Abstract

Structured illumination microscopy is able to improve the spatial resolution of wide-field fluorescence imaging by applying sinusoidal stripe pattern illumination to the sample. The corresponding computational image reconstruction requires precise knowledge of the pattern’s parameters, which are its phase (ϕ) and wave vector (p). Here, a computationally inexpensive method for estimation of p from the raw data is proposed and illustrated with simulations. The method estimates p through a selective discrete Fourier transform at tunable subpixel precision. This results in an accurate p estimation for all the illumination patterns and subsequently improves the superresolution image recovery by a factor of 10 around sharp edges as compared to an integer pixel approach. The technique as presented here is of major interest to the large variety of custom-build systems that are used. The feasibility of the presented method is proven in comparison with published data.

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

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  5. P. Křížek, T. Lukeš, M. Ovesný, K. Fliegel, and G. M. Hagen, “SIMToolbox: A MATLAB toolbox for structured illumination fluorescence microscopy,” Bioinformatics 32, 318–320 (2015).
  6. M. Müller, V. Mönkemöller, S. Hennig, W. Hübner, and T. Huser, “Open-source image reconstruction of super-resolution structured illumination microscopy data in ImageJ,” Nat. Comms. 7, 10980 (2016).
    [Crossref]
  7. K. Wicker, O. Mandula, G. Best, R. Fiolka, and R. Heintzmann, “Phase optimisation for structured illumination microscopy,” Opt. Express 21, 2032–2049 (2013).
    [Crossref]
  8. K. Wicker, “Non-iterative determination of pattern phase in structured illumination microscopy using auto-correlations in Fourier space,” Opt. Express 21, 24692–24701 (2013).
    [Crossref]
  9. S. A. Shroff, J. R. Fienup, and D. R. Williams, “Phase-shift estimation in sinusoidally illuminated images for lateral superresolution,” J. Opt. Soc. Am. A 26, 413–424 (2009).
    [Crossref]
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    [Crossref]
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    [Crossref]
  12. M. Singh and K. Khare, “Accurate efficient carrier estimation for single-shot digital holographic imaging,” Opt. Lett. 41, 4871–4874 (2016).
    [Crossref]
  13. L. Condat, J. Boulanger, N. Pustelnik, S. Sahnoun, and L. Sengmanivong, “A 2-D spectral analysis method to estimate the modulation parameters in structured illumination microscopy,” in IEEE 11th International Symposium on Biomedical Imaging (ISBI), 2014, vol. 11, pp. 604–607.
  14. E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
    [Crossref]
  15. J. T. Frohn, “Super-resolution fluorescence microscopy by structured light illumination” Ph.D. dissertation (Swiss Federal Institute of Technology, 2000).

2016 (2)

M. Müller, V. Mönkemöller, S. Hennig, W. Hübner, and T. Huser, “Open-source image reconstruction of super-resolution structured illumination microscopy data in ImageJ,” Nat. Comms. 7, 10980 (2016).
[Crossref]

M. Singh and K. Khare, “Accurate efficient carrier estimation for single-shot digital holographic imaging,” Opt. Lett. 41, 4871–4874 (2016).
[Crossref]

2015 (1)

P. Křížek, T. Lukeš, M. Ovesný, K. Fliegel, and G. M. Hagen, “SIMToolbox: A MATLAB toolbox for structured illumination fluorescence microscopy,” Bioinformatics 32, 318–320 (2015).

2013 (2)

2012 (1)

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

2010 (1)

2009 (1)

2008 (1)

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]

2006 (1)

R. Soummer, L. Pueyo, A. Sivaramakristnan, and R. J. Vanderbei, “Fast computation of Lyot-style coronagraph propagation,” Astrophys. J. Suppl. Ser. 167, 81–99 (2006).
[Crossref]

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]

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]

1873 (1)

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Archiv für mikroskopische Anatomie 9, 413–418 (1873).
[Crossref]

Abbe, E.

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Archiv für mikroskopische Anatomie 9, 413–418 (1873).
[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]

Allain, M.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Belkebir, K.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Best, G.

Boulanger, J.

