Abstract

The Strehl definition along the axis of a birefringent lens sandwiched between two polarizers is studied analytically. The optic axis of the birefringent lens made of a uniaxial crystal is perpendicular to the lens axis, and the system behaves like a bifocus lens for proper orientation of the polarizers. The Sparrow criterion is employed for designing an imaging system with high depth of focus. It is shown that, when the two foci are separated by the Sparrow limit of resolution, the focal depth is maximum and the intensity point-spread function remains almost identical within this limit. The resolution according to the Rayleigh criterion in this zone is more than that of an ideal lens.

© 2000 Optical Society of America

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References

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    [CrossRef]

1999

S. Sanyal, A. Ghosh, “Imaging characteristics of birefringent lenses under focused and defocused condition,” Optik 110, 513–520 (1999).

1998

S. Sanyal, P. Bandyopadhyay, A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592–599 (1998).
[CrossRef]

1997

M. Schmitz, O. Bryngdahl, “A new type of lens with binary subwavelength structures,” Opt. Photon. News 8(12), 18 (1997).
[CrossRef]

1994

K. Bhattacharya, A. K. Chakraborty, 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]

1992

1988

1986

1985

1984

1983

1972

G. Hausler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
[CrossRef]

1971

1961

1960

1875

J. L. Soret, “Ueber die durch Kreisgitter Diffractionsphanomene,” Ann. Phys. Chem. 156, 99–113 (1875).
[CrossRef]

Andres, P.

Bai, H. X.

Bandyopadhyay, P.

S. Sanyal, P. Bandyopadhyay, A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592–599 (1998).
[CrossRef]

Basu, D. K.

A. K. Chakraborty, S. Das, D. K. Basu, A. Ghosh, “Imaging characteristics of a birefringent lens,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. SPIE1166, 130–134 (1990).
[CrossRef]

Berriel-Valdos, L. R.

Bhattacharya, K.

K. Bhattacharya, A. K. Chakraborty, 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]

Bryngdahl, O.

M. Schmitz, O. Bryngdahl, “A new type of lens with binary subwavelength structures,” Opt. Photon. News 8(12), 18 (1997).
[CrossRef]

Chakraborty, A. K.

K. Bhattacharya, A. K. Chakraborty, 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]

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

A. K. Chakraborty, S. Das, D. K. Basu, A. Ghosh, “Imaging characteristics of a birefringent lens,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. SPIE1166, 130–134 (1990).
[CrossRef]

Das, S.

A. K. Chakraborty, S. Das, D. K. Basu, A. Ghosh, “Imaging characteristics of a birefringent lens,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. SPIE1166, 130–134 (1990).
[CrossRef]

Díaz, A.

Farn, M. W.

Ghosh, A.

S. Sanyal, A. Ghosh, “Imaging characteristics of birefringent lenses under focused and defocused condition,” Optik 110, 513–520 (1999).

S. Sanyal, P. Bandyopadhyay, A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592–599 (1998).
[CrossRef]

K. Bhattacharya, A. K. Chakraborty, 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]

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

A. K. Chakraborty, S. Das, D. K. Basu, A. Ghosh, “Imaging characteristics of a birefringent lens,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. SPIE1166, 130–134 (1990).
[CrossRef]

Hausler, G.

G. Hausler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
[CrossRef]

Hazra, L. N.

L. N. Hazra, “Diffractive optical elements: past, present, and future,” in Selected Papers from International Conference on Optics and Optoelectronics ’98, K. Singh, O. P. Nijhawan, A. K. Gupta, A. K. Musla, eds., Proc. SPIE3729, 198–212 (1999).
[CrossRef]

Indebetouw, G.

Korpel, A.

McCrickerd, J. T.

Miyamoto, K.

Montes, E. L.

Murata, K.

Ojeda-Castañeda, J.

Pieper, R. J.

Sanyal, S.

S. Sanyal, A. Ghosh, “Imaging characteristics of birefringent lenses under focused and defocused condition,” Optik 110, 513–520 (1999).

S. Sanyal, P. Bandyopadhyay, A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592–599 (1998).
[CrossRef]

Schmitz, M.

M. Schmitz, O. Bryngdahl, “A new type of lens with binary subwavelength structures,” Opt. Photon. News 8(12), 18 (1997).
[CrossRef]

Soret, J. L.

J. L. Soret, “Ueber die durch Kreisgitter Diffractionsphanomene,” Ann. Phys. Chem. 156, 99–113 (1875).
[CrossRef]

Tsujiuchi, J.

