Abstract

Phase-only spatial light modulators (SLMs) are widely used in holographic display applications, including holographic image projection (HIP). Most phase computer generated hologram (CGH) calculation algorithms have an iterative structure with a high computational load, and also are prone to speckle noise, as a result of the random phase terms applied on the desired images to mitigate the encoding noise. In this paper, we present a non-iterative algorithm, where simple Discrete Fourier Transform (DFT) relations are exploited to compute phase CGHs that exactly control half of the desired image samples (those on even - or odd - indexed rows - or columns) via a single Fast Fourier Transform (FFT) and trivial arithmetic operations. The encoding noise appearing on the uncontrolled half of the image samples is reduced by the application of structured, non-random initial phase terms so that speckle noise is also kept low. High quality reconstructions are obtained under temporal averaging of several SLM frames. Interlaced video within half of the addressable image area is readily deliverable without frame rate division. Our algorithm provides about 6X and 20X reduction in computational cost compared to IFTA and FIDOC algorithms, respectively. Simulations and experiments verify that the algorithm constitutes a promising option for real-time computation of phase CGHs.

© 2016 Optical Society of America

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References

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2015 (4)

2014 (1)

2012 (1)

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109(20), 203903 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (2)

2009 (1)

2008 (2)

2006 (1)

2005 (1)

2004 (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

2003 (1)

R. Tudela, E. Martin-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A Pure Appl. Opt. 5(5), s189 (2003).
[Crossref]

1999 (1)

1998 (2)

1992 (1)

1990 (1)

1989 (1)

1988 (1)

1987 (1)

1986 (1)

1982 (1)

1980 (1)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19(3), 193297 (1980).
[Crossref]

1978 (2)

1969 (2)

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13(2), 150–155 (1969).
[Crossref]

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13(2), 160–168 (1969).
[Crossref]

1967 (1)

Abookasis, D.

Allebach, J. P.

Arie, A.

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109(20), 203903 (2012).
[Crossref] [PubMed]

Arrizón, V.

Booth, M. J.

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

Brown, B. R.

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13(2), 160–168 (1969).
[Crossref]

Bryngdahl, O.

Buckley, E.

E. Buckley, “Holographic laser projection,” J. Disp. Technol. 7(3), 135–140 (2011).
[Crossref]

E. Buckley, “Holographic projector using one lens,” Opt. Lett. 35(20), 3399–3401 (2010).
[Crossref] [PubMed]

Carnicer, A.

R. Tudela, E. Martin-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A Pure Appl. Opt. 5(5), s189 (2003).
[Crossref]

Chellappan, K. V.

Christmas, J.

Collings, N.

Crossland, W. A.

Davey, A.

Diep, J.

Dolev, I.

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109(20), 203903 (2012).
[Crossref] [PubMed]

Dong, B. Z.

Ducin, I.

Efron, U.

U. Efron, Spatial Light Modulator Technology: Materials, Devices, and Applications (Marcel Dekker, 1994).

Endo, Y.

Epstein, I.

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109(20), 203903 (2012).
[Crossref] [PubMed]

Erden, E.

Fajst, A.

Fienup, J. R.

Georgiou, A.

Goto, Y.

Gu, B. Y.

Guo, Z.

Haist, T.

Hasegawa, S.

Hermerschmidt, A.

G. Lazarev, A. Hermerschmidt, S. Krüger, and S. Osten, “LCOS spatial light modulators: Trends and applications,” in Optical Imaging and Metrology: Advanced Technologies, W. Osten and N. Reingand, eds. (Wiley-VCH, 2012), chap. 1, pp. 130.

Hirayama, R.

Hirsch, P. M.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13(2), 150–155 (1969).
[Crossref]

Hiyama, D.

Honma, S.

Hsu, K. Y.

K. Y. Hsu, H. Y. Li, and D. Psaltis, “Holographic implementation of a fully connected neural network,” in Proceedings of the IEEE (IEEE, 1990) 78(10), pp. 1637–1645.
[Crossref]

Hsueh, C. K.

Ito, T.

Jeziorska-Chapman, A.