L. Condat, J. Boulanger, N. Pustelnik, S. Sahnoun, and L. Sengmanivong, “A 2-D spectral analysis method to estimate the modulation parameters in structured illumination microscopy,” in IEEE 11th International Symposium on Biomedical Imaging (ISBI), 2014, vol. 11, pp. 604–607.

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]

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]

Condat, L.

L. Condat, J. Boulanger, N. Pustelnik, S. Sahnoun, and L. Sengmanivong, “A 2-D spectral analysis method to estimate the modulation parameters in structured illumination microscopy,” in IEEE 11th International Symposium on Biomedical Imaging (ISBI), 2014, vol. 11, pp. 604–607.

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]

Fienup, J. R.

Fiolka, R.

Fliegel, K.

P. Křížek, T. Lukeš, M. Ovesný, K. Fliegel, and G. M. Hagen, “SIMToolbox: A MATLAB toolbox for structured illumination fluorescence microscopy,” Bioinformatics 32, 318–320 (2015).

Frohn, J. T.

J. T. Frohn, “Super-resolution fluorescence microscopy by structured light illumination” Ph.D. dissertation (Swiss Federal Institute of Technology, 2000).

Girard, J.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Golubovskaya, I. N.

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]

Gustafsson, M. G. L.

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]

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]

Hagen, G. M.

P. Křížek, T. Lukeš, M. Ovesný, K. Fliegel, and G. M. Hagen, “SIMToolbox: A MATLAB toolbox for structured illumination fluorescence microscopy,” Bioinformatics 32, 318–320 (2015).

Heintzmann, R.

K. Wicker, O. Mandula, G. Best, R. Fiolka, and R. Heintzmann, “Phase optimisation for structured illumination microscopy,” Opt. Express 21, 2032–2049 (2013).
[Crossref]

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]

Hennig, S.

M. Müller, V. Mönkemöller, S. Hennig, W. Hübner, and T. Huser, “Open-source image reconstruction of super-resolution structured illumination microscopy data in ImageJ,” Nat. Comms. 7, 10980 (2016).
[Crossref]

Hübner, W.

M. Müller, V. Mönkemöller, S. Hennig, W. Hübner, and T. Huser, “Open-source image reconstruction of super-resolution structured illumination microscopy data in ImageJ,” Nat. Comms. 7, 10980 (2016).
[Crossref]

Huser, T.

M. Müller, V. Mönkemöller, S. Hennig, W. Hübner, and T. Huser, “Open-source image reconstruction of super-resolution structured illumination microscopy data in ImageJ,” Nat. Comms. 7, 10980 (2016).
[Crossref]

Khare, K.

Krížek, P.

P. Křížek, T. Lukeš, M. Ovesný, K. Fliegel, and G. M. Hagen, “SIMToolbox: A MATLAB toolbox for structured illumination fluorescence microscopy,” Bioinformatics 32, 318–320 (2015).

Le Moal, E.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Lukeš, T.

P. Křížek, T. Lukeš, M. Ovesný, K. Fliegel, and G. M. Hagen, “SIMToolbox: A MATLAB toolbox for structured illumination fluorescence microscopy,” Bioinformatics 32, 318–320 (2015).

Mandula, O.

Mönkemöller, V.

M. Müller, V. Mönkemöller, S. Hennig, W. Hübner, and T. Huser, “Open-source image reconstruction of super-resolution structured illumination microscopy data in ImageJ,” Nat. Comms. 7, 10980 (2016).
[Crossref]

Mudry, E.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Müller, M.

M. Müller, V. Mönkemöller, S. Hennig, W. Hübner, and T. Huser, “Open-source image reconstruction of super-resolution structured illumination microscopy data in ImageJ,” Nat. Comms. 7, 10980 (2016).
[Crossref]

Nicoletti, C.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Ovesný, M.

P. Křížek, T. Lukeš, M. Ovesný, K. Fliegel, and G. M. Hagen, “SIMToolbox: A MATLAB toolbox for structured illumination fluorescence microscopy,” Bioinformatics 32, 318–320 (2015).

Pueyo, L.

R. Soummer, L. Pueyo, A. Sivaramakristnan, and R. J. Vanderbei, “Fast computation of Lyot-style coronagraph propagation,” Astrophys. J. Suppl. Ser. 167, 81–99 (2006).
[Crossref]

Pustelnik, N.

