Abstract

A simple formalism relating image fields to object fields, similar to that of the scalar and paraxial case, is presented for an aplanatic system obeying the sine condition, which shows that the vector plane-wave spectrum of image fields is equal to the product of the vector coherent transfer function due to the x- and y-polarized point electric field source and the scalar spectrum of the corresponding transverse object fields. Utilizing this formula and dyadic Green’s function, a rigorous imaging theory of an aplanatic system for the point electric current source through a stratified medium is readily developed.

© 2006 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  9. H. Guo, J. Chen, and S. Zhuang, "Resolution of aplanatic systems with various semiapertures, viewed from the two sides of the diffracting aperture," J. Opt. Soc. Am. A (to be published).
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    [CrossRef] [PubMed]
  11. S. Barkeshli and P. H. Pathak, IEEE Trans. Microwave Theory Tech. 40, 128 (1992).
    [CrossRef]
  12. R. L. Hartman, J. Opt. Soc. Am. A 17, 1067 (2000).
    [CrossRef]
  13. P. Török, Opt. Lett. 25, 1463 (2000).
    [CrossRef]

2006 (1)

2005 (1)

2004 (1)

O. Haeberlé, Opt. Commun. 235, 1 (2004).
[CrossRef]

2003 (2)

2000 (2)

1998 (1)

P. Török, P. D. Higdon, and T. Wilson, J. Mod. Opt. 45, 1681 (1998).
[CrossRef]

1997 (1)

P. Török and T. Wilson, Opt. Commun. 137, 127 (1997).
[CrossRef]

1992 (1)

S. Barkeshli and P. H. Pathak, IEEE Trans. Microwave Theory Tech. 40, 128 (1992).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Ammar, M.

Barkeshli, S.

S. Barkeshli and P. H. Pathak, IEEE Trans. Microwave Theory Tech. 40, 128 (1992).
[CrossRef]

Chen, J.

H. Guo, J. Chen, and S. Zhuang, Opt. Express 14, 2095 (2006).
[CrossRef] [PubMed]

H. Guo, J. Chen, and S. Zhuang, "Resolution of aplanatic systems with various semiapertures, viewed from the two sides of the diffracting aperture," J. Opt. Soc. Am. A (to be published).

Foley, J. T.

Furukawa, H.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Guo, H.

H. Guo, J. Chen, and S. Zhuang, Opt. Express 14, 2095 (2006).
[CrossRef] [PubMed]

H. Guo, J. Chen, and S. Zhuang, "Resolution of aplanatic systems with various semiapertures, viewed from the two sides of the diffracting aperture," J. Opt. Soc. Am. A (to be published).

Haeberlé, O.

Hartman, R. L.

Higdon, P. D.

P. Török, P. D. Higdon, and T. Wilson, J. Mod. Opt. 45, 1681 (1998).
[CrossRef]

Pathak, P. H.

S. Barkeshli and P. H. Pathak, IEEE Trans. Microwave Theory Tech. 40, 128 (1992).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Tenjimbayashi, K.

Török, P.

Wilson, T.

P. Török, P. D. Higdon, and T. Wilson, J. Mod. Opt. 45, 1681 (1998).
[CrossRef]

P. Török and T. Wilson, Opt. Commun. 137, 127 (1997).
[CrossRef]

Wolf, E.

J. T. Foley and E. Wolf, Opt. Lett. 30, 1312 (2005).
[CrossRef] [PubMed]

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Zhuang, S.

H. Guo, J. Chen, and S. Zhuang, Opt. Express 14, 2095 (2006).
[CrossRef] [PubMed]

H. Guo, J. Chen, and S. Zhuang, "Resolution of aplanatic systems with various semiapertures, viewed from the two sides of the diffracting aperture," J. Opt. Soc. Am. A (to be published).