Jordan, J. A.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13(2), 150–155 (1969).
[Crossref]

Juvells, I.

R. Tudela, E. Martin-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A Pure Appl. Opt. 5(5), s189 (2003).
[Crossref]

Kakue, T.

Kolodziejczyk, A.

Krüger, S.

G. Lazarev, A. Hermerschmidt, S. Krüger, and S. Osten, “LCOS spatial light modulators: Trends and applications,” in Optical Imaging and Metrology: Advanced Technologies, W. Osten and N. Reingand, eds. (Wiley-VCH, 2012), chap. 1, pp. 130.

Labastida, I.

R. Tudela, E. Martin-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A Pure Appl. Opt. 5(5), s189 (2003).
[Crossref]

Lazarev, G.

G. Lazarev, A. Hermerschmidt, S. Krüger, and S. Osten, “LCOS spatial light modulators: Trends and applications,” in Optical Imaging and Metrology: Advanced Technologies, W. Osten and N. Reingand, eds. (Wiley-VCH, 2012), chap. 1, pp. 130.

Lesem, L. B.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13(2), 150–155 (1969).
[Crossref]

Li, H. Y.

K. Y. Hsu, H. Y. Li, and D. Psaltis, “Holographic implementation of a fully connected neural network,” in Proceedings of the IEEE (IEEE, 1990) 78(10), pp. 1637–1645.
[Crossref]

Li, Q.

Liu, H. K.

Liu, R.

Lohmann, A. W.

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13(2), 160–168 (1969).
[Crossref]

A. W. Lohmann and D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6(10), 1739–1748 (1967).
[Crossref] [PubMed]

Makowski, M.

Martin-Badosa, E.

R. Tudela, E. Martin-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A Pure Appl. Opt. 5(5), s189 (2003).
[Crossref]

Méndez, G.

Mengu, D.

D. Mengu, E. Ulusoy, and H. Urey, “Holographic Image Projection with Phase Only Spatial Light Modulators via Non-Iterative CGH Computation Method,” Digital Holography and Three-Dimensional Imaging Conference, (Optical Society of America, 2015), pp. DT2A–5.

Mok, F.

Moore, J.

Nagahama, Y.

Neil, M. A. A.

Nobukawa, T.

Nomura, T.

Okamoto, A.

Onural, L.

Osten, S.

G. Lazarev, A. Hermerschmidt, S. Krüger, and S. Osten, “LCOS spatial light modulators: Trends and applications,” in Optical Imaging and Metrology: Advanced Technologies, W. Osten and N. Reingand, eds. (Wiley-VCH, 2012), chap. 1, pp. 130.

Ozaktas, H. M.

Paris, D. P.

Psaltis, D.

F. Mok, J. Diep, H. K. Liu, and D. Psaltis, “Real-time computer-generated hologram by means of liquid-crystal television spatial light modulator,” Opt. Lett. 11(11), 748–750 (1986).
[Crossref] [PubMed]

K. Y. Hsu, H. Y. Li, and D. Psaltis, “Holographic implementation of a fully connected neural network,” in Proceedings of the IEEE (IEEE, 1990) 78(10), pp. 1637–1645.
[Crossref]

Reicherter, M.

Rosen, J.

Sánchez-de-La-Llave, D.

Sano, M.

Sawchuk, A. A.

Seldowitz, M. A.

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

Shibukawa, A.

Shimobaba, T.

Siemion, A.

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

Sugie, T.

Suszek, J.

Sweeney, D. W.

Sypek, M.

Tiziani, H. J.

Tomita, A.

Tudela, R.

R. Tudela, E. Martin-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A Pure Appl. Opt. 5(5), s189 (2003).
[Crossref]

Ulusoy, E.

E. Ulusoy, L. Onural, and H. M. Ozaktas, “Synthesis of three-dimensional light fields with binary spatial light modulators,” J. Opt. Soc. Am. A 28, (6) 1211–1223 (2011).
[Crossref]

D. Mengu, E. Ulusoy, and H. Urey, “Holographic Image Projection with Phase Only Spatial Light Modulators via Non-Iterative CGH Computation Method,” Digital Holography and Three-Dimensional Imaging Conference, (Optical Society of America, 2015), pp. DT2A–5.

