Abstract

By using previously established methods based on linear programming (MLP), we design and fabricate two types of diffractive superresolution element (DSE). The structure parameters and superresolution performances of the fabricated DSEs are tested. The test results agree well with the design results and are applicable to a writable or a read-only optical disk. Thus the application validity of the MLP is experimentally verified.

© 2006 Optical Society of America

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References

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  13. H. Liu, Y. Yan, D. Yi, and G. Jin, "Theories for the design of a hybrid refractive-diffractive superresolution lens with high numerical aperture," J. Opt. Soc. Am. A 20, 913-924 (2003).
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  14. H. Liu, Y. Yan, and G. Jin, "Design theories and performance limits of diffractive superresolution elements with the highest sidelobe suppressed," J. Opt. Soc. Am. A 22, 828-838 (2005).
    [CrossRef]
  15. H. Liu, "Investigations of design methods of diffractive optical elements to implement optical superresolution," Ph.D. dissertation (Tsinghua University, Beijing, 2004), Chap. 2.
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    [CrossRef]
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2005 (1)

2003 (2)

H. Liu, Y. Yan, D. Yi, and G. Jin, "Theories for the design of a hybrid refractive-diffractive superresolution lens with high numerical aperture," J. Opt. Soc. Am. A 20, 913-924 (2003).
[CrossRef]

N. Wei, M. Gong, and R. Cui, "Numerical solution of sidelobe intensity for phase-shifting apodizers," Jpn. J. Appl. Phys. 42, 104-108 (2003).
[CrossRef]

2002 (2)

2000 (2)

1998 (1)

1997 (1)

1986 (1)

1984 (1)

1982 (1)

1980 (1)

R. Boivin and A. Boivin, "Optimized amplitude filtering for superresolution over a restricted field: I. Achievement of maximum central irradiance under an energy constraint," Opt. Acta 27, 587-610 (1980).
[CrossRef]

Akduman, I.

Bertero, M.

Blyth, T. S.

T. S. Blyth and E. F. Robertson, Further Linear Algebra (Springer, 2002), Chap. 1.
[CrossRef]

Boivin, A.

R. Boivin and A. Boivin, "Optimized amplitude filtering for superresolution over a restricted field: I. Achievement of maximum central irradiance under an energy constraint," Opt. Acta 27, 587-610 (1980).
[CrossRef]

Boivin, R.

R. Boivin and A. Boivin, "Optimized amplitude filtering for superresolution over a restricted field: I. Achievement of maximum central irradiance under an energy constraint," Opt. Acta 27, 587-610 (1980).
[CrossRef]

Brand, U.

Caballero, M. T.

Cox, I. J.

Cui, R.

N. Wei, M. Gong, and R. Cui, "Numerical solution of sidelobe intensity for phase-shifting apodizers," Jpn. J. Appl. Phys. 42, 104-108 (2003).
[CrossRef]

Elsgolc, L. E.

L. E. Elsgolc, Calculus of Variations (Pergamon, 1961), Chap. I.

Gong, M.

N. Wei, M. Gong, and R. Cui, "Numerical solution of sidelobe intensity for phase-shifting apodizers," Jpn. J. Appl. Phys. 42, 104-108 (2003).
[CrossRef]

Grochmalicki, J.

Hegedus, Z. S.

Hester, G.

Jin, G.

Juskaitis, R.

Laczik, Z. J.

Liu, H.

Martinez-Corral, M.

Morris, G. M.

Neil, M. A. A.

Pike, R.

Robertson, E. F.

T. S. Blyth and E. F. Robertson, Further Linear Algebra (Springer, 2002), Chap. 1.
[CrossRef]

Sales, T. R. M.

Sarafis, V.

Sheppard, C. J. R.

Stelzer, E. H. K.

Strayer, J. K.

J. K. Strayer, Linear Programming and Its Applications (Springer-Verlag, 1989), Chap. 2.
[CrossRef]

Swoger, J.

Tan, Q.

Wei, N.

N. Wei, M. Gong, and R. Cui, "Numerical solution of sidelobe intensity for phase-shifting apodizers," Jpn. J. Appl. Phys. 42, 104-108 (2003).
[CrossRef]

Wilson, T.

Wu, M.

G. Jin, Y. Yan, and M. Wu, Binary Optics (National Defense Industry Press, Beijing, 1998), Chap. 9.1.

Yan, Y.

Yi, D.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (6)

Jpn. J. Appl. Phys. (1)

N. Wei, M. Gong, and R. Cui, "Numerical solution of sidelobe intensity for phase-shifting apodizers," Jpn. J. Appl. Phys. 42, 104-108 (2003).
[CrossRef]

Opt. Acta (1)

R. Boivin and A. Boivin, "Optimized amplitude filtering for superresolution over a restricted field: I. Achievement of maximum central irradiance under an energy constraint," Opt. Acta 27, 587-610 (1980).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (5)

J. K. Strayer, Linear Programming and Its Applications (Springer-Verlag, 1989), Chap. 2.
[CrossRef]

H. Liu, "Investigations of design methods of diffractive optical elements to implement optical superresolution," Ph.D. dissertation (Tsinghua University, Beijing, 2004), Chap. 2.

T. S. Blyth and E. F. Robertson, Further Linear Algebra (Springer, 2002), Chap. 1.
[CrossRef]

L. E. Elsgolc, Calculus of Variations (Pergamon, 1961), Chap. I.

G. Jin, Y. Yan, and M. Wu, Binary Optics (National Defense Industry Press, Beijing, 1998), Chap. 9.1.

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Figures (6)

Fig. 1
Fig. 1

DSE at the exit pupil of an imaging system used to achieve optical superresolution.

Fig. 2
Fig. 2

Chemical erosion technique used to fabricate the designed DSEs.

Fig. 3
Fig. 3

Photograph of the fabricated DSEs.

Fig. 4
Fig. 4

Solid curves show the measured profiles of the fabricated DSEs. The dotted lines show the approximate step heights: (a) DSE1 and (b) DSE2.

Fig. 5
Fig. 5

Experimental setup used to measure the intensity of the PSF modulated by the fabricated DSEs.

Fig. 6
Fig. 6

Measured PSF intensity modulated by the fabricated DSEs. (a) Measured two-dimensional PSF intensity for DSE1, (b) average one-dimensional PSF intensity for DSE1, (c) measured two-dimensional PSF intensity for DSE2, (d) average one-dimensional PSF intensity for DSE2.

Tables (2)

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Table 1 Design Results with MLP

Tables Icon

Table 2 Measured Superresolution Performances of the Fabricated DSEs

Equations (5)

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I ( η ) = 4 | 0 1 U ( ρ ) J 0 ( x J ηρ ) ρdρ | 2 ,
max U ( ρ ) S   subject to   I ( η i ) = 0 , i = 1 , 2 , , N , 0 < η i < η i + 1 , | U ( ρ ) | 1 ,
min U ( ρ ) G   subject to   S S l , M M u , | U ( ρ ) | 1 ,
| Δ M | / M | Δ I M | / I M + | Δ I C | / I C ,
| Δ G | / G | Δ r G | / r G + | Δ r A | / r A ,

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