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References

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  1. E. Wolf and K. Miyamoto, J. Opt. Soc. Am. 50, 1131 (1960).
    [Crossref]
  2. K. Miyamoto and E. Wolf, J. Opt. Soc. Am. 52, 615, 626 (1962).
    [Crossref]
  3. A. Rubinowicz, Ann. Physik 53, 257 (1917).
    [Crossref]
  4. A. Rubinowicz, Die Beugungswelle in der Kirchhoffschen Theorie der Beugung (Państwowe Wydawnictwo Naukowe, Warszawa, 1957).
  5. A. Rubinowicz, J. Opt. Soc. Am. 52, 717 (1962).
    [Crossref]

1962 (2)

1960 (1)

E. Wolf and K. Miyamoto, J. Opt. Soc. Am. 50, 1131 (1960).
[Crossref]

1917 (1)

A. Rubinowicz, Ann. Physik 53, 257 (1917).
[Crossref]

Miyamoto, K.

K. Miyamoto and E. Wolf, J. Opt. Soc. Am. 52, 615, 626 (1962).
[Crossref]

E. Wolf and K. Miyamoto, J. Opt. Soc. Am. 50, 1131 (1960).
[Crossref]

Rubinowicz, A.

A. Rubinowicz, J. Opt. Soc. Am. 52, 717 (1962).
[Crossref]

A. Rubinowicz, Ann. Physik 53, 257 (1917).
[Crossref]

A. Rubinowicz, Die Beugungswelle in der Kirchhoffschen Theorie der Beugung (Państwowe Wydawnictwo Naukowe, Warszawa, 1957).

Wolf, E.

K. Miyamoto and E. Wolf, J. Opt. Soc. Am. 52, 615, 626 (1962).
[Crossref]

E. Wolf and K. Miyamoto, J. Opt. Soc. Am. 50, 1131 (1960).
[Crossref]

Ann. Physik (1)

A. Rubinowicz, Ann. Physik 53, 257 (1917).
[Crossref]

J. Opt. Soc. Am. (3)

Other (1)

A. Rubinowicz, Die Beugungswelle in der Kirchhoffschen Theorie der Beugung (Państwowe Wydawnictwo Naukowe, Warszawa, 1957).

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Figures (1)

Fig. 1
Fig. 1

Conical frustrum bounded by the covering surface S and the lateral area L. Point P is the vertex of the cone belonging to L, B is the boundary curve of S and L. A vector surface element on L is given by n d f = d r × d s ( r / r Q ).

Equations (11)

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u ( P ) = S n · V ( P , Q ) d f ,
V ( P , Q ) = 1 4 π [ e i k r r grad Q u ( Q ) u ( Q ) grad Q e i k r r ] .
V ( P , Q ) = rot Q W ( P , Q ) .
W ( P , Q ) = i r × 1 4 π 1 r Q r Q + e i k r grad Q u ( Q ) d r .
S + L n · V ( P , Q ) d f = 0.
n d f = d r × d s ( r / r Q ) ,
L n · V ( P , Q ) d f = 1 4 π L e i k r r n · grad Q u ( Q ) d f .
n · grad Q e i k r r = n ( e i k r r ) = 0
L n · V ( P , Q ) d f = B r Q + 1 4 π 1 r Q e i k r ( d r × d s ) · grad Q u ( Q ) = B W ( P , Q ) · d s ,
W ( P , Q ) = i r × 1 4 π 1 r Q r Q + e i k r grad Q u ( Q ) d r .
S n · V ( P , Q ) d f = S n · rot Q W ( P , Q ) d f .