Abstract

Computer-generated holography (CGH) is a technique for converting a three-dimensional (3D) object scene into a two-dimensional (2D), complex-valued hologram. One of the major bottlenecks of CGH is the intensive computation that is involved in the hologram generation process. To overcome this problem, numerous research works have been conducted with the aim of reducing arithmetic operations involved in CGH. In this paper, we shall review a number of fast CGH methods that have been developed in the past decade. These methods, which are commonly referred to as point-based CGH, are applied to compute digital Fresnel holograms for an object space that is represented in a point cloud model. While each method has its own strength and weakness, trading off conflicting issues, such as computation efficiency and memory requirement, they also exhibit potential grounds of synergy. We hope that this paper will bring out the essence of each method and provide some insight on how different methods may crossover into better ones.

© 2018 Chinese Laser Press

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References

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    [Crossref]

2018 (2)

H. Sato, T. Kakue, Y. Ichihashi, Y. Endo, K. Wakunami, R. Oi, K. Yamamoto, H. Nakayama, T. Shimobaba, and T. Ito, “Real-time colour hologram generation based on ray-sampling plane with multi-GPU acceleration,” Sci. Rep. 8, 1500 (2018).
[Crossref]

B. Jackin, S. Watanabe, K. Ootsu, T. Ohkawa, T. Yokota, Y. Hayasaki, T. Yatagai, and T. Baba, “Decomposition method for fast computation of gigapixel-sized Fresnel holograms on a graphics processing unit cluster,” Appl. Opt. 57, 3134–3145 (2018).
[Crossref]

2017 (6)

2015 (5)

2014 (5)

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, T. Kakue, and T. Ito, “Fast calculation of a computer-generated hologram for RGB and depth images using a wavefront recording plane method,” Photon. Lett. Poland 6, 90–92 (2014).
[Crossref]

A.-H. Phan, M. A. Alam, S.-H. Jeon, J.-H. Lee, and N. Kim, “Fast hologram generation of long-depth object using multiple wavefront recording planes,” Proc. SPIE 9006, 900612 (2014).
[Crossref]

K. Murano, T. Shimobaba, A. Sugiyama, N. Takada, T. Kakue, M. Oikawa, and T. Ito, “Fast computation of computer-generated hologram using Xeon Phi coprocessor,” Comput. Phys. Commun. 185, 2742–2757 (2014).
[Crossref]

X. Dong, S. Kim, and E. Kim, “MPEG-based novel look-up table for rapid generation of video holograms of fast-moving three-dimensional objects,” Opt. Express 22, 8047–8067 (2014).
[Crossref]

A. Phan, M. Piao, S. Gil, and N. Kim, “Generation speed and reconstructed image quality enhancement of a long-depth object using double wavefront recording planes and a GPU,” Appl. Opt. 53, 4817–4824 (2014).
[Crossref]

2013 (5)

2012 (6)

2011 (4)

P. W. M. Tsang, K. W. K. Cheung, and T.-C. Poon, “Near computation-free compression of Fresnel holograms based on adaptive delta modulation,” Opt. Eng. 50, 085802 (2011).
[Crossref]

P. W. M. Tsang, W. K. Cheung, T. Kim, Y. S. Kim, and T.-C. Poon, “Low-complexity compression of holograms based on delta modulation,” Opt. Commun. 284, 2113–2117 (2011).
[Crossref]

S. Kim, J. Kim, and E. Kim, “Effective reduction of the novel look-up table memory size based on a relationship between the pixel pitch and reconstruction distance of a computer-generated hologram,” Appl. Opt. 50, 3375–3382 (2011).
[Crossref]

P. W. M. Tsang, W. Cheung, T.-C. Poon, and C. Zhou, “Holographic video at 40 frames per second for 4-million object points,” Opt. Express 19, 15205–15211 (2011).
[Crossref]

2010 (3)

2009 (5)

2008 (1)

1993 (1)

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28–34 (1993).
[Crossref]

1977 (1)

J. Bresenham, “A linear algorithm for incremental digital display of circular arcs,” Commun. ACM 20, 100–106 (1977).
[Crossref]

1969 (1)

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 160–168 (1969).
[Crossref]

1967 (3)

J. J. Burch, “A computer algorithm for the synthesis of spatial frequency filters,” Proc. IEEE 55, 599–601 (1967).
[Crossref]

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9, 405–407 (1967).
[Crossref]

A. W. Lohmann and D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
[Crossref]

1966 (1)

Alam, M. A.

