Abstract

Display-sized full-parallax holograms with large viewing angles require resolutions surpassing tens of Gigapixels. Unfortunately, computer-generated holography is computationally intensive, particularly for these huge display resolutions. Existing algorithms designed for diffraction of typical Megapixel-sized holograms do not scale well for these large resolutions. Furthermore, since the holograms will not fit in the RAM of most of today’s computers, the algorithms should be modified to minimize disk access. We propose two novel algorithms respectively for short-distance and long-distance propagation, and accurately compute the diffraction of a 17.2 Gigapixel hologram on a standard desktop machine. We report a 500-fold speedup over the reference rectangular tiling algorithm for the short-distance version, and a 50-fold speedup for the long-distance version.

© 2019 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]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  22. Y.-H. Kim, C.-W. Byun, H. Oh, J.-E. Pi, J.-H. Choi, G. H. Kim, M.-L. Lee, H. Ryu, and C.-S. Hwang, “Off-axis angular spectrum method with variable sampling interval,” Opt. Commun. 348, 31–37 (2015).
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    [Crossref]
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    [Crossref]

2019 (3)

D. Blinder, A. Ahar, S. Bettens, T. Birnbaum, A. Symeonidou, H. Ottevaere, C. Schretter, and P. Schelkens, “Signal processing challenges for digital holographic video display systems,” Signal Process. Image Commun. 70, 114–130 (2019).
[Crossref]

H. Zhang, L. Cao, and G. Jin, “Three-dimensional computer-generated hologram with fourier domain segmentation,” Opt. Express 27(8), 11689–11697 (2019).
[Crossref]

D. Blinder, “Direct calculation of computer-generated holograms in sparse bases,” Opt. Express 27(16), 23124–23137 (2019).
[Crossref]

2018 (4)

2017 (3)

2016 (4)

2015 (2)

Y.-H. Kim, C.-W. Byun, H. Oh, J.-E. Pi, J.-H. Choi, G. H. Kim, M.-L. Lee, H. Ryu, and C.-S. Hwang, “Off-axis angular spectrum method with variable sampling interval,” Opt. Commun. 348, 31–37 (2015).
[Crossref]

A. Symeonidou, D. Blinder, A. Munteanu, and P. Schelkens, “Computer-generated holograms by multiple wavefront recording plane method with occlusion culling,” Opt. Express 23(17), 22149–22161 (2015).
[Crossref]

2014 (1)

2013 (1)

2012 (1)

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

2010 (1)

2009 (2)

2007 (1)

1993 (1)

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–31 (1993).
[Crossref]

Ahar, A.

D. Blinder, A. Ahar, S. Bettens, T. Birnbaum, A. Symeonidou, H. Ottevaere, C. Schretter, and P. Schelkens, “Signal processing challenges for digital holographic video display systems,” Signal Process. Image Commun. 70, 114–130 (2019).
[Crossref]

A. Symeonidou, D. Blinder, A. Ahar, C. Schretter, A. Munteanu, and P. Schelkens, “Speckle noise reduction for computer generated holograms of objects with diffuse surfaces,” Proc. SPIE 9896, 98960F (2016).
[Crossref]

Askari, M.

Bettens, S.

D. Blinder, A. Ahar, S. Bettens, T. Birnbaum, A. Symeonidou, H. Ottevaere, C. Schretter, and P. Schelkens, “Signal processing challenges for digital holographic video display systems,” Signal Process. Image Commun. 70, 114–130 (2019).
[Crossref]

Birnbaum, T.

D. Blinder, A. Ahar, S. Bettens, T. Birnbaum, A. Symeonidou, H. Ottevaere, C. Schretter, and P. Schelkens, “Signal processing challenges for digital holographic video display systems,” Signal Process. Image Commun. 70, 114–130 (2019).
[Crossref]

Blinder, D.

