Abstract

In this paper, we propose the simulation of polarized speckle fields using the Stokes formalism, which allows the description of partially polarized electromagnetic waves. We define a unique parameter which determines the partial decorrelation of the involved fields, allowing to simulate the polarized speckles produced by all types of scatterers, from simple to multiple scatterers. We validate this model by comparison with experimental measurements. We use that simulation model to study the impact of the imaging device parameters on polarimetric measurements: first we emphasize a limit of resolution on retardance measurements, then we study the spatial depolarization, which appears when an observer is measuring any space-variant polarization map.

© 2016 Optical Society of America

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References

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  1. W. Wang, T. Yokozeki, R. Ishijima, A. Wada, Y. Miyamoto, and M. Takeda, “Optical vortex metrology for nanometric speckle displacement measurement,” Opt. Express 14, 120–127 (2006).
    [Crossref] [PubMed]
  2. X. Wang, Y. Liu, L. Guo, and H. Li, “Potential of vortex beams with orbital angular momentum modulation for deep-space optical communication,” Opt. Eng. 53, 056107 (2014).
    [Crossref]
  3. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
    [Crossref]
  4. C. AbouNader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
    [Crossref]
  5. L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, D. I. McLean, and T. L. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 18, 061211 (2013).
    [Crossref]
  6. G. D. Lewis and D. L. Jordan, “Remote sensing of polarimetric speckle,” J. Phys. D: Appl. Phys. 34, 1399–1407 (2001).
    [Crossref]
  7. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Pub., 2006), pp. 25–40.
  8. A. Doronin, A. J. Radosevich, V. Backman, and I. Meglinski, “Two electric field Monte Carlo models of coherent backscattering of polarized light,” J. Opt. Soc. Am. A 31, 2394–2400 (2014).
    [Crossref]
  9. M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213, 201–221 (2002).
    [Crossref]
  10. F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Polarization Singularities in 2D and 3D Speckle Fields,” Phys. Rev. Lett. 100, 203902 (2008).
    [Crossref] [PubMed]
  11. D. Goldstein, Polarized Light (CRC Press, 2003), pp. 32–42.
  12. A. Ghabbach, M. Zerrad, G. Soriano, and C. Amra, “Accurate metrology of polarization curves measured at the speckle size of visible light scattering,” Opt. Express 22, 14594–14609 (2014).
    [Crossref] [PubMed]
  13. J. Dupont, X. Orlik, A. Gabbach, M. Zerrad, G. Soriano, and C. Amra, “Polarization analysis of speckle field below its transverse correlation width : application to surface and bulk scattering,” Opt. Express 22, 24133–24141 (2014).
    [Crossref] [PubMed]
  14. J. Dupont and X. Orlik, “Polarized vortices in optical speckle field: observation of rare polarization singularities,” Opt. Express 23, 6041–6049 (2015).
    [Crossref] [PubMed]
  15. J. Dupont and X. Orlik, “Speckle fields polarimetry: statistical analysis and polarization singularities measurements,” Proc. SPIE 9660, 96601B (2015).
    [Crossref]
  16. J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: Implications in tissue optics,” J. Biomed. Opt. 7, 307–312 (2002).
    [Crossref] [PubMed]
  17. M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: Electromagnetic prediction,” Opt. Express 18, 15832–15843 (2010).
    [Crossref] [PubMed]
  18. A. Ghabbach, M. Zerrad, G. Soriano, S. Liukaityte, and C. Amra, “Depolarization and enpolarization DOP histograms measured for surface and bulk speckle patterns,” Opt. Express 22, 21427–21440 (2014).
    [Crossref] [PubMed]
  19. M. Zerrad, H. Tortel, G. Soriano, A. Ghabbach, and C. Amra, “Spatial depolarization of light from the bulks: electromagnetic prediction,” Opt. Express 23, 8246–8260 (2015).
    [Crossref] [PubMed]

2015 (4)

C. AbouNader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

J. Dupont and X. Orlik, “Polarized vortices in optical speckle field: observation of rare polarization singularities,” Opt. Express 23, 6041–6049 (2015).
[Crossref] [PubMed]

J. Dupont and X. Orlik, “Speckle fields polarimetry: statistical analysis and polarization singularities measurements,” Proc. SPIE 9660, 96601B (2015).
[Crossref]

