Abstract

Computer-generated holography at high resolutions is a computationally intensive task. Efficient algorithms are needed to generate holograms at acceptable speeds, especially for real-time and interactive applications such as holographic displays. We propose a novel technique to generate holograms using a sparse basis representation in the short-time Fourier space combined with a wavefront-recording plane placed in the middle of the 3D object. By computing the point spread functions in the transform domain, we update only a small subset of the precomputed largest-magnitude coefficients to significantly accelerate the algorithm over conventional look-up table methods. We implement the algorithm on a GPU, and report a speedup factor of over 30. We show that this transform is superior over wavelet-based approaches, and show quantitative and qualitative improvements over the state-of-the-art WASABI method; we report accuracy gains of 2dB PSNR, as well improved view preservation.

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

Full Article  |  PDF Article
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References

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2017 (2)

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,” Optics Communications 393, 107–112 (2017).
[Crossref]

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

2016 (2)

A. Gilles, P. Gioia, R. Cozot, and L. Morin, “Hybrid approach for fast occlusion processing in computer-generated hologram calculation,” Appl. Opt. 55, 5459–5470 (2016).
[Crossref] [PubMed]

H. Niwase, N. Takada, H. Araki, Y. Maeda, M. Fujiwara, H. Nakayama, T. Kakue, T. Shimobaba, and T. Ito, “Real-time electroholography using a multiple-graphics processing unit cluster system with a single spatial light modulator and the infiniband network,” Optical Engineering 55, 55–56 (2016).
[Crossref]

2015 (2)

2014 (2)

2013 (3)

2012 (1)

2009 (3)

2008 (2)

2006 (1)

E. Darakis and J. J. Soraghan, “Use of fresnelets for phase-shifting digital hologram compression,” IEEE transactions on image processing 15, 3804–3811 (2006).
[Crossref] [PubMed]

1996 (1)

A. van der Schaaf and J. van Hateren, “Modelling the power spectra of natural images: Statistics and information,” Vision Research 36, 2759–2770 (1996).
[Crossref] [PubMed]

1993 (1)

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

1976 (1)

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,” Optics Communications 393, 107–112 (2017).
[Crossref]

Araki, H.

H. Niwase, N. Takada, H. Araki, Y. Maeda, M. Fujiwara, H. Nakayama, T. Kakue, T. Shimobaba, and T. Ito, “Real-time electroholography using a multiple-graphics processing unit cluster system with a single spatial light modulator and the infiniband network,” Optical Engineering 55, 55–56 (2016).
[Crossref]

H. Niwase, N. Takada, H. Araki, H. Nakayama, A. Sugiyama, T. Kakue, T. Shimobaba, and T. Ito, “Real-time spatiotemporal division multiplexing electroholography with a single graphics processing unit utilizing movie features,” Opt. Express 22, 28052–28057 (2014).
[Crossref] [PubMed]

Blinder, D.

Chong, T.-C.

Cozot, R.

Darakis, E.

E. Darakis and J. J. Soraghan, “Use of fresnelets for phase-shifting digital hologram compression,” IEEE transactions on image processing 15, 3804–3811 (2006).
[Crossref] [PubMed]

Fujiwara, M.

H. Niwase, N. Takada, H. Araki, Y. Maeda, M. Fujiwara, H. Nakayama, T. Kakue, T. Shimobaba, and T. Ito, “Real-time electroholography using a multiple-graphics processing unit cluster system with a single spatial light modulator and the infiniband network,” Optical Engineering 55, 55–56 (2016).
[Crossref]

Gilles, A.

Gioia, P.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2004), 3rd ed.

Honda, T.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” (SPIE,1993).

Hoshino, H.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” (SPIE,1993).

Ichihashi, Y.

Ito, T.

