Abstract

Two methods to achieve super-resolution with complex masks displayed in one-phase-only liquid crystal display (LCD) are described. The first method decomposes the complex mask into two phase-only elements with a posterior recombination using an interferometer, and the second method simultaneously encodes the amplitude and the phase by modulating the amplitude of the carrier phase. Experimental results are presented using a liquid crystal on silicon spatial light modulator under reflection.

© 2013 Optical Society of America

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References

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2013 (1)

Y. Calderón-Hermosillo, N. Alcalá Ochoa, E. N. Arias, and J. García-Márquez, Opt. Lasers Eng. 51, 610 (2013).

2012 (1)

2007 (1)

2006 (1)

2005 (1)

1999 (1)

1998 (1)

T. R. M. Sales, Phys. Rev. Lett. 81, 3844 (1998).
[CrossRef]

1992 (1)

1978 (1)

1952 (1)

G. T. di Francia, Nuovo Cimento Suppl. 9, 426 (1952).
[CrossRef]

Alcalá Ochoa, N.

Y. Calderón-Hermosillo, N. Alcalá Ochoa, E. N. Arias, and J. García-Márquez, Opt. Lasers Eng. 51, 610 (2013).

Arias, E. N.

Y. Calderón-Hermosillo, N. Alcalá Ochoa, E. N. Arias, and J. García-Márquez, Opt. Lasers Eng. 51, 610 (2013).

Arrizón, V.

Cagigal, M. P.

Calderón-Hermosillo, Y.

Y. Calderón-Hermosillo, N. Alcalá Ochoa, E. N. Arias, and J. García-Márquez, Opt. Lasers Eng. 51, 610 (2013).

Campos, J.

Canales, V. F.

Carrada, R.

Cottrell, D. M.

Davis, J. A.

di Francia, G. T.

G. T. di Francia, Nuovo Cimento Suppl. 9, 426 (1952).
[CrossRef]

Fütterer, G.

García-Márquez, J.

Y. Calderón-Hermosillo, N. Alcalá Ochoa, E. N. Arias, and J. García-Márquez, Opt. Lasers Eng. 51, 610 (2013).

González, L. A.

Gregory, D. A.

Gundu, P. N.

Hack, E.

Häussler, R.

Hueh, C. K.

Kanbayashi, Y.

Kato, H.

Kirsch, J. C.

Leister, N.

Moreno, I.

Rastogi, P.

Reichelt, S.

Ruiz, U.

Sales, T. R. M.

T. R. M. Sales, Phys. Rev. Lett. 81, 3844 (1998).
[CrossRef]

Sawchuk, A. A.

Tam, E. C.

Usukura, N.

Yzuel, M. J.

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Figures (6)

Fig. 1.
Fig. 1.

Phase decomposition of a complex mask with carrier terms included. From method one (a) φ1(x,y) and (b) φ2(x,y); (c) with the Davis method and (d) with the Arrizón method.

Fig. 2.
Fig. 2.

Optical setup for demonstrating super-resolution via the decomposition of a complex mask into two phase-only masks (method one).

Fig. 3.
Fig. 3.

PSF reduction obtained using method one (dotted line). The PSF corresponding to a free pupil is shown for comparison purposes (continuous line).

Fig. 4.
Fig. 4.

PSF reduction obtained using methods from Davis (dashed) and Arrizón (dotted). The PSF corresponding to a free pupil is shown with the continuous line.

Fig. 5.
Fig. 5.

Experimental PSFs obtained from method one. (a) Free pupil. (b) Superposition.

Fig. 6.
Fig. 6.

Experimental PSFs obtained from method two. (a) The free pupil. (b) Davis method. (c) Arrizón method.

Equations (13)

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h(x,y)=1/2exp[i(φ+ψ)]+1/2exp[i(φψ)],
φ1,2(x,y)=mod{[φ(x,y)±arccosA(x,y)],2π}.
H(u,v)=F[h1(u,v)+h2(u,v)]=H1(u,v)+H2(u,v),
g1,2(x,y)=exp{iL1,2[φ1,2(x,y)+2π(a1,2x+b1,2y)]},
eizφ=n=Sn(z)einφ,
Sn(z)=exp[i(nz)π]sinc(nz),
eig1,2(x,y)=n=Sn(L1,2)ein[φ1,2(x,y)+2πa1,2x+2πb1,2y].
S1(L1,2)exp[iφ1,2(x,y)]exp[i2π(a1,2x+b1,2y)].
S1(L1,2)H1,2(ua1,2,wb1,2),
sinc[1M(x,y)]exp[iϕ(x,y)]exp{iπ[1M(x,y)]}C(x,y),
eizcosθ=n=Jn(z)einθ,
n=Jn[M(x,y)]exp{in[ϕ(x,y)+2π(ax+by)]}
J1[M(x,y)]exp[iϕ(x,y)]exp[i(2πax+2πby)].

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