ASTM_F_1811_-_97.pdf

Designation:F 1811 97Standard Practice forEstimating the Power Spectral Density Function and RelatedFinish Parameters from Surface Profile Data1This standard is issued under the fixed designation F 1811;the number immediately following the designation indicates the year oforiginal adoption or,in the case of revision,the year of last revision.A number in parentheses indicates the year of last reapproval.Asuperscript epsilon(e)indicates an editorial change since the last revision or reapproval.1.Scope1.1 This practice defines the methodology for calculating aset of commonly used statistical parameters and functions ofsurface roughness from a set of measured surface profile data.Its purposes are to provide fundamental procedures and nota-tion for processing and presenting data,to alert the reader torelated issues that may arise in user-specific applications,andto provide literature references where further details can befound.1.2 The present practice is limited to the analysis of one-dimensional or profile data taken at uniform intervals alongstraight lines across the surface under test,although referenceis made to the more general case of two-dimensional measure-ments made over a rectangular array of data points.1.3 The data analysis procedures described in this practiceare generic and are not limited to specific surfaces,surface-generation techniques,degrees of roughness,or measuringtechniques.Examples of measuring techniques that can be usedto generate profile data for analysis are mechanical profilinginstruments using a rigid contacting probe,optical profilinginstruments that sample over a line or an array over an area ofthe surface,optical interferometry,and scanning-microscopytechniques such as atomic-force microscopy.The distinctionsbetween different measuring techniques enter the presentpractice through various parameters and functions that aredefined in Sections 3 and 5,such as their sampling intervals,bandwidths,and measurement transfer functions.1.4 The primary interest here is the characterization ofrandom or periodic aspects of surface finish rather than isolatedsurface defects such as pits,protrusions,scratches or ridges.Although the methods of data analysis described here can beequally well applied to profile data of isolated surface features,the parameters and functions that are derived using theprocedures described in this practice may have a differentphysical significance than those derived from random orperiodic surfaces.1.5 The statistical parameters and functions that are dis-cussed in this practice are,in fact,mathematical abstractionsthat are generally defined in terms of an infinitely-long linearprofile across the surface,or the“ensemble”average of aninfinite number of finite-length profiles.In contrast,real profiledata are available in the form of one or more sets of digitizedheight data measured at a finite number of discrete positions onthe surface under test.This practice gives both the abstractdefinitions of the statistical quantities of interest,and numericalprocedures for determining values of these abstract quantitiesfrom sets of measured data.In the notation of this practicethese numerical procedures are called“estimators”and theresults that they produce are called“estimates”.1.6 This practice gives“periodogram”estimators for deter-mining the root-mean-square(rms)roughness,rms slope,andpower spectral density(PSD)of the surface directly fromprofile height or slope measurements.The statistical literatureuses a circumflex to distinguish an estimator or estimate fromits abstract or ensemble-average value.For example,denotesan estimate of the quality A.However,some word-processorscannot place a circumflex over consonants in text.Anysymbolic or verbal device may be used instead.1.7 The quality of estimators of surface statistics are,inturn,characterized by higher-order statistical properties thatdescribe their“bias”and“fluctuation”properties with respectto their abstract or ensemble-average versions.This practicedoes not discuss the higher-order statistical properties of theestimators given here since their practical significance and useare application-specific and beyond the scope of this document.Details of these and related subjects can be found in References(110)2at the end of this practice.1.8 Raw measured profile data generally contain trendingcomponents that are independent of the microtopography of thesurface being measured.These components must be subtractedbefore the difference or residual errors are subjected to thestatistical-estimation routines given here.These trending com-ponents originate from both extrinsic and intrinsic sources.Extrinsic trends arise from the rigid-body positioning of thepart under test in the measuring apparatus.In optics thesedisplacement and rotation contributions are called“piston”and“tilt”errors.In contrast,intrinsic trends arise from deliberate oraccidental shape errors inherent in the surface under test,suchas a circular or parabolic curvatur