IEEE Trans. Microwave Theory Tech. (1)

S. Barkeshli and P. H. Pathak, IEEE Trans. Microwave Theory Tech. 40, 128 (1992).
[CrossRef]

J. Mod. Opt. (1)

P. Török, P. D. Higdon, and T. Wilson, J. Mod. Opt. 45, 1681 (1998).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (3)

O. Haeberlé, Opt. Commun. 216, 55 (2003).
[CrossRef]

O. Haeberlé, Opt. Commun. 235, 1 (2004).
[CrossRef]

P. Török and T. Wilson, Opt. Commun. 137, 127 (1997).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Proc. R. Soc. London, Ser. A (1)

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Other (2)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

H. Guo, J. Chen, and S. Zhuang, "Resolution of aplanatic systems with various semiapertures, viewed from the two sides of the diffracting aperture," J. Opt. Soc. Am. A (to be published).

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Figures (1)

Fig. 1
Fig. 1

Geometry of imaging of an aplanatic system for the point electric current source through a stratified medium.

Equations (22)

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E ( r ) = λ 2 E ̃ ( s ) exp ( j k s r ) d s x d s y ,
E ̃ ( s ) = [ x E x + y E y z s z 1 ( s x E x + s y E y ) ] exp [ j k ( s x x + s y y ) ] d x d y ,
F { E ( x x o , y y o ) } = E ̃ ( s ) exp [ j k ( s x x o + s y y o ) ] ,
E o ( x , y ) = E o ( x o , y o ) δ ( x x o , y y o ) d x o d y o .
E i ( x , y ) = E o ( x o , y o ) h ( x , y ; x o , y o ) d x o d y o ,
E ̃ i ( s i x , s i y ) = E o ( x o , y o ) h ̃ ( s i x , s i y ; x o , y o ) d x o d y o ,
h ̃ ( s i x , s i y ; x o , y o ) = [ H ̃ c 1 ( s i x , s i y ) e o x ( x o , y o ) + H ̃ c 2 ( s i x , s i y ) e o y ( x o , y o ) ] exp [ j k i M ( s i x x o + s i y y o ) ] ,
H ̃ c 1 x ( s i x , s i y ) = j Γ ( cos θ o sin 2 φ + cos θ i cos 2 φ ) ,
H ̃ c 1 y ( s i x , s i y ) = j Γ ( cos θ i cos θ o ) sin φ cos φ ,
H ̃ c 1 z ( s i x , s i y ) = j Γ sin θ i cos φ ,
H ̃ c 2 x ( s i x , s i y ) = H ̃ c 1 y ( s i x , s i y ) ,
H ̃ c 2 y ( s i x , s i y ) = j Γ ( cos θ o cos 2 φ + cos θ i sin 2 φ ) ,
H ̃ c 2 z ( s i x , s i y ) = j Γ sin θ i sin φ ,
E ̃ i ( s i x , s i y ) = H ̃ c 1 ( s i x , s i y ) E ̃ o x ( s o x , s o y ) + H ̃ c 2 ( s i x , s i y ) E ̃ o y ( s o x , s o y ) .
E m ( r , 0 ) = j ω μ 1 G m , 1 ( r , 0 ) p e .
G m , 1 ( r , 0 ) = j 4 π 2 d k x d k y exp ( j κ 1 z 1 ) 2 κ 1 [ n n Υ m , 1 > + n m n 1 Υ m , 1 > ( k m κ 1 k 1 κ m ) ] exp [ j ( k x x + k y y ) ] ,
E ̃ o x = A ( k 1 s m y A Υ m , 1 > + s m x s 1 z B Υ m , 1 > ) ,
E ̃ o y = A ( k 1 s m x A Υ m , 1 > s m y s 1 z B Υ m , 1 > ) ,
E i x ( r ) = j C [ k 1 p e x A 0 a + j 2 M k i p e z cos ϕ A 1 a + k 1 ( p e x cos 2 ϕ + p e y sin 2 ϕ ) A 2 a ] ,
E i y ( r ) = j C [ k 1 p e y A 0 a + j 2 M k i p e z sin ϕ A 1 a + k 1 ( p e x sin 2 ϕ p e y cos 2 ϕ ) A 2 a ] ,
E i z ( r ) = 2 C [ j M k i p e z A 0 b k 1 ( p e x cos ϕ + p e y sin ϕ ) A 1 b ] ,
A n a , b = 0 Φ i cos ( 1 2 ) θ m cos 1 2 θ i sin θ i B n a , b exp ( j Ψ ) × J n ( k i ρ sin θ i ) exp ( j k i cos θ i z ) d θ i ,

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