Abstract

Intensity correlation microscopy (ICM), which is prominently known through antibunching microscopy or super-resolution optical fluctuation imaging (SOFI), provides super-resolution through a correlation analysis of antibunching of independent quantum emitters or temporal fluctuations of blinking fluorophores. For correlation order m the PSF in the signal is effectively taken to the mth power, and is thus directly shrunk by the factor m. Combined with deconvolution, a close to linear resolution improvement of factor m can be obtained. Yet, analysis of high correlation orders is challenging, which limits the achievable resolutions. Here we propose to use three dimensional structured illumination along with mth-order correlation analysis to obtain an enhanced scaling of up to m + m = 2m. Including the stokes shift or plasmonic sub-wavelength illumination enhancements beyond 2m can be achieved. Hence, resolutions far below the diffraction limit in full 3D imaging and with already low correlation orders, can potentially be achieved. Since ICM operates in the linear regime our approach may be particularly promising for enhancing the resolution in biological imaging at low illumination levels.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

E. A. Ingerman, R. A. London, R. Heintzmann, and M. G. L. Gustafsson, “Signal, noise and resolution in linear and nonlinear structured-illumination microscopy,” J. Microsc. 0, 1–23 (2018).

2017 (3)

2016 (1)

2015 (1)

X. Zhang, X. Chen, Z. Zeng, M. Zhang, Y. Sun, P. Xi, J. Peng, and P. Xu, “Development of a reversibly switchable fluorescent protein for super-resolution optical fluctuation imaging (SOFI),” ACS Nano 9, 2659–2667 (2015).
[Crossref] [PubMed]

2014 (4)

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref] [PubMed]

J. H. Park, S.-W. Lee, E. S. Lee, and J. Y. Lee, “A method for super-resolved CARS microscopy with structured illumination in two dimensions,” Opt. Express 22, 9854–9870 (2014).
[Crossref] [PubMed]

X. Zeng, M. Al-Amri, and M. S. Zubairy, “Nanometer-scale microscopy via graphene plasmons,” Phys. Rev. B 90, 235418 (2014).
[Crossref]

F. Wei, D. Lu, H. Shen, W. Wan, J. L. Ponsetto, E. Huang, and Z. Liu, “Wide field super-resolution surface imaging through plasmonic structured illumination microscopy,” Nano Lett. 14, 4634–4639 (2014).
[Crossref] [PubMed]

2013 (1)

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13, 5832–5836 (2013).
[Crossref] [PubMed]

2012 (3)

P. Dedecker, G. C. H. Mo, T. Dertinger, and J. Zhang, “Widely accessible method for superresolution fluorescence imaging of living systems,” Proc. Natl. Acad. Sci USA 109, 10909–10914 (2012).
[Crossref] [PubMed]

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1, 4 (2012).
[Crossref]

T. Dertinger, J. Xu, O. F. Naini, R. Vogel, and S. Weiss, “SOFI-based 3D superresolution sectioning with a widefield microscope,” Opt. Nanoscopy 1, 2 (2012).
[Crossref]

2011 (1)

2010 (1)

2009 (1)

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. USA 106, 22287–22292 (2009).
[Crossref] [PubMed]

2008 (2)

L. Shao, B. Isaac, S. Uzawa, D. A. Agard, J. W. Sedat, and M. G. L. Gustafsson, “I5S: Wide-field light microscopy with 100-nm-scale resolution in three dimensions,” Biophys. J. 94, 4971–4983 (2008).
[Crossref] [PubMed]

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
[Crossref] [PubMed]

2006 (3)

S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation,” Biophys. J. 91, 4258–4272 (2006).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Meth. 3, 793–796 (2006).
[Crossref]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

2005 (2)

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” Proc. Natl. Acad. Sci. USA 102, 17565–17569 (2005).
[Crossref] [PubMed]

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. USA 102, 13081–13086 (2005).
[Crossref] [PubMed]

2002 (1)

2000 (1)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
[Crossref] [PubMed]

1999 (1)

R. Heintzmann and C. G. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185–196 (1999).
[Crossref]

1997 (2)

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, and W. E. Moerner, “On/off blinking and switching behaviour of single molecules of green fluorescent protein,” Nature 388, 355–358 (1997).
[Crossref] [PubMed]

R. Freimann, S. Pentz, and H. Hörler, “Development of a standing-wave fluorescence microscope with high nodal plane flatness,” J. Microsc. 187, 193–200 (1997).
[Crossref] [PubMed]

1995 (1)

S. W. Hell and M. Kroug, “Ground-state-depletion fluorscence microscopy: A concept for breaking the diffraction resolution limit,” Appl. Phys. B 60, 495–497 (1995).
[Crossref]

1994 (2)

1993 (1)

B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature 366, 44–48 (1993).
[Crossref] [PubMed]

1963 (1)

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[Crossref]

Agard, D. A.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
[Crossref] [PubMed]

L. Shao, B. Isaac, S. Uzawa, D. A. Agard, J. W. Sedat, and M. G. L. Gustafsson, “I5S: Wide-field light microscopy with 100-nm-scale resolution in three dimensions,” Biophys. J. 94, 4971–4983 (2008).
[Crossref] [PubMed]

M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “I5M: 3D widefield light microscopy with better than 100 nm axial resolution,” J. Microsc.195, 10–16.
[PubMed]

Agarwal, G. S.

