<P> Slope parameters describe characteristics of the slope of the roughness profile . Spacing and counting parameters describe how often the profile crosses certain thresholds . These parameters are often used to describe repetitive roughness profiles, such as those produced by turning on a lathe . </P> <Table> <Tr> <Th> Parameter </Th> <Th> Description </Th> <Th> Formula </Th> </Tr> <Tr> <Td> R, R </Td> <Td> the RMS slope of the profile within the sampling length </Td> <Td> R d q = 1 N ∑ i = 1 N Δ i 2 (\ displaystyle R_ (dq) = (\ sqrt ((\ frac (1) (N)) \ sum _ (i = 1) ^ (N) \ Delta _ (i) ^ (2)))) </Td> </Tr> <Tr> <Td> R, R </Td> <Td> the average absolute slope of the profile within the sampling length </Td> <Td> R d a = 1 N ∑ i = 1 N Δ i (\ displaystyle R_ (da) = (\ frac (1) (N)) \ sum _ (i = 1) ^ (N) \ Delta _ (i)) </Td> </Tr> <Tr> <Td> Δ i (\ displaystyle \ Delta _ (i) \!) </Td> <Td> where delta i is calculated according to ASME B46. 1 and is a 5th order Savitzky--Golay smoothing filter </Td> <Td> Δ i = 1 60 d x (y i + 3 − 9 y i + 2 + 45 y i + 1 − 45 y i − 1 + 9 y i − 2 − y i − 3) (\ displaystyle \ Delta _ (i) = (\ frac (1) (60dx)) (y_ (i + 3) - 9y_ (i + 2) + 45y_ (i + 1) - 45y_ (i - 1) + 9y_ (i - 2) - y_ (i - 3))) </Td> </Tr> </Table> <Tr> <Th> Parameter </Th> <Th> Description </Th> <Th> Formula </Th> </Tr> <Tr> <Td> R, R </Td> <Td> the RMS slope of the profile within the sampling length </Td> <Td> R d q = 1 N ∑ i = 1 N Δ i 2 (\ displaystyle R_ (dq) = (\ sqrt ((\ frac (1) (N)) \ sum _ (i = 1) ^ (N) \ Delta _ (i) ^ (2)))) </Td> </Tr>

Which of the following is the definition of roughness