Urey, H.

K. V. Chellappan, E. Erden, and H. Urey, “Laser-based displays: a review,” Appl. Opt. 49(25), F79–F98 (2010).
[Crossref] [PubMed]

D. Mengu, E. Ulusoy, and H. Urey, “Holographic Image Projection with Phase Only Spatial Light Modulators via Non-Iterative CGH Computation Method,” Digital Holography and Three-Dimensional Imaging Conference, (Optical Society of America, 2015), pp. DT2A–5.

Vallmitjana, S.

R. Tudela, E. Martin-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A Pure Appl. Opt. 5(5), s189 (2003).
[Crossref]

Wagemann, E. U.

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

Wani, Y.

Weissbach, S.

Wilson, T.

Wyrowski, F.

Xing, Y.

Yan, J.

Yang, G. Z.

Appl. Opt. (8)

IBM J. Res. Dev. (2)

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13(2), 150–155 (1969).
[Crossref]

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13(2), 160–168 (1969).
[Crossref]

IEEE T. Image Process. (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

J. Disp. Technol. (1)

E. Buckley, “Holographic laser projection,” J. Disp. Technol. 7(3), 135–140 (2011).
[Crossref]

J. Opt. A Pure Appl. Opt. (2)

R. Tudela, E. Martin-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A Pure Appl. Opt. 5(5), s189 (2003).
[Crossref]

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A Pure Appl. Opt. 10, 035302 (2008).
[Crossref]

J. Opt. Soc. Am. A (5)

Opt. Eng. (1)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19(3), 193297 (1980).
[Crossref]

Opt. Express (6)

Opt. Lett. (6)

Phys. Rev. Lett. (1)

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109(20), 203903 (2012).
[Crossref] [PubMed]

Other (4)

K. Y. Hsu, H. Y. Li, and D. Psaltis, “Holographic implementation of a fully connected neural network,” in Proceedings of the IEEE (IEEE, 1990) 78(10), pp. 1637–1645.
[Crossref]

D. Mengu, E. Ulusoy, and H. Urey, “Holographic Image Projection with Phase Only Spatial Light Modulators via Non-Iterative CGH Computation Method,” Digital Holography and Three-Dimensional Imaging Conference, (Optical Society of America, 2015), pp. DT2A–5.

U. Efron, Spatial Light Modulator Technology: Materials, Devices, and Applications (Marcel Dekker, 1994).

G. Lazarev, A. Hermerschmidt, S. Krüger, and S. Osten, “LCOS spatial light modulators: Trends and applications,” in Optical Imaging and Metrology: Advanced Technologies, W. Osten and N. Reingand, eds. (Wiley-VCH, 2012), chap. 1, pp. 130.

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Figures (9)

Fig. 1
Fig. 1

a) 2-f setup for holographic image projection (HIP) with a spatial light modulator (SLM). b) Decomposition of an arbitrary complex number H ( with | H | 2 ) as the summation of two unit magnitude (phase-only) numbers P 1 and P 2, showing that two phase-only pixels constitute one degree of freedom.

Fig. 2
Fig. 2

Basics of the proposed phase CGH computation method. All signals are discrete. a) Desired field S. b) Ideal full-complex CGH H with two halves named HU and HL. c) Downsampling of S. Only even rows (rows with even index such as k = 0,2,…) are preserved. d) Corresponding CGH, aliased as a result of downsampling. e) Downsampling of S. Only odd rows are preserved. f) Corresponding CGH. h) A phase CGH satisfying PU + PL = HU + HL (|HU + HL| 2), computed as in Fig. 1(b). g) The field generated by h. In accordance with c and d, h generates the same even rows with H. Odd rows however are left uncontrolled and appear noisy. I–j) Counterpart of g–h for perfect reconstruction of odd rows. Phase CGHs exactly control half of the degrees of freedom, as expected.