Al-Amri, M.

X. Zeng, M. Al-Amri, and M. S. Zubairy, “Nanometer-scale microscopy via graphene plasmons,” Phys. Rev. B 90, 235418 (2014).
[Crossref]

Bailey, B.

B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature 366, 44–48 (1993).
[Crossref] [PubMed]

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Meth. 3, 793–796 (2006).
[Crossref]

Berclaz, C.

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1, 4 (2012).
[Crossref]

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

Bezryadina, A.

J. L. Ponsetto, A. Bezryadina, F. Wei, K. Onishi, H. Shen, E. Huang, L. Ferrari, Q. Ma, Y. Zou, and Z. Liu, “Experimental demonstration of localized plasmonic structured illumination microscopy,” ACS Nano 11, 5344–5350 (2017).
[Crossref] [PubMed]

Bocchio, N. L.

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1, 4 (2012).
[Crossref]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

Brida, G.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref] [PubMed]

Cande, W. Z.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
[Crossref] [PubMed]

Carlton, P. M.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
[Crossref] [PubMed]

Chen, X.

X. Zhang, X. Chen, Z. Zeng, M. Zhang, Y. Sun, P. Xi, J. Peng, and P. Xu, “Development of a reversibly switchable fluorescent protein for super-resolution optical fluctuation imaging (SOFI),” ACS Nano 9, 2659–2667 (2015).
[Crossref] [PubMed]

Classen, A.

Colyer, R.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. USA 106, 22287–22292 (2009).
[Crossref] [PubMed]

Cremer, C.

Cremer, C. G.

R. Heintzmann and C. G. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185–196 (1999).
[Crossref]

Cubitt, A. B.

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, and W. E. Moerner, “On/off blinking and switching behaviour of single molecules of green fluorescent protein,” Nature 388, 355–358 (1997).
[Crossref] [PubMed]

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

Dedecker, P.

P. Dedecker, G. C. H. Mo, T. Dertinger, and J. Zhang, “Widely accessible method for superresolution fluorescence imaging of living systems,” Proc. Natl. Acad. Sci USA 109, 10909–10914 (2012).
[Crossref] [PubMed]

Degiovanni, I. P.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref] [PubMed]

Dellagiacoma, C.

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1, 4 (2012).
[Crossref]

S. Geissbuehler, C. Dellagiacoma, and T. Lasser, “Comparison between SOFI and STORM,” Biomed. Opt. Express 2, 408–420 (2011).
[Crossref] [PubMed]

Dertinger, T.

T. Dertinger, J. Xu, O. F. Naini, R. Vogel, and S. Weiss, “SOFI-based 3D superresolution sectioning with a widefield microscope,” Opt. Nanoscopy 1, 2 (2012).
[Crossref]

P. Dedecker, G. C. H. Mo, T. Dertinger, and J. Zhang, “Widely accessible method for superresolution fluorescence imaging of living systems,” Proc. Natl. Acad. Sci USA 109, 10909–10914 (2012).
[Crossref] [PubMed]

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. USA 106, 22287–22292 (2009).
[Crossref] [PubMed]

Deutsch, Z.

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13, 5832–5836 (2013).
[Crossref] [PubMed]

Dickson, R. M.

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, and W. E. Moerner, “On/off blinking and switching behaviour of single molecules of green fluorescent protein,” Nature 388, 355–358 (1997).
[Crossref] [PubMed]

Eggeling, C.

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” Proc. Natl. Acad. Sci. USA 102, 17565–17569 (2005).
[Crossref] [PubMed]

Enderlein, J.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. USA 106, 22287–22292 (2009).
[Crossref] [PubMed]

S. C. Stein, A. Huss, I. Gregor, and J. Enderlein, Super-Resolution Imaging in Biomedicine (CRC Press, 2016).

Farkas, D. L.

B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature 366, 44–48 (1993).
[Crossref] [PubMed]

Ferrari, L.

J. L. Ponsetto, A. Bezryadina, F. Wei, K. Onishi, H. Shen, E. Huang, L. Ferrari, Q. Ma, Y. Zou, and Z. Liu, “Experimental demonstration of localized plasmonic structured illumination microscopy,” ACS Nano 11, 5344–5350 (2017).
[Crossref] [PubMed]

Forneris, J.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref] [PubMed]

Freimann, R.

R. Freimann, S. Pentz, and H. Hörler, “Development of a standing-wave fluorescence microscope with high nodal plane flatness,” J. Microsc. 187, 193–200 (1997).
[Crossref] [PubMed]

Gatto Monticone, D.

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Sedat, J. W.