A.-H. Phan, M. A. Alam, S.-H. Jeon, J.-H. Lee, and N. Kim, “Fast hologram generation of long-depth object using multiple wavefront recording planes,” Proc. SPIE 9006, 900612 (2014).
[Crossref]

Arai, D.

D. Arai, T. Shimobaba, T. Nishitsuji, T. Kakue, N. Masuda, and T. Ito, “An accelerated hologram calculation using the wavefront recording plane method and wavelet transform,” Opt. Commun. 393, 107–112 (2017).
[Crossref]

D. Arai, T. Shimobaba, K. Murano, Y. Endo, R. Hirayama, D. Hiyama, T. Kakue, and T. Ito, “Acceleration of computer-generated holograms using tilted wavefront recording plane method,” Opt. Express 23, 1740–1747 (2015).
[Crossref]

Awazu, S.

Baba, T.

Bayraktar, M.

Blinder, D.

Bresenham, J.

J. Bresenham, “A linear algorithm for incremental digital display of circular arcs,” Commun. ACM 20, 100–106 (1977).
[Crossref]

Brown, B. R.

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 160–168 (1969).
[Crossref]

B. R. Brown and A. W. Lohmann, “Complex spatial filtering with binary mask,” Appl. Opt. 5, 967–969 (1966).
[Crossref]

Burch, J. J.

J. J. Burch, “A computer algorithm for the synthesis of spatial frequency filters,” Proc. IEEE 55, 599–601 (1967).
[Crossref]

Cao, L.

Chen, J.

Cheung, K.

Cheung, K. W. K.

P. W. M. Tsang, K. W. K. Cheung, and T.-C. Poon, “Fast numerical generation and hybrid encryption of a computer-generated Fresnel holographic video sequence,” Chin. Opt. Lett. 11, 020901 (2013).

P. W. M. Tsang, K. W. K. Cheung, and T.-C. Poon, “Near computation-free compression of Fresnel holograms based on adaptive delta modulation,” Opt. Eng. 50, 085802 (2011).
[Crossref]

P. W. M. Tsang, J.-P. Liu, K. W. K. Cheung, and T.-C. Poon, “An enhanced method for fast generation of hologram sub-lines,” Chin. Opt. Lett. 7, 1092–1096 (2009).

P. W. M. Tsang, J.-P. Liu, K. W. K. Cheung, and T.-C. Poon, “Fast generation of Fresnel holograms based on multirate filtering,” Appl. Opt. 48, H23–H30 (2009).
[Crossref]

P. W. M. Tsang, J.-P. Liu, T.-C. Poon, and K. W. K. Cheung, “Fast generation of hologram sublines based on field programmable gate array,” in Holography and Three-Dimensional Imaging, OSA Technical Digest Series (2009), paper Dwc2.

Cheung, W.

Cheung, W. K.

P. W. M. Tsang, W. C. Situ, W. K. Cheung, T.-C. Poon, and C. Zhou, “Fast generation of hologram from range camera images based on the sub-lines and holographic interpolation,” Proc. SPIE 8556, 85560R (2012).
[Crossref]

P. W. M. Tsang, W. K. Cheung, T. Kim, Y. S. Kim, and T.-C. Poon, “Low-complexity compression of holograms based on delta modulation,” Opt. Commun. 284, 2113–2117 (2011).
[Crossref]

Chong, T.

Chu, D.

Dong, X.

Endo, Y.

H. Sato, T. Kakue, Y. Ichihashi, Y. Endo, K. Wakunami, R. Oi, K. Yamamoto, H. Nakayama, T. Shimobaba, and T. Ito, “Real-time colour hologram generation based on ray-sampling plane with multi-GPU acceleration,” Sci. Rep. 8, 1500 (2018).
[Crossref]

D. Arai, T. Shimobaba, K. Murano, Y. Endo, R. Hirayama, D. Hiyama, T. Kakue, and T. Ito, “Acceleration of computer-generated holograms using tilted wavefront recording plane method,” Opt. Express 23, 1740–1747 (2015).
[Crossref]

Fan, Q.

Z. Yang, Q. Fan, Y. Zhang, J. Liu, and J. Zhou, “A new method for producing computer generated holograms,” J. Opt. 14, 095702 (2012).
[Crossref]

Gao, C.

