Abstract

Expressions for the scalar field in the focal volume are derived for the case of a uniform, converging, spherical wave incident upon a circular aperture. The intensity exhibits a reflection asymmetry with respect to the focal plane.

© 1981 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975).
  2. E. Collett and E. Wolf, “Symmetry properties of focused fields,” Opt. Lett. 5, 264–266 (1980).
    [Crossref] [PubMed]
  3. E. Wolf, “Phase conjugacy and symmetries in spatially bandlimited wavefields containing no evanescent components,” J. Opt. Soc. Am. 70, 1311–1319 (1980).
    [Crossref]
  4. D. A. Holmes and et al., “Parametric study of apertured focused Gaussian beams,” Appl. Opt. 11, 565–574 (1972).
    [Crossref] [PubMed]

1980 (2)

1972 (1)

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Figures (1)

Fig. 1
Fig. 1

Notation used for diffraction of converging spherical wave.

Equations (16)

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s f + z + ( x 2 + y 2 ) / 2 ( f + z ) - ( x ξ + y η ) / ( f + z ) - z ρ 2 / 2 f ( f + z ) ,
ρ 2 f 2 ,             ρ 2 ( f + z ) 2 ,             and             r 2 ( f + z ) 2 .
U ( P ) = ( - i A / λ f ) exp ( - i k f ) exp ( i k s ) s d S ,
U ( P ) = [ - i A / λ f ( f + z ) ] exp ( i k z ) exp [ i k r 2 / 2 ( f + z ) ] × exp { - i k z ρ 2 / [ 2 f ( f + z ) ] - i k r ρ × cos ( θ - ψ ) / ( f + z ) } ρ d ρ d θ ,
ξ = ρ sin θ ,             η = ρ cos θ ,             x = r sin ψ ,             and y = r cos ψ .
U ( P ) = ( - i A / λ f ) [ ( k a 2 - f u ) / k f ] × exp [ i k f ( f u + v 2 / 2 k ) / ( k a 2 - f u ) ] J ( u , v ) ,
J ( u , v ) = 0 1 exp ( - i u α 2 / 2 ) α d α × 0 2 π exp [ - i v α cos ( θ - ψ ) ] d θ
u = k a 2 z / [ f ( f + z ) ] ,             v = k a r / ( f + z ) .
J ( u , v ) = 2 π 0 1 J 0 ( v α ) exp ( - i u α 2 / 2 ) α d α .
f a
k a u ,             k a v .
k a ( f / a ) u .
I ( u , v ) = U ( P ) U * ( P ) ,
I ( u , v ) = ( A / 2 π f 2 ) 2 ( k a 2 - f u ) 2 J ( u , v ) J * ( u , v ) .
I ( u , 0 ) = ( 2 A 2 / f 2 ) W ( u ) ,
W ( u ) = { [ ( k a 2 / f ) - u ] 2 / u 2 } ( 1 - cos u / 2 ) .