# Application of Areal Topography Parameters in Surface Characterization
## 2 Areal Topography Parameters from Definition to Application  
A surface condition is characterized by numerous areal topography parameters, which can be classified into several categories: height, spatial, hybrid, functional, and miscellaneous [26]. Most of these parameters are defined in the ISO 25178-2:2021 standard Geometrical Product Specifications (GPS)--Surface Texture: Areal--Part 2: Terms, Definitions, and Surface Texture Parameters [26]. Although surface texture is inherently multidimensional and complex, industry and practice still rely heavily on a limited set of parameters namely \(Ra\) or \(Sa\) and \(Rz\) or \(Sz\) due to their simplicity, standardization, and ease of interpretation. Most technical drawings, specifications, and standards require only \(Ra\) or \(Sa\), which reinforces their widespread use in quality control and production. The most commonly used roughness parameters \(Ra\) in 2D and \(Sa\) in 3D represent the arithmetical mean deviation of the surface profile or area. Mathematically, they quantify the average absolute deviation of height values from the mean plane, but do not capture the spatial distribution, shape, or frequency of surface features. As a result, entirely different surface profiles--for example, one with smooth, widely spaced undulations and another with sharp, densely packed peaks and valleys--can exhibit the same \(Ra\) or \(Sa\) value, despite having vastly different functional or morphological properties. Illustrative examples of surfaces with identical \(Sa\) values but distinct topographies are shown in Figure 1. Figure 1 shows three different surface profiles (sinusoidal, randomly rough, and sharply peaked) that all share the same \(Sa\) value (approximately 18 nm). In all images, color indicates surface height: brighter colors represent higher regions, while darker tones correspond to deeper regions. It is well known that two surfaces can share the same \(Sa\) value while differing significantly in structure, function, or manufacturing quality. However, it is less often emphasized that the magnitude and reliability of the \(Sa\) parameter as well as other surface parameters do not depend solely on their mathematical definitions, but critically on the measurement conditions, instrument calibration, and data resolution. This is particularly evident in high-precision instruments such as atomic force microscopes (AFMs), where even minimal calibration errors in the \(x\)- or \(y\)-axis can distort dimensions, alter feature spacing, and lead to incorrect parameter estimation. To provide a broader basis for surface characterization, Table 1 presents a summary of the most relevant 3D areal parameters as defined in ISO 25178-2, along with their mathematical definitions and typical applications. Figure 1: Surfaces with identical \(Sa\) values but different structures: (**a**) sinusoidal profile, (**b**) random surface, (**c**) spiked features. The following section provides a literature review of the application of surface texture parameters in industry and research. \begin{table}
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The \(Sa\) and \(Sq\) parameters provide an overall measure of surface texture. However, they do not differentiate between peaks and valleys, nor do they account for the spatial distribution of surface features. Consequently, surfaces with significantly different topographic features can exhibit identical \(Sa\) and \(Sq\) values. Figure 2 illustrates two distinctly different surfaces with identical \(Sa\) and \(Sq\) values, highlighting the limitations and insensitivity of these parameters when used in isolation. Nevertheless, once the surface type or functional context is known, \(Sa\) and \(Sq\) can still serve as useful indicators of significant deviations in surface characteristics.