AlphaThe Surfalize web app is in active development. Features, the user interface and computed results may change at any time, and this documentation may lag behind the app.
Surface texture parameters
Surfalize computes the areal (S) parameter families of ISO 25178-2:2021, validated against reference software and against analytic soft gauges (validation results), plus the ISO 21920 profile (R) set on any extracted profile. This page explains what each supported parameter measures and how it is defined. All areal parameters are evaluated over the area A of the scale-limited surface, that is, the surface after your chosen levelling and filtering. Heights z(x,y) are measured from the mean plane unless noted. Each S-parameter has a 1D profile analogue (Sa ↔ Ra, Sq ↔ Rq, and so on), available on extracted profiles.
How to compute them in the app (the Parameters panel, profiles, batch tables) is covered in the user guide.
Height (amplitude) parameters
Height parameters describe the statistical distribution of the ordinate values, that is, how far the surface departs vertically from its mean plane. They say nothing about the lateral arrangement of the texture: two very different-looking surfaces can share the same Sa.
The mean absolute deviation from the mean plane. The most widely used, most robust roughness number: stable, easy to interpret, but insensitive to the shape of the texture (it cannot tell peaks from valleys, or a few big features from many small ones).
The standard deviation of the heights (RMS roughness). Equivalent to Sa for a Gaussian surface (Sq ≈ 1.25 Sa) but weights large excursions more heavily, so it is more sensitive to outliers. Sq is the natural scale for statistical and optical work.
Sp is the single highest peak above the mean plane, Sv the depth of the single lowest pit (a positive number), and Sz their sum, the total peak-to-valley height. These are extreme-value parameters: informative about the worst-case feature, but sensitive to noise and single spikes, so they pair well with outlier removal beforehand.
The asymmetry of the height distribution (a pure number). Ssk < 0: a full, plateau-like surface with valleys cut into it, typical of a good bearing or sealing surface. Ssk > 0: a surface dominated by peaks or spikes standing above the bulk. Ssk ≈ 0: symmetric (a Gaussian surface).
The peakedness of the height distribution. Sku = 3 for a Gaussian surface; Sku > 3 means a spiky surface with heavy tails (sharp peaks or deep pits standing out); Sku < 3 means a bumpy, evenly-distributed, flat-topped surface.
Spatial parameters
Spatial parameters describe the lateral texture, its length scale and directionality. Sal and Str come from the surface autocorrelation function (ACF), shown in the app's ACF panel, with a default correlation threshold s = 0.2. Std and Ssw come from the Fourier transform F(p, q) of the mean-centred heights.
The shortest lateral distance over which the surface decorrelates (the ACF first drops to s). A small Sal means fine, quickly-varying texture; a large Sal means long-wavelength, gently-varying texture. It is the dominant lateral wavelength of the roughness.
The ratio of the shortest to the longest decay length, between 0 and 1. Str → 1: isotropic texture, the same in every direction (for example bead-blasted or electropolished surfaces). Str → 0: strongly anisotropic, lay-dominated texture (for example turned, ground or rolled surfaces). By convention Str > 0.5 is called isotropic, < 0.3 anisotropic.
The direction in which the angular amplitude density of the spectrum is largest, in 0–180°, measured counter-clockwise from +x with y pointing up the map (ISO 25178-2:2021, 3.2.15.1). It is the direction of the dominant spatial-frequency vector, so it lies perpendicular to the lay: grooves running along y give Std = 0°. The spectrum is binned in 0.5° steps over all frequencies except the zero frequency. Meaningful only for surfaces with a lay (low Str).
The wavelength of the strongest spatial-frequency component. A clear answer for periodic textures (turning marks, laser structures); for random surfaces the largest component is often just the longest wavelength in the field and Ssw is not meaningful (ISO 25178-2:2021, 4.3.5, note 1).
Hybrid parameters
Hybrid parameters combine height and lateral information through the surface slope. Because they involve derivatives they are sensitive to short-wavelength content and to the sampling interval, so they are best compared between surfaces measured and filtered the same way.
The RMS of the local surface slope. A dimensionless (or radian) measure of how steep the texture is: relevant to sealing, adhesion, wetting, gloss and optical scattering. Two surfaces with equal Sa but different Sdq feel and behave differently: higher Sdq means sharper, steeper features.
