| 7 | | <I^2^(q)> = |
| | 7 | <I^2^(q)> = pi/2 ∫ ∫ I2(q,θ,ϕ)P1(q,θ)P2(q,ϕ)|cos(θ)| dθ dϕ |
| | 8 | |
| | 9 | I can't find a reference that includes the cosine term, or the pi/2 |
| | 10 | |
| | 11 | Perhaps the confusion arose from the different forms of the ellipsoid of revolution. Eq 2.32 gives the ellipsoid of revolution as: |
| | 12 | |
| | 13 | i(h) = ∫,,0,,^pi/2^ Phi2(h a √(cos2 θ + v2 sin2 θ) cos θ dθ |
| | 14 | |
| | 15 | but the 1-D ellipsoid kernel employs the substitution u = sin theta so it is evaluated as |
| | 16 | |
| | 17 | i(h) = ∫,,0,,^1^ Phi2(h a √(1 + u2(v2 - 1)) du |
| | 18 | |
| | 19 | [Note: the u variable above is incorrectly named as cos_alpha in the code.] |
