Richard Leach - Fundamental prinsiples of engineering nanometrology (778895), страница 52
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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.
This grouping gives the impression that surface texture shouldbe part of a coherent scheme with roughness at the smaller scale and errorsof form at the larger scale.The primary definition of surface texture has, until recently, been basedon the profile (ISO 4287 [9]). To ensure consistency of the irregularities in theAreal surface texture characterizationmeasured profile, the direction of that profile was specified to be orthogonalto the lay (the direction of the prominent pattern). This direction is notnecessarily related to the datum of the surface, whereas errors of form, suchas straightness, are always specified parallel to a datum of the surface [37].Hence, profile surface texture and profile errors of form usually have differentcoordinate systems and do not form a coherent specification.This situation has now changed since the draft standardization of arealsurface methods, in which the primary definition of surface texture ischanged from one being based on profiles to one based on areal surfaces.
Thismeans that there is no consistency requirement for the coordinate system tobe related to the lay. Therefore, a unified coordinate system has beenestablished for both surface texture and form measurement [26]. Surfacetexture is now truly part of a coherent scheme, with surface texture at thesmaller scale. The system is part of what is referred to as the geometricalproduct specification (GPS).8.3.5 Areal parametersThere are two main classes of areal parameters:-Field parameters – defined from all the points on a scale-limitedsurface;-Feature parameters – defined from a subset of predefined topologicalfeatures from the scale-limited surface.A further class of areal parameters are those based on fractal analysis.Fractal parameters are essentially field parameters but are given their ownsection in this book as they have certain distinguishing characteristics.Some examples of the use of areal parameters can be found in [38] for thetreatment of steel surfaces, [39] for the characterization of dental implants,[40] for the monitoring of milling tool wear and [41] for the analysis ofbiofilms.8.3.6 Field parametersThe field or S- and V-parameter set has been divided into height, spacing,hybrid, functions and related parameters, and one miscellaneous parameter.A great deal of the physical arguments discussed for the profile parametersalso apply to their areal equivalents, for example, Rsk and Ssk.
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