Abstract

The polarization phase shift (PPS) has emerged as an important analytical tool in optical metrology. The present study utilizes the concept of controlling the polarization phase in applications such as focal shift and automatic focusing. When elliptically polarized light, in general, is incident upon a circularly symmetric polarization mask consisting of circular and annular zones with each zone having a unique linear polarizability, the polarization-phase difference introduced between the polarization-masked zones is also circularly symmetric. With the mask at the lens aperture, the polarization phase introduced is multiplicative with the lens function and is shown to result in a shift of the Gaussian focus plane. Because the polarization phase can be controlled by variation of the polarization parameters, the effective focal length of the imaging system can be varied within a small range. A study of the point-spread functions at the shifted focal planes has shown that the quality of the focal patch in these planes is comparable with that produced by a diffraction-limited imaging system at Gaussian focus. The shift of focus can be achieved by control of the polarization of the input beam. It is anticipated that this technique may find application in areas for which dynamic focusing within a small range is required.

© 2003 Optical Society of America

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References

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  1. Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
    [CrossRef]
  2. Y. Li, “Dependence of the focal shift on Fresnel number and f number,” J. Opt. Soc. Am. 72, 770–774 (1982).
    [CrossRef]
  3. G. Hausler, E. Korner, “Simple focusing error,” Appl. Opt. 23, 2468–2471 (1984).
    [CrossRef]
  4. J. Odeja-Castaneda, L. R. Berriel-Valdos, E. Montes, “Line spread function relatively insensitive to defocus,” Opt. Lett. 8, 458–460 (1983).
    [CrossRef]
  5. G. Indebetouw, H. Bai, “Imaging with Fresnel zone pupil masks: extended depth of field,” Appl. Opt. 23, 4299–4302 (1984).
    [CrossRef] [PubMed]
  6. C. Varamit, G. Indebetouw, “Imaging properties of defocused partitioned pupils,” J. Opt. Soc. Am. A 2, 799–802 (1985).
    [CrossRef]
  7. J. Odeja-Castaneda, L. R. Berriel-Valdos, “Arbitrarily high focal depth with finite apertures,” Opt. Lett. 13, 183–185 (1988).
    [CrossRef]
  8. P. Jaquinot, B. Roizen-Dossier, “Apodization,” in Progress in OpticsE. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. III, pp. 29–186.
  9. T. Asakura, S. Mishina, “Diffraction by circular apertures with a ring shaped π phase change,” Jpn. J. Appl. Phys. 9, 195–202 (1970).
    [CrossRef]
  10. T. Asakura, H. Nagai, “Further studies of far field diffraction by modified annular and annulas apertures,” Jpn. J. Appl. Phys. 10, 879–885 (1970).
    [CrossRef]
  11. M. Mino, Y. Okano, “Improvement in the OTF of a defocused optical system through the use of shaded apertures,” Appl. Opt. 10, 2219–2225 (1971).
    [CrossRef] [PubMed]
  12. J. T. McCrickerd, “Coherent processing and depth of focus of annular aperture imagery,” Appl. Opt. 10, 2226–2231 (1971).
    [CrossRef] [PubMed]
  13. A. Ghosh, K. Murata, A. K. Chakroborty, “Frequency response characteristics of a perfect lens masked by polarizing devices,” J. Opt. Soc. Am. A 5, 277–284 (1988).
    [CrossRef]
  14. K. Bhattacharya, A. Ghosh, A. K. Chakroborty, “Vector wave imagery with a lens masked by polarisers,” J. Mod. Opt. 40, 379–390 (1993).
    [CrossRef]
  15. K. Bhattacharya, A. K. Chakroborty, A. Ghosh, “Simulation of effects of phase and amplitude coatings on the lens aperture with polarization masks,” J. Opt. Soc. Am. A 2, 586–592 (1994).
    [CrossRef]
  16. A. K. Chakroborty, H. Mukherjee, “Modification of PSF by polarisation mask,” J. Opt. (Paris) 9, 251–254 (1978).
  17. A. Ghosh, J. Basu, P. P. Goswami, A. K. Chakroborty, “Frequency response characteristic of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1978).
    [CrossRef]
  18. A. Ghosh, A. K. Chakroborty, K. Murata, “Imaging characteristics of a perfect lens partially masked by a linear polariser,” Optik (Stuttgart) 76, 153–156 (1987).
  19. S. N. Datta, A. Ghosh, A. K. Chakroborty, “Imaging characteristics of a lens zonally masked by polarizers and retarders,” Optik 100, 1–7 (1995).
  20. D. Roy Chowdhury, K. Bhattacharya, S. Sanyal, A. K. Chakraborty, “Performance of a polarization-masked lens aperture in the presence of spherical aberration,” J. Opt. A 4, 98–104 (2002).
    [CrossRef]
  21. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1985), pp. 436–441.