J. Tsujiuchi, “Correction of optical images by compensation of aberrations and by spatial frequency filtering,” in Progress in Optics II, E. Wolf, ed. (North-Holland, Amsterdam, 1963), pp. 131–180.
[CrossRef]

Welford, W. T.

Ann. Phys. Chem.

J. L. Soret, “Ueber die durch Kreisgitter Diffractionsphanomene,” Ann. Phys. Chem. 156, 99–113 (1875).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

K. Bhattacharya, A. K. Chakraborty, 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]

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

Opt. Commun.

G. Hausler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
[CrossRef]

Opt. Eng.

S. Sanyal, P. Bandyopadhyay, A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592–599 (1998).
[CrossRef]

Opt. Lett.

Opt. Photon. News

M. Schmitz, O. Bryngdahl, “A new type of lens with binary subwavelength structures,” Opt. Photon. News 8(12), 18 (1997).
[CrossRef]

Optik

S. Sanyal, A. Ghosh, “Imaging characteristics of birefringent lenses under focused and defocused condition,” Optik 110, 513–520 (1999).

Other

J. Tsujiuchi, “Correction of optical images by compensation of aberrations and by spatial frequency filtering,” in Progress in Optics II, E. Wolf, ed. (North-Holland, Amsterdam, 1963), pp. 131–180.
[CrossRef]

Lord Rayleigh, Experimental Notebook 1870–1878 (U.S. Air Force Geophysics Laboratory Research Library, Hanscom Air Force Base, Bedford, Mass., 01731).

L. N. Hazra, “Diffractive optical elements: past, present, and future,” in Selected Papers from International Conference on Optics and Optoelectronics ’98, K. Singh, O. P. Nijhawan, A. K. Gupta, A. K. Musla, eds., Proc. SPIE3729, 198–212 (1999).
[CrossRef]

A. K. Chakraborty, S. Das, D. K. Basu, A. Ghosh, “Imaging characteristics of a birefringent lens,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. SPIE1166, 130–134 (1990).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Proposed system.

Fig. 2
Fig. 2

Strehl definition versus effective defocus coefficient for α = 0.3142λ (plot 1) and α = 1.5λ (plot 2) in parallel-polarizer configuration. For α = 0.3142λ: 1a, first sinc square term of Eq. (7); 1b, second sinc square term of Eq. (7); 1c, product of two sinc terms of Eq. (7); 1d, sum of two sinc square terms of Eq. (7).

Fig. 3
Fig. 3

Strehl definition versus effective defocus coefficient for α = 0.6044λ (plot 1) and α = 1.5λ (plot 2) in crossed-polarizer configuration. For α = 0.6044λ: 1a, first sinc square term of Eq. (7); 1b, second sinc square term of Eq. (7); 1c, product of two sinc terms of Eq. (7); 1d, sum of two sinc square terms of Eq. (7).

Fig. 4
Fig. 4

(a) Variation of IPSF of an ideal lens with defocus. (b) Variation of IPSF of a birefringent lens (α = 0.3142λ, parallel-polarizer configuration) with defocus. (c) Variation of IPSF of a birefringent lens (α = 0.6044λ, crossed-polarizer configuration) with defocus. The defocus coefficient is expressed in terms of λ.

Fig. 5
Fig. 5

(a) IPSF of the birefringent lens with α = 0.3142λ in parallel-polarizer configuration for different values of defocusing, (b) IPSF of the birefringent lens with α = 0.6044λ in crossed-polarizer configuration for different values of defocusing. The defocus coefficient is expressed in terms of λ.

Equations (11)

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A-+r, α=cossinkα1-r2,
I-+ρ, α, W¯20=2 01 r cossinkα1-r2×expikW¯20r2J02πρrdr2,
I-+0, α, W¯20=2 01 r cossinkα1-r2×expikW¯20r2dr2.
Tt-+α=2 01 A-+2r, αrdr=121±sinc4α/λ,
S-+α, W¯20=I-+0, α, W¯20/Tt-+α.
S-+α, W20=1Tt-+α-rectz-12cossinkαz×exp-ikW¯20zdz2, rectz=1for-12<z<120otherwise.
S-+α, W¯20=14sinc2W¯20-αλ+sinc2W¯20+αλ±12sincW¯20-αλsincW¯20+αλ×cos2π αλ121±sinc4α/λ-1.
S+α, 0=2 sinc22α/λ/1+sinc4α/λ,
S-α, 0=2πα/λsinc2α/λ2/1-sinc4α/λ.
dS-+α, W¯20dW¯20W¯20=0
d2S-+dW¯202W¯20=0=5-cos4πp-4 cos2πp-8πp sin2πp7+cos4πp+8π2p2-1cos2πp-8πp sin2πp=0,

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