Abstract

We show that the amplitude and phase information from a two-dimensional complex field can be synthesized from a phase-only optical element with micrometric resolution. The principle of the method is based on the combination of two spatially sampled phase elements by using a low-pass filter at the Fourier plane of a 4f optical system. The proposed encoding technique was theoretically demonstrated, as well as experimentally validated with the help of a phase-only spatial light modulator for phase encoding, a conventional CMOS camera to measure the amplitude of the complex field, and a Shack–Hartmann wavefront sensor to determine its phase.

© 2014 Optical Society of America

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2013 (3)

2012 (3)

2011 (1)

2007 (2)

2006 (1)

2003 (2)

2001 (1)

2000 (2)

1999 (1)

1994 (2)

1993 (1)

1990 (1)

1985 (1)

1978 (1)

1971 (1)

Andilla, J.

Arrizón, V.

Awwal, A. A. S.

Belyi, V.

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[CrossRef]

Bent, N.

Bianco, V.

Birch, P.

Bolduc, E.

Boyd, R. W.

Budgett, D.

Campos, J.

Carrada, R.

Chatwin, C.

Choi, S.

Cohn, R. W.

Cottrell, D. M.

Davis, J. A.

Dudley, A.

A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, Opt. Commun. 285, 5 (2012).
[CrossRef]

Erdei, G.

Ferraro, P.

Finizio, A.

Forbes, A.

A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, Opt. Commun. 285, 5 (2012).
[CrossRef]

Fütterer, G.

Glückstad, J.

González, L. A.

Göröcs, Z.

Häussler, R.

Horner, J. L.

Hsieh, W.-Y.

Hsueh, C. K.

Jahan, S. R.

Javidi, B.

Jones, A. L.

Kanbayashi, Y.

Karim, M. A.

Karimi, E.

Kato, H.

Kettinger, Á.

Khilo, N.

A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, Opt. Commun. 285, 5 (2012).
[CrossRef]

Kim, H.

Kirk, J. P.

Koppa, P.

Leaird, D. E.

Lee, H.-S.

Leger, J. R.

Leister, N.

Liang, M.

Liu, J.-P.

Lórincz, E.

Márquez, A.

Martín-Badosa, E.

Memmolo, P.

Mogensen, P. C.

Montes-Usategui, M.

Moreno, I.

Oudin, S.

Paturzo, M.

Pleguezuelos, E.

Poon, T.-C.

Reichelt, S.

Reitze, D. H.

Reményi, J.

Ropot, P.

A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, Opt. Commun. 285, 5 (2012).
[CrossRef]

Ruiz, U.

Santamato, E.

Sarkadi, T.

Sawchuk, A. A.

Song, H.

Sung, G.

Tsang, P.

Ujhelyi, F.

Usukura, N.

Vasilyeu, R.

A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, Opt. Commun. 285, 5 (2012).
[CrossRef]

Weiner, A. M.

Won, K.

Young, R.

Yzuel, M. J.

Appl. Opt. (8)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, Opt. Commun. 285, 5 (2012).
[CrossRef]

Opt. Express (2)

Opt. Lett. (9)

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Figures (3)

Fig. 1.
Fig. 1.

Checkerboard patterns obtained with functions (a) M1(x,y) and (b) M2(x,y), respectively.

Fig. 2.
Fig. 2.

Schematic setup used to measure the amplitude and phase of a complex field.

Fig. 3.
Fig. 3.

Experimental results. (a), (e) Initial amplitude and (c), (g) phase of the complex field, and corresponding (b), (f) amplitude and (d), (h) phase measured. All data are shown within a square window of [3mm×3mm].

Equations (11)

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

M1,2(x,y)=12n=m=Λ1,2(n,m)ei2πnxpei2πmyp,
Λ1,2(n,m)cos[π(n±m)2]sinc(n2)sinc(m2).
M1(x,y)eiθ(x,y)+M2(x,y)eiϑ(x,y)=eiα(x,y),
α(x,y)=M1(x,y)θ(x,y)+M2(x,y)ϑ(x,y).
H(u,v)=F{eiα(x,y)}eiα(x,y)ei2π(xx+yy)fλdxdy.
H(u,v)=12[H1(u,v)+H2(u,v)],
H1(u,v)=n=m=Λ1(n,m)Ψ(unp,vmp),
H2(u,v)=n=m=Λ2(n,m)Ω(unp,vmp).
H(u,v)P(u,v)=12F{U(x,y)},
F{U(x,y)}Ψ(u,v)+Ω(u,v).
F{rect(x/ε,y/ε)}sin(πpMagx)πxsin(πpMagy)πy.

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