Abstract

Two examples are presented to illustrate the advantages of polarization coded apertures, in which the incoming light will rotate its polarization at a portion of an aperture. In the first example the depth of field of a diffraction limited lens is increased without sacrificing the light throughput; in the second example the axial focal intensity of a pixelated Fresnel zone plate is increased by 100%. Both examples work for linearly polarized or unpolarized illumination.

© 2006 Optical Society of America

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References

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  1. A. Ghosh, K. Murata, and A. K. Chakraborty, “Frequency-response characteristics of a perfect lens masked by polarizing devices,” J. Opt. Soc. Am. A 5, 277–284 (1988).
    [Crossref]
  2. D. R. Chowdhury, K. Bhattacharya, S. Sanyal, and A. K. Chakraborty, “Performance of a polarization-masked lens aperture in the presence of spherical aberration,” J. Opt. A: Pure and Applied Optics,  4, 98–104 (2002).
    [Crossref]
  3. A. Zlotnik, Z. Zalevsky, and E. Marom, “Superresolution with nonorthogonal polarization coding,” Appl. Opt. 44, 3705–3715 (2005).
    [Crossref] [PubMed]
  4. E. H. Linfoot and E. Wolf, “Diffraction images in systems with an annular aperture,” Proc. Phys. Soc. B 66, 145–149 (1953).
    [Crossref]
  5. T-C Poon and M. Motamedi, “Optical digital incoherent image-processing for extended depth of field,” Appl. Opt. 26, 4612–4615 (1987).
    [Crossref] [PubMed]
  6. J. Ojeda-Castaneda and L. R. Berriel Valdos, “Abitrarily high focal depth with finite aperture,” Opt. Lett. 13, 183–185 (1988).
    [Crossref] [PubMed]
  7. E. R. Dowski and W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34, 1859–1866 (1995).
    [Crossref] [PubMed]
  8. W. Chi and N. George, “Computational imaging with the logarithmic asphere: theory,” J. Opt. Soc. Am. A 20, 2260–2273 (2003).
    [Crossref]
  9. P. Yeh and C. Gu, Optics of Liquid Crystal Displays, (John Wiley & Sons, Inc., New York, 1999). Chapter 9 and references therein.
  10. T. D. Beynon, I. Kirk, and T. R. Mathews, “Gabor zone plate with binary transmittance values,” Opt. Lett. 17, 544–546 (1992).
    [Crossref] [PubMed]
  11. P. W. McOwan, M. S. Gordon, and W. J. Hossack, “A switchable liquid crystal binary Gabor lens,” Opt. Commun. 103, 189–193 (1993).
    [Crossref]
  12. R. E. English and N. George, “Diffraction from a circular aperture: on axis field strength,” Appl. Opt. 26, 2360–2363 (1987).
    [Crossref] [PubMed]

2005 (1)

2003 (1)

2002 (1)

D. R. Chowdhury, K. Bhattacharya, S. Sanyal, and A. K. Chakraborty, “Performance of a polarization-masked lens aperture in the presence of spherical aberration,” J. Opt. A: Pure and Applied Optics,  4, 98–104 (2002).
[Crossref]

1995 (1)

1993 (1)

P. W. McOwan, M. S. Gordon, and W. J. Hossack, “A switchable liquid crystal binary Gabor lens,” Opt. Commun. 103, 189–193 (1993).
[Crossref]

1992 (1)

1988 (2)

1987 (2)

1953 (1)

E. H. Linfoot and E. Wolf, “Diffraction images in systems with an annular aperture,” Proc. Phys. Soc. B 66, 145–149 (1953).
[Crossref]

Berriel Valdos, L. R.

Beynon, T. D.

Bhattacharya, K.

D. R. Chowdhury, K. Bhattacharya, S. Sanyal, and A. K. Chakraborty, “Performance of a polarization-masked lens aperture in the presence of spherical aberration,” J. Opt. A: Pure and Applied Optics,  4, 98–104 (2002).
[Crossref]

Cathey, W. T.

Chakraborty, A. K.

D. R. Chowdhury, K. Bhattacharya, S. Sanyal, and A. K. Chakraborty, “Performance of a polarization-masked lens aperture in the presence of spherical aberration,” J. Opt. A: Pure and Applied Optics,  4, 98–104 (2002).
[Crossref]

A. Ghosh, K. Murata, and A. K. Chakraborty, “Frequency-response characteristics of a perfect lens masked by polarizing devices,” J. Opt. Soc. Am. A 5, 277–284 (1988).
[Crossref]

Chi, W.

Chowdhury, D. R.

D. R. Chowdhury, K. Bhattacharya, S. Sanyal, and A. K. Chakraborty, “Performance of a polarization-masked lens aperture in the presence of spherical aberration,” J. Opt. A: Pure and Applied Optics,  4, 98–104 (2002).
[Crossref]

Dowski, E. R.

English, R. E.

George, N.

Ghosh, A.

Gordon, M. S.