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E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
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O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13, 5832–5836 (2013).
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D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113, 143602 (2014).
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F. Wei, D. Lu, H. Shen, W. Wan, J. L. Ponsetto, E. Huang, and Z. Liu, “Wide field super-resolution surface imaging through plasmonic structured illumination microscopy,” Nano Lett. 14, 4634–4639 (2014).
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J. L. Ponsetto, A. Bezryadina, F. Wei, K. Onishi, H. Shen, E. Huang, L. Ferrari, Q. Ma, Y. Zou, and Z. Liu, “Experimental demonstration of localized plasmonic structured illumination microscopy,” ACS Nano 11, 5344–5350 (2017).
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Figures (3)

Fig. 1
Fig. 1 Illustrations of total OTF supports of 3D-SIM (left column) and second-order 3D SI-ICM (right column). Image (a) depicts the OTF of a widefield microscope and (b) the 3D Gaussian H(k) as approximation. (c) shows the Fourier transform of the structured illumination of Eq. (10) with the center positions kj = (kρ, kz)j (j = 1, . . ., 7) given in the main text (see the central blue and outer green dots). Combining (a) and (c) yields the images in (d), where the OTF support of widefield microscopy, 2D SIM for one single orientation α, 3D-SIM for one α and 3D-SIM for three orientations α = 0, π 3, 2 π 3 are shown. The final image of (d) provides a two-fold enlarged support along all axes. Image (e) shows the OTF H2(k) of second-order ICM, which is enlarged by the factor 2 along all axes. Image (f) depicts the Fourier transform of the squared structured illumination, where the outer (red) dots represent the contributions from the first higher harmonics. Again, combining images (e) and (f) yields the OTF supports displayed in g), i.e., of second-order ICM, second-order ICM with 2D-SIM for a single α, second-order ICM with 3D SIM for a single α and second-order ICM with 3D-SIM for four orientations α = 0, π 4, 2 π 4, 3 π 4. The total support for this case is already enhanced by the factor 4 along all axes.
Fig. 2
Fig. 2 Schematic setup of an SI-ICM experiment (left side) and the corresponding flowchart to obtain the sought-after superresolving images (right side). For details see text.
Fig. 3
Fig. 3 The figure shows (a) an object consisting of three emitters at positions r1 = (−0.16, 0.16, 0.05), r2 = (0.26, −0.26, 0.57) and r3 = (0.26, −0.26, 0.68) (in units of Δρmin) and (b) the 3D PSF of Eq. (1) utilized in the simulation. The images (c) – (i) are obtained by the methods (c) widefield microscopy, (d) second-order ICM, (e) second-order ICM + Deconvolution, (f) 3D-SIM, (g) 16th-order ICM, (h) fourth-order ICM + Deconvolution, and (i) second-order 3D-SI-ICM. For details on the simulation see text.

Equations (14)

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h ( r ) = exp [ x 2 + y 2 w ρ 2 z 2 w z 2 ] ,
Δ ρ min = 0.61 λ 𝒜 Δ z min = 2 n λ 𝒜 2 .
I ( r , t ) I ( r ) = h ( r ) * n ( r ) = I 0 i = 1 N h ( r r i ) .
[ G ( 1 ) ( r ) ] 2 = I 0 2 i , j = 1 N h ( r r i ) h ( r r j ) I 0 2 i = 1 N h 2 ( r r i ) + I 0 2 i j N h ( r r i ) h ( r r j ) .
Antibunching : G ( 2 ) ( r ) I 0 2 i j N h ( r r i ) h ( r r j ) SOFI : G 2 ( r ) I 0 2 i , j = 1 N h ( r r i ) h ( r r j ) + i = 1 N h 2 ( r r i ) Δ I i ( t ) 2
Antibunching : ICM 2 ( r ) = [ G ( 1 ) ( r ) ] 2 G ( 2 ) ( r ) = I 0 2 i = 1 N h 2 ( r r i ) , SOFI : ICM 2 ( r ) = G 2 ( r ) [ G ( 1 ) ( r ) ] 2 = ( Δ I ) 2 ¯ i = 1 N h 2 ( r r i ) .
ICM m ( r ) = i = 1 N h m ( r r i ) ,
SIM ( r ) = h ( r ) * [ n ( r ) × I str ( r , α , φ r ) ] = i = 1 N h ( r r i ) × I str ( r i , α , φ r ) .
E ( x , y , z ) = e i ( k x x + k y y φ r ) + i k z z + e i ( k z + φ z ) + e i ( k x x + k y y φ r ) + i k z z ,
I str ( r ) = 3 + 2 cos [ 2 ( k x x + k y y ) + 2 φ r ] + 4 cos [ ( k x x + k y y ) + φ r ] cos [ ( k k z ) z + φ z ] ,
FT { SIM ( r ) } = H ( k ) × j = 1 7 c j e i φ j n ˜ ( k k j ) ,
n ˜ new ( k ) = j n ˜ j ( k + k j ) [ j H ( k + k j ) ] + γ A ( k ) ,
SI-ICM m ( r ) = i = 1 N h m ( r r i ) × I str ( r i , α , φ j ) m .
FT { SI-ICM 2 ( r ) } = H 2 ( k ) × j = 1 19 c j e i φ j n ˜ ( k k j ) ,

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