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The curve tells the user how much of the profile lies ata particular height, in a histogram sense.The profile height amplitude curve illustrates the relative total lengths overwhich the profile graph attains any selected range of heights above or below themean line. This is illustrated in Figure 8.13. The horizontal lengths of theFIGURE 8.11 Profile section level separation.Surface profile characterizationFIGURE 8.12 Profile height amplitude distribution curve.FIGURE 8.13 Amplitude distribution curve.profile included within the narrow band dz at a height z are a, b, c, d and e.
Byexpressing the sum of these lengths as a percentage of the evaluation length,a measure of the relative amount of the profile at a height z can be obtained.Figure 8.13 is termed the amplitude distribution at height z. By plotting densityagainst height the amplitude density distributed over the whole profile can beseen. This produces the amplitude density distribution curve.8.2.10 Profile specification standardsThere are nine ISO specification standards relating to the measurement andcharacterization of surface profile. These standards only cover the use of227228C H A P T ER 8 : Surface topography characterizationstylus instruments. The details of the standards are presented in [8] and theircontent is briefly described in this section.
It should be noted that the currentISO plan for surface texture is that the profile standards will become a sub-setof the areal standards (see section 8.3.4). Whilst the basic standards anddetails will probably not change significantly, the reader should keep abreastof the latest developments in standards.ISO 3274 [15] describes a typical stylus instrument and its metrologicalcharacteristics. ISO 4287 [9] presents the definitions of the surface profileparameters (i.e. the P, W and R parameters – see section 8.2.3) and how tocalculate the parameters.
ISO 4288 [12] describes the various default values,and basic rules and procedures for surface texture profile analysis. ISO 11562[10] describes the phase correct Gaussian filter that is applied for the variouscut-off filters used for surface profile analysis. ISO 12179 [16] presents themethods for calibrating contact stylus instruments for profile measurementand ISO 5436 part 1 [17] describes the artefacts that are used to calibratestylus instruments (see section 6.10.2). ISO 5436 part 2 [18] describes theconcepts and use of software measurement standards (see section 6.13). ISO1302 [19] presents the rules for the indication of surface texture in technicalproduct documentation such as drawings, specifications, contracts andreports.Note that there are no specification standards that relate to themeasurement of surface profile using optical instruments.
However, in manycases where a profile can be mathematically extracted from an areal opticalscan, the profile characterization and analysis standards can be applied. It isimportant, however, to understand how the surface data are filtered, especially when trying to compare contact stylus and optical results.There are no methods specified in ISO standards on how to remove formprior to surface texture analysis. The most common form removal filter is thelinear least squares method and this method is applied on some commercialinstruments as a default.
However, the linear least squares method may bethe most appropriate in a large range of cases (especially where low slopeangle tilt needs to be removed) but can sometimes lead to significant errors.For example, a linear least squares form removal process will introduce tiltinto a sinusoidal surface with few periods within the sampling length. Leastsquares can also be calculated in two different manners, both leading topotentially different results (see [20] for details).ISO 13565 parts 1 [21], 2 [22] and 3 [23] relate to the measurement ofsurfaces having stratified functional properties. The roughness profilegenerated using the filter defined in ISO 11562 [10] (see section 8.2.3) sufferssome undesirable distortions, when the measured surface consists of relatively deep valleys beneath a more finely finished plateau with minimalAreal surface texture characterizationwaviness.
This type of surface is very common, for example in cylinder linersfor internal combustion engines. ISO 13565 part 1 provides a method ofgreatly reducing these distortions, thus enabling the parameters defined inISO 13565 part 2 and part 3 to be used for evaluating these types of surfaces,with minimal influence from these distortions.In 1970s France, engineers from the school of ‘Arts et Métiers’ togetherwith Peugeot and Renault conceived a graphical method for analysingmotifs, adapted to the characterization of functional surface texture. Thismethod takes the functional requirements of the surface into account andattempts to find relationships between peak and valley locations and theserequirements.
