a(e) » u + V • co8(2 • (e-Qg)) 



the three term regression technique yields estimates for u, v, and 9^. 

 These terms have definite physical meaning. u represents the simple 

 mean roughness level of the surface, that is the mean a(6) of the signal 

 sampled In all directions. This could be visualized as the "Isotropic" 

 component of the surface, v determines the amplitude of the sinusoidal 

 component of the regression model and represents a measure of the degree 

 of anlsotropy of the surface. 6 estimates the normal to the true azi- 

 muth of the linear trend. Frequency Is not estimated since the perio- 

 dicity of 1 cycle/ 180' Is known. 



Unfortunately, It Is not possible to decompose more than one linear 

 trend In a surface using this method. Envision a surface consisting of 

 two linear trends of differing orientation (6^ and 6g), "anlsotropy" 

 levels (VA and vb), and "Isotropy" levels (ua and ug). The surface, 

 being a simple linear combination of the two component trends can be 

 expressed as 



a(e) » (u^ + ub) + VA • co8(2 • (9-8^)) + vb • cos(2 • B-Sb)) 



In this example, u^ and ub are both presumably equal to zero for "per- 

 fect" linear trends. However, even In non-perfect cases In which some 

 energies are available parallel to strike, the u components are linearly 

 combined and can not be differentiated. The "anlsotropy" components 

 also combine linearly to yield another sinusoid whose amplitude and 

 phase are dependent on the relative amplitudes and phases of the orlg- 



86 