L. Condat, J. Boulanger, N. Pustelnik, S. Sahnoun, and L. Sengmanivong, “A 2-D spectral analysis method to estimate the modulation parameters in structured illumination microscopy,” in IEEE 11th International Symposium on Biomedical Imaging (ISBI), 2014, vol. 11, pp. 604–607.

Sahnoun, S.

L. Condat, J. Boulanger, N. Pustelnik, S. Sahnoun, and L. Sengmanivong, “A 2-D spectral analysis method to estimate the modulation parameters in structured illumination microscopy,” in IEEE 11th International Symposium on Biomedical Imaging (ISBI), 2014, vol. 11, pp. 604–607.

Savatier, J.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Sedat, J. W.

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]

Sengmanivong, L.

L. Condat, J. Boulanger, N. Pustelnik, S. Sahnoun, and L. Sengmanivong, “A 2-D spectral analysis method to estimate the modulation parameters in structured illumination microscopy,” in IEEE 11th International Symposium on Biomedical Imaging (ISBI), 2014, vol. 11, pp. 604–607.

Sentenac, A.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Shao, L.

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]

Shroff, S. A.

Singh, M.

Sivaramakristnan, A.

R. Soummer, L. Pueyo, A. Sivaramakristnan, and R. J. Vanderbei, “Fast computation of Lyot-style coronagraph propagation,” Astrophys. J. Suppl. Ser. 167, 81–99 (2006).
[Crossref]

Soummer, R.

R. Soummer, L. Pueyo, A. Sivaramakristnan, and R. J. Vanderbei, “Fast computation of Lyot-style coronagraph propagation,” Astrophys. J. Suppl. Ser. 167, 81–99 (2006).
[Crossref]

Vanderbei, R. J.

R. Soummer, L. Pueyo, A. Sivaramakristnan, and R. J. Vanderbei, “Fast computation of Lyot-style coronagraph propagation,” Astrophys. J. Suppl. Ser. 167, 81–99 (2006).
[Crossref]

Wang, C. J. R.

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]

Wicker, K.

Williams, D. R.

Archiv für mikroskopische Anatomie (1)

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Archiv für mikroskopische Anatomie 9, 413–418 (1873).
[Crossref]

Astrophys. J. Suppl. Ser. (1)

R. Soummer, L. Pueyo, A. Sivaramakristnan, and R. J. Vanderbei, “Fast computation of Lyot-style coronagraph propagation,” Astrophys. J. Suppl. Ser. 167, 81–99 (2006).
[Crossref]

Bioinformatics (1)

P. Křížek, T. Lukeš, M. Ovesný, K. Fliegel, and G. M. Hagen, “SIMToolbox: A MATLAB toolbox for structured illumination fluorescence microscopy,” Bioinformatics 32, 318–320 (2015).

Biophys. J. (1)

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]

J. Microsc. (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]

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

Nat. Comms. (1)

M. Müller, V. Mönkemöller, S. Hennig, W. Hübner, and T. Huser, “Open-source image reconstruction of super-resolution structured illumination microscopy data in ImageJ,” Nat. Comms. 7, 10980 (2016).
[Crossref]

Nat. Photonics (1)

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Proc. SPIE (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]

Other (2)

J. T. Frohn, “Super-resolution fluorescence microscopy by structured light illumination” Ph.D. dissertation (Swiss Federal Institute of Technology, 2000).

L. Condat, J. Boulanger, N. Pustelnik, S. Sahnoun, and L. Sengmanivong, “A 2-D spectral analysis method to estimate the modulation parameters in structured illumination microscopy,” in IEEE 11th International Symposium on Biomedical Imaging (ISBI), 2014, vol. 11, pp. 604–607.

