Abstract

By using a Jones matrix, the precise expression for the pupil function of a two-adjustable-mode superresolving filter, a combination of a radial birefringent plate and a glass annular plate, is obtained. This filter can provide superresolution in both radial and axial adjustment operations, which can supplement each other in setting accuracy and superresolution range in practical use. As an adjustable filter, it is less dependent on wavelength. With the relative radius of the inner plate set to be ε=0.52 and the rotating angle set to be 45°, this type of filter can achieve better superresolution performance than the continuous-phase filters reported in Opt. Lett. 28, 607 (2003) .

© 2007 Optical Society of America

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References

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  1. G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento, Suppl. 9, 426-435 (1952).
    [CrossRef]
  2. F. Xiao, J. Yuan, G. Wang, and Z. Xu, "Tunable phase-only optical filters with a uniaxial crystal," Appl. Opt. 43, 3415-3419 (2004).
    [CrossRef]
  3. M. Yun, L. Liu, J. Sun, and D. Liu, "Transverse or axial superresolution with radial birefringent filter," J. Opt. Soc. Am. A 21, 1869-1874 (2004).
    [CrossRef]
  4. H. Zhu, H. Gan, H. Gao, J. Chen, and Z. Xu, "Design of adjustable superresolving filters based on birefringent crystals," Appl. Opt. 45, 104-109 (2006).
    [CrossRef]
  5. C. J. R. Sheppard and Z. S. Hegedus, "Axial behavior of pupil-plane filters," J. Opt. Soc. Am. A 5, 643 (1988).
    [CrossRef]
  6. X. Zhu, "Explicit Jones transformation matrix for a tilted birefringent plate with its optic axis parallel to the plate surfaces," Appl. Opt. 33, 3502-3506 (1994).
    [CrossRef] [PubMed]
  7. http://www.crystran.co.uk/qutzdata.htm.
  8. http://www.mellesgriot.com/products/optics/mp-3-1.htm.
  9. D. M. de Juana, J. E. Oti, V. F. Canales, and M. P. Cagigal, "Design of superresolving continuous phase filters," Opt. Lett. 28, 607-609 (2003).
    [CrossRef] [PubMed]

2006

2004

2003

1994

1988

1952

G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento, Suppl. 9, 426-435 (1952).
[CrossRef]

Cagigal, M. P.

Canales, V. F.

Chen, J.

de Juana, D. M.

Gan, H.

Gao, H.

Hegedus, Z. S.

Liu, D.

Liu, L.

Oti, J. E.

Sheppard, C. J. R.

Sun, J.

Toraldo di Francia, G.

G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento, Suppl. 9, 426-435 (1952).
[CrossRef]

Wang, G.

Xiao, F.

Xu, Z.

Yuan, J.

Yun, M.

Zhu, H.

Zhu, X.

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Figures (6)

Fig. 1
Fig. 1

Sketch of (a) the DAMSF and (b) the TZPF. The double-headed arrow represents the direction of the optical axis of the crystal.

Fig. 2
Fig. 2

Dependence of (a) G and (b) S on the rotation angle θ in RLA mode for different thicknesses of the TZPF, denoted m.

Fig. 3
Fig. 3

Dependence of (a) G and (b) S on tilting angle α in TTA for different thicknesses ( m ) of the TZPF.

Fig. 4
Fig. 4

Transversal and axial intensity for different superresolved patterns. The rotation angles have values of 0 ° , 20 ° , 40 ° , and 60 ° in the RLA mode, and the tilting angles have values of 0 ° , 1.5 ° , 3 ° , 4.5 ° , and 6 ° in the TTA mode.

Fig. 5
Fig. 5

Dependence of G and S on the rotation angle θ in RLA mode for wavelengths λ of 442, 532, 694, and 1550 nm (a), (b) for the RLA mode and (c), (d) for the TTA mode. Solid curve, λ = 442 nm ; dashed curve, λ = 1550 nm ; dashed–dotted curve, λ = 532 nm ; dotted curve with circles, λ = 694 nm .

Fig. 6
Fig. 6

Comparison of transverse intensities of our filter under ε = 0.52 with the continuous-phase filter of Ref. [9]. Dashed curve, our filter, dotted curve, continuous-phase filter.

Tables (1)

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Table 1 Refractive Indices for Quartz ( SiO 2 ) and BK7 Glasses at Different Wavelengths

Equations (11)

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U ( v , u ) = 2 0 1 P ( ρ ) J 0 ( v ρ ) exp ( j u p 2 2 ) ρ d ρ .
M = ( 1 cos 2 θ sin 2 α w n e 2 ) 1 [ a cos 2 θ exp ( i δ e ) + sin 2 θ exp ( i δ o ) a sin θ cos θ [ exp ( i δ e ) exp ( i δ o ) ] a sin θ cos θ [ exp ( i δ e ) exp ( i δ o ) ] sin 2 θ exp ( i δ e ) + a cos 2 θ exp ( i δ o ) ] ,
δ e = 2 π d λ [ n e ( 1 sin 2 α sin 2 θ n e 2 sin 2 α cos 2 θ n o 2 ) 1 2 n o ( 1 sin 2 α n o 2 ) 1 2 n o ( 1 sin 2 α n o 2 ) 1 2 ] ,
δ o = 2 π n o d [ λ ( 1 sin 2 α n o 2 ) 1 2 ]
d = ( 2 m 1 ) λ 2 Δ n
P 1 = P 2 = [ 1 0 0 0 ] .
E 0 = [ 1 0 ]
E = P 1 M P 2 E 0 = [ 1 cos 2 θ sin 2 α w n e 2 ] 1 [ a cos 2 θ exp ( i δ e ) + sin 2 θ exp ( i δ o ) 0 ] .
P i = [ 1 ( cos 2 θ sin 2 α ) ( w n e 2 ) ] 1 [ a cos 2 θ exp ( i δ e ) + sin 2 θ exp ( i δ o ) ] ,
P o = exp ( i δ ) ,
P ( ρ ) = { [ 1 ( cos 2 θ sin 2 α ) ( w n e 2 ) ] 1 [ a cos 2 θ exp ( i δ e ) + sin 2 θ exp ( i δ o ) ] ( 0 ρ ε ) exp ( i δ ) ( ε < ρ 1 ) ,

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