D. Blinder, A. Ahar, S. Bettens, T. Birnbaum, A. Symeonidou, H. Ottevaere, C. Schretter, and P. Schelkens, “Signal processing challenges for digital holographic video display systems,” Signal Process. Image Commun. 70, 114–130 (2019).
[Crossref]

D. Blinder, “Direct calculation of computer-generated holograms in sparse bases,” Opt. Express 27(16), 23124–23137 (2019).
[Crossref]

A. Symeonidou, D. Blinder, and P. Schelkens, “Colour computer-generated holography for point clouds utilizing the phong illumination model,” Opt. Express 26(8), 10282–10298 (2018).
[Crossref]

A. Symeonidou, D. Blinder, A. Ahar, C. Schretter, A. Munteanu, and P. Schelkens, “Speckle noise reduction for computer generated holograms of objects with diffuse surfaces,” Proc. SPIE 9896, 98960F (2016).
[Crossref]

A. Symeonidou, D. Blinder, A. Munteanu, and P. Schelkens, “Computer-generated holograms by multiple wavefront recording plane method with occlusion culling,” Opt. Express 23(17), 22149–22161 (2015).
[Crossref]

Byun, C.-W.

Y.-H. Kim, C.-W. Byun, H. Oh, J.-E. Pi, J.-H. Choi, G. H. Kim, M.-L. Lee, H. Ryu, and C.-S. Hwang, “Off-axis angular spectrum method with variable sampling interval,” Opt. Commun. 348, 31–37 (2015).
[Crossref]

Cao, L.

Choi, J.-H.

Y.-H. Kim, C.-W. Byun, H. Oh, J.-E. Pi, J.-H. Choi, G. H. Kim, M.-L. Lee, H. Ryu, and C.-S. Hwang, “Off-axis angular spectrum method with variable sampling interval,” Opt. Commun. 348, 31–37 (2015).
[Crossref]

Cozot, R.

Gilles, A.

Gioia, P.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (W.H. Freeman, 2017).

Honda, T.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–31 (1993).
[Crossref]

Hoshino, H.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–31 (1993).
[Crossref]

Hwang, C.-S.

Y.-H. Kim, C.-W. Byun, H. Oh, J.-E. Pi, J.-H. Choi, G. H. Kim, M.-L. Lee, H. Ryu, and C.-S. Hwang, “Off-axis angular spectrum method with variable sampling interval,” Opt. Commun. 348, 31–37 (2015).
[Crossref]

Igarashi, S.

Ito, T.

Jin, G.

Ju, Y.-G.

Kang, H.

Kim, G. H.

Y.-H. Kim, C.-W. Byun, H. Oh, J.-E. Pi, J.-H. Choi, G. H. Kim, M.-L. Lee, H. Ryu, and C.-S. Hwang, “Off-axis angular spectrum method with variable sampling interval,” Opt. Commun. 348, 31–37 (2015).
[Crossref]

Kim, S.-B.

Kim, S.-H.

Kim, Y.-H.

Y.-H. Kim, C.-W. Byun, H. Oh, J.-E. Pi, J.-H. Choi, G. H. Kim, M.-L. Lee, H. Ryu, and C.-S. Hwang, “Off-axis angular spectrum method with variable sampling interval,” Opt. Commun. 348, 31–37 (2015).
[Crossref]

Ko, S.-B.

Lee, B. R.

J. Y. Son, H. Lee, B. R. Lee, and K. H. Lee, “Holographic and light-field imaging as future 3-d displays,” Proc. IEEE 105(5), 789–804 (2017).
[Crossref]

Lee, H.

J. Y. Son, H. Lee, B. R. Lee, and K. H. Lee, “Holographic and light-field imaging as future 3-d displays,” Proc. IEEE 105(5), 789–804 (2017).
[Crossref]

Lee, K. H.

J. Y. Son, H. Lee, B. R. Lee, and K. H. Lee, “Holographic and light-field imaging as future 3-d displays,” Proc. IEEE 105(5), 789–804 (2017).
[Crossref]

Lee, M.-L.

Y.-H. Kim, C.-W. Byun, H. Oh, J.-E. Pi, J.-H. Choi, G. H. Kim, M.-L. Lee, H. Ryu, and C.-S. Hwang, “Off-axis angular spectrum method with variable sampling interval,” Opt. Commun. 348, 31–37 (2015).
[Crossref]

Liao, H.-K.

Liu, J.-P.