2002 (1)

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

1995 (1)

S. N. Datta, A. Ghosh, A. K. Chakroborty, “Imaging characteristics of a lens zonally masked by polarizers and retarders,” Optik 100, 1–7 (1995).

1994 (1)

K. Bhattacharya, A. K. Chakroborty, A. Ghosh, “Simulation of effects of phase and amplitude coatings on the lens aperture with polarization masks,” J. Opt. Soc. Am. A 2, 586–592 (1994).
[CrossRef]

1993 (1)

K. Bhattacharya, A. Ghosh, A. K. Chakroborty, “Vector wave imagery with a lens masked by polarisers,” J. Mod. Opt. 40, 379–390 (1993).
[CrossRef]

1988 (2)

1987 (1)

A. Ghosh, A. K. Chakroborty, K. Murata, “Imaging characteristics of a perfect lens partially masked by a linear polariser,” Optik (Stuttgart) 76, 153–156 (1987).

1985 (1)

1984 (2)

1983 (1)

1982 (1)

1981 (1)

Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
[CrossRef]

1978 (2)

A. K. Chakroborty, H. Mukherjee, “Modification of PSF by polarisation mask,” J. Opt. (Paris) 9, 251–254 (1978).

A. Ghosh, J. Basu, P. P. Goswami, A. K. Chakroborty, “Frequency response characteristic of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1978).
[CrossRef]

1971 (2)

1970 (2)

T. Asakura, S. Mishina, “Diffraction by circular apertures with a ring shaped π phase change,” Jpn. J. Appl. Phys. 9, 195–202 (1970).
[CrossRef]

T. Asakura, H. Nagai, “Further studies of far field diffraction by modified annular and annulas apertures,” Jpn. J. Appl. Phys. 10, 879–885 (1970).
[CrossRef]

Asakura, T.

T. Asakura, H. Nagai, “Further studies of far field diffraction by modified annular and annulas apertures,” Jpn. J. Appl. Phys. 10, 879–885 (1970).
[CrossRef]

T. Asakura, S. Mishina, “Diffraction by circular apertures with a ring shaped π phase change,” Jpn. J. Appl. Phys. 9, 195–202 (1970).
[CrossRef]

Bai, H.

Basu, J.

A. Ghosh, J. Basu, P. P. Goswami, A. K. Chakroborty, “Frequency response characteristic of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1978).
[CrossRef]

Berriel-Valdos, L. R.

Bhattacharya, K.

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

K. Bhattacharya, A. K. Chakroborty, A. Ghosh, “Simulation of effects of phase and amplitude coatings on the lens aperture with polarization masks,” J. Opt. Soc. Am. A 2, 586–592 (1994).
[CrossRef]

K. Bhattacharya, A. Ghosh, A. K. Chakroborty, “Vector wave imagery with a lens masked by polarisers,” J. Mod. Opt. 40, 379–390 (1993).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1985), pp. 436–441.

Chakraborty, A. K.

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

Chakroborty, A. K.

S. N. Datta, A. Ghosh, A. K. Chakroborty, “Imaging characteristics of a lens zonally masked by polarizers and retarders,” Optik 100, 1–7 (1995).

K. Bhattacharya, A. K. Chakroborty, A. Ghosh, “Simulation of effects of phase and amplitude coatings on the lens aperture with polarization masks,” J. Opt. Soc. Am. A 2, 586–592 (1994).
[CrossRef]

K. Bhattacharya, A. Ghosh, A. K. Chakroborty, “Vector wave imagery with a lens masked by polarisers,” J. Mod. Opt. 40, 379–390 (1993).
[CrossRef]

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

A. Ghosh, A. K. Chakroborty, K. Murata, “Imaging characteristics of a perfect lens partially masked by a linear polariser,” Optik (Stuttgart) 76, 153–156 (1987).