The percentage of extra surface area contributed by the texture, relative to a perfectly flat area of the same footprint. A flat surface has Sdr = 0; Sdr = 10 % means the true surface area exceeds its projection by 10 %. It matters wherever the real contact area drives behaviour: coating adhesion, catalysis, cell attachment, heat transfer.
Functional parameters (Abbott–Firestone)
The functional parameters come from the areal material ratio curve (the Abbott–Firestone curve): for every height c, it plots the fraction of the surface that lies above c. Reading from the top down, the curve sweeps from 0 % (above the highest peak) to 100 % (below the deepest pit). Following ISO 25178-2 Annex B, a straight equivalent line is fitted to the flattest 40 %-wide window of the curve (the core). Where that line meets 0 % and 100 % material ratio defines the core band, and the regions outside it define the peaks and valleys.
The peak-to-valley height of the core (the working part of the surface), read as the vertical extent of the equivalent line. Sk is the roughness that remains once the removable peaks and valleys are set aside: it governs load-bearing behaviour and wear in the running-in state.
The mean height of the protruding peaks above the core, as the height of the equal-area triangle over area A1. These are the tips that are worn away first during running-in and that carry initial contact. Low Spk is wanted on sliding or sealing surfaces.
The mean depth of the valleys below the core, as the equal-area triangle over area A2. Deep valleys act as reservoirs and debris traps, so a controlled Svk is desirable for lubricant retention on cylinder liners and similar surfaces.
The material ratios at the upper and lower limits of the core. Smrk1 is the small fraction of the area occupied by the peaks above the core; Smrk2 is the material ratio at the top of the valleys (so 100 − Smrk2 is the fraction taken up by valleys). They locate where peaks end and valleys begin. (Called Smr1 and Smr2 before ISO 25178-2:2021; older workflows are renamed when loaded.)
The height of the highest point above the core and the depth of the deepest point below it, before the equal-area reduction that gives Spk and Svk. They show how far single extreme features reach beyond the core.
The areas between the material ratio curve and the core limits, i.e. the triangles that define Spk and Svk. Sak1 scales with the material in the peaks, Sak2 with the void in the valleys (oil retention).
The material ratio curve read at one point. Since ISO 25178-2:2021 the reference height c0 is the highest point unless another is specified (4.5.1), so Smr(c) is the bearing fraction after removing c of material, and Smc(p) is how much has to be removed to reach the ratio p. The cut depth c (default 1 µm) and the ratio p (default 10 %) are settings of the Parameters dialog.
The height difference between two material ratios. With the defaults p = 2.5 % and q = 50 % it measures how far the extreme peaks rise above the median level (the former Sxp, which ISO 25178-2:2021 replaced by the general Sdc; older workflows are renamed when loaded).
Material probability parameters
On a material probability curve the material ratio is plotted as a Gaussian probability, in multiples of the standard deviation s, against height. A Gaussian height distribution then becomes a straight line whose slope is its Sq. A stratified surface made by two processes, for example a plateau-honed cylinder liner (a fine plateau finish cut by deep honing grooves), shows two straight regions joined by a knee. ISO 25178-2:2021 (4.5.5, Annex B.4) defines three parameters on it and refers to ISO 21920-2:2021 Annex D.6 for the procedure, which is also used for the profile twins Rpq, Rvq and Rmq.
The slopes of straight lines regressed over the plateau and valley regions: the Sq of the process that made the plateau and of the one that made the valleys. A small Spq means a fine, smooth plateau; Svq describes the depth spread of the grooves.
The material ratio where the two regression lines cross: the share of the surface that belongs to the plateau. The rest is taken up by the valleys.
The regions (ISO 21920-2 D.6). A hyperbola is fitted to the whole curve; the bisector of its asymptotes meets it at a first estimate of the plateau–valley transition. Moving outwards from there on each side, the second derivative of the curve is screened, and a point whose |d²| exceeds six times the spread of the values before it ends the region (upper plateau limit UPL, lower valley limit LVL). This drops outlying peaks (deposits, dirt) and deep scratches at the ends of the curve. A second hyperbola, fitted to the curve between UPL and LVL normalized to a square, gives the inner limits: its asymptotes are bisected three times towards each side, and those lines meet the hyperbola at the lower plateau limit LPL and the upper valley limit UVL.
