Symbol Parameter Name Unit

Definition Comments

Illustrations

R_a

average roughness

µm

$R_{\text{a}}=\frac{1}{l}{\displaystyle {\int }_0^l\left|z\left(x\right)\right|\text{d}x}$

It is the average surface roughness of the scanned profile around the mean line (the least squares mean line or that generated by a standard filter). It represents the average absolute deviation of the scanned profile points from a mean line.

R_q

root mean squared

µm

$R_{\text{q}}=\sqrt{\frac{1}{l}{\displaystyle {\int }_0^l\left|z^2\left(x\right)\right|\text{d}x}}$

It is the root mean square deviation of a scanned profile on a mean line. This is a statistically meaningful parameter that is only recently gaining acceptance for industrial surface measurement but is widely used within the optical surface community. This value is typically 11% higher than R_a.

It is further sensitive to peaks and valleys than R_a as the amplitudes are squared.

Ÿ Profile roughness (2D): R_q/R_a = 1.22

Ÿ Profile roughness (3D): R_q/R_a = 1.25

R_sk

skewness

$R_{\text{sk}}=\frac{1}{R_{\text{q}}^3}\left[\frac{1}{l}{\displaystyle {\int }_0^l{z}^3\left(x\right)\text{d}x}\right]$

It is the roughness amplitude distribution and is a measure of the (a) symmetry processes produce near-Gaussian distributions, with a skewness value close to 0.0. For asymmetric height distribution, the skewness can be negative or positive values.

Ÿ +ve for steep peaks and flat valleys.

Ÿ −ve for flat peaks and steep valleys.

R_ku

kurtosis

$R_{\text{ku}}=\frac{1}{R_{\text{q}}^4}\left[\frac{1}{l}{\displaystyle {\int }_0^l{z}^4\left(x\right)\text{d}x}\right]$

It is the roughness amplitude distribution and is a measure of the “peakedness” of the surface asperity heights about the profile mean line. A surface with a high kurtosis value tends to be peaky (large numbers of high asperities, and deep valleys) and produces a narrow asperity distribution.

Ÿ True Gaussian distribution has a kurtosis = 3

R_k

core roughness depth

µm

The depth of the roughness core profile.

R_pk

reduced peak height

µm

The average height of protruding peaks above roughness core profile.

R_vk

reduced valley depth

µm

The average depth of valleys is projecting through roughness core profile.

M_r1

material portion 1

%

The level in %, determined for the intersection line which separates the protruding peaks from the roughness core profile.