A. K. Chakroborty, H. Mukherjee, “Modification of PSF by polarisation mask,” J. Opt. (Paris) 9, 251–254 (1978).

A. Ghosh, J. Basu, P. P. Goswami, A. K. Chakroborty, “Frequency response characteristic of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1978).
[CrossRef]

Datta, S. N.

S. N. Datta, A. Ghosh, A. K. Chakroborty, “Imaging characteristics of a lens zonally masked by polarizers and retarders,” Optik 100, 1–7 (1995).

Ghosh, A.

S. N. Datta, A. Ghosh, A. K. Chakroborty, “Imaging characteristics of a lens zonally masked by polarizers and retarders,” Optik 100, 1–7 (1995).

K. Bhattacharya, A. K. Chakroborty, A. Ghosh, “Simulation of effects of phase and amplitude coatings on the lens aperture with polarization masks,” J. Opt. Soc. Am. A 2, 586–592 (1994).
[CrossRef]

K. Bhattacharya, A. Ghosh, A. K. Chakroborty, “Vector wave imagery with a lens masked by polarisers,” J. Mod. Opt. 40, 379–390 (1993).
[CrossRef]

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

A. Ghosh, A. K. Chakroborty, K. Murata, “Imaging characteristics of a perfect lens partially masked by a linear polariser,” Optik (Stuttgart) 76, 153–156 (1987).

A. Ghosh, J. Basu, P. P. Goswami, A. K. Chakroborty, “Frequency response characteristic of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1978).
[CrossRef]

Goswami, P. P.

A. Ghosh, J. Basu, P. P. Goswami, A. K. Chakroborty, “Frequency response characteristic of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1978).
[CrossRef]

Hausler, G.

Indebetouw, G.

Jaquinot, P.

P. Jaquinot, B. Roizen-Dossier, “Apodization,” in Progress in OpticsE. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. III, pp. 29–186.

Korner, E.

Li, Y.

Y. Li, “Dependence of the focal shift on Fresnel number and f number,” J. Opt. Soc. Am. 72, 770–774 (1982).
[CrossRef]

Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
[CrossRef]

McCrickerd, J. T.

Mino, M.

Mishina, S.

T. Asakura, S. Mishina, “Diffraction by circular apertures with a ring shaped π phase change,” Jpn. J. Appl. Phys. 9, 195–202 (1970).
[CrossRef]

Montes, E.

Mukherjee, H.

A. K. Chakroborty, H. Mukherjee, “Modification of PSF by polarisation mask,” J. Opt. (Paris) 9, 251–254 (1978).

Murata, K.

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

A. Ghosh, A. K. Chakroborty, K. Murata, “Imaging characteristics of a perfect lens partially masked by a linear polariser,” Optik (Stuttgart) 76, 153–156 (1987).

Nagai, H.

T. Asakura, H. Nagai, “Further studies of far field diffraction by modified annular and annulas apertures,” Jpn. J. Appl. Phys. 10, 879–885 (1970).
[CrossRef]

Odeja-Castaneda, J.

Okano, Y.

Roizen-Dossier, B.

P. Jaquinot, B. Roizen-Dossier, “Apodization,” in Progress in OpticsE. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. III, pp. 29–186.

Roy Chowdhury, D.

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

Sanyal, S.

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

Varamit, C.

Wolf, E.

Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1985), pp. 436–441.

Appl. Opt. (4)

J. Mod. Opt. (2)

K. Bhattacharya, A. Ghosh, A. K. Chakroborty, “Vector wave imagery with a lens masked by polarisers,” J. Mod. Opt. 40, 379–390 (1993).
[CrossRef]

A. Ghosh, J. Basu, P. P. Goswami, A. K. Chakroborty, “Frequency response characteristic of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1978).
[CrossRef]

J. Opt. (Paris) (1)

A. K. Chakroborty, H. Mukherjee, “Modification of PSF by polarisation mask,” J. Opt. (Paris) 9, 251–254 (1978).

J. Opt. A (1)

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

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Jpn. J. Appl. Phys. (2)

T. Asakura, S. Mishina, “Diffraction by circular apertures with a ring shaped π phase change,” Jpn. J. Appl. Phys. 9, 195–202 (1970).
[CrossRef]

T. Asakura, H. Nagai, “Further studies of far field diffraction by modified annular and annulas apertures,” Jpn. J. Appl. Phys. 10, 879–885 (1970).
[CrossRef]

Opt. Commun. (1)

Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
[CrossRef]

Opt. Lett. (2)

Optik (1)

S. N. Datta, A. Ghosh, A. K. Chakroborty, “Imaging characteristics of a lens zonally masked by polarizers and retarders,” Optik 100, 1–7 (1995).

