Abstract

To take advantage of phase-only filters to reduce reflected stray light, two phase plates are used in a synthetic complex superresolving pupil filter to get a small spot for laser direct writing. The amplitude modulation in a conventional complex superresolving pupil filter (CCSPF) is substituted by an equivalent phase modulation. The equivalence between the proposed filter and a CCSPF is established for a general design. The effectiveness of the proposed filter was proven through experiments to obtain a small main lobe width of 0.86 times the size of the airy spot.

© 2008 Optical Society of America

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References

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2007

C. J. R. Sheppard, “Fundamentals of superresolution,” Micron 38, 165-169 (2007).
[CrossRef]

2005

2004

2003

1999

M. Martinez-Corral, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267-278 (1999).
[CrossRef]

1997

1994

C. K. Seiracki, “A leaky annular pupil for improved lateral resolution,” Proc. SPIE 2184, 120-126 (1994).
[CrossRef]

1990

1977

C. J. R. Sheppard, “The use of lens with annular aperture in scanning optical microscopy,” Optik 48, 329-334 (1977).

Cagigal, M. P.

Canales, V. F.

de Juana, D. M.

Gundu, P. N.

Hack, E.

Luo, H.

Martinez-Corral, M.

M. Martinez-Corral, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267-278 (1999).
[CrossRef]

Morris, G. M.

Oti, J. E.

Rastogi, P.

Seiracki, C. K.

C. K. Seiracki, “A leaky annular pupil for improved lateral resolution,” Proc. SPIE 2184, 120-126 (1994).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard, “Fundamentals of superresolution,” Micron 38, 165-169 (2007).
[CrossRef]

C. J. R. Sheppard, “The use of lens with annular aperture in scanning optical microscopy,” Optik 48, 329-334 (1977).

Yamanaka, Y.

Yun, M.

Zhou, C.

Zhou, S.

Appl. Opt.

J. Opt. Soc. Am. A

Micron

C. J. R. Sheppard, “Fundamentals of superresolution,” Micron 38, 165-169 (2007).
[CrossRef]

Opt. Commun.

M. Martinez-Corral, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267-278 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

Optik

C. J. R. Sheppard, “The use of lens with annular aperture in scanning optical microscopy,” Optik 48, 329-334 (1977).

Proc. SPIE

C. K. Seiracki, “A leaky annular pupil for improved lateral resolution,” Proc. SPIE 2184, 120-126 (1994).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of synthetic complex superresolution based on double-beam phase modulation.

Fig. 2
Fig. 2

Superresolving performance of the SCSPF shown in Table 1 compared with known filters.

Fig. 3
Fig. 3

Theoretical profiles of the phase plates shown in Table 2.

Fig. 4
Fig. 4

Photograph of the phase plates. The substrates are 12.7 mm in diameter, and the effective modulation zones are 5 mm in diameter.

Fig. 5
Fig. 5

Stability analysis for δ M .

Fig. 6
Fig. 6

Images detected by the CCD at 40 times amplification.

Fig. 7
Fig. 7

Two-dimensional cross sections of the airy spot image and superresolving spot image shown in Fig. 6 ( A = 45 ° ).

Tables (3)

Tables Icon

Table 1 Design Examples of Synthetic Complex Superresolving Pupil Filters Corresponding with Other Known Filters ( T 3 = 1 , R 3 = 1 )

Tables Icon

Table 2 Theoretical and Experimental Parameters of Phase Plates a

Tables Icon

Table 3 Equivalent Transmittance and Phase Values Corresponding with the Synthetic Complex Superresolving Pupil Filters Shown in Table 2 at Actual Depth

Equations (10)

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E 1 = [ E 1 x E 1 y ] = J BST J P 1 J M 1 J P 1 J BSR [ E 1 x 0 E 1 y 0 ] ,
E 2 = [ E 2 x E 2 y ] = J BSR J P 2 J M 1 e i δ M J P 2 J BST [ E 2 x 0 E 2 y 0 ] .
U 1 = 1 2 e i 2 φ 1 ( ρ ) ,
U 2 = 1 2 e i [ 2 φ 2 ( ρ ) + δ M ] ,
U = U 1 + U 2 = 0 1 ( e i 2 φ 1 ( ρ ) + e i 2 φ 2 ( ρ ) ) J 0 ( v ρ ) exp ( i u ρ 2 / 2 ) ρ d ρ ,
e i 2 φ 1 ( ρ ) = cos ( 2 φ 1 ( ρ ) ) + i sin ( 2 φ 1 ( ρ ) ) , e i 2 φ 2 ( ρ ) = cos ( 2 φ 2 ( ρ ) ) + i sin ( 2 φ 2 ( ρ ) ) ,
e i 2 φ 1 ( ρ ) + e i 2 φ 2 ( ρ ) = 2 cos ( φ 1 ( ρ ) φ 2 ( ρ ) ) × [ cos ( φ 1 ( ρ ) + φ 2 ( ρ ) ) + i sin ( φ 1 ( ρ ) + φ 2 ( ρ ) ) ] = 2 cos ( φ 1 ( ρ ) φ 2 ( ρ ) ) e i ( φ 1 ( ρ ) + φ 2 ( ρ ) ) ,
U = 2 0 1 cos ( α ( ρ ) ) e i β ( ρ ) J 0 ( v ρ ) exp ( i u ρ 2 / 2 ) ρ d ρ ,
α ( ρ ) = φ 1 ( ρ ) φ 2 ( ρ ) , β ( ρ ) = φ 1 ( ρ ) + φ 2 ( ρ ) ,
A ( ρ ) = cos ( α ( ρ ) ) , ϕ ( ρ ) = β ( ρ ) .

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