M. Zerrad, H. Tortel, G. Soriano, A. Ghabbach, and C. Amra, “Spatial depolarization of light from the bulks: electromagnetic prediction,” Opt. Express 23, 8246–8260 (2015).
[Crossref] [PubMed]

2014 (5)

2013 (1)

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, D. I. McLean, and T. L. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 18, 061211 (2013).
[Crossref]

2010 (1)

2008 (1)

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Polarization Singularities in 2D and 3D Speckle Fields,” Phys. Rev. Lett. 100, 203902 (2008).
[Crossref] [PubMed]

2006 (1)

2002 (3)

M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213, 201–221 (2002).
[Crossref]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: Implications in tissue optics,” J. Biomed. Opt. 7, 307–312 (2002).
[Crossref] [PubMed]

2001 (1)

G. D. Lewis and D. L. Jordan, “Remote sensing of polarimetric speckle,” J. Phys. D: Appl. Phys. 34, 1399–1407 (2001).
[Crossref]

Abboud, M.

C. AbouNader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

AbouNader, C.

C. AbouNader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

Amra, C.

Backman, V.

Dennis, M. R.

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Polarization Singularities in 2D and 3D Speckle Fields,” Phys. Rev. Lett. 100, 203902 (2008).
[Crossref] [PubMed]

M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213, 201–221 (2002).
[Crossref]

Dhadwal, G.

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, D. I. McLean, and T. L. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 18, 061211 (2013).
[Crossref]

Doronin, A.

Dupont, J.

Flossmann, F.

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Polarization Singularities in 2D and 3D Speckle Fields,” Phys. Rev. Lett. 100, 203902 (2008).
[Crossref] [PubMed]

Gabbach, A.

Ghabbach, A.

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Goldstein, D.

D. Goldstein, Polarized Light (CRC Press, 2003), pp. 32–42.

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Pub., 2006), pp. 25–40.

Guo, L.

X. Wang, Y. Liu, L. Guo, and H. Li, “Potential of vortex beams with orbital angular momentum modulation for deep-space optical communication,” Opt. Eng. 53, 056107 (2014).
[Crossref]

Ishijima, R.

Jordan, D. L.

G. D. Lewis and D. L. Jordan, “Remote sensing of polarimetric speckle,” J. Phys. D: Appl. Phys. 34, 1399–1407 (2001).
[Crossref]

Kalia, S.

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, D. I. McLean, and T. L. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 18, 061211 (2013).
[Crossref]

Le Brun, G.

C. AbouNader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

Le Jeune, B.

C. AbouNader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

Lee, T. L.

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, D. I. McLean, and T. L. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 18, 061211 (2013).
[Crossref]

Lewis, G. D.

G. D. Lewis and D. L. Jordan, “Remote sensing of polarimetric speckle,” J. Phys. D: Appl. Phys. 34, 1399–1407 (2001).
[Crossref]

Li, H.

X. Wang, Y. Liu, L. Guo, and H. Li, “Potential of vortex beams with orbital angular momentum modulation for deep-space optical communication,” Opt. Eng. 53, 056107 (2014).
[Crossref]

Li, J.

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: Implications in tissue optics,” J. Biomed. Opt. 7, 307–312 (2002).
[Crossref] [PubMed]

Liu, Y.

X. Wang, Y. Liu, L. Guo, and H. Li, “Potential of vortex beams with orbital angular momentum modulation for deep-space optical communication,” Opt. Eng. 53, 056107 (2014).
[Crossref]

Liukaityte, S.

Loutfi, H.

C. AbouNader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

Lui, H.

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, D. I. McLean, and T. L. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 18, 061211 (2013).
[Crossref]

Mansour, R.

C. AbouNader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

McLean, D. I.

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, D. I. McLean, and T. L. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 18, 061211 (2013).
[Crossref]

Meglinski, I.

Miyamoto, Y.

O’Holleran, K.

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Polarization Singularities in 2D and 3D Speckle Fields,” Phys. Rev. Lett. 100, 203902 (2008).
[Crossref] [PubMed]

Orlik, X.

Padgett, M. J.

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Polarization Singularities in 2D and 3D Speckle Fields,” Phys. Rev. Lett. 100, 203902 (2008).
[Crossref] [PubMed]

Pellen, F.

C. AbouNader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

Radosevich, A. J.

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Soriano, G.

Sorrentini, J.

Takeda, M.

Tchvialeva, L.

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, D. I. McLean, and T. L. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 18, 061211 (2013).
[Crossref]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Tortel, H.

Wada, A.