Optik (Stuttgart) (1)

A. Ghosh, A. K. Chakroborty, K. Murata, “Imaging characteristics of a perfect lens partially masked by a linear polariser,” Optik (Stuttgart) 76, 153–156 (1987).

Other (2)

P. Jaquinot, B. Roizen-Dossier, “Apodization,” in Progress in OpticsE. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. III, pp. 29–186.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1985), pp. 436–441.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the proposed optical setup: P, polarizer; C, compensator; I, focusing lens; M, polarization mask; A, analyzer; S, screen.

Fig. 2
Fig. 2

Normalized axial irradiance for several values of δ. For a polarization-masked lens aperture the polarization parameters are α = 0°, β = 90°, and γ = 45°. a = b = 1 and ε = 0.707. Curve O, δ = 0°, 360°; curve A, δ = 45°; curve B, δ = 90°; curve C, δ = 135°; curve D, δ = 180°; curve E, δ = 225°; curve F, δ = 270°; curve G, δ = 315°.

Fig. 3
Fig. 3

In each case: top, comparison of the intensity PSF of a polarization-masked lens with an ideal lens for several values of δ; bottom, computed focal patch, as follows: (a) δ = 45°, (b) δ = 90°, (c) δ = 135°, (d) δ = 180°, (e) δ = 225°, (f) δ = 270°, (g) δ = 315°. Other parameters as in Fig. 2.

Fig. 4
Fig. 4

Focal shift (in micrometers) plotted against input beam parameter δ.

Fig. 5
Fig. 5

Normalized axial irradiance for several values of γ for a = b = 1, δ = 90°, α = 0°, β = 90°, ε = 0.707.

Fig. 6
Fig. 6

In each case: top, comparison of the intensity PSF of a polarization-masked lens with an ideal lens for several values of γ; bottom, Computed focal patch, as follows: (a) γ = 45°, (b) γ = 135°, (c) γ = 75°, (d) γ = 105°, (e) γ = 160°. Other parameters as in Fig. 5.

Fig. 7
Fig. 7

Focal shift (in micrometers) plotted against analyzer orientation γ (in degrees).

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

UPx, y, z0=-2πiR2Aλf2expifR2u×01expiur2/2J0ρrrdr =KR201expiur2/2J0ρrrdr,
K=-2πiAλf2expifR2u,
u=2πλRf2z,
ρ=2πλRfx2+y21/2.
w20=u/2k,
z=8w20fno2,
UPx, y, z0=KR201expikw20r2J0ρrrdr,
GcP=KR20εexpikw20r2J0ρrrdr.
GaP=KR201expikw20r2J0ρrrdr-0εexpikw20r2J0ρrrdr.
εi=abeiδ,
Uc=GcPαabeiδ,
Ua=GaPβabeiδ.
Uc=PγUc,
Ua=PγUa.
Uc=GcR1 expiΔ1cos γsin γ,
Ua=GaR2 expiΔ2cos γsin γ,
R1=cosγ-αa2 cos2 α+b2 sin2 α+ab sin 2α cos δ1/2,
R2=cosγ-βa2 cos2 β+b2 sin2 β+ab sin 2β cos δ1/2,
Δ1=tan-1b sin α sin δ/a cos α+b sin α cos δ,
Δ2=tan-1b sin β sin δ/a cos β+b sin β cos δ.
Δ=tan-1ab sin δ sinα-β/a2 cos α cos β+b2 sin α sin β+ab sin(α+βcos δ.
U=|Ua+Uc|2,
U=C12R12 cos2α-γ+R22C22 cos2β-γ+2C1C2R1R2 cosα-γcosβ-γcosθ1-θ3+Δ,
C1=U1ε2+U2ε21/2, C2=U112+U2121/2, C2=C12+C22-2C1C2 cosθ1-θ21/2,
U1l=0lcos kw20r2J0ρrrdr, U2l=0lsin kw20r2J0ρrrdr.
θ1=tan-1U2εU1ε, θ2=tan-1U21U11, θ3=tan-1C2 sin θ1-C1 sin θ2C2 cos θ1-C1 cos θ2.

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