• Arithmetical mean deviation of the assessed topographic surface [1][2][3][4]

where L_x and L_y are the size of a definition area
 
Digitized form :


where N_x and N_y are number of data points in x and y direction.

• Root mean square deviation of the assessed topographic surface [1][2][3][4]

Root mean square of the ordinate value Z(x,y) within a definition area
 
AnaLytical Form:


where L_x and L_y are the size of a definition area
 
Digitized form :


where N_x and N_y are number of data points in x and y direction.

• Skewness of the assessed topographic surface [1][2][3][4]

Skewness of the ordinate value Z(x,y) within a definition area

AnaLytical Form:

where L_x and L_y are the size of a definition area
 
Digitized form :


where N_x and N_y are number of data points in x and y direction.

• Kurtosis of the assessed topographic surface [1][2][3][4]

Kurtosis of the ordinate value Z(x,y) within a definition area


 where L_x and L_y are the size of a definition area

Digitized form :


where N_x and N_y are number of data points in x and y direction.

• Root mean square slope of the assessed topographic surface [3]

Root mean square slope of the ordinate value Z(x,y) within a definition area


 where L_x and L_y are the size of a definition area

Digitized form :


where


N_x and N_y are number of data points in x and y direction.

• Developed interfacial area ratio [2][3]
  

 where L_x and L_y are the size of a definition area

Digitized form :



where



N_x and N_y are number of data points in x and y direction.

• Arithmetic Mean Summit Curvature of the surface [2]
  

 
for any summit located at and n is a number of summits. Eight nearest neighbors are used to determine summits of areal topographic data.

• Maximum peak height, Sp [1][2][3][4]: largest peak height value within a definition area


• Maximum pit height, Sv [1][2][3][4]: largest pit height value within a definition area

• Maximum height of the topographic surface [1][2][3][4], St = |Sp| + |Sv|

• Ten point height of the surface [4]

where Sp is peak height and Sv is pit height. Eight nearest neighbors are used to determine summits and valleys of areal topographic data.

• Density of summits, Sds [2][3][4]: number of peaks per unit area. Eight nearest neighbors are used to determine summits of areal topographic data.

References

1. Surface Texture (Surface Roughness, Waviness, and Lay), an American National Standard, ASME B46.1-2002, New York, NY

2. K. J. Stout, P. J. Sullivan, W. P. Dong, E. Mainsah, N. Lou, T. Mathia and H. Zahouani, The Development of Methods for The Characterisation of Roughness in Three Dimensions, Report EUR 15178 EN. EC Brussels, 1993

3. L. Blunt and X. Jiang, Advanced Techniques for Assessment Surface Topography, 1st edition, London Penton Press, 2003, ISBN 1903996112

4. ISO/TC 213 N057 2004 Draft ISO/WD Surface texture: Geometrical Product Specification (GPS) - Surface texture: Areal - Part 1: Terms, definitions and surface texture parameters (International Standard Organization)