- ij-S 



n^(x^,y^,t) ^ -±k I I cose F(a)e^^^''^~\^l~'^y^l^8e 3a (4.26) 



The cross-spectrum of water surface displacement and slope as 

 measured, then, would be 



s* (a) = -ik r cose|F(a,e)|V^f'^x^^i-^o^-'^^^i-^o)]de .^ ,7) 



1 



However, the analysis requires that 



r2lT 



S (CT) = - ik cose|F{o,e) 1^ dO (A. 28) 



X ■'0 



Hence, the measured spectrum is corrected using 



c2tt 

 X X -"O 



Similarly, the correction, for a slope measurement along the y-axis at. 

 (xj.yg) would be 



S (a) = S* (o) f"" e^^^x(^2-^0^-'^(y2-yo^^ dG (A. 30) 



y ^\o ■'o 



