ID: 609807
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Roughness ConceptsRMS, Correlation Lengths, and the Height-Height Correlation FunctionBy Max Bloomfield, June 2006 ©2006,Max Bloomfield How rough are these surfaces? ©2006,Max Bloomfield Distances below the mean plane are negative (yellow arrows) and distances above are positive (purple arrows). And we chosethe mean planes position so these values all add to zero! (We did that when we used the rule that the amount of surface above and below the mean plane should be equal.) ©2006,Max Bloomfield RMS roughness turns out to be good for comparing how rough things are when they have similar structures.For example, here B has 3 times the wof A, and C has 6 times the wof A.(Thats good, because B and C are just A stretched vertically by a factor of 3 and 6 respectively.)BC ©2006,Max Bloomfield Which of these is rougher?ABJust using RMS can be deceiving. Above, A and B have the same RMS roughness!B was constructed by scaling A horizontally, so by the same amount on average. So why does B seemso much rougher? Its the quicker variation in the vertical as a function of horizontal position. ©2006,Max Bloomfield 1.Pick a point on the surface. Call that horizontal position (a) ©2006,Max Bloomfield3.Average the squared difference in height for a large a1 1 b1 a2 b2 r rb2 a3 b3 r rb3 ©2006,Max Bloomfield 2w2Strong dependence on r ©2006,Max Bloomfieldnoisy surface, bump widthis not a well defined term.