Proceedings with Extended Abstracts (single PDF file) - Radio ...

F 13 (ξ x ′) = (1 − cos 2ψ N) cot α 12 cot α 23 + (1 + cos 2ψ N ) − sin 2ψ N (cot α 12 + cot α 23 )sin 2 α 13 (cot α 12 − cot α 13 ) (cot α 23 − cot α 13 )F 23 (ξ x ′) = (1 − cos 2ψ N) cot α 12 cot α 13 + (1 + cos 2ψ N ) − sin 2ψ N (cot α 12 + cot α 13 )sin 2 α 23 (cot α 12 − cot α 23 ) (cot α 13 − cot α 23 )similarly for F ij (ξ y ′) where terms in psi N change sign. Variance of ψ N is:Var [ψ N ] =3(i≠j) (1 ∑ 1( ) 21− 1 i,j=1Bij2ξ 2 x ′ ξ 2 y ′) 2Pij2 Var [c ij ]c 2 ij(4)whereP 12 = sin 2ψ N (cot α 13 cot α 23 − 1) − cos 2ψ N (cot α 13 + cot α 23 )sin 2 α 12 (cot α 13 − cot α 12 ) (cot α 23 − cot α 12 )P 13 = sin 2ψ N (cot α 12 cot α 23 − 1) − cos 2ψ N (cot α 12 + cot α 23 )sin 2 α 13 (cot α 12 − cot α 13 ) (cot α 23 − cot α 13 )P 23 = sin 2ψ N (cot α 12 cot α 13 − 1) − cos 2ψ N (cot α 12 + cot α 13 )sin 2 α 23 (cot α 12 − cot α 23 ) (cot α 13 − cot α 23 )Variances of refractive index perturbation horizontal correlation lengths are:( 1Var [ρ x ′] =4ξ x ′ρ x ′) 2Var [ξ x ′] (5)and similarly for variance of ρ y ′. Covariance terms Cov[c ij , c ik ] have been neglected,the results in Figure 2 for SA configuration Case 1 [Hassenpflug et al., 2003] show thattheoretical estimates using the given expressions agree well with experimental data. θ x ′,θ y ′ are angular aspect sensitivity of the correlation ellipse.(a)yx |(b)Ψ Νy | ρ x|Ψxρ y|Figure 1: (a) Horizontal correlation ellipse parameters, (b) Zero-lag CCF coefficientvariance per Awe, Zhang. Peak CCF coefficient c ij (τ p )=1, τ p is varied to change c ij (0).157