Masuda, N.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

T. Shimobaba, N. Masuda, and T. Ito, “Simple and fast calculation algorithm for computer-generated hologram with wavefront recording plane,” Opt. Lett. 34(20), 3133–3135 (2009).
[Crossref]

Matsushima, K.

Morin, L.

Muffoletto, R. P.

Munteanu, A.

A. Symeonidou, D. Blinder, A. Ahar, C. Schretter, A. Munteanu, and P. Schelkens, “Speckle noise reduction for computer generated holograms of objects with diffuse surfaces,” Proc. SPIE 9896, 98960F (2016).
[Crossref]

A. Symeonidou, D. Blinder, A. Munteanu, and P. Schelkens, “Computer-generated holograms by multiple wavefront recording plane method with occlusion culling,” Opt. Express 23(17), 22149–22161 (2015).
[Crossref]

Nakahara, S.

Nakamura, M.

Nakamura, T.

Nishitsuji, T.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Oh, H.

Y.-H. Kim, C.-W. Byun, H. Oh, J.-E. Pi, J.-H. Choi, G. H. Kim, M.-L. Lee, H. Ryu, and C.-S. Hwang, “Off-axis angular spectrum method with variable sampling interval,” Opt. Commun. 348, 31–37 (2015).
[Crossref]

Ohyama, N.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–31 (1993).
[Crossref]

Okada, N.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Ottevaere, H.

D. Blinder, A. Ahar, S. Bettens, T. Birnbaum, A. Symeonidou, H. Ottevaere, C. Schretter, and P. Schelkens, “Signal processing challenges for digital holographic video display systems,” Signal Process. Image Commun. 70, 114–130 (2019).
[Crossref]

Park, D.-Y.

Park, J.-H.

Pi, J.-E.

Y.-H. Kim, C.-W. Byun, H. Oh, J.-E. Pi, J.-H. Choi, G. H. Kim, M.-L. Lee, H. Ryu, and C.-S. Hwang, “Off-axis angular spectrum method with variable sampling interval,” Opt. Commun. 348, 31–37 (2015).
[Crossref]

Ryu, H.

Y.-H. Kim, C.-W. Byun, H. Oh, J.-E. Pi, J.-H. Choi, G. H. Kim, M.-L. Lee, H. Ryu, and C.-S. Hwang, “Off-axis angular spectrum method with variable sampling interval,” Opt. Commun. 348, 31–37 (2015).
[Crossref]

Sakurai, T.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Schelkens, P.

D. Blinder, A. Ahar, S. Bettens, T. Birnbaum, A. Symeonidou, H. Ottevaere, C. Schretter, and P. Schelkens, “Signal processing challenges for digital holographic video display systems,” Signal Process. Image Commun. 70, 114–130 (2019).
[Crossref]

A. Symeonidou, D. Blinder, and P. Schelkens, “Colour computer-generated holography for point clouds utilizing the phong illumination model,” Opt. Express 26(8), 10282–10298 (2018).
[Crossref]

A. Symeonidou, D. Blinder, A. Ahar, C. Schretter, A. Munteanu, and P. Schelkens, “Speckle noise reduction for computer generated holograms of objects with diffuse surfaces,” Proc. SPIE 9896, 98960F (2016).
[Crossref]

A. Symeonidou, D. Blinder, A. Munteanu, and P. Schelkens, “Computer-generated holograms by multiple wavefront recording plane method with occlusion culling,” Opt. Express 23(17), 22149–22161 (2015).
[Crossref]

Schretter, C.

D. Blinder, A. Ahar, S. Bettens, T. Birnbaum, A. Symeonidou, H. Ottevaere, C. Schretter, and P. Schelkens, “Signal processing challenges for digital holographic video display systems,” Signal Process. Image Commun. 70, 114–130 (2019).
[Crossref]

A. Symeonidou, D. Blinder, A. Ahar, C. Schretter, A. Munteanu, and P. Schelkens, “Speckle noise reduction for computer generated holograms of objects with diffuse surfaces,” Proc. SPIE 9896, 98960F (2016).
[Crossref]

Shimobaba, T.

Shin, K.-S.

