# Roughness Evaluation of Burnished Topography with a Precise Definition of the S-L Surface
## 1 Introduction
This type of surface can be proposed by the application of the least-squares fitting methods [38]. When cylindrical details are measured, the reference plane can be obviously fitted by the cylindrical shape [39], polynomials with different degrees [40], or other planes suitable for representing the waviness [41; 42]. The application of least-square fitting procedures can reduce the distortion of the deep or wide features, especially when they are located near (on) the edge of the analysed detail [43; 44], compared to the regular digital filtering methods. However, guidance on how to use regular (e.g., those available in the commercial software) methods in the definition of a proper L-surface is required. Second, the S-surface received when an S-operator (e.g., S-filter [45]) is applied must also consider that it has been found that the occurrence of S-components can radically influence the values of the ST parameters [46]. One of the components included in the small-scale lateral surface (S-surface) is the high-frequency measurement noise. Generally, according to the ISO standard [47], measurement noise can be defined as the noise added to the output signal occurring during the normal use of the measuring instrument. When creating a standard reference frame for describing and reducing the measurement noise, it is necessary to define it, along with the associated measurement bandwidth [48; 49]. One of the often analysed bandwidths for measurement noise studies is in the high-frequency domain. Generally, the high-frequency measurement noise can be caused by the instability of the mechanics with any influences from the environment [50]. Nevertheless, in most cases, the high-frequency noise is caused by vibrations [51]. This problem seems to be even more significant when in situ measurement is provided [52; 53]. Some solutions can be proposed with the isolation [54; 55; 56] or suppression [57] of vibration sources. However, it is difficult to provide a general procedure for the selection of the method for the S-surface definition. One of the crucial tasks required to be resolved is to propose a method for a precise definition of the S-L surface for the textures containing some deep or wide features. It was observed in previous studies that the false estimation of the L-surface can enlarge the errors in the evaluation of the ISO 25178 surface topography parameters for various surfaces (e.g., turned [58], ground [59], laser-textured [60] and other topographies [61]). Plenty of detailed proposals can be presented with a thresholding method [62]. Generally, the threshold function can be used to segment the top and bottom surfaces (e.g., when the instrument calibration is provided [63]). This technique can be applied when a separation of the plateau and valley part of the laser-textured surfaces is proposed to also minimize the errors of the measurement errors [64]. In the whole process of calculating the surface roughness parameters, the accuracy of the ST evaluation increases when the precision in the S-L surface definition also increases. Reducing the errors in the S-L surface evaluation can be especially significant when functional properties are studied. The results of the calculation of surface topography parameters can be significantly influenced by the precision in the definition of the S-L surface. Both errors, those received when the S-surface and L-surface are defined, can be valuable in the dimple characterisation. There are many procedures for the elimination of the irrelevant components (like form, shape, waviness, and measurement noise) from the raw measured data, nevertheless, errors in the ISO 25178 parameter calculation were not studied in detail when the distortion of selected features (e.g., dimples) was considered. The effect of the type of surface, after various finishing treatments (e.g., plateau-honed, turned, or isotropic), containing additionally burnished oil pockets on the results of dimple distortion are presented in this paper.