Abstract

A new technique for encoding the amplitude and phase of diffracted fields in digital holography is proposed. It is based on a random spatial multiplexing of two phase-only diffractive patterns. The first one is the phase information of the intended pattern, while the second one is a diverging optical element whose purpose is the control of the amplitude. A random number determines the choice between these two diffractive patterns at each pixel, and the amplitude information of the desired field governs its discrimination threshold. This proposed technique is computationally fast and does not require iterative methods, and the complex field reconstruction appears on axis. We experimentally demonstrate this new encoding technique with holograms implemented onto a flicker-free phase-only spatial light modulator (SLM), which allows the axial generation of such holograms. The experimental verification includes the phase measurement of generated patterns with a phase-shifting polarization interferometer implemented in the same experimental setup.

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

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References

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2017 (1)

J. L. Martínez, P. García-Martínez, and I. Moreno, “Microscope system with on axis programmable Fourier transform filtering,” Opt. Lasers Eng. 89, 116–122 (2017).
[Crossref]

2016 (2)

2015 (4)

2014 (1)

2013 (3)

2012 (1)

2011 (1)

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5(1), 81–101 (2011).
[Crossref]

2010 (2)

E. J. Fernández, P. M. Prieto, and P. Artal, “Adaptive optics binocular visual simulator to study stereopsis in the presence of aberrations,” J. Opt. Soc. Am. A 27(11), A48–A55 (2010).
[Crossref] [PubMed]

I. Moreno, A. Martínez-García, L. Nieradko, J. Albero, and C. Gorecki, “Low cost production of computer-generated holograms: from design to optical evaluation,” J. Eur. Opt. Soc. Rapid. Pub. 5, 10011 (2010).
[Crossref]

2009 (2)

2008 (3)

I. Moreno, A. Lizana, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express 16(21), 16711–16722 (2008).
[Crossref] [PubMed]

A. Hermeschmidt, S. Krüger, T. Haist, S. Zwick, M. Warber, and W. Osten, “Holographic optical tweezers with real-time hologram calculation using a phase-only modulating LCOS-based SLM at 1064 nm,” Proc. SPIE 6905, 690508 (2008).
[Crossref]

A. Martínez, I. Moreno, and M. M. Sánchez-López, “Comparative analysis of time and spatially multiplexed diffractive optical elements in a ferroelectric liquid crystal display,” Jpn. J. Appl. Phys. 47(3), 1589–1594 (2008).
[Crossref]

2006 (1)

2003 (2)

2002 (1)

2000 (2)

1999 (1)

1997 (1)

F. Fetthauer, C. Stroot, and O. Bryngdahl, “On the quantization of holograms with the iterative Fourier transform algorithm,” Opt. Commun. 136(1-2), 7–10 (1997).
[Crossref]

1996 (2)

1995 (2)

J. Amako, H. Miura, and T. Sonehara, “Speckle-noise reduction on kinoform reconstruction using a phase-only spatial light modulator,” Appl. Opt. 34(17), 3165–3171 (1995).
[Crossref] [PubMed]

D. Roberge, L. G. Neto, and Y. Sheng, “Full-complex modulation spatial light modulator using two coupled-mode modulation liquid crystal televisions,” Proc. SPIE 2490, 407–415 (1995).
[Crossref]

1994 (2)

1993 (1)

1990 (1)

1988 (1)

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 349–393 (1988).
[Crossref]

1978 (1)

1971 (1)

J. P. Kirk and A. L. Jones, “Phase-only complex-valued spatial filter,” J. Opt. Soc. Am 61(8), 1023–1028 (1971).
[Crossref]

1970 (2)

1969 (1)

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

1954 (1)

Aguirre-Olivas, D.

Albero, J.

I. Moreno, A. Martínez-García, L. Nieradko, J. Albero, and C. Gorecki, “Low cost production of computer-generated holograms: from design to optical evaluation,” J. Eur. Opt. Soc. Rapid. Pub. 5, 10011 (2010).
[Crossref]

Alieva, T.

Amako, J.

Ando, T.