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Figures (8)

Fig. 1.
Fig. 1. Illustration of the subpixel peak localization in Fourier space. Panel (a) shows a raw data image of the sample pirate under stripe pattern illumination as described in the text. The edges of the image have been dampened to avoid discontinuities. In (b), the Fourier spectrum of (a) calculated by the FFT routine is shown. The pattern wave vector p is indicated in green. Estimating p based on the integer pixel location of the maximum in the Fourier spectrum will lead to a peak location mismatch as shown in the cropped Fourier spectrum (c). The red cross is the location of the maximum, the green cross the actual peak location based on the numerical value of the fringe period and orientation used. Panel (d) shows the result of the proposed selective Fourier transform of (a). The center has been selected to be the location of the maximum found in (c). The upsampling factor is α = 10 , and the size of the area is the same as in (c). Now the maximum (red) is much closer to the actual peak position (green).
Fig. 2.
Fig. 2. Spectral overlap. The separated components C ˜ 0 and C ˜ 1 in Fourier space ( k x , k y ). If C ˜ 1 is shifted by p (red arrow) to its correct position in Fourier space, both bands will have a region of overlap k in which they differ only by a complex factor [see Eq. (10)].
Fig. 3.
Fig. 3. Samples (a) pirate and (b) Siemens star as they have been used in the simulations. They are represented in a size of 256 × 256    px .
Fig. 4.
Fig. 4. (a) Deviation of the pattern orientation and (b) fringe spacing calculated from the detected peak position from the actual value for oversampling factors of 1–10. The calculations are performed for a maximum expected photon count of 5 × 10 1 in the brightest pixel. The solid line represents the mean deviation for all 60 samples, and the shaded area shows the standard deviation. This is done for two different samples [Siemens star (red) and pirate (blue)].
Fig. 5.
Fig. 5. Relative phase error at oversampling of 1–10 for four different photon levels (a)  5 × 10 1 , (b)  5 × 10 2 , (c)  5 × 10 3 , and (d)  5 × 10 4 , and two different samples [Siemens star (red) and pirate (blue)]. The solid lines represent the mean value and the shaded areas the standard deviation of the phase error.
Fig. 6.
Fig. 6. Absolute phase error at oversampling of 1–10 for four different photon levels (a)  5 × 10 1 , (b)  5 × 10 2 , (c)  5 × 10 3 , and (d)  5 × 10 4 , and two different samples [Siemens star (red) and pirate (blue)]. The solid lines represent the mean value and the shaded areas the standard deviation of the phase error.
Fig. 7.
Fig. 7. Reconstruction of simulated SIM data. For a raw data set of nine images (three orientations with three phases each), parameter estimation and reconstruction were performed for oversampling factors of 1 and 10. Panel (a) shows the result of a conventional wide-field deconvolution under plain illumination. The SIM reconstruction with known pattern parameters in (b) shows the expected resolution enhancement. In (c) and (d), the image reconstruction based on the proposed parameter estimation for oversampling of 1 and 10, respectively, is shown. In (e) and (f), the absolute deviation of the reconstruction as shown in (c) and (d) from the reconstruction with known pattern parameters is presented.
Fig. 8.
Fig. 8. Similar to Figs. 7(e) and 7(f), the absolute deviation of the reconstruction from the reconstruction with known pattern parameters is presented for oversampling factors of (a) 1 and (b) 10.

Equations (13)

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

γ = arctan ( p y / p x ) ,
L = ( p x 2 + p y 2 ) 1 / 2 ,
D ( r ) = [ S ( r ) I ( r ) ] h ( r ) ,
I ( r ) = m = 1 1 a m exp [ i m ( 2 π pr + ϕ ) ]
D ˜ ( k ) = m = 1 1 exp ( i m ϕ ) a m S ˜ ( k m p ) h ˜ ( k ) C ˜ m ( k ) .
D ˜ ( k ) = M C ˜ ( k ) ,
C ˜ ( k ) = M 1 D ˜ ( k ) .
S ˜ ^ ( k ) = m , d a m C ˜ m , d ( k + m p d ) h ˜ * ( k + m p d ) m , d | a m h ˜ ( k + m p d ) | 2 + w A ( k ) .
[ C ˜ 0 C ˜ m ] ( p ) = k C ˜ 0 * ( k ) C ˜ m ( k + m p ) ,
a m = k C ˜ 0 * ( k ) C ˜ m ( k + m p ) k | C ˜ 0 ( k ) | 2 .
ϕ n = arg [ D ˜ n ( p ) ] ,
ϕ n = arg [ ( D ˜ n D ˜ n ) ( p ) ] ,
D ˜ ( u ^ , v ^ ) = exp ( 2 π i N y v ^ y ) D ( x , y ) exp ( 2 π i N x x u ^ ) ,

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