Wang, L. V.

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: Implications in tissue optics,” J. Biomed. Opt. 7, 307–312 (2002).
[Crossref] [PubMed]

Wang, W.

Wang, X.

X. Wang, Y. Liu, L. Guo, and H. Li, “Potential of vortex beams with orbital angular momentum modulation for deep-space optical communication,” Opt. Eng. 53, 056107 (2014).
[Crossref]

Yao, G.

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: Implications in tissue optics,” J. Biomed. Opt. 7, 307–312 (2002).
[Crossref] [PubMed]

Yokozeki, T.

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Zeng, H.

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, D. I. McLean, and T. L. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 18, 061211 (2013).
[Crossref]

Zerrad, M.

J. Biomed. Opt. (3)

C. AbouNader, F. Pellen, H. Loutfi, R. Mansour, B. Le Jeune, G. Le Brun, and M. Abboud, “Early diagnosis of teeth erosion using polarized laser speckle imaging,” J. Biomed. Opt. 21, 071103 (2015).
[Crossref]

L. Tchvialeva, G. Dhadwal, H. Lui, S. Kalia, H. Zeng, D. I. McLean, and T. L. Lee, “Polarization speckle imaging as a potential technique for in vivo skin cancer detection,” J. Biomed. Opt. 18, 061211 (2013).
[Crossref]

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: Implications in tissue optics,” J. Biomed. Opt. 7, 307–312 (2002).
[Crossref] [PubMed]

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

J. Phys. D: Appl. Phys. (1)

G. D. Lewis and D. L. Jordan, “Remote sensing of polarimetric speckle,” J. Phys. D: Appl. Phys. 34, 1399–1407 (2001).
[Crossref]

Opt. Commun. (1)

M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213, 201–221 (2002).
[Crossref]

Opt. Eng. (1)

X. Wang, Y. Liu, L. Guo, and H. Li, “Potential of vortex beams with orbital angular momentum modulation for deep-space optical communication,” Opt. Eng. 53, 056107 (2014).
[Crossref]

Opt. Express (7)

J. Dupont and X. Orlik, “Polarized vortices in optical speckle field: observation of rare polarization singularities,” Opt. Express 23, 6041–6049 (2015).
[Crossref] [PubMed]

M. Zerrad, H. Tortel, G. Soriano, A. Ghabbach, and C. Amra, “Spatial depolarization of light from the bulks: electromagnetic prediction,” Opt. Express 23, 8246–8260 (2015).
[Crossref] [PubMed]

W. Wang, T. Yokozeki, R. Ishijima, A. Wada, Y. Miyamoto, and M. Takeda, “Optical vortex metrology for nanometric speckle displacement measurement,” Opt. Express 14, 120–127 (2006).
[Crossref] [PubMed]

M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: Electromagnetic prediction,” Opt. Express 18, 15832–15843 (2010).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, and C. Amra, “Accurate metrology of polarization curves measured at the speckle size of visible light scattering,” Opt. Express 22, 14594–14609 (2014).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, S. Liukaityte, and C. Amra, “Depolarization and enpolarization DOP histograms measured for surface and bulk speckle patterns,” Opt. Express 22, 21427–21440 (2014).
[Crossref] [PubMed]

J. Dupont, X. Orlik, A. Gabbach, M. Zerrad, G. Soriano, and C. Amra, “Polarization analysis of speckle field below its transverse correlation width : application to surface and bulk scattering,” Opt. Express 22, 24133–24141 (2014).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Polarization Singularities in 2D and 3D Speckle Fields,” Phys. Rev. Lett. 100, 203902 (2008).
[Crossref] [PubMed]

Proc. SPIE (1)

J. Dupont and X. Orlik, “Speckle fields polarimetry: statistical analysis and polarization singularities measurements,” Proc. SPIE 9660, 96601B (2015).
[Crossref]

Rev. Mod. Phys. (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Other (2)

D. Goldstein, Polarized Light (CRC Press, 2003), pp. 32–42.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Pub., 2006), pp. 25–40.

