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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).
It has been easily extrapolatedfrom the linear profile Gaussian filter standard into the areal filter byinstrument manufacturers for at least a decade and allows users to separatewaviness and roughness in surface measurement.For surfaces produced using a range of manufacturing methods, theroughness data have differing degrees of precision that contains some verydifferent observations or outliers. In this case, a robust Gaussian filter (basedon the maximum likelihood estimation) can be used to suppress the influence of the outliers.
The robust Gaussian filter can also be found in mostinstrument software.It should be noted that the Gaussian filter is not applicable for all functional aspects of a surface, for example, in contact phenomena, where theupper envelope of the surface is more relevant. A standardized framework forfilters has been established, which gives a mathematical foundation for231232C H A P T ER 8 : Surface topography characterizationfiltration, together with a toolbox of different filters. Information concerningthese filters will soon be published as a series of technical specifications (ISO/TS 16610 series [27]), to allow metrologists to assess the utility of the recommended filters according to applications. So far only Gaussian filters havebeen published, but the toolbox will contain the following classes of filters:Linear filters: the mean line filters (M-system) belong to this class andinclude the Gaussian filter, spline filter and the spline-wavelet filter;Morphological filters: the envelope filters (E-system) belong to this classand include closing and opening filters using either a disk or a horizontal line;Robust filters: filters that are robust with respect to specific profilephenomena such as spikes, scratches and steps.
These filters include therobust Gaussian filter and the robust spline filter;Segmentation filters: filters that partition a profile into portionsaccording to specific rules. The motif approach belongs to this class and hasnow been put on a firm mathematical basis.Filtering is a complex subject that will probably warrant a book of its ownfollowing the introduction of the ISO/TS 16610 series [27] of specificationstandards. The user should consider filtering options on a case-by-case basisbut the simple rule of thumb is that if you want to compare two surfacemeasurements, it is important that both sets use the same filtering methodsand nesting indexes (or that appropriate corrections are applied).
Table 8.2presents the default nesting indices in ISO 25178 part 3 [26]. The usershould consult the latest version of ISO 25178 part 3 because at the time ofwriting there is still debate in the standards committees as to the values inTable 8.2.8.3.3 Areal specification standardsThe areal specification standards are at various stages of development. Theplan is to have the profile standards (see section 8.2.10) as a subset of theareal standards (with appropriate re-numbering). Hence, the profile standards will be re-published after the areal standards (with some omissions,ambiguities and errors corrected) under a new numbering scheme that isconsistent with that of the areal standards. All the areal standards are part ofISO 25178, which will consist of at least the following parts, under thegeneral title Geometrical product specification (GPS) – Surface texture: Areal:-Part 1: Areal surface texture drawing indications-Part 2: Terms, definitions and surface texture parameters [25]Areal surface texture characterizationTable 8.2Relationships between nesting index value, S-filter nesting index,sampling distance and ball radiusNesting indexvalue(F-operator/L-filter) (mm)S-filter nestingindex (mm)Max.
samplingdistance (mm)Max. ballradius (mm).0.10.20.250.50.81.02.02.55.08.01020255080100..1.02.02.55.08.010202550801002002505008001000..0.30.60.81.52.53.06.08.01525306080150250300..0.81.52.04.06.08.01520406080150200400600800.-Part 3: Specification operators [26]-Part 4: Comparison rules-Part 5: Verification operators-Part 6: Classification of methods for measuring surface texture [28]-Part 70: Measurement standards for areal surface texturemeasurement instruments-Part 71: Software measurement standards [29]-Part 72: Software measurement standards – XML file format-Part 601: Nominal characteristics of contact (stylus) instruments [30]-Part 602: Nominal characteristics of non-contact (confocal chromaticprobe) instruments [31]233234C H A P T ER 8 : Surface topography characterization-Part 603: Nominal characteristics of non-contact (phase-shiftinginterferometric microscopy) instruments [32]-Part 604: Nominal characteristics of non-contact (coherence scanninginterferometry) instruments [33]-Part 605: Nominal characteristics of non-contact (point autofocus)instruments-Part 606: Nominal characteristics of non-contact (variable focus)instruments-Part 701: Calibration and measurement standards for contact (stylus)instruments [34]-Part 702: Calibration and measurement standards for non-contact(confocal chromatic probe) instruments-Part 703: Calibration and measurement standards for non-contact(phase-shifting interferometric microscopy) instruments-Part 704: Calibration and measurement standards for non-contact(coherence scanning interferometry) instruments-Part 705: Calibration and measurement standards for non-contact(point autofocus) instruments-Part 706: Calibration and measurement standards for non-contact(variable focus) instrumentsThe American National Standards Institute has also published specification standards [35] that include some areal analyses (mainly fractalbased).8.3.4 Unified coordinate system for surface texture and formSurface irregularities have traditionally been divided into three groupsloosely based on scale [36]: (i) roughness, generated by the materialremoval mechanism such as tool marks; (ii) waviness, produced byimperfect operation of a machine tool; and (iii) errors of form, generated byerrors of a machine tool, distortions such as gravity effects, thermal effects,set-up, etc.
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