Analytical calculation of the solid angle defined by a cylindrical detector and a point cosine source with orthogonal axes

Prata, M. J.

doi:10.1016/s0969-806x(03)00006-9

Cited by 9 publications

(3 citation statements)

References 10 publications

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“…In a recent work (Prata, 2003a) we derived analytical expressions for the solid angle subtended by a cylinder at a point cosine source, under the restriction that the source and cylinder axes are orthogonal to each other. In the present work we obtain similar expressions in the case where the source direction is parallel to the cylinder axis.…”

Section: Introductionmentioning

confidence: 99%

Analytical calculation of the solid angle defined by a cylindrical detector and a point cosine source with parallel axes

Prata¹

2004

Radiation Physics and Chemistry

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We derive analytical expressions for the solid angle subtended by a right finite circular cylinder at a point source with cosine angular distribution in the case where the source direction is parallel to the cylinder axis. As a subsidiary result, an expression for the solid angle subtended by a disc detector at a spread disc source is also provided, in the case where the two discs have a common symmetry axis which is also coincident with the source direction.

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Section: Introductionmentioning

confidence: 99%

Analytical calculation of the solid angle defined by a cylindrical detector and a point cosine source with parallel axes

Prata¹

2004

Radiation Physics and Chemistry

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“…In two recent works we obtained analytical expressions for the solid angle subtended by a cylindrical shaped detector at a point cosine source in the cases where the source axis is orthogonal [1] or parallel [2] to the cylinder axis of revolution. As ancillary results we also derived expressions for the solid angle defined by a circular disc in the cases where the source axis is orthogonal (Ω ⊥ ) or parallel (Ω ) to the symmetry axis of the disc.…”

Section: Introductionmentioning

confidence: 99%

Analytical calculation of the solid angle subtended by a circular disc detector at a point cosine source

Prata

2004

Nuclear Instruments and Methods in Physics Research Section A:

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We derive analytical expressions for the solid angle subtended by a circular disc at a point source with cosine angular distribution (f (µ) = µ/π) under the sole condition that the disc lies in the half-space illuminated by the source (µ ≥ 0). The expressions are given with reference to two alternative coordinate systems (S and S'), S being such that the z axis is parallel to the symmetry axis of the disc and S' such that the z ′ axis is aligned with the source direction. Sample plots of the expressions are presented.

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“…In a recent work (Prata, 2002) we describe the analytical calculation of the solid angle subtended by a cylinder at a point cosine source. Combining these results with those presented here, the case of an axially symmetric point source with an angular distribution given by f k (Ω) = 1 + a Ω · k can be treated analitically when the source axis (k) is orthogonal to that of the cylinder.…”

Section: Introductionmentioning

confidence: 99%

Solid angle subtended by a cylindrical detector at a point source in terms of elliptic integrals

Prata

2003

Radiation Physics and Chemistry

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The solid angle subtended by a right circular cylinder at a point source located at an arbitrary position generally consists of a sum of two terms: that defined by the cylindrical surface (Ω cyl ) and the other by either of the end circles (Ω circ ). We derive an expression for Ω cyl in terms of elliptic integrals of the first and third kinds and give similar expressions for Ω circ using integrals of the first and second kinds. These latter can be used alternatively to an expression also in terms of elliptic integrals, due to Philip A. Macklin and included as a footnote in Masket (Rev. Sci. Instr., 28 (3), 191-197, 1957). The solid angle subtended by the whole cylinder when the source is located at an arbitrary location can then be calculated using elliptic integrals.

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Analytical calculation of the solid angle defined by a cylindrical detector and a point cosine source with orthogonal axes

Abstract: We derive analytical expressions for the solid angle subtended by a right circular cylinder at a point source with cosine angular distribution in the case where the source and the cylinder axes are mutually orthogonal.

Cited by 9 publications

References 10 publications

Analytical calculation of the solid angle defined by a cylindrical detector and a point cosine source with parallel axes

Analytical calculation of the solid angle defined by a cylindrical detector and a point cosine source with parallel axes

Analytical calculation of the solid angle subtended by a circular disc detector at a point cosine source

Solid angle subtended by a cylindrical detector at a point source in terms of elliptic integrals

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