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Figures (7)

Fig. 1
Fig. 1 Schematic representation of the transverse planes used for the simulation of the far field amplitude of subjective speckle fields. Coordinates in the object plane are xo, yo, xp, yp in the pupil plane and xi, yi in the image plane. The distances between each transverse plane are large enough to use a far field approximation.
Fig. 2
Fig. 2 Comparison between simulation and experimental measurement of the polarization map scattered by a black lambertian scatterer under SLM illumination. (a) RGB polarization map obtained by the simulation with σ = π/6 rad. The SOP probability density function is represented in the inset. (b) Measured polarization map scattered by the sample illuminated with a 532 nm SLM laser source. The SOP probability density function is represented in the inset. (c) Simulated relative phase shifts in the image plane, in the inset is represented its probability density function (red) and the measured one (blue). (d) Measured relative phase shifts.
Fig. 3
Fig. 3 Results of the simulation for a surface scatterer in the image plane. (a) Scalar intensity I. (b) Relative phase shift ϕ between the two orthogonal directions x and y. In the inset is represented its normalized probability density function. (c) RGB representation of the polarization map. (d) Representation of the scattered SOP in the Poincaré sphere, the black dot is representing the illumination SOP (vertical). (e) Representation of the polarization ellipses corresponding to the area in the white square in (c), the ellipse color is representative of the scalar intensity in a logarithmic scale, a darker background represents right handed SOP, the others are left handed ones.
Fig. 4
Fig. 4 Results of the simulation for a multiple scatterer in the image plane. (a) Scalar intensity I. (b) Relative phase shift ϕ between the two orthogonal directions x and y. In the inset is represented its normalized probability density function. (c) RGB representation of the polarization map. (d) Representation of the scattered SOP in the Poincaré sphere, the black dot is representing the illumination SOP (vertical). (e) Representation of the polarization ellipses corresponding to the area in the white square in (c), the ellipse color is representative of the scalar intensity in a logarithmic scale, a darker background represents right handed SOP, the others are left handed ones.
Fig. 5
Fig. 5 Simulation of the speckle field produced by the scattering on a surface scatterer with additional Gaussian retardance. (a) Representation of the retardance ψ applied to the plane waves polarized along the x axis. (b) Representation of the relative phase shift ϕ in the image plane. (c) RGB representation of the polarimetric states. (d, e, f) Same representations in case of a retardance with a 10 times higher spatial frequency, but imaged with the same PSF size.
Fig. 6
Fig. 6 (a) Representation of the normalized speckle intensity I′, after a sampling of the initial map on 2 × 2 pixels. (b) Representation of the speckle intensity I′, after a sampling of the initial map on 10 × 10 pixels. (c) Representation of the speckle intensity I′, after a sampling of the initial map on 70 × 70 pixels, which is roughly the surface of a single speckle grain. (d, e, f) Representation of the corresponding spatially depolarized intensities Isdp.
Fig. 7
Fig. 7 (a) Representation of the normalized spatially depolarized intensity, calculated with Eq. (13) on the 1 × 1 polarization map. (b) Representation of the normalized spatially depolarized intensity, after a sampling of the 1 × 1 polarization map on 45 × 45 pixels. One can see that the spatial variations of the two maps are similar.

Tables (1)

Tables Icon

Table 1 Contrast value of the speckle scalar intensity I′, defined by std(I′)/mean(I′), and depolarization ratio, defined by mean(Isdp)/mean(I′), in function of the spatial sampling of a given field produced by multiple scattering.

Equations (13)

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E o ( x o , y o ) = A 0 ( x o , y o ) e j φ ( x o , y o )
E p ( x p , y p ) = p u p ( x p , y p ) F T { E o ( x o , y o ) }
E i ( x i , y i ) = F T { E p ( x p , y p ) }
S = { I = | E ix | 2 + | E iy | 2 + C 2 Q = 2 | E ix | | E iy | cos ( ϕ ) U = | E ix | 2 | E iy | 2 V = 2 | E ix | | E iy | sin ( ϕ )
D O P = Q 2 + U 2 + V 2 I
D O P = | E ix | 2 + | E iy | 2 | E ix | 2 + | E iy | 2 + C 2 = 1 C 2 I
φ y ( x o , y o ) = φ x ( x o , y o ) + G ( ρ , σ )
ϕ ( x i , y i ) = a tan 2 ( Im { E ix ( x i , y i ) } , Re { E ix ( x i , y i ) } ) a tan 2 ( Im { E iy ( x i , y i ) } , Re { E iy ( x i , y i ) } )
φ y ( x o , y o ) = φ x ( x o , y o ) + G ( ψ ( x o , y o ) , σ )
I s d p = I Q 2 + U 2 + V 2
g x i = S i x
g y i = S i y
I s d p I p . i ( g x i 2 + g y i 2 )

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