Abstract

A new type of phase-only superresolving pupil filter with a discrete continuous-phase profile is presented that is a combination of discrete multilevel-phase modulation and continuous-phase modulation. This type of filter can achieve better superresolution performance than the continuous-phase filters reported in Opt. Lett. 28, 607 (2003). Therefore, with regard to the superresolution effect, this type of filter deserves study for practical applications. More importantly, the diffraction performance of this type of filter can explain the effect of a discrete-phase filter illuminated with a continuous wave front, whose superresolving performance cannot be analyzed with previous superresolution methods.

© 2004 Optical Society of America

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References

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  1. T. R. M. Sales and G. M. Morris, J. Opt. Soc. Am. A 14, 1637 (1997).
    [CrossRef]
  2. D. M. de Juana, V. F. Canales, P. J. Valle, and M. P. Cagigal, Opt. Commun. 229, 71 (2004).
    [CrossRef]
  3. J. Jia, C. Zhou, and L. Liu, Opt. Commun. 228, 271 (2003).
    [CrossRef]
  4. J. Jia, C. Zhou, X. Sun, and L. Liu, Appl. Opt. 43, 2112 (2004).
    [CrossRef] [PubMed]
  5. C. Zhou, J. Jia, and L. Liu, Opt. Lett. 28, 2174 (2003).
    [CrossRef] [PubMed]
  6. D. M. de Juana, J. E. Oti, V. F. Canales, and M. P. Cagigal, Opt. Lett. 28, 607 (2003).
    [CrossRef] [PubMed]
  7. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).
  8. M. A. A. Neil, F. Massournian, R. Juskaitis, and T. Wilson, Opt. Lett. 27, 1929 (2002).
    [CrossRef]

2004 (2)

J. Jia, C. Zhou, X. Sun, and L. Liu, Appl. Opt. 43, 2112 (2004).
[CrossRef] [PubMed]

D. M. de Juana, V. F. Canales, P. J. Valle, and M. P. Cagigal, Opt. Commun. 229, 71 (2004).
[CrossRef]

2003 (3)

2002 (1)

1997 (1)

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Cagigal, M. P.

D. M. de Juana, V. F. Canales, P. J. Valle, and M. P. Cagigal, Opt. Commun. 229, 71 (2004).
[CrossRef]

D. M. de Juana, J. E. Oti, V. F. Canales, and M. P. Cagigal, Opt. Lett. 28, 607 (2003).
[CrossRef] [PubMed]

Canales, V. F.

D. M. de Juana, V. F. Canales, P. J. Valle, and M. P. Cagigal, Opt. Commun. 229, 71 (2004).
[CrossRef]

D. M. de Juana, J. E. Oti, V. F. Canales, and M. P. Cagigal, Opt. Lett. 28, 607 (2003).
[CrossRef] [PubMed]

de Juana, D. M.

D. M. de Juana, V. F. Canales, P. J. Valle, and M. P. Cagigal, Opt. Commun. 229, 71 (2004).
[CrossRef]

D. M. de Juana, J. E. Oti, V. F. Canales, and M. P. Cagigal, Opt. Lett. 28, 607 (2003).
[CrossRef] [PubMed]

Jia, J.

Juskaitis, R.

Liu, L.

Massournian, F.

Morris, G. M.

Neil, M. A. A.

Oti, J. E.

Sales, T. R. M.

Sun, X.

Valle, P. J.

D. M. de Juana, V. F. Canales, P. J. Valle, and M. P. Cagigal, Opt. Commun. 229, 71 (2004).
[CrossRef]

Wilson, T.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Zhou, C.

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Figures (3)

Fig. 1
Fig. 1

Phase profile of the discrete continuous filter that is a combination of a continuous filter (Ref. 6) and a discrete filter (Ref. 3) (Filter 6 in Table 2).

Fig. 2
Fig. 2

Comparison of normalized transverse intensities of this filter (Filter 6 in Table 2; solid curve) with the continuous phase filter of Ref. 6 (dashed curve).

Fig. 3
Fig. 3

Schematic of a discrete (multilevel) phase filter illuminated with the continuous wave front of a laser beam for the superresolution effect that can be explained with our hybrid filter.

Tables (2)

Tables Icon

Table 1 Comparison of Superresolution Performance of This Filter, ϕρ=a sin2πbρ+θi, the Continuous-Phase Filters in Ref. 6, and the Discrete-Phase Filter in Ref. 3

Tables Icon

Table 2 Numerical Results of Binary Discrete Continuous Filters with Parameters a, b, ρ1, ρ2 and θ1=π, θ2=0, θ3=π in Comparison with Ref. 6

Equations (8)

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ϕρ=a sin2πbρ+θi,
θi=θ1ρ0,ρ1θ2ρρ1,ρ2θNρρN-1,ρN=1.
Uv,u=201PρJ0vρexpjuρ2/2ρdρ,
In=201Pρρ2n+1dρ,
GT=2ReI0I1*-uf ImI0*I2S,S=I02-uf ImI0*I1,
In=2 expiθ10ρ1expia sin2πρbρ2n+1dρ+2 expiθ2ρ1ρ2expia sin2πρbρ2n+1dρ+2 expiθ3ρ21expia sin2πρbρ2n+1dρ.
Iv,uf=n=0r2nv2n2,
r2n=-1nIn/a2n+-1njufIn+1/2a2n+-1n+1uf2In+2/8a2n, a0=1, a2=4, a2n=a2n-22n2 n=1,2,3,.

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