Gil, S.

Hariharan, P.

P. Hariharan, Optical Holography: Principles, Techniques and Applications (Cambridge University, 1996).

Hasegawa, N.

Hayasaki, Y.

Hirayama, R.

Hiyama, D.

Ichihashi, Y.

H. Sato, T. Kakue, Y. Ichihashi, Y. Endo, K. Wakunami, R. Oi, K. Yamamoto, H. Nakayama, T. Shimobaba, and T. Ito, “Real-time colour hologram generation based on ray-sampling plane with multi-GPU acceleration,” Sci. Rep. 8, 1500 (2018).
[Crossref]

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, T. Kakue, and T. Ito, “Fast calculation of a computer-generated hologram for RGB and depth images using a wavefront recording plane method,” Photon. Lett. Poland 6, 90–92 (2014).
[Crossref]

H. Nakayama, N. Takada, Y. Ichihashi, S. Awazu, T. Shimobaba, N. Masuda, and T. Ito, “Real-time color electroholography using multiple graphics processing units and multiple high-definition liquid-crystal display panels,” Appl. Opt. 49, 5993–5996 (2010).
[Crossref]

Ito, T.

H. Sato, T. Kakue, Y. Ichihashi, Y. Endo, K. Wakunami, R. Oi, K. Yamamoto, H. Nakayama, T. Shimobaba, and T. Ito, “Real-time colour hologram generation based on ray-sampling plane with multi-GPU acceleration,” Sci. Rep. 8, 1500 (2018).
[Crossref]

D. Arai, T. Shimobaba, T. Nishitsuji, T. Kakue, N. Masuda, and T. Ito, “An accelerated hologram calculation using the wavefront recording plane method and wavelet transform,” Opt. Commun. 393, 107–112 (2017).
[Crossref]

N. Hasegawa, T. Shimobaba, T. Kakue, and T. Ito, “Acceleration of hologram generation by optimizing the arrangement of wavefront recording planes,” Appl. Opt. 56, A97–A103 (2017).
[Crossref]

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

D. Arai, T. Shimobaba, K. Murano, Y. Endo, R. Hirayama, D. Hiyama, T. Kakue, and T. Ito, “Acceleration of computer-generated holograms using tilted wavefront recording plane method,” Opt. Express 23, 1740–1747 (2015).
[Crossref]

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, T. Kakue, and T. Ito, “Fast calculation of a computer-generated hologram for RGB and depth images using a wavefront recording plane method,” Photon. Lett. Poland 6, 90–92 (2014).
[Crossref]

K. Murano, T. Shimobaba, A. Sugiyama, N. Takada, T. Kakue, M. Oikawa, and T. Ito, “Fast computation of computer-generated hologram using Xeon Phi coprocessor,” Comput. Phys. Commun. 185, 2742–2757 (2014).
[Crossref]

J. Weng, T. Shimobaba, N. Okada, H. Nakayama, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express 20, 4018–4023 (2012).
[Crossref]

T. Nishitsuji, T. Shimobaba, T. Kakue, N. Masuda, and T. Ito, “Fast calculation of computer-generated hologram using the circular symmetry of zone plates,” Opt. Express 20, 27496–27502 (2012).
[Crossref]

H. Nakayama, N. Takada, Y. Ichihashi, S. Awazu, T. Shimobaba, N. Masuda, and T. Ito, “Real-time color electroholography using multiple graphics processing units and multiple high-definition liquid-crystal display panels,” Appl. Opt. 49, 5993–5996 (2010).
[Crossref]

T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express 18, 19504–19509 (2010).
[Crossref]

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

Jackin, B.

Jeon, S.-H.

A.-H. Phan, M. A. Alam, S.-H. Jeon, J.-H. Lee, and N. Kim, “Fast hologram generation of long-depth object using multiple wavefront recording planes,” Proc. SPIE 9006, 900612 (2014).
[Crossref]

Ji, Y.

Jia, J.

Jiang, W.

Jiao, S.

Jin, G.

Kakue, T.