Arnold, A. S.

Arrizón, V.

Artal, P.

Bandres, M. A.

Bentley, J. B.

Bernet, S.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5(1), 81–101 (2011).
[Crossref]

Birch, P. M.

Brown, B. R.

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

Bryngdahl, O.

F. Fetthauer, C. Stroot, and O. Bryngdahl, “On the quantization of holograms with the iterative Fourier transform algorithm,” Opt. Commun. 136(1-2), 7–10 (1997).
[Crossref]

Budgett, D.

Burckhardt, C. B.

Burger, L.

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
[Crossref] [PubMed]

Calvo, M. L.

Campos, J.

Chang, C.

Chatwin, C.

Chen, J.

Clark, T. W.

Cohn, R. W.

Cottrell, D. M.

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 349–393 (1988).
[Crossref]

Daley, R. C.

Davis, J. A.

Fernández, E.

Fernández, E. J.

Fetthauer, F.

F. Fetthauer, C. Stroot, and O. Bryngdahl, “On the quantization of holograms with the iterative Fourier transform algorithm,” Opt. Commun. 136(1-2), 7–10 (1997).
[Crossref]

Forbes, A.

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
[Crossref] [PubMed]

Franke-Arnold, S.

Fukuchi, N.

Fütterer, G.

García-Martínez, P.

J. L. Martínez, P. García-Martínez, and I. Moreno, “Microscope system with on axis programmable Fourier transform filtering,” Opt. Lasers Eng. 89, 116–122 (2017).
[Crossref]

Gorecki, C.

I. Moreno, A. Martínez-García, L. Nieradko, J. Albero, and C. Gorecki, “Low cost production of computer-generated holograms: from design to optical evaluation,” J. Eur. Opt. Soc. Rapid. Pub. 5, 10011 (2010).
[Crossref]

Guertin, J.

Gutiérrez-Vega, J. C.

Haist, T.

T. Haist and W. Osten, “Holography using pixelated spatial light modulators—part 1: theory and basic considerations,” J. Micro/Nanolith. MEMS MOEMS 14(4), 041310 (2015).
[Crossref]

A. Hermeschmidt, S. Krüger, T. Haist, S. Zwick, M. Warber, and W. Osten, “Holographic optical tweezers with real-time hologram calculation using a phase-only modulating LCOS-based SLM at 1064 nm,” Proc. SPIE 6905, 690508 (2008).
[Crossref]

Hassebrook, L. G.

Häussler, R.

Hermeschmidt, A.

A. Hermeschmidt, S. Krüger, T. Haist, S. Zwick, M. Warber, and W. Osten, “Holographic optical tweezers with real-time hologram calculation using a phase-only modulating LCOS-based SLM at 1064 nm,” Proc. SPIE 6905, 690508 (2008).
[Crossref]

Hsueh, C. K.

Hussain, A.

Iemmi, C.

Inoue, T.

Jesacher, A.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5(1), 81–101 (2011).
[Crossref]

Jia, J.

Jones, A. L.

J. P. Kirk and A. L. Jones, “Phase-only complex-valued spatial filter,” J. Opt. Soc. Am 61(8), 1023–1028 (1971).
[Crossref]

Kanbayashi, Y.

Kato, H.

Kirk, J. P.

J. P. Kirk and A. L. Jones, “Phase-only complex-valued spatial filter,” J. Opt. Soc. Am 61(8), 1023–1028 (1971).
[Crossref]

Krüger, S.

A. Hermeschmidt, S. Krüger, T. Haist, S. Zwick, M. Warber, and W. Osten, “Holographic optical tweezers with real-time hologram calculation using a phase-only modulating LCOS-based SLM at 1064 nm,” Proc. SPIE 6905, 690508 (2008).
[Crossref]

Lancis, J.

Lee, W. H.

Lei, W.

Leister, N.

Lhamon, M. E.

Li, X.

Liang, M.

Litvin, I.

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
[Crossref] [PubMed]

Liu, J.

Lizana, A.

Lohmann, A. W.

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

Márquez, A.