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,” Optics Communications 393, 107–112 (2017).
[Crossref]

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

H. Niwase, N. Takada, H. Araki, Y. Maeda, M. Fujiwara, H. Nakayama, T. Kakue, T. Shimobaba, and T. Ito, “Real-time electroholography using a multiple-graphics processing unit cluster system with a single spatial light modulator and the infiniband network,” Optical Engineering 55, 55–56 (2016).
[Crossref]

H. Niwase, N. Takada, H. Araki, H. Nakayama, A. Sugiyama, T. Kakue, T. Shimobaba, and T. Ito, “Real-time spatiotemporal division multiplexing electroholography with a single graphics processing unit utilizing movie features,” Opt. Express 22, 28052–28057 (2014).
[Crossref] [PubMed]

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21, 9192–9197 (2013).
[Crossref] [PubMed]

N. Takada, T. Shimobaba, H. Nakayama, A. Shiraki, N. Okada, M. Oikawa, N. Masuda, and T. Ito, “Fast high-resolution computer-generated hologram computation using multiple graphics processing unit cluster system,” Appl. Opt. 51, 7303–7307 (2012).
[Crossref] [PubMed]

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] [PubMed]

Ji, Y.-M.

Jia, J.

Kakue, T.

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,” Optics Communications 393, 107–112 (2017).
[Crossref]

H. Niwase, N. Takada, H. Araki, Y. Maeda, M. Fujiwara, H. Nakayama, T. Kakue, T. Shimobaba, and T. Ito, “Real-time electroholography using a multiple-graphics processing unit cluster system with a single spatial light modulator and the infiniband network,” Optical Engineering 55, 55–56 (2016).
[Crossref]

H. Niwase, N. Takada, H. Araki, H. Nakayama, A. Sugiyama, T. Kakue, T. Shimobaba, and T. Ito, “Real-time spatiotemporal division multiplexing electroholography with a single graphics processing unit utilizing movie features,” Opt. Express 22, 28052–28057 (2014).
[Crossref] [PubMed]

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21, 9192–9197 (2013).
[Crossref] [PubMed]

Kang, H.

Kim, E.-S.

Kim, H.-J.

Kim, S.-B.

Kim, S.-C.

Kim, S.-H.

Ko, S.-B.

Li, B.

Li, X.

Liang, X.

Liu, J.

Lucente, M. E.

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

Maeda, Y.

H. Niwase, N. Takada, H. Araki, Y. Maeda, M. Fujiwara, H. Nakayama, T. Kakue, T. Shimobaba, and T. Ito, “Real-time electroholography using a multiple-graphics processing unit cluster system with a single spatial light modulator and the infiniband network,” Optical Engineering 55, 55–56 (2016).
[Crossref]

Masuda, N.

Matsushima, K.

Morin, L.

Munteanu, A.

Nakahara, S.

Nakamura, M.

Nakayama, H.

Nishitsuji, T.

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,” Optics Communications 393, 107–112 (2017).
[Crossref]

Niwase, H.

H. Niwase, N. Takada, H. Araki, Y. Maeda, M. Fujiwara, H. Nakayama, T. Kakue, T. Shimobaba, and T. Ito, “Real-time electroholography using a multiple-graphics processing unit cluster system with a single spatial light modulator and the infiniband network,” Optical Engineering 55, 55–56 (2016).
[Crossref]

H. Niwase, N. Takada, H. Araki, H. Nakayama, A. Sugiyama, T. Kakue, T. Shimobaba, and T. Ito, “Real-time spatiotemporal division multiplexing electroholography with a single graphics processing unit utilizing movie features,” Opt. Express 22, 28052–28057 (2014).
[Crossref] [PubMed]

Ohyama, N.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” (SPIE,1993).

Oi, R.

Oikawa, M.

Okada, N.

Pan, Y.

Park, J.-H.

Schelkens, P.

Shimobaba, T.

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

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,” Optics Communications 393, 107–112 (2017).
[Crossref]

H. Niwase, N. Takada, H. Araki, Y. Maeda, M. Fujiwara, H. Nakayama, T. Kakue, T. Shimobaba, and T. Ito, “Real-time electroholography using a multiple-graphics processing unit cluster system with a single spatial light modulator and the infiniband network,” Optical Engineering 55, 55–56 (2016).
[Crossref]

H. Niwase, N. Takada, H. Araki, H. Nakayama, A. Sugiyama, T. Kakue, T. Shimobaba, and T. Ito, “Real-time spatiotemporal division multiplexing electroholography with a single graphics processing unit utilizing movie features,” Opt. Express 22, 28052–28057 (2014).
[Crossref] [PubMed]

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21, 9192–9197 (2013).
[Crossref] [PubMed]

N. Takada, T. Shimobaba, H. Nakayama, A. Shiraki, N. Okada, M. Oikawa, N. Masuda, and T. Ito, “Fast high-resolution computer-generated hologram computation using multiple graphics processing unit cluster system,” Appl. Opt. 51, 7303–7307 (2012).
[Crossref] [PubMed]

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] [PubMed]

Shiraki, A.