H. Sato, T. Kakue, Y. Ichihashi, Y. Endo, K. Wakunami, R. Oi, K. Yamamoto, H. Nakayama, T. Shimobaba, and T. Ito, “Real-time colour hologram generation based on ray-sampling plane with multi-GPU acceleration,” Sci. Rep. 8, 1500 (2018).
[Crossref]

D. Arai, T. Shimobaba, T. Nishitsuji, T. Kakue, N. Masuda, and T. Ito, “An accelerated hologram calculation using the wavefront recording plane method and wavelet transform,” Opt. Commun. 393, 107–112 (2017).
[Crossref]

N. Hasegawa, T. Shimobaba, T. Kakue, and T. Ito, “Acceleration of hologram generation by optimizing the arrangement of wavefront recording planes,” Appl. Opt. 56, A97–A103 (2017).
[Crossref]

D. Arai, T. Shimobaba, K. Murano, Y. Endo, R. Hirayama, D. Hiyama, T. Kakue, and T. Ito, “Acceleration of computer-generated holograms using tilted wavefront recording plane method,” Opt. Express 23, 1740–1747 (2015).
[Crossref]

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K. Murano, T. Shimobaba, A. Sugiyama, N. Takada, T. Kakue, M. Oikawa, and T. Ito, “Fast computation of computer-generated hologram using Xeon Phi coprocessor,” Comput. Phys. Commun. 185, 2742–2757 (2014).
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P. W. M. Tsang, W. K. Cheung, T. Kim, Y. S. Kim, and T.-C. Poon, “Low-complexity compression of holograms based on delta modulation,” Opt. Commun. 284, 2113–2117 (2011).
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P. W. M. Tsang, W. K. Cheung, T. Kim, Y. S. Kim, and T.-C. Poon, “Low-complexity compression of holograms based on delta modulation,” Opt. Commun. 284, 2113–2117 (2011).
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Kwon, M.

Lee, J.-H.

A.-H. Phan, M. A. Alam, S.-H. Jeon, J.-H. Lee, and N. Kim, “Fast hologram generation of long-depth object using multiple wavefront recording planes,” Proc. SPIE 9006, 900612 (2014).
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P. W. M. Tsang and T.-C. Poon, “Review on theory and applications of wavefront recording plane framework in generation and processing of digital holograms,” Chin. Opt. Lett. 11, 010902 (2013).
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P. W. M. Tsang, T.-C. Poon, and K. Cheung, “Enhancing the pictorial content of digital holograms at 100 frames per second,” Opt. Express 20, 14183–14188 (2012).
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P. W. M. Tsang, K. Cheung, and T.-C. Poon, “Real-time relighting of digital holograms based on wavefront recording plane method,” Opt. Express 20, 5962–5967 (2012).
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P. W. M. Tsang, W. C. Situ, W. K. Cheung, T.-C. Poon, and C. Zhou, “Fast generation of hologram from range camera images based on the sub-lines and holographic interpolation,” Proc. SPIE 8556, 85560R (2012).
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P. W. M. Tsang, K. W. K. Cheung, and T.-C. Poon, “Near computation-free compression of Fresnel holograms based on adaptive delta modulation,” Opt. Eng. 50, 085802 (2011).
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H. Sato, T. Kakue, Y. Ichihashi, Y. Endo, K. Wakunami, R. Oi, K. Yamamoto, H. Nakayama, T. Shimobaba, and T. Ito, “Real-time colour hologram generation based on ray-sampling plane with multi-GPU acceleration,” Sci. Rep. 8, 1500 (2018).
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H. Sato, T. Kakue, Y. Ichihashi, Y. Endo, K. Wakunami, R. Oi, K. Yamamoto, H. Nakayama, T. Shimobaba, and T. Ito, “Real-time colour hologram generation based on ray-sampling plane with multi-GPU acceleration,” Sci. Rep. 8, 1500 (2018).
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D. Arai, T. Shimobaba, K. Murano, Y. Endo, R. Hirayama, D. Hiyama, T. Kakue, and T. Ito, “Acceleration of computer-generated holograms using tilted wavefront recording plane method,” Opt. Express 23, 1740–1747 (2015).
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P. W. M. Tsang, K. Cheung, and T.-C. Poon, “Real-time relighting of digital holograms based on wavefront recording plane method,” Opt. Express 20, 5962–5967 (2012).
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P. W. M. Tsang, T.-C. Poon, and K. Cheung, “Enhancing the pictorial content of digital holograms at 100 frames per second,” Opt. Express 20, 14183–14188 (2012).
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P. W. M. Tsang, W. Cheung, T.-C. Poon, and C. Zhou, “Holographic video at 40 frames per second for 4-million object points,” Opt. Express 19, 15205–15211 (2011).
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J. Weng, T. Shimobaba, N. Okada, H. Nakayama, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express 20, 4018–4023 (2012).
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Opt. Lett. (1)