Martínez, A.

A. Martínez, I. Moreno, and M. M. Sánchez-López, “Comparative analysis of time and spatially multiplexed diffractive optical elements in a ferroelectric liquid crystal display,” Jpn. J. Appl. Phys. 47(3), 1589–1594 (2008).
[Crossref]

Martínez, J. L.

J. L. Martínez, P. García-Martínez, and I. Moreno, “Microscope system with on axis programmable Fourier transform filtering,” Opt. Lasers Eng. 89, 116–122 (2017).
[Crossref]

A. Hussain, J. L. Martínez, A. Lizana, and J. Campos, “Super resolution imaging achieved by using on-axis interferometry based on a spatial light modulator,” Opt. Express 21(8), 9615–9623 (2013).
[Crossref] [PubMed]

Martínez-García, A.

I. Moreno, A. Martínez-García, L. Nieradko, J. Albero, and C. Gorecki, “Low cost production of computer-generated holograms: from design to optical evaluation,” J. Eur. Opt. Soc. Rapid. Pub. 5, 10011 (2010).
[Crossref]

Matsumoto, N.

Maurer, C.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5(1), 81–101 (2011).
[Crossref]

McLeod, J. H.

Mellado-Villaseñor, G.

Mendoza-Yero, O.

Mínguez-Vega, G.

Miura, H.

Moreno, I.

J. L. Martínez, P. García-Martínez, and I. Moreno, “Microscope system with on axis programmable Fourier transform filtering,” Opt. Lasers Eng. 89, 116–122 (2017).
[Crossref]

I. Moreno, A. Martínez-García, L. Nieradko, J. Albero, and C. Gorecki, “Low cost production of computer-generated holograms: from design to optical evaluation,” J. Eur. Opt. Soc. Rapid. Pub. 5, 10011 (2010).
[Crossref]

A. Martínez, I. Moreno, and M. M. Sánchez-López, “Comparative analysis of time and spatially multiplexed diffractive optical elements in a ferroelectric liquid crystal display,” Jpn. J. Appl. Phys. 47(3), 1589–1594 (2008).
[Crossref]

I. Moreno, A. Lizana, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express 16(21), 16711–16722 (2008).
[Crossref] [PubMed]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38(23), 5004–5013 (1999).
[Crossref] [PubMed]

Neto, L. G.

D. Roberge, L. G. Neto, and Y. Sheng, “Full-complex modulation spatial light modulator using two coupled-mode modulation liquid crystal televisions,” Proc. SPIE 2490, 407–415 (1995).
[Crossref]

Ngcobo, S.

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
[Crossref] [PubMed]

Nieradko, L.

I. Moreno, A. Martínez-García, L. Nieradko, J. Albero, and C. Gorecki, “Low cost production of computer-generated holograms: from design to optical evaluation,” J. Eur. Opt. Soc. Rapid. Pub. 5, 10011 (2010).
[Crossref]

Offer, R. F.

Ohtake, Y.

Osten, W.

T. Haist and W. Osten, “Holography using pixelated spatial light modulators—part 1: theory and basic considerations,” J. Micro/Nanolith. MEMS MOEMS 14(4), 041310 (2015).
[Crossref]

A. Hermeschmidt, S. Krüger, T. Haist, S. Zwick, M. Warber, and W. Osten, “Holographic optical tweezers with real-time hologram calculation using a phase-only modulating LCOS-based SLM at 1064 nm,” Proc. SPIE 6905, 690508 (2008).
[Crossref]

Pan, Y.

Prieto, P. M.

Qi, Y.

Radwell, N.

Reichelt, S.

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5(1), 81–101 (2011).
[Crossref]

Roberge, D.

D. Roberge, L. G. Neto, and Y. Sheng, “Full-complex modulation spatial light modulator using two coupled-mode modulation liquid crystal televisions,” Proc. SPIE 2490, 407–415 (1995).
[Crossref]

Rodrigo, J. A.

Sánchez-de-la-Llave, D.

Sánchez-López, M. M.