Solanki, S.

Soraghan, J. J.

E. Darakis and J. J. Soraghan, “Use of fresnelets for phase-shifting digital hologram compression,” IEEE transactions on image processing 15, 3804–3811 (2006).
[Crossref] [PubMed]

Sugiyama, A.

Symeonidou, A.

Takada, N.

Tan, C.

Tanjung, R. B. A.

van der Schaaf, A.

A. van der Schaaf and J. van Hateren, “Modelling the power spectra of natural images: Statistics and information,” Vision Research 36, 2759–2770 (1996).
[Crossref] [PubMed]

van Hateren, J.

A. van der Schaaf and J. van Hateren, “Modelling the power spectra of natural images: Statistics and information,” Vision Research 36, 2759–2770 (1996).
[Crossref] [PubMed]

Wakunami, K.

Wang, Y.

Wolf, K.

K. Wolf, Geometric Optics on Phase Space, Theoretical and Mathematical Physics (SpringerBerlin Heidelberg, 2004).

Xu, X.

Yamaguchi, M.

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

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” (SPIE,1993).

Yamaguchi, T.

Yamamoto, K.

Yamashita, H.

Yatagai, T.

Yeom, H.-J.

Yoshikawa, H.

Zhang, H.

Appl. Opt. (7)

IEEE transactions on image processing (1)

E. Darakis and J. J. Soraghan, “Use of fresnelets for phase-shifting digital hologram compression,” IEEE transactions on image processing 15, 3804–3811 (2006).
[Crossref] [PubMed]

Journal of Electronic Imaging (1)

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

Opt. Express (8)

Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. A. Tanjung, C. Tan, and T.-C. Chong, “Fast cgh computation using s-lut on gpu,” Opt. Express 17, 18543–18555 (2009).
[Crossref]

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21, 9192–9197 (2013).
[Crossref] [PubMed]

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

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, 24450–24465 (2014).
[Crossref] [PubMed]

H. Niwase, N. Takada, H. Araki, H. Nakayama, A. Sugiyama, T. Kakue, T. Shimobaba, and T. Ito, “Real-time spatiotemporal division multiplexing electroholography with a single graphics processing unit utilizing movie features,” Opt. Express 22, 28052–28057 (2014).
[Crossref] [PubMed]

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

J.-H. Park, S.-B. Kim, H.-J. Yeom, H.-J. Kim, H. Zhang, B. Li, Y.-M. Ji, S.-H. Kim, and S.-B. Ko, “Continuous shading and its fast update in fully analytic triangular-mesh-based computer generated hologram,” Opt. Express 23, 33893–33901 (2015).
[Crossref]

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

Opt. Lett. (1)

Optical Engineering (1)

H. Niwase, N. Takada, H. Araki, Y. Maeda, M. Fujiwara, H. Nakayama, T. Kakue, T. Shimobaba, and T. Ito, “Real-time electroholography using a multiple-graphics processing unit cluster system with a single spatial light modulator and the infiniband network,” Optical Engineering 55, 55–56 (2016).
[Crossref]

Optics Communications (1)

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,” Optics Communications 393, 107–112 (2017).
[Crossref]

Vision Research (1)

A. van der Schaaf and J. van Hateren, “Modelling the power spectra of natural images: Statistics and information,” Vision Research 36, 2759–2770 (1996).
[Crossref] [PubMed]

Other (3)

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” (SPIE,1993).

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2004), 3rd ed.