Details the standard leaves open: the curve is sampled at up to 10 000 material ratios; the hyperbola is fitted as the branch z = a + b·u − c·√(u² + δ²), u = x − x0, by least squares in z on axes scaled to a square; the second derivative is that of a local quadratic over ±0.025 s. The parameters are only defined for surfaces with two height processes: a single Gaussian distribution (no knee), or a curve whose regions cannot be found, gives N/A.
Volume parameters
Volume parameters also come from the material ratio curve, but integrate it to give volumes per unit area (reported in µm³/µm² = µm). The curve is split at two material ratios, by default p = 10 % and q = 80 %, into peak, core and valley zones. The area to the left of the curve is material; the area to the right is void.
The material volume contained in the peaks (above the 10 % material-ratio height). Small and worn off early; a large Vmp signals a peaky surface that will lose material during running-in.
The material volume of the core zone, the bulk that carries the load once the peaks are worn. A stable, functionally important quantity for contact and stiffness.
The void volume of the core zone, the space available to hold and transport lubricant across the working surface.
The void volume in the deep valleys (below the 80 % material-ratio height). These reservoirs retain lubricant and trap wear debris, so a controlled Vvv is beneficial on sealing and sliding surfaces.
Feature parameters
Feature parameters do not come from a single formula; they are computed by segmenting the surface into hills and dales with a watershed algorithm, then keeping only significant features via Wolf pruning (small features whose local height is below a threshold, by default 5 % of Sz, are merged away). Statistics are then taken over the surviving peaks and pits. This makes them robust to noise but dependent on the pruning threshold.
The number of significant peaks (Spd) or pits (Svd) per unit area. High peak density means many small asperities sharing the contact load; it correlates with real contact area and, for example, friction and electrical contact behaviour.
The mean principal (local mean) curvature at the peak summits (Spc) or pit bottoms (Svc). Sharp peaks give a large Spc; rounded, blunt peaks give a small one. Sharp asperities concentrate stress and deform or wear faster under load.
S5p is the mean height of the five highest significant peaks, S5v the mean depth of the five deepest significant pits, and S10z their sum. Like Sz they characterise extreme features, but averaging five of each makes them far more robust to a single spurious spike than the single-point Sp, Sv and Sz.
Motif statistics and shape
Besides the seven named feature parameters, ISO 25178-2:2021 (5.9, Tables 6 and 7) names statistics of the hills and dales left after Wolf pruning (the motifs). Each name is S, then h (hills) or d (dales), then the attribute, then the statistic: no suffix = mean, x = maximum, q = standard deviation (of the population). For example Sda is the mean dale area and Shhx the largest local hill height. Shn and Sdn count the motifs. Motifs touching the border of the measurement are left out, as for Spd and Svd, because they are truncated.
The local height of a hill is the height of its peak above its saddle (the point where it joins its neighbour; for a dale the depth of the pit below its pour point). The area is the motif's horizontal area. The volume is the material of a hill above the plane through its saddle, and the void of a dale below it, i.e. the fluid a dale holds before it overflows. (The standard names the volume attribute without a formula; this is the volume that matches the local height.)
Roundness is 1 for a disc and smaller for elongated motifs; the form factor compares the area with the perimeter Π (1 for a disc, near 0 for a thin or ragged outline); the equivalent diameter is that of the disc of equal area; the aspect ratio is the largest over the smallest diameter (1 for a disc). The perimeter is the length of the motif's outline traced between pixel centres, and Dmax, Dmin are its largest and smallest caliper (Feret) diameters. Useful for structured surfaces, e.g. the dimples of a laser-textured part.
Significant motifs (Table 3). By default all motifs count. Alternatively only those that are open or closed at a height c, given as a material ratio: a dale is open when its lowest saddle lies below c (fluid at that level reaches the neighbouring dale) and closed when its pit lies below c and its whole ridge line above (it holds fluid). Hills mirror this: a closed hill is an island above c. The Wolf pruning threshold and the significance are settings of the Parameters dialog.
Defaults
Defaults follow ISO 25178-3 and surfalize: material ratios p = 10 %, q = 80 % for the volume parameters, Sdc between 2.5 % and 50 %, an ACF threshold s = 0.2 for Sal and Str, and Wolf pruning at 5 % of Sz for the feature and motif parameters (all motifs significant). Smr is read 1 µm below the highest point and Smc at 10 %. Every one of these except s can be changed in the Parameters dialog; the values used are stored with the parameter table and shown under each result.
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