A. Martínez, I. Moreno, and M. M. Sánchez-López, “Comparative analysis of time and spatially multiplexed diffractive optical elements in a ferroelectric liquid crystal display,” Jpn. J. Appl. Phys. 47(3), 1589–1594 (2008).
[Crossref]

Sawchuk, A. A.

Sheng, Y.

D. Roberge, L. G. Neto, and Y. Sheng, “Full-complex modulation spatial light modulator using two coupled-mode modulation liquid crystal televisions,” Proc. SPIE 2490, 407–415 (1995).
[Crossref]

Sonehara, T.

Stroot, C.

F. Fetthauer, C. Stroot, and O. Bryngdahl, “On the quantization of holograms with the iterative Fourier transform algorithm,” Opt. Commun. 136(1-2), 7–10 (1997).
[Crossref]

Usukura, N.

Wang, J.

L. Zhu and J. Wang, “Arbitrary manipulation of spatial amplitude and phase using phase-only spatial light modulators,” Sci. Rep. 4(1), 7441 (2015).
[Crossref] [PubMed]

Wang, Y.

Warber, M.

A. Hermeschmidt, S. Krüger, T. Haist, S. Zwick, M. Warber, and W. Osten, “Holographic optical tweezers with real-time hologram calculation using a phase-only modulating LCOS-based SLM at 1064 nm,” Proc. SPIE 6905, 690508 (2008).
[Crossref]

Weiner, A. M.

A. M. Weiner, “Femtosecond pulse shaping using spatial Light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000).
[Crossref]

Wyrowski, F.

Xia, J.

Yang, L.

Yang, Z.

Young, R.

Yzuel, M. J.

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Supplementary Material (1)

NameDescription
» Visualization 1       Propagation of complex Hermite-Gauss 11 mode (HG11) generated by the proposed random encoding masks. The field propagates from 0m to 4m, and it is calculated for creating the minimum waist at 2m (as it can be checked in the simulation). The undesire

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Figures (9)

Fig. 1
Fig. 1 (a) Amplitude distribution of the desired reconstruction. (b) Random phase distribution added to spread its Fourier transform. Corresponding (c) amplitude A(u) and (d) phase ϕ(u) = arg{F(u)}, of its Fourier transform. (e) 160 cycle negative axicon used as the diverging element D(u). (f) A realization of the corresponding random multiplexed phase mask M(u).
Fig. 2
Fig. 2 Hologram reconstructions (the intensity has been equally oversaturated in them all to clearly appreciate the noise features) for (a) the phase-only simple hologram shown in Fig. 1(d), (b) a single realization of the random multiplexed phase hologram given at Fig. 1(f), and (c) the average of 10 different realizations of the random multiplexed phase hologram.
Fig. 3
Fig. 3 (a) SNR and (b) diffraction efficiency for the proposed method in the case of the “Ñ” image reconstruction. Data points are obtained by sweeping both mean value μ and deviation σ of signal rnd(u) in the interval [0,1].
Fig. 4
Fig. 4 Schematic representation of the optical system used to test the designed masks.
Fig. 5
Fig. 5 (a) Experimental verification of hologram reconstruction plane. (b) Central detail of the diffracted field. (c) Distorted reconstruction happening when amplitude and phase corresponding to different hologram realizations are bundled together into a single mask. (d) Average integration of 10 realizations. (e) Average integration of 10 different realizations of a simple phase-only hologram.
Fig. 6
Fig. 6 Experimental reconstruction of different HG modes with indices pq indicated on the left. From left to right, columns show the expected intensity and phase distributions, and the corresponding measured intensity and phase distributions. The four remaining columns to the right represent phase-shifted interferograms used to retrieve phase patterns of each mode.
Fig. 7
Fig. 7 Experimental reconstruction of different LG modes with indices pl indicated on the left. From left to right, columns show the expected intensity and phase distributions, and the corresponding measured intensity and phase distributions. The four remaining columns to the right represent phase-shifted interferograms used to retrieve phase patterns of each mode.
Fig. 8
Fig. 8 (a) Graphic of possible values of the random number rnd(u). The probability of having A(u)>rnd(u), i.e., the probability of R(u) = 1 is represented by the number of steps over the shadowed area (including the ground or ‘0’ step). (b) Traces of a given realization of 1024 samples of binary multiplexing mask R(u) (first, blue trace), amplitude pattern A(u) (second, red trace), and NA(u) (third, green trace), and (c) averaged and normalized (30-level) histogram for 10 realizations of NA(u).
Fig. 9
Fig. 9 In left column, images corresponding to: (a) pixelated structure of NA(u) (pixel size P = 8 and Ns = 32x32 samples), (b) autocorrelation RNN(ξ), and (c) spectral power density |ÑA(ν)|2, (d) modulus of diffraction spectrum ÑA(ν). In the right column: (e) cross section of the central part of autocorrelation function, exhibiting a triangular peak shape with maximum value of 11099.10, and (f) histogram representing the phase value occurrence of ÑA(ν).

