3271 metrology 01-02/pt/jr - buecher.de quantify a surface accurately,we can only hope ... related...

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Surface texture:two-dimensional

“Errors, like straws, upon the surface flow;He who would search for pearls must dive below.”

(All for Love, Prologue, 25; John Dryden 1631–1700)

1

Surface texture: an overview

The concept of surface technology has previouslyvaried according to whether a scientist, technologist,or engineer has inspected a surface. An individual’sviewpoint differs depending upon their specificinterest and technical emphasis. Therefore, a surfacecannot be thought of in isolation from otherfeatures, because each is valid and necessary andneeds to be considered to gain an overall impressionof its industrial, or scientific usage.

Surface technology encompasses a wide range ofdisciplines that includes: metrology; metallurgy;materials science; physics; chemistry; tribology andmechanical design. Moreover, it has become appar-ent that this topic, and associated characteristics thatrelate to surface technology needs to be recognisedas a subject in its own right.

Surface technology provides an important andvaluable insight into the practical and theoreticalapplications of a manufactured surface, most not-ably for the following reasons:

� the surface is the final link from the originaldesign concept through to its manufacture, withthe industrial engineer being the last person toadd value to the product prior to shipment;

� industry is continually attempting to improvecomponent power-to-weight ratios, drive downmanufacturing costs and find efficient ways ofeither producing or improving surfaces – this hasbecome an established goal of world-classcompeting companies today;

� internationally, there is growing demand torecognise the legal implications of a product’sperformance. Product liability is directly relatedto the production process technique and, hence,to a surface’s quality;

� technical data that in the past was consideredvalid, has of late been found to be either unreli-able or may give insufficient detailed informationon surface phenomena. By way of an example,originally it was thought that the surface tex-ture was directly related to a component’s fatiguelife; however, it has been shown that surfacetopography must be extended to include sub-surface metallurgical transformations, namelysurface integrity;

� the production process selected for the manu-facture of a part has been shown to have someinfluence on the likely in-service reliability ofcomponents.

1.1 Introduction

On the macro scale the natural world mimicssurfaces found in engineering. Typical of these isthat shown in Figure 1, where the desert sand is comprised of sand grains – roughness; ripples inthe surface – waviness; together with the undulatingnature of the land – profile. From an engineeringpoint of view, surfaces are boundaries between twodistinct media, namely, the component and itsworking environment. When a designer develops afeature for a part – whether on a computer-aideddesign (CAD) system, or drawing board – neat linesdelineate the desired surface condition, which isfurther specified by its specific geometric tolerance.In reality, this theoretical surface condition cannotexist, as it results from process-induced surfacetexture modifications. Regardless of the method ofmanufacture, an engineering surface must have

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Surface texture: two-dimensional 3

Figure 1. The natural world – the desert – can exhibit a large-scalecombination of surface characteristics, for instance: � agglomeration (i.e. clusters) of sand – roughness;� ripples – waviness; and� the undulating nature of the land – profile.(Source: James Smith, Prayer in the desert, circa 1920s.)

some form of texture associated with it, this being a combination of several interrelated factors, suchas:

� the influence of the material’s microstructure;� the surface generation method, the tool’s cutting

action, tool geometry, cutting speed, feedrate andthe effect of cutting fluid;

� instability during the manufacturing process,promoted by induced chatter – poor loop-stiff-ness between the machine-tool–workpiece sys-tem, or imbalance in a grinding wheel;

� inherent residual stresses within the part, pro-moted by stress patterns causing deformations inthe component.

Within the limitations resulting from the com-ponent’s manufacture, a designer must select a func-tional surface condition that will satisfy the

operational constraints, which might be a require-ment for either a “smooth” or “rough” surface. Thisthen begs the question posed many years ago: “Howsmooth is smooth?” This is not as superficial a state-ment as it might initially seem, because unless wecan quantify a surface accurately, we can only hopethat it will function correctly in service. In fact, asurface’s texture, as illustrated in Figure 2, is acomplex condition resulting from a combination of:

� roughness – comprising of irregularities thatoccur due to the mechanism of the materialremoval production process; tool geometry,wheel grit, or the EDM spark;

� waviness – that component of the surface textureupon which roughness is superimposed, resultingfrom factors such as machine or part deflections,vibrations and chatter, material strain and ex-traneous effects;

Industrial metrology4

Lay

Roughness

Waviness

Waviness spacing

Roughness spacing

Profile – long-frequency components:

Waviness – medium-frequency components:

Roughness – short-frequency components:

Figure 2. The major components that constitute a typical surface texture, also exhibiting some degree of directionality (lay).