Shiraki, A.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Son, J. Y.

J. Y. Son, H. Lee, B. R. Lee, and K. H. Lee, “Holographic and light-field imaging as future 3-d displays,” Proc. IEEE 105(5), 789–804 (2017).
[Crossref]

Stoykova, E.

Symeonidou, A.

D. Blinder, A. Ahar, S. Bettens, T. Birnbaum, A. Symeonidou, H. Ottevaere, C. Schretter, and P. Schelkens, “Signal processing challenges for digital holographic video display systems,” Signal Process. Image Commun. 70, 114–130 (2019).
[Crossref]

A. Symeonidou, D. Blinder, and P. Schelkens, “Colour computer-generated holography for point clouds utilizing the phong illumination model,” Opt. Express 26(8), 10282–10298 (2018).
[Crossref]

A. Symeonidou, D. Blinder, A. Ahar, C. Schretter, A. Munteanu, and P. Schelkens, “Speckle noise reduction for computer generated holograms of objects with diffuse surfaces,” Proc. SPIE 9896, 98960F (2016).
[Crossref]

A. Symeonidou, D. Blinder, A. Munteanu, and P. Schelkens, “Computer-generated holograms by multiple wavefront recording plane method with occlusion culling,” Opt. Express 23(17), 22149–22161 (2015).
[Crossref]

Takada, N.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Tohline, J. E.

Tyler, J. M.

Wakunami, K.

Weng, J.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Yamaguchi, M.

Yamashita, H.

Yeom, H.-J.

Yoshikawa, H.

Zhang, H.

Appl. Opt. (5)

Comput. Phys. Commun. (1)

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Opt. Commun. (1)

Y.-H. Kim, C.-W. Byun, H. Oh, J.-E. Pi, J.-H. Choi, G. H. Kim, M.-L. Lee, H. Ryu, and C.-S. Hwang, “Off-axis angular spectrum method with variable sampling interval,” Opt. Commun. 348, 31–37 (2015).
[Crossref]

Opt. Express (12)

H. Zhang, L. Cao, and G. Jin, “Three-dimensional computer-generated hologram with fourier domain segmentation,” Opt. Express 27(8), 11689–11697 (2019).
[Crossref]

K. Wakunami, H. Yamashita, and M. Yamaguchi, “Occlusion culling for computer generated hologram based on ray-wavefront conversion,” Opt. Express 21(19), 21811–21822 (2013).
[Crossref]

S. Igarashi, T. Nakamura, K. Matsushima, and M. Yamaguchi, “Efficient tiled calculation of over-10-gigapixel holograms using ray-wavefront conversion,” Opt. Express 26(8), 10773–10786 (2018).
[Crossref]

R. P. Muffoletto, J. M. Tyler, and J. E. Tohline, “Shifted fresnel diffraction for computational holography,” Opt. Express 15(9), 5631–5640 (2007).
[Crossref]

K. Matsushima, “Shifted angular spectrum method for off-axis numerical propagation,” Opt. Express 18(17), 18453–18463 (2010).
[Crossref]

K. Matsushima, M. Nakamura, and S. Nakahara, “Silhouette method for hidden surface removal in computer holography and its acceleration using the switch-back technique,” Opt. Express 22(20), 24450–24465 (2014).
[Crossref]

H.-J. Yeom and J.-H. Park, “Calculation of reflectance distribution using angular spectrum convolution in mesh-based computer generated hologram,” Opt. Express 24(17), 19801–19813 (2016).
[Crossref]

M. Askari, S.-B. Kim, K.-S. Shin, S.-B. Ko, S.-H. Kim, D.-Y. Park, Y.-G. Ju, and J.-H. Park, “Occlusion handling using angular spectrum convolution in fully analytical mesh based computer generated hologram,” Opt. Express 25(21), 25867–25878 (2017).
[Crossref]

T. Shimobaba and T. Ito, “Fast generation of computer-generated holograms using wavelet shrinkage,” Opt. Express 25(1), 77–87 (2017).
[Crossref]

D. Blinder, “Direct calculation of computer-generated holograms in sparse bases,” Opt. Express 27(16), 23124–23137 (2019).
[Crossref]

