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References

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  1. G. Lansraux, Rev. optique 26, 24 (1947).
  2. H. H. Hopkins, Proc. Phys. Soc. (London) B,  62, 22 (1949).
    [Crossref]
  3. N. Nielsen, Handbuch der Theorie der Gammafunktion (B. G. Teubner, Leipzig, 1906).

1949 (1)

H. H. Hopkins, Proc. Phys. Soc. (London) B,  62, 22 (1949).
[Crossref]

1947 (1)

G. Lansraux, Rev. optique 26, 24 (1947).

Hopkins, H. H.

H. H. Hopkins, Proc. Phys. Soc. (London) B,  62, 22 (1949).
[Crossref]

Lansraux, G.

G. Lansraux, Rev. optique 26, 24 (1947).

Nielsen, N.

N. Nielsen, Handbuch der Theorie der Gammafunktion (B. G. Teubner, Leipzig, 1906).

Proc. Phys. Soc. (London) B (1)

H. H. Hopkins, Proc. Phys. Soc. (London) B,  62, 22 (1949).
[Crossref]

Rev. optique (1)

G. Lansraux, Rev. optique 26, 24 (1947).

Other (1)

N. Nielsen, Handbuch der Theorie der Gammafunktion (B. G. Teubner, Leipzig, 1906).

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Figures (1)

Fig. 1
Fig. 1

Method for studying the effect of spherical aberrations on the diffraction pattern.

Equations (11)

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U P = exp [ - i 2 π λ ( r - δ ) ] d S ,
δ = ( λ / 2 π ) ψ ( ρ / a ) m ,
r = ( R 2 + x 2 ) 1 2 - ϑ ρ cos φ             with             x R .
U P = 0 2 π 0 a exp [ i 2 π λ ϑ ρ cos φ ] exp [ i ψ ( ρ / a ) m ] ρ d ρ d φ .
0 2 π exp [ i 2 π λ ϑ ρ cos φ ] d φ = 2 π J 0 ( l ρ ) ,             where             l = 2 π λ ϑ .
U P = 0 a exp [ i ψ ( ρ / a ) m ] J 0 ( l ρ ) ρ d ρ .
v 2 j + 1 J 0 ( v ) d v ,
U P = n = 1 b n J n ( z ) z n - i n = 1 b n J n ( z ) z n             with             z = l a ,
D i f k ( ψ ) = 2 k ψ - 4 k ψ 3 3 ! + 6 k ψ 5 5 ! - 8 k ψ 7 7 ! +
D o f k ( ψ ) = 1 k - 3 k ψ 2 2 ! + 5 k ψ 4 4 ! - 7 k ψ 6 6 ! + ,
D i f k ( ψ ) = Im [ e i ψ j = 1 k + 1 S k + 1 j ( i ψ ) j - 1 ] , D o f k ( ψ ) = Re [ e i ψ j = 1 k + 1 S k + 1 j ( i ψ ) j - 1 ] ,