3D Surface Roughness and Wear Measurement, Analysis and Inspection

Legacy Parameters

Rpm, Rvm and Rz (Average Max Peak Height, Valley Depth and Height of Surface)

The RpmRvm, and Rz  parameters are evaluated from an average of the heights and depths of  a number of extreme peaks and valleys. Rpm the Average Maximum Peak Height,  is found by averaging the heights of the ten (10) highest peaks found over the complete 3D image. Rvm, the Average Maximum Valley Depth, is found by averaging the depths of the ten (10) lowest valleys found over the complete 3D image. Rz, the Average Maximum Height of the Surface,  is found from RpmRvm. Note that in determining the peaks and valleys, the analysis software eliminates a grid of 11 x 11 pixels around a given peak/valley before searching for the next peak/valley, thus assuring that significantly separated peaks/valleys are found.


Rpm may be useful in establishing the height of the dominant peaked structures which may easily be plastically deformed under contact or penetrate a coating. Rvm provides an estimate of the average valley depths and may be useful in understanding fluid flow through an interface and space for debris entrapment. Rz provides an estimate of the overall peak to valley magnitude of a surface and may serve to predict the thickness of coating needed to completely cover and level a surface.

X Slope Rq and Y Slope Rq (X and Y Root Mean Squared Slope)

X Slope Rq and Y Slope Rq, the Root Mean Squared X Slope and Root Mean Squared Y Slope are found by calculating the standard deviation (i.e. rms) of the slopes of the surface along the X and Y directions respectively. The slope is found by taking the derivative of the surface profiles along each direction, using the lateral resolution of the measurement area as the point spacing.  Analytically, X Slope Rq and Y Slope Rq are given by:

Where the brackets,  <   >, represent the average value of all slopes in the relevant direction.


Slopes may be used to investigate the behavior of various surface texture forming techniques in that material and process conditions may change the slopes considerably, whereas the height parameters such as Ra are relatively unaffected. The surface slope may also be useful in relating the nature of the surface when used in coating and visual appearance applications.

NormVolume (Normalized Surface Volume)

NormVolume, the Normalized Surface Volume, is found by calculating the volume contained by the surface and a “plane” that is placed near the top of the surface. The placement of the reference plane is done on a statistical basis to ensure that the very high peak locations are not used as the reference point for the plane.  Once the volume is calculated (e.g. in units of cm3), the volume result is “normalized” to the cross sectional area of the plane (e.g. units of m2).  Other units of NormVolume are BCM which is an acronym for “Billions of Cubic Microns per Inch Squared”. The BCM units are typically used in the printing industry.


NormVolume finds application in the printing industry, by providing a measure of the fluid holding properties of printing device surfaces (e.g. anilox rolls, Lithoplates, etc. ) and the printed media (e.g. paper). Other applications, such as in the tribology field use the NormVolume to establish the volume of space a surface provides for lubricant containment. The measurement of various wear patters may result in a structure in which NormVolume may quantify the amount of material removed from a surface or displaced along a surface.

SAI (Surface Area Index)

SAI, the Surface Area Index, is the surface area at the lateral resolution of the measured/filtered surface as compared to that of a perfectly flat/smooth surface. The calculation involves fitting triangular patches between the measured points and adding up the total area of all patches. A ratio is then formed of the total surface area measured and the nominal flat area of measurement. This analysis is a precursor to a complete fractal analysis of the surface.i Since SAI is a ratio, it is a unitless quantity.

Depiction of the calculation of the Surface Area Index (SAI).  Demonstrating only a few triangular patches whereas the complete analysis involves fitting patches over the complete image.


The combination of different surface texture amplitudes and spacings are further manifested in the overall surface provided by the texture. The SAI parameter finds application for issues relating to  surface wetting, fluid flow, coating adhesion, printing etc.  

i C.A. Brown, P.D. Charles, W.A. Johnsen, S. Chester, fractal analysis of topographic data by the patchwork method, Wear 161 (1993) 61-67.

Parameter NameSymbolFamily
2D Average Roughness Ra Legacy Parameters
Average Maximum Height of the Surface Rz Legacy Parameters
Average Maximum Peak Height Rpm Legacy Parameters
Average Maximum Valley Depth Rvm Legacy Parameters
Normalized Surface Volume NormVolume Legacy Parameters
Root Mean Square Slope in X,Y Slope Rq (X,Y) Legacy Parameters
Surface Area Index SAI Legacy Parameters