Photon. Lett. Poland (1)

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, T. Kakue, and T. Ito, “Fast calculation of a computer-generated hologram for RGB and depth images using a wavefront recording plane method,” Photon. Lett. Poland 6, 90–92 (2014).
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Proc. IEEE (1)

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Proc. SPIE (2)

A.-H. Phan, M. A. Alam, S.-H. Jeon, J.-H. Lee, and N. Kim, “Fast hologram generation of long-depth object using multiple wavefront recording planes,” Proc. SPIE 9006, 900612 (2014).
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Sci. Rep. (1)

H. Sato, T. Kakue, Y. Ichihashi, Y. Endo, K. Wakunami, R. Oi, K. Yamamoto, H. Nakayama, T. Shimobaba, and T. Ito, “Real-time colour hologram generation based on ray-sampling plane with multi-GPU acceleration,” Sci. Rep. 8, 1500 (2018).
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P. W. M. Tsang, J.-P. Liu, T.-C. Poon, and K. W. K. Cheung, “Fast generation of hologram sublines based on field programmable gate array,” in Holography and Three-Dimensional Imaging, OSA Technical Digest Series (2009), paper Dwc2.

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Figures (8)

Fig. 1.
Fig. 1. Spatial relation between object points and the hologram plane.
Fig. 2.
Fig. 2. Novel look-up-table (N-LUT) method.
Fig. 3.
Fig. 3. (a) Retrieving an N-point PFP of a segment of the 3D surface. (b) An example showing the partitioning of pixels in the source image into horizontal segments, each having similar properties.
Fig. 4.
Fig. 4. Line-scan method for generating the PFP.
Fig. 5.
Fig. 5. Computing a hologram pixel with the S-LUT method.
Fig. 6.
Fig. 6. Computing a hologram pixel with the C-LUT method.
Fig. 7.
Fig. 7. Spatial relation between the object space, the WRP, and the hologram plane.
Fig. 8.
Fig. 8. Partitioning the object into scan planes, each contributing to a sub-line on the hologram plane.

Tables (1)

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Table 1. Arithmetic Calculations of a Single Operation for Computing the Hologram with Eq. (2)

Equations (23)

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F(m,n;zo)=expi2π(mδ)2+(nδ)2+zo2λ=expiwnmx2+ny2+zo2,
H(m,n)=p=0PApF(mup,nvp;zp),
H(m,n;zo)=I(m,n;zo)*F(m,n;zo).
H(m,n;zo)=I1[I˜(ωm,ωn;zo)F˜(ωm,ωn;zo)].
H(m,n)=I1[k=0K1I˜(ωm,ωn;zk)F˜(ωm,ωn;zk)].
F(r,θ;zo)=exp[iwn(rcosθ)2+(rsinθ)2+zo2]=exp[iwnr2+zo2].
F(m,n;zo)=F(rcosθ,rsinθ;zo).
F(m,n;zo)|m0;n0=F(|m|,n;zo),
F(m,n;zo)|n0=F(m,|n|;zo).
H(m,n)=p=1PApexp(iwnΔm2+Δn2+zp2),
H(m,n)=p=1PApOH(Δm,zp)OV(Δn,zp),
OH(Δm,zp)=exp(iwnΔm2+zp2),
OV(Δn,zp)=exp(iwnΔn2+zp2)
HF(m,n)=p=0P1Apexp[i2πλ(m2+n22zpmup+nvpzp)].
HF(m,n)=p=0P1ApL(m,n;zp)OH(m,up)OV(n,vp),
wp(m,n)|(m,n)Sp=Aprpexp(i2πrpλ),
W(m,n)=p=0P1wp(m,n).
H(m,n)=W(m,n)*h(m,n;zo),
wj(m,n)|(m,n)Sj=pμjarm;n;pexp(i2πrm;n;pλ),
W(m,n)=j=0T1wj(m,n),
O(m,t)|0t<L=p=0T(t)At;prt;pexp(iπrt;p2λzt;p),
O(m,n)=O(m,nDv)*g(n).
H(m,n)=O(m,n)*Fv(n),

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