The motif method had success in French industry and wasincorporated into an international standard in 1996 [24]. These motifmethods are the basis for the segmentation used in areal feature parameteranalysis (see section 8.3.7).8.3 Areal surface texture characterizationThere are inherent limitations with 2D surface measurement and characterization.
A fundamental problem is that a 2D profile does not necessarilyindicate functional aspects of the surface. For example, consider the mostcommonly used parameter for 2D surface characterization, Ra. Figure 6.4shows the profiles of two surfaces, both of which return the same Ra valuewhen filtered under the same conditions. It can be seen that the two surfaceshave very different features and consequently very different functionalproperties. With profile measurement and characterization it is also oftendifficult to determine the exact nature of a topographic feature.8.3.1 Scale-limited surfaceDistinct from the 2D profile system, areal surface characterization does notrequire three different groups (profile, waviness and roughness) of surfacetexture parameters as defined in section 8.2.3.
For example, in arealparameters only Sq is defined for the root mean square parameter rather thanthe primary surface Pq, waviness Wq and roughness Rq as in the profile case.The meaning of the Sq parameter depends on the type of scale-limitedsurface used.Two filters are defined, the S-filter and the L-filter [25]. The S-filter is definedas a filter that removes unwanted small-scale lateral components of themeasured surface such as measurement noise or functionally irrelevant smallfeatures.
The L-filter is used to remove unwanted large-scale lateral229230C H A P T ER 8 : Surface topography characterizationcomponents of the surface, and the F-operator removes the nominal form(by default using a least squares method [26]). The scale at which the filtersoperate is controlled by the nesting index. The nesting index is an extension ofthe notion of the original cut-off wavelength, and is suitable for all types offilters. For example, for a Gaussian filter the nesting index is equivalent to thecut-off wavelength. These filters are used in combination to create SF and SLsurfaces.An SF surface (equivalent to a primary surface) results from using anS-filter and an F-operator in combination on a surface, and an SL surface(equivalent to a roughness surface) by using an L-filter on an SF surface. Bothan SF surface and an SL surface are called scale-limited surfaces.
The scalelimited surface depends on the filters or an operator used, with the scalesbeing controlled by the nesting indices of those filters.8.3.2 Areal filteringA Gaussian filter is a good general-purpose filter and it is the current standardized approach for the separation of the roughness and wavinesscomponents from a primary surface (see section 8.2.3). Both roughness andwaviness surfaces can be acquired from a single filtering procedure withminimal phase distortion. The weighting function of an areal filter is theGaussian function given by"#1p x2y2exp 2sðx; yÞ ¼ 2þ(8.8)a lcxlcya lcx2 lcy 2lcx x lcx; lcy y lcywhere x, y are the two-dimensional distance from the centre (maximum) ofthe weighting function, lc is the cut-off wavelength, a is a constant, toprovide 50 % transmission characteristic at the cut-off lc, and a is given byrffiffiffiffiffiffiffiffiln2z 0:4697:(8.9)pWith the separability and symmetry of the Gaussian function, a twodimensional Gaussian filtered surface can be obtained by convoluting twoone-dimensional Gaussian filters through rows and columns of a measuredsurface, thusXXz0 ðx n1 ; y n2 Þsðn1 Þsðn2 Þ :zðx; yÞ ¼ z0 ðx; yÞ (8.10)Figure 8.14 shows a raw measured epitaxial wafer surface (a), and itsshort-scale SL surface (roughness) (b) and middle-scale SF surface (waviness)Areal surface texture characterizationFIGURE 8.14Epitaxial wafer surfacetopographies indifferent transmissionbands: (a) the rawmeasured surface;(b) roughness surface(short-scale SL-surface)S-filter ¼ 0.36 mm(sampling space), Lfilter ¼ 8 mm); (c) wavysurface (middle-scaleSF-surface) S-filter ¼8 mm, F-operator; and(d) form error surface(long-scale formsurface), F-operator.(c) and long-scale form surface (form error surface) (d) by using Gaussianfiltering with an automatic correct edged process.The international standard for the areal Gaussian filter (ISO 16610-61[27]) is currently being developed (the areal Gaussian filter has been widelyused by almost all instrument manufacturers).
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