Fig. 3
Fig. 3

Verification of the basic phase CGH computation method. (a) Desired field S. Only magnitude is shown. Phase is random. (b) Magnitude of ideal full-complex CGH H. (c) Phase CGH satisfying PU + PL = HU + HL, shown as a gray scale image. (d) Reconstruction of c and its downsampled versions. (e) Counterpart of c–d for phase CGH satisfying PUPL = HUHL.

Fig. 4
Fig. 4

Examined HIP scenarios. (a) Desired image is specified over the entire central diffraction order (CDO). Phase freedom on the image plane is exploited to decrease encoding error. (b) Desired image is specified over half of the CDO. The unused part of CDO is reserved for encoding noise.

Fig. 5
Fig. 5

Initial phase terms (Quadratic Phase Functions - QPF) applied on the desired images to obtain a smooth energy distribution on the SLM plane. Desired image occupies (a) the entire CDO, (b) half of the CDO. In both cases, desired image is split into two parts with almost equal energies E1 and E2. In general, the two parts have different sizes. The upper (lower) part is mapped to upper (lower) half of the SLM via a suitable QPF term, which actually acts as a lens term that locally adjusts the ray directions for the mapping. In this way, image energy is distributed uniformly on the SLM, enabling a low encoding noise. The middle region of the SLM is left relatively empty to avoid diffraction artifacts during the calculation of phase CGHs.

Fig. 6
Fig. 6

Assignment of P 1 and P 2 to PU and PL in (a) Case A (b) Case B, where pixels on a checkerboard pattern are flipped with respect to Case A.

Fig. 7
Fig. 7

Simulation results for Case A. a) Desired image specified within the entire CDO. b,c) Ideal full-complex CGHs respectively for the row and column cases, obtained by the application of the QPF terms in Fig. 5(a). d,e) Reconstructions by phase CGHs designed respectively for even rows and even columns. Reconstructions by phase CGHs for odd rows and columns look similar. f) Time averaged reconstruction by two phase CGHs designed for even and odd rows. g) Time averaged reconstruction by two phase CGHs designed for even and odd columns. In f and g, two SLM frames are required to form each video frame. h) The average of f and g, requiring 4 SLM frames per video frame. In d and e, there are missing pixels and artifacts, hence reconstruction error is high. Note also that the artifacts in d and e appear at different locations. In f and g, information is completed, but artifacts appear persistent since only reconstructions by row or column type CGHs are averaged. In h, information is complete and artifacts are relatively suppressed, hence best image quality is achieved.

Fig. 8
Fig. 8

Simulation results of Case B. (a) Desired image within the CDO. Dark regions are reserved for encoding noise. (b) Corresponding ideal full-complex CGH, obtained by the application of the QPF terms in Fig. 5(b). (c) Reconstruction by a phase CGH designed for even columns. Encoding noise mainly appears in the unused part of CDO, and odd columns within the image area appear as missing, rather than noisy, similar to that in interlaced video format. (d) Zoom-in version of c. (e) Average of the reconstructions of two phase CGHs for even and odd columns. (f) Zoom-in version of (e). In e and f, full information is restored, and speckle and encoding noise is quite low.

Fig. 9
Fig. 9

a) Experimental HIP setup. Camera is placed slightly off-axis to avoid the unmodulated beam of the SLM. b) HIP Case A, average of reconstructions of four phase CGHs. Experimental version of Fig. 7(f). c) HIP Case B, average of reconstructions of two phase CGHs. Experimental version of Fig. 8(e). The lower quality in comparison to simulation results is due to SLM pixel cross-talk and flicker effects. d) HIP Case A obtained with IFTA algorithm, which makes the speckle reduction ability of our algorithm quite evident.

Tables (2)

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Table 1 Performance of the proposed HIP algorithm for Case A. The average Mean Squared Error (MSE) and Structured Similarity Index Measure (SSIM) values of a set of desired images is reported.

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Table 2 IFTA configurations that achieve the MSE performance of the last row of Table 1.

Equations (4)

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S k , l = DFT { H m , n } .
P 1 = e j ( H α )
P 2 = e j ( H + α )
α = arccos ( | H | 2 ) .

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