K. Wolf, Geometric Optics on Phase Space, Theoretical and Mathematical Physics (SpringerBerlin Heidelberg, 2004).

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Figures (9)

Fig. 1
Fig. 1 Diagram illustrating how distance to a plane will affect the PSF support size. Given the hologram pixel pitch, the corresponding maximum diffraction angle will determine the geometry of the cone of influence shown on the left. The classic WRP method will reduce the support of PSFs w.r.t. the hologram plane, as shown on the right. By placing the WRP in the middle of the point cloud, the average PSF support will be reduced further.
Fig. 2
Fig. 2 Representation of a 1D PSF as a red curve η(x), and the affected Heisenberg boxes for the (a) spatial, (b) orthogonal wavelets and (c) STFT bases. Affected coefficients are colored blue. The total colored surface area is an indication of the sparsity of the transform for a particular signal. Wavelets outperform the spatial (i.e. conventional WRP method), which are in turn outperformed by the STFT. The wavelets are suboptimal because of (1) the lack of frequency symmetry and (2) the inability of distinguishing postive and negative frequencies, indicated by the green boxes.
Fig. 3
Fig. 3 NMSE of various sparsified transforms, keeping the 64 highest-magnitude coefficients. The sparsification is applied on a PSF of a point placed at z going from 0 to 25 mm, sampled with 512 × 512 pixels, on a hologram with a pixel pitch of 6 µm and a wavelength λ =×633 nm.
Fig. 4
Fig. 4 Schematic representation of the spatial version CGH pipeline. Look-up table entries are chosen based on each point’s z-value and are directly added to the WRP.
Fig. 5
Fig. 5 Schematic representation of the STFT version CGH pipeline. Here, the look-up table entries only contain the non-zero STFT coefficients. An entry is chosen not only based on the distance z, but also based on its relative (x, y)-translation w.r.t. the STFT blocks. The amount of affected STFT blocks depends on z. Three partially overlapping (color-coded) entries will only update a small amount of STFT coefficients. In this example, the red PSF has the largest support, followed by the blue and then the green one, according to their respective z. Finally, the blocks are inverse-STFT-transformed before propagation.
Fig. 6
Fig. 6 Because the STFT is not translation-invariant, we need to store STFT coefficients for B × B shifted PSF instances. For every STFT block, we store the 2 × 2 grouped highest-magnitude coefficients and the associated position index.
Fig. 7
Fig. 7 Depiction of views and the Fourier domain of renderings of the Venus CGH using various methods. The top row (a,b,c) display the backpropagated left view, the middle row (d,e,f) the backpropagated right view, and the bottom row (g,h,i) are the Fourier magnitudes. The left column (a,d,g) is the WASABI method, the middle column (b,e,h) is the STFT method, and the right column (c,f,i) is the reference spatial method.
Fig. 8
Fig. 8 Phase of the (sparsified) LUT entries of PSFs with dimensions 320 × 320. (a) reconstructed PSF with 1.6% of largest weighted db4 coefficients, (b) reconstructed PSF with 1.6% of largest STFT coefficients (16 × 16 blocks), (c) original PSF.
Fig. 9
Fig. 9 Quality comparison of the generated Venus hologram using the STFT method and WASABI, w.r.t. the conventional LUT method, for various levels of sparsity.

Tables (1)

Tables Icon

Table 1 Computation times of both tested pipelines, shown for every stage. The spatial version does not have an STFT transform.

Equations (10)

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

U ( x , y ) = j a j e i k r j r j
U ( x , y , z ) = 1 [ [ U ( x , y , 0 ) ] e 2 π i z λ 2 ω x 2 ω y 2 ]
e i k z i λ z exp ( i k x 2 2 z ) η ( x ) = 1 2 π x k x 2 2 z = k x 2 π z = x λ z
NMSE ( R , S ) = j R j S j 2 j R j 2
sin ( θ ) = λ 2 p
w k = 2 | z k | tan ( θ ) = 2 | z k | tan ( sin 1 λ 2 p ) = 2 | z k | λ 4 p 2 λ 2
( [ q x p ] mod B , [ q y p ] mod B , K ( q z z WRP + z max ) 2 z max )
O ( α K z max 2 ) with α = λ 2 4 p 2 λ 2 .
O ( α s B 2 K z max 2 )
O ( s P ) + O ( N log B ) + O ( N log N )

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