loktev, V. Volostnikov, “Singular wavefields and phase retrieval problem,” Proc. SPIE 3487, 141–147 (1998).
[CrossRef]

Lukin, V. P.

V. P. Lukin, B. V. Fortes, “Phase-correction of turbulent distortions of an optical wave propagating under conditions of strong intensity fluctuations,” Appl. Opt. 41(27), 5616–5624 (2002).
[CrossRef] [PubMed]

V. A. Tartakovsky, V. A. Sennikov, P. A. Konyaev, V. P. Lukin, “Wave reversal under strong scintillation conditions and sequential phasing in adaptive optics,” Atmos. Oceanic Opt. 15, 1104–1113 (2002).

F. Yu. Kanev, V. P. Lukin, L. N. Lavrinova, “Correction of turbulent distortions based on the phase conjugation in the presence of phase dislocations in a reference beam,” Atmos. Oceanic Opt. 14, 1132–1169 (2001).

Mamaev, A. V.

Mokhun, I.

Y. Galushko, I. Mokhun, “Characteristics of scalar random field and its vortex networks. Recovery of the optical phase,” J. Opt. A: Pure Appl. Opt. 11094017 (2009).

Oldfield, M. A.

Patorski, K.

Pilipetsky, H. F.

Sennikov, V. A.

V. A. Tartakovsky, V. A. Sennikov, P. A. Konyaev, V. P. Lukin, “Wave reversal under strong scintillation conditions and sequential phasing in adaptive optics,” Atmos. Oceanic Opt. 15, 1104–1113 (2002).

Shkunov, V. V.

Shvartsman,

N. Freund, Shvartsman, V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101(3–4), 247–264 (1993).
[CrossRef]

Soskin, M. S.

V. I. Vasil’ev, M. S. Soskin, “Analysis of dynamics of topological peculiarities of varying random vector fields,” Ukr. J. Phys. 52, 1123–1129 (2007).

M. S. Soskin, M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).

Tartakovsky, V. A.

V. A. Tartakovsky, V. A. Sennikov, P. A. Konyaev, V. P. Lukin, “Wave reversal under strong scintillation conditions and sequential phasing in adaptive optics,” Atmos. Oceanic Opt. 15, 1104–1113 (2002).

Trusiak, M.

Vasil’ev, V. I.

V. I. Vasil’ev, M. S. Soskin, “Analysis of dynamics of topological peculiarities of varying random vector fields,” Ukr. J. Phys. 52, 1123–1129 (2007).

Vasnetsov, M. V.

M. S. Soskin, M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).

Volostnikov, V.

M. Loktev, V. Volostnikov, “Singular wavefields and phase retrieval problem,” Proc. SPIE 3487, 141–147 (1998).
[CrossRef]

V. Volostnikov, “Phase problem in optics,” J. Sov. Laser Research 11(6), 601–626 (1990).
[CrossRef]

E. Abramochkin, V. Volostnikov, “Relationship between two-dimensional intensity and phase in a Fresnel diffraction zone,” Opt. Commun. 74(3–4), 144–148 (1989).
[CrossRef]

E. Abramochkin, V. Volostnikov, “Two-dimensional phase problem: differential approach,” Opt. Commun. 74(3–4), 139–143 (1989).
[CrossRef]

Wielgus, M.

Zel’dovich, B. Y.

Appl. Opt. (3)

Atmos. Oceanic Opt. (2)

V. A. Tartakovsky, V. A. Sennikov, P. A. Konyaev, V. P. Lukin, “Wave reversal under strong scintillation conditions and sequential phasing in adaptive optics,” Atmos. Oceanic Opt. 15, 1104–1113 (2002).

F. Yu. Kanev, V. P. Lukin, L. N. Lavrinova, “Correction of turbulent distortions based on the phase conjugation in the presence of phase dislocations in a reference beam,” Atmos. Oceanic Opt. 14, 1132–1169 (2001).

IEEE Trans. Signal Processing Acoust. Speech Signal Processing (1)

R. Keys, “Cubic convolution interpolation for digital image processing,” IEEE Trans. Signal Processing Acoust. Speech Signal Processing 29(6), 1153–1160 (1981).
[CrossRef]

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

Y. Galushko, I. Mokhun, “Characteristics of scalar random field and its vortex networks. Recovery of the optical phase,” J. Opt. A: Pure Appl. Opt. 11094017 (2009).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Sov. Laser Research (1)

V. Volostnikov, “Phase problem in optics,” J. Sov. Laser Research 11(6), 601–626 (1990).
[CrossRef]

Opt. Commun. (3)

E. Abramochkin, V. Volostnikov, “Two-dimensional phase problem: differential approach,” Opt. Commun. 74(3–4), 139–143 (1989).
[CrossRef]

E. Abramochkin, V. Volostnikov, “Relationship between two-dimensional intensity and phase in a Fresnel diffraction zone,” Opt. Commun. 74(3–4), 144–148 (1989).
[CrossRef]

N. Freund, Shvartsman, V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101(3–4), 247–264 (1993).
[CrossRef]

Opt. Express (3)

Proc. SPIE (1)

M. Loktev, V. Volostnikov, “Singular wavefields and phase retrieval problem,” Proc. SPIE 3487, 141–147 (1998).
[CrossRef]

Prog. Opt. (1)

M. S. Soskin, M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).

Ukr. J. Phys. (1)

V. I. Vasil’ev, M. S. Soskin, “Analysis of dynamics of topological peculiarities of varying random vector fields,” Ukr. J. Phys. 52, 1123–1129 (2007).

Other (3)

I. Mokhun, “Introduction to linear singular optics,” in Optical Correlation Techniques and Applications, Ed. O. V. Angelsky, (2007), Chap. 1, TA 1630.A6, 1–133.

R. H. T. Bates and M. J. McDonnell, Image Restoration and Reconstruction (Caledon Oxford, 1986).

T. Acharya and A. K. Ray, Image Processing – Principles and Applications (Wiley InterScience, 2006).

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Figures (4)

Fig. 1
Fig. 1

Saddle point of intensity (blue) with two maxima and two minima (red and green, respectively) in its vicinity. Green lines are the iso-intensity lines.

Fig. 2
Fig. 2

Gradient lines of intensity in the vicinity of the saddle point S. Solid lines are the iso-intensity lines.

Fig. 3
Fig. 3

a. Spatial intensity distribution with the saddle points and the gradient lines of intensity (a) and spatial phase distribution associated with frame 3 a with the saddle points and the gradient lines of intensity.

Fig. 4
Fig. 4

Histograms for phase distribution of the analyzed speckle field: distributions of phase deviation along the phase gradient line from a phase at the initial saddle point for mean: 0°, confidence interval with probability 95%: – 1.71° -> + 1.71° (a), mean: −10.31°, confidence interval with probability 95%: – 12.03° -> −8.60° (b), mean: −10.31°, confidence interval with probability 95%: – 12.03° -> −8.60°, and mean: 4.25°, confidence interval with probability 95%: 2.85° -> 5.66°.

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