P. W. McOwan, M. S. Gordon, and W. J. Hossack, “A switchable liquid crystal binary Gabor lens,” Opt. Commun. 103, 189–193 (1993).
[Crossref]

Gu, C.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays, (John Wiley & Sons, Inc., New York, 1999). Chapter 9 and references therein.

Hossack, W. J.

P. W. McOwan, M. S. Gordon, and W. J. Hossack, “A switchable liquid crystal binary Gabor lens,” Opt. Commun. 103, 189–193 (1993).
[Crossref]

Kirk, I.

Linfoot, E. H.

E. H. Linfoot and E. Wolf, “Diffraction images in systems with an annular aperture,” Proc. Phys. Soc. B 66, 145–149 (1953).
[Crossref]

Marom, E.

Mathews, T. R.

McOwan, P. W.

P. W. McOwan, M. S. Gordon, and W. J. Hossack, “A switchable liquid crystal binary Gabor lens,” Opt. Commun. 103, 189–193 (1993).
[Crossref]

Motamedi, M.

Murata, K.

Ojeda-Castaneda, J.

Poon, T-C

Sanyal, S.

D. R. Chowdhury, K. Bhattacharya, S. Sanyal, and A. K. Chakraborty, “Performance of a polarization-masked lens aperture in the presence of spherical aberration,” J. Opt. A: Pure and Applied Optics,  4, 98–104 (2002).
[Crossref]

Wolf, E.

E. H. Linfoot and E. Wolf, “Diffraction images in systems with an annular aperture,” Proc. Phys. Soc. B 66, 145–149 (1953).
[Crossref]

Yeh, P.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays, (John Wiley & Sons, Inc., New York, 1999). Chapter 9 and references therein.

Zalevsky, Z.

Zlotnik, A.

Appl. Opt. (4)

J. Opt. A: Pure and Applied Optics (1)

D. R. Chowdhury, K. Bhattacharya, S. Sanyal, and A. K. Chakraborty, “Performance of a polarization-masked lens aperture in the presence of spherical aberration,” J. Opt. A: Pure and Applied Optics,  4, 98–104 (2002).
[Crossref]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

P. W. McOwan, M. S. Gordon, and W. J. Hossack, “A switchable liquid crystal binary Gabor lens,” Opt. Commun. 103, 189–193 (1993).
[Crossref]

Opt. Lett. (2)

Proc. Phys. Soc. B (1)

E. H. Linfoot and E. Wolf, “Diffraction images in systems with an annular aperture,” Proc. Phys. Soc. B 66, 145–149 (1953).
[Crossref]

Other (1)

P. Yeh and C. Gu, Optics of Liquid Crystal Displays, (John Wiley & Sons, Inc., New York, 1999). Chapter 9 and references therein.

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Figures (9)

Fig. 1.
Fig. 1.

The extended depth of field imaging setup with a polarization coded aperture.

Fig. 2.
Fig. 2.

The IPSFs of diffraction limited lens for central aperture; ring aperture and full aperture.

Fig. 3.
Fig. 3.

The IPSFs of diffraction limited lens for a lens with polarization coded aperture.

Fig. 4.
Fig. 4.

The IPSFs of diffraction limited lens for a lens with conventional aperture.

Fig. 5.
Fig. 5.

The OTFs of diffraction limited lens for a lens with polarization coded aperture.

Fig. 6.
Fig. 6.

The OTFs of diffraction limited lens for a lens with conventional circular aperture.

Fig. 7.
Fig. 7.

The setup for pixelated zone plate. Left: setup; Right: pixelated zone plate

Fig. 8.
Fig. 8.

A pixelated Fresnel zone plate. White pixel: no change in polarization; black pixel: polarization rotate 90°.

Fig. 9.
Fig. 9.

Axial intensity of pixelated zone plates with and without polarization coded aperture. Thick red line: pixelated zone plate with polarization coded aperture as shown in Fig. 8; Thin blue line: pixelated zone plate without polarization coding.

Equations (8)

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I ( ρ ) = 0 r r J 0 ( 2 πr ρ λt ) exp [ i 2 πW λ ( r R ) 2 ] dr 2 + r R r J 0 ( 2 πr ρ λt ) exp [ i 2 πW λ ( r R ) 2 ] dr 2 ,
E mn = A y n a 2 y n + a 2 x m a 2 x m a 2 f f 2 + x 2 + y 2 exp ( i 2 π λ f 2 + x 2 + y 2 ) dxdy ,
I P = π 2 ϕ mn < π 2 E mn 2 + π ϕ mn < π 2 or π 2 ϕ mn < π E mn 2 .
I P 2 π 2 ϕ mn < π 2 E mn 2 .
t ( r ) = n = 1 2 N 1 ( 1 ) n + 1 circ ( r r n ) ,
E ( z ) = n = 1 2 N 1 ( 1 ) n + 1 E z n ,
E z n = E 0 [ exp ( i 2 π λ z ) z z 2 + r n 2 exp ( i 2 π λ z 2 + r n 2 ) ] .
I ( z ) = C e i 2 π λ z + n = 1 2 N 1 ( 1 ) n z z 2 + nλf exp ( i 2 π λ z 2 + nλf ) 2 ,

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