Changes between Version 3 and Version 4 of Ticket #332, comment 2


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Timestamp:
Jan 7, 2016 8:13:11 AM (9 years ago)
Author:
pkienzle
Comment:

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  • Ticket #332, comment 2

    v3 v4  
    55!SasView is using: 
    66 
    7     <I^2^(q)> = pi/2 ∫ ∫ I2(q,θ,ϕ)P1(q,θ)P2(q,ϕ)|cos(θ)| dθ dϕ 
     7    <I(q)> = pi/2 ∫ ∫ I(q,θ,ϕ)P,,1,,(q,θ)P,,2,,(q,ϕ)|cos(θ)| dθ dϕ 
    88 
    99I can't find a reference that includes the cosine term, or the pi/2 
    … …  
    1111Perhaps the confusion arose from the different forms of the ellipsoid of revolution. Eq 2.32 gives the ellipsoid of revolution as: 
    1212 
    13     i(h) = ∫,,0,,^pi/2^ Phi2(h a √(cos2 θ + v2 sin2 θ) cos θ dθ 
     13    i(h) = ∫,,0,,^pi/2^ Phi^2^(h a √(cos2 θ + v2 sin2 θ) cos θ dθ 
    1414 
    1515but the 1-D ellipsoid kernel employs the substitution u = sin theta so it is evaluated as 
    1616 
    17     i(h) = ∫,,0,,^1^ Phi2(h a √(1 + u2(v2 - 1)) du 
     17    i(h) = ∫,,0,,^1^ Phi^2^(h a √(1 + u2(v2 - 1)) du 
    1818 
    1919[Note: the u variable above is incorrectly named as cos_alpha in the code.]