Tables (1)

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Table 1 Comparison of SNR, efficiency and computation time with different approaches.

Equations (25)

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T( u )=A( u )exp[ iφ( u ) ]=A( u )F( u ),
M( u )=R( u )F( u )+ R ¯ ( u )D( u ),
R( u )={ 1if A( u )>rnd( u ) 0if A( u )rnd( u ) ,
E{ M( u ) }=Ε{ R( u ) }F( u )+Ε{ R ¯ ( u ) }D( u )=A( u )exp[ iφ( u ) ]+[ 1A( u ) ]D( u ).
R( u )=A( u )+ N A ( u ),
M( u )=A( u )F( u )+ N A ( u )F( u )+[ 1A( u ) ]D( u ) N A ( u )D( u ) =T( u )+[ A ¯ ( u ) N A ( u ) ]D( u )+ N A ( u )F( u ).
N ˜ A ( ν ) WP 6 sinc( νP )exp( i2π·rnd( ν ) ),
BG( ν )= N ˜ A ( ν ) F ˜ ( ν )= WP 6 sinc( νP )exp( i2π·rnd( ν ) ) F ˜ ( ν ),
SNR=10log( d ij 2 [ d ij β r ij ] 2 ),
β= r ij d ij / | r ij | 2 ,
EFFIC= d ij r ij 2 d ij 2 r ij 2 ,
f p,q ( x,y, w 0 )= H p ( 2 w 0 x ) H q ( 2 w 0 y ) e ( x 2 + y 2 )/ w 0 2 ,
f p,l ( r,ϕ, w 0 )= ( r 2 w 0 ) | l | L p | l | ( 2 r 2 w 0 2 ) e ( r/ w 0 ) 2 e ilφ ,
P[ R( u )=1 ]P[ rnd( u )<A( u ) ]= n N A( u ),
P[ R( u )=0 ]= Nn N 1A( u ).
E{ R( u ) }=1·P[ R( u )=1 ]+0·P[ R( u )=0 ]A( u ),
P[ N A ( u )= n N ]=P[ R( u )=0|A( u )=n/N ]= N( 1A( u ) ) N 2 = N( 1 n N ) N 2 .
P[ N A ( u )= n N ]=P[ R( u )=1|A( u )=1 n N ]= NA( u ) N 2 = N( 1 n N ) N 2 ,
P[ N A ( u )= n N ]= 1| n N | N ,n[ N,N ].
P[ N A ( u )=x ]= lim N ( 1| n N | N )=( 1| x | )dx f NA ( x )dx.
μ NA = 1 1 x( 1| x | )dx 0.
σ NA 2 = 1 1 ( x μ NA ) 2 ( 1| x | )dx 1 6 .
R NN ( ξ )= N A ( u ) N A ( u+ξ )du W σ NA 2 Λ P ( ξ/ 2P ),
| N ˜ A ( ν ) | 2 =FT{ R NN ( ξ ) } WP 6 sin c 2 ( νP ) WP 6 ,P0.
N ˜ A ( ν ) WP 6 sinc( νP )exp( i2π·rnd( ν ) ).

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