A. Symeonidou, D. Blinder, A. Munteanu, and P. Schelkens, “Computer-generated holograms by multiple wavefront recording plane method with occlusion culling,” Opt. Express 23(17), 22149–22161 (2015).
[Crossref]

A. Symeonidou, D. Blinder, and P. Schelkens, “Colour computer-generated holography for point clouds utilizing the phong illumination model,” Opt. Express 26(8), 10282–10298 (2018).
[Crossref]

Opt. Lett. (1)

Proc. IEEE (1)

J. Y. Son, H. Lee, B. R. Lee, and K. H. Lee, “Holographic and light-field imaging as future 3-d displays,” Proc. IEEE 105(5), 789–804 (2017).
[Crossref]

Proc. SPIE (2)

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–31 (1993).
[Crossref]

A. Symeonidou, D. Blinder, A. Ahar, C. Schretter, A. Munteanu, and P. Schelkens, “Speckle noise reduction for computer generated holograms of objects with diffuse surfaces,” Proc. SPIE 9896, 98960F (2016).
[Crossref]

Signal Process. Image Commun. (1)

D. Blinder, A. Ahar, S. Bettens, T. Birnbaum, A. Symeonidou, H. Ottevaere, C. Schretter, and P. Schelkens, “Signal processing challenges for digital holographic video display systems,” Signal Process. Image Commun. 70, 114–130 (2019).
[Crossref]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (W.H. Freeman, 2017).

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Figures (7)

Fig. 1.
Fig. 1. Diagram of the rectangular tiling algorithm using shifted Fresnel diffraction. The dark blue example tile in the source plane has to be numerically propagated to every tile in the destination plane. This process has to be repeated over for every source plane tile.
Fig. 2.
Fig. 2. Diagram of the short-distance based diffraction algorithm. (a) Every tile has a region of influence, indicated by the red edge with edge width $w$. (b) The blue grid indicates the tiles that are transferred to the GPU for propagation. After diffraction, only the corresponding block in the overlapping red grid is known, as the remaining information will still be affected by neighboring tiles. The horizontal and vertical buffers, denoted in red and green respectively, represent the temporary data stored on the GPU for signalling data across subsequent tiles and tile rows.
Fig. 3.
Fig. 3. Diagram of the Long-distance strip-based diffraction using ASM, with zeropadding. This version uses two intermediate stored versions on disk. In Phase 1, strips are read and directly transferred on GPU, where they are zeropadded, FFT-transformed and transposed. Phase 2 is similar to the previous phase, but here the ASM transfer function is applied. The second FFT is undone, and the only the relevant data is sent back to disk after transposing the data once more. The final Phase 3 will undo the FFT from Phase 1, crop the data and write the final hologram.
Fig. 4.
Fig. 4. Summary of the multi-WRP algorithm. (a) Diagram of the main steps of the algorithm, depicting how the scene is divided into WRP zones, each containing its own set of 3D points. The LUT consists of entries of varying sizes, depending on their respective distance to the WRP plane. (b) Example of a single point accumulation, showing the real part of the holographic signal. First the occlusion mask is applied on the point location, followed by the LUT entry addition at that location.
Fig. 5.
Fig. 5. Schematic of the main program components. The left region contains components running on the CPU, the right region contains those who run on GPU. The annotated black arrows indicate how the components communicate with each other.
Fig. 6.
Fig. 6. Diagram of the scene geometry (not to scale). (a) front view, showing the plane’s lateral dimensions. (b) top view, showing the distance to the hologram plane and the depth of the model.
Fig. 7.
Fig. 7. Three rendered views taken from the same hologram, backpropagated at $z= 27.0\;\textrm{mm}$.

Equations (3)

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k 4 O ( B 2 log ( B 2 ) ) = O ( k 2 N 2 log B )
w = d tan ( θ ) = d tan ( sin 1 λ 2 p ) = d λ 4 p 2 λ 2
k 2 O ( ( B + 2 w ) 2 log ( ( B + 2 w ) 2 ) ) = O ( ( N + 2 k w ) 2 log ( B + 2 w ) ) O ( N 2 log B )

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