Abstract

The optical transfer function of a perfect-lens aperture masked by linear retarders or rotators with an analyzer at the output side is studied. The beam of light considered is a polarized polychromatic beam with a Gaussian spectral profile.

© 1988 Optical Society of America

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References

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  1. P. Jacquinot, B. Roizen-Dossier, “Apodization,” in Progress in Optics III, E. Wolf, ed. (North-Holland, Amsterdam, 1964).
  2. A. K. Chakraborty, H. Mukherjee, “Modification of PSF by polarization masks,”J. Opt. (India) 5, 71–74 (1976).
  3. A. K. Chakraborty, B. Mondal Adhikari, R. Roy Choudhury, “The optical transfer function of a perfect lens with polarization masks,”J. Opt. (Paris) 9, 251–254 (1978).
    [CrossRef]
  4. B. Chakraborty, “Effect of polarizers used as masks on the perfect-lens aperture,” J. Opt. Soc. Am. A 2, 743–746 (1985).
    [CrossRef]
  5. A. Ghosh, J. Basu, P. P. Groswami, A. K. Chakraborty, “Frequency response characteristics of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1987).
    [CrossRef]
  6. A. K. Chakraborty, “Propagation of a polarized polychromatic beam through a birefringent plate,” Opt. Commun. 10, 374–377 (1974).
    [CrossRef]
  7. B. Chakraborty, “Depolarizing effect of propagation of a polarized polychromatic beam through an optically active medium: a generalized study,” J. Opt. Soc. Am. A 3, 1422–1427 (1986).
    [CrossRef]
  8. G. G. Slyusarev, Aberration and Optical Design Theory, 2nd ed. (Adam Hilger, Bristol, UK, 1984).
  9. W. A. Schurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1966), Table 4.1.

1987 (1)

A. Ghosh, J. Basu, P. P. Groswami, A. K. Chakraborty, “Frequency response characteristics of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1987).
[CrossRef]

1986 (1)

1985 (1)

1978 (1)

A. K. Chakraborty, B. Mondal Adhikari, R. Roy Choudhury, “The optical transfer function of a perfect lens with polarization masks,”J. Opt. (Paris) 9, 251–254 (1978).
[CrossRef]

1976 (1)

A. K. Chakraborty, H. Mukherjee, “Modification of PSF by polarization masks,”J. Opt. (India) 5, 71–74 (1976).

1974 (1)

A. K. Chakraborty, “Propagation of a polarized polychromatic beam through a birefringent plate,” Opt. Commun. 10, 374–377 (1974).
[CrossRef]

Basu, J.

A. Ghosh, J. Basu, P. P. Groswami, A. K. Chakraborty, “Frequency response characteristics of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1987).
[CrossRef]

Chakraborty, A. K.

A. Ghosh, J. Basu, P. P. Groswami, A. K. Chakraborty, “Frequency response characteristics of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1987).
[CrossRef]

A. K. Chakraborty, B. Mondal Adhikari, R. Roy Choudhury, “The optical transfer function of a perfect lens with polarization masks,”J. Opt. (Paris) 9, 251–254 (1978).
[CrossRef]

A. K. Chakraborty, H. Mukherjee, “Modification of PSF by polarization masks,”J. Opt. (India) 5, 71–74 (1976).

A. K. Chakraborty, “Propagation of a polarized polychromatic beam through a birefringent plate,” Opt. Commun. 10, 374–377 (1974).
[CrossRef]

Chakraborty, B.

Ghosh, A.

A. Ghosh, J. Basu, P. P. Groswami, A. K. Chakraborty, “Frequency response characteristics of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1987).
[CrossRef]

Groswami, P. P.

A. Ghosh, J. Basu, P. P. Groswami, A. K. Chakraborty, “Frequency response characteristics of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1987).
[CrossRef]

Jacquinot, P.

P. Jacquinot, B. Roizen-Dossier, “Apodization,” in Progress in Optics III, E. Wolf, ed. (North-Holland, Amsterdam, 1964).

Mondal Adhikari, B.

A. K. Chakraborty, B. Mondal Adhikari, R. Roy Choudhury, “The optical transfer function of a perfect lens with polarization masks,”J. Opt. (Paris) 9, 251–254 (1978).
[CrossRef]

Mukherjee, H.

A. K. Chakraborty, H. Mukherjee, “Modification of PSF by polarization masks,”J. Opt. (India) 5, 71–74 (1976).

Roizen-Dossier, B.

P. Jacquinot, B. Roizen-Dossier, “Apodization,” in Progress in Optics III, E. Wolf, ed. (North-Holland, Amsterdam, 1964).

Roy Choudhury, R.

A. K. Chakraborty, B. Mondal Adhikari, R. Roy Choudhury, “The optical transfer function of a perfect lens with polarization masks,”J. Opt. (Paris) 9, 251–254 (1978).
[CrossRef]

Schurcliff, W. A.

W. A. Schurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1966), Table 4.1.

Slyusarev, G. G.

G. G. Slyusarev, Aberration and Optical Design Theory, 2nd ed. (Adam Hilger, Bristol, UK, 1984).

J. Mod. Opt. (1)

A. Ghosh, J. Basu, P. P. Groswami, A. K. Chakraborty, “Frequency response characteristics of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1987).
[CrossRef]

J. Opt. (India) (1)

A. K. Chakraborty, H. Mukherjee, “Modification of PSF by polarization masks,”J. Opt. (India) 5, 71–74 (1976).

J. Opt. (Paris) (1)

A. K. Chakraborty, B. Mondal Adhikari, R. Roy Choudhury, “The optical transfer function of a perfect lens with polarization masks,”J. Opt. (Paris) 9, 251–254 (1978).
[CrossRef]

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

Opt. Commun. (1)

A. K. Chakraborty, “Propagation of a polarized polychromatic beam through a birefringent plate,” Opt. Commun. 10, 374–377 (1974).
[CrossRef]

Other (3)

G. G. Slyusarev, Aberration and Optical Design Theory, 2nd ed. (Adam Hilger, Bristol, UK, 1984).

W. A. Schurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1966), Table 4.1.

P. Jacquinot, B. Roizen-Dossier, “Apodization,” in Progress in Optics III, E. Wolf, ed. (North-Holland, Amsterdam, 1964).

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Figures (5)

Fig. 1
Fig. 1

OTF curves for two different values of θ and for = 0.707, β = 0°, K = 1, δ = 0°, (Δλ)hw = 422 nm, and δ = 90°.

Fig. 2
Fig. 2

OTF curves for two different values of (Δλ)hw and δ, with = 0.707, θ = 0°, K = 1, δ = 10°, and β = 60°.

Fig. 3
Fig. 3

OTF curves for different values of β, with = 0.50, K = 1, δ = 10°, t = 1.53 mm, and (Δλ)hw = 422 nm.

Fig. 4
Fig. 4

OTF curves for different values of β, with = 0.707, K = 1, δ = 10°, t = 1.53 mm, and (Δλ)hw = 422 nm.

Fig. 5
Fig. 5

OTF curves for different values of t, with = 0.707, K = 1, δ = 10°, β = 0°, and (Δλ)hw = 422 nm.

Tables (1)

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Table 1 Variation of F(ω) as a Function of ωa

Equations (18)

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J i = [ K e i δ ] [ I ( ν ) d ν ] 1 / 2 ( K 2 + 1 ) 1 / 2 ,
central = C ( δ , θ ) J i ,
C ( δ , θ ) = [ cos δ + i sin δ cos 2 θ i sin δ sin 2 θ i sin δ sin 2 θ cos δ i sin δ cos 2 θ ]
J central = π 2 J 1 ( X ) ( X ) × [ cos δ + i sin δ cos 2 θ i sin δ sin 2 θ i sin δ sin 2 θ cos δ i sin δ cos 2 θ ] J i .
J annular = [ π J 1 ( X ) X π 2 J 1 ( X ) ( X ) ] J i .
J = J central + J annular .
P ( β ) = [ K 1 ( λ ) cos 2 β + K 2 ( λ ) sin 2 β { K 1 ( λ ) K 2 ( λ ) } sin β cos β { K 1 ( λ ) K 2 ( λ ) } sin β cos β K 1 ( λ ) sin 2 β + K 2 ( λ ) cos 2 β ] ,
I ( X ) = { J 1 2 ( X ) X 2 ( K 1 2 + K 2 2 ) + 2 4 J 1 2 ( X ) ( X ) 2 [ ( K 1 2 + K 2 2 ) ( K 1 2 + K 2 2 ) cos δ + 0.25 ( K 1 2 K 2 2 ) sin 4 θ 0.25 ( K 1 2 K 2 2 ) sin 4 θ cos 2 δ ] + 2 2 J 1 ( X ) X J 1 ( X ) ( X ) × ( K 1 2 + K 2 2 ) cos δ ( K 1 2 + K 2 2 ) } I ( ν ) d ν .
I ( X ) = ( J 1 2 ( X ) X 2 [ K 2 ( K 1 2 cos 2 β + K 2 2 sin 2 β ) + ( K 1 2 sin 2 β + K 2 2 cos 2 β ) + 2 K cos δ sin β cos β × ( K 1 2 + K 2 2 ) ] + 4 J 1 2 ( X ) ( X ) 2 { 2 K 2 ( 1 cos δ ) × ( K 1 2 cos 2 β + K 2 2 sin 2 β ) + 2 ( 1 cos δ ) ( K 1 2 sin 2 β + K 2 2 cos 2 β ) + 2 K ( K 1 2 K 2 2 ) sin β cos β [ cos ( δ 2 δ ) 2 cos ( δ δ ) + cos δ ] } + 2 2 J 1 ( X ) X J 1 ( X ) ( X ) × { K 2 ( cos δ 1 ) ( K 1 2 cos 2 β + K 2 2 sin 2 β ) + 2 K ( K 1 2 K 2 2 ) sin β cos β [ cos ( δ δ ) cos δ ] + ( K 1 2 sin 2 β + K 2 2 cos 2 β ) ( cos δ 1 ) } ) I ( ν ) d ν ( K 2 + 1 ) .
F UN ( ω ) = Δ ( ω , 1,1 ) Δ ν { Δ ν I ( ν ) [ K 1 2 ( ν ) + K 2 2 ( ν ) ] d ν } + 2 4 Δ ( ω , , ) Δ ν { Δ ν I ( ν ) [ K 1 2 ( ν ) + K 2 2 ( ν ) ] d ν Δ ν I ( ν ) [ K 1 2 ( ν ) + K 2 2 ( ν ) ] cos δ ( ν ) d ν + 0.25 sin 4 θ Δ ν I ( ν ) [ K 1 2 ( ν ) + K 2 2 ( ν ) ] d ν 0.25 sin 4 θ Δ ν I ( ν ) [ K 1 2 ( ν ) + K 2 2 ( ν ) ] cos 2 δ ( ν ) d ν } + 2 4 Δ ( ω , 1 , ) Δ ν { Δ ν I ( ν ) [ K 1 2 ( ν ) + K 2 2 ( ν ) ] cos δ ( ν ) d ν Δ ν I ( ν ) [ K 1 2 ( ν ) + K 2 2 ( ν ) ] d ν }
F UN ( ω ) = Δ ( ω , 1,1 ) Δ ν ( K 2 + 1 ) { ( K 2 cos 2 β + sin 2 β ) Δ ν I ( ν ) K 1 2 ( ν ) d ν + ( K 2 sin 2 β + cos 2 β ) Δ ν I ( ν ) K 2 2 ( ν ) d ν + 2 K cos δ sin β cos β Δ ν I ( ν ) [ K 1 2 ( ν ) K 2 2 ( ν ) ] d ν } + 2 4 Δ ( ω , , ) Δ ν ( K 2 + 1 ) { ( K 2 cos 2 β + sin 2 β ) Δ ν I ( ν ) K 1 2 ( ν ) d ν + ( K 2 sin 2 β + cos 2 β ) Δ ν I ( ν ) K 2 2 ( ν ) d ν ( K 2 cos 2 β + sin 2 β ) Δ ν I ( ν ) K 1 2 ( ν ) cos δ ( ν ) d ν ( K 2 sin 2 β + cos 2 β ) Δ ν I ( ν ) K 2 2 ( ν ) cos δ ( ν ) d ν + K sin β cos β Δ ν I ( ν ) [ K 1 2 ( ν ) K 2 2 ( ν ) ] × cos [ δ 2 δ ( ν ) ] d ν 2 K sin β cos β Δ ν I ( ν ) [ K 1 2 ( ν ) K 2 2 ( ν ) ] cos [ δ δ ( ν ) ] d ν + K sin β cos β cos δ × Δ ν I ( ν ) [ K 1 2 ( ν ) K 2 2 ( ν ) ] d ν } + 2 4 Δ ( ω , 1 , ) Δ ν ( K 2 + 1 ) × { ( K 2 cos 2 β + sin 2 β ) Δ ν I ( ν ) K 1 2 ( ν ) cos δ ( ν ) d ν + ( K 2 sin 2 β + cos 2 β ) Δ ν I ( ν ) K 2 2 ( ν ) cos δ ( ν ) d ν ( K 2 cos 2 β + sin 2 β ) Δ ν I ( ν ) K 1 2 ( ν ) d ν ( K 2 sin 2 β + cos 2 β ) Δ ν I ( ν ) K 2 2 ( ν ) d ν + 2 K sin β cos β Δ ν I ( ν ) [ K 1 2 ( ν ) K 2 2 ( ν ) ] × cos [ δ δ ( ν ) ] d ν 2 K sin β cos β cos δ Δ ν I ( ν ) × [ K 1 2 ( ν ) K 2 2 ( ν ) ] d ν } .
F ( ω ) = F UN ( ω ) F UN ( 0 ) .
central = R ( θ ) J j ,
R ( θ ) = [ cos θ ( ν ) sin θ ( ν ) sin θ ( ν ) cos θ ( ν ) ]
annular = R ( θ ) J i .
J central = π 2 J 1 ( X ) ( X ) R ( θ ) J i ,
J annular = [ π J 1 ( X ) X π 2 J 1 ( X ) ( X ) ] R ( θ ) J i .
F UN ( ω ) = π 2 Δ ( ω , 1,1 ) 2 ( K 2 + 1 ) Δ ν { ( K 2 + 1 ) Δ ν I ( ν ) [ K 1 2 ( ν ) + K 2 2 ( ν ) ] d ν + [ ( K 2 1 ) cos 2 β + 2 K cos δ sin 2 β ] × Δ ν I ( ν ) [ K 1 2 ( ν ) K 2 2 ( ν ) ] cos 2 t θ ( ν ) d ν + [ ( 1 K ) sin 2 β + 2 K cos δ cos 2 β ] × Δ ν I ( ν ) [ K 1 2 ( ν ) K 2 2 ( ν ) ] sin 2 t θ ( ν ) d ν } + 2 π 2 4 Δ ( ω , , ) ( K 2 + 1 ) Δ ν { ( cos 2 β + K 2 sin 2 β ) × Δ ν I ( ν ) K 1 2 ( ν ) d ν + ( sin 2 β + K 2 cos 2 β ) × Δ ν I ( ν ) K 2 2 ( ν ) d ν K cos δ sin 2 β × Δ ν I ( ν ) [ K 1 2 ( ν ) K 2 2 ( ν ) ] d ν [ cos 2 β + K 2 sin 2 β K cos δ sin 2 β ] × Δ ν I ( ν ) K 1 2 ( ν ) cos 2 t θ ( ν ) d ν [ sin 2 β + K 2 cos 2 β + K cos δ sin 2 β ] × Δ ν I ( ν ) K 2 2 ( ν ) cos 2 t θ ( ν ) d ν } + 2 π 2 4 Δ ( ω , 1 , ) ( K 2 + 1 ) Δ ν × { [ 1 2 ( K 2 1 ) sin 2 β K cos δ cos 2 β ] × Δ ν I ( ν ) [ K 1 2 ( ν ) K 2 2 ( ν ) ] sin 2 t θ ( ν ) d ν ( K cos δ sin 2 β K 2 sin 2 β cos 2 β ) × Δ ν I ( ν ) K 1 2 ( ν ) cos 2 t θ ( ν ) d ν + ( K cos δ sin 2 β + K 2 cos 2 β + sin 2 β ) × Δ ν I ( ν ) K 2 2 ( ν ) cos 2 t θ ( ν ) d ν + ( K cos δ sin 2 β K 2 sin 2 β cos 2 β ) × Δ ν I ( ν ) K 1 2 ( ν ) d ν ( K cos δ sin 2 β + K 2 cos 2 β + sin 2 β Δ ν I ( ν ) K 2 2 ( ν ) d ν } ,

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