# Application of Areal Topography Parameters in Surface Characterization
## 1 Introduction and Terminological Framework  
Modern advancements in surface nanotechnology and scanning probe microscopy (SPM) have opened new avenues for detailed surface characterization at micro- and nanoscales. Areal topography parameters (3D surface parameters) provide a more comprehensive and spatially resolved description of surface geometry compared to conventional two-dimensional (2D) profile parameters, which often fail to capture the complexity of functional surface features [1, 2]. This enhanced capability is essential for linking surface characteristics with critical functional properties, such as adhesion, friction, wettability, and optical performance [3]. Surface topography can be quantified through a wide array of parameters, both filtered and unfiltered, using 2D profilometry or advanced 3D measurement techniques. Traditional 2D roughness parameters (R) and waviness parameters (W) rely on filtering the measured profile according to standardized cut-off values. However, areal topography parameters--commonly referred to as 3D roughness parameters--are often left unfiltered due to the lack of established guidelines regarding appropriate cut-off values in areal measurements [4]. This has led to inconsistent terminology and interpretation across variousstudies [5]. The lack of standardized terminology sometimes leads to misinterpretation of results. Several surface topography parameters describe the surface condition. In surface nanotechnology, areal topography parameters serve as a powerful tool for characterizing a wide variety of surfaces produced through techniques such as laser surface modification, thin film deposition, and micro- or nano-fabrication processes [6; 7]. Surface integrity, which encompasses both microstructural and topographical features, is critical in applications where wear resistance, adhesion, and corrosion resistance are of primary importance, as surface defects can act as initiation sites for failure [8]. In this context, areal topography data can significantly influence manufacturing outcomes and, ultimately, determine the quality of the final product [9; 10]. Quantitative assessment of surfaces using areal topography parameters is essential for understanding the interactions between manufacturing processes and the resulting surface properties [11; 12]. Areal topography parameters are particularly vital for characterizing the surface condition of materials in additive manufacturing (AM) and machining processes [13]. The use of areal topography parameters to enhance the reliability of AM components has been demonstrated in [13]. [PERSON] et al. reported that the surface roughness and material removal rates of nanoparticle-reinforced powder metallurgy alloys were significantly affected by variations in machining parameters such as depth of cut and feed rate, demonstrating the utility of areal topographic analysis in optimizing manufacturing processes [14]. Surface topography also plays a significant role in powder metallurgy [15; 16]. In [17], the effects of laser beam micromachining on the surface characteristics of compacted titanium samples, produced using hydride-dehydride (HDH) titanium powder compaction, are investigated, with a specific focus on applications in dental implantology. Surface topography characterization typically relies on areal parameters, which provide a comprehensive representation of surface features, including both roughness and waviness. In [18], the authors investigate how to accurately and efficiently measure the irregular surfaces of metallic components produced via additive manufacturing, employing an advanced optical method known as coherence scanning interferometry (CSI). The integration of high-resolution techniques such as atomic force microscopy (AFM), a prominent SPM method, allows for nanoscale mapping of surface topography, providing detailed insight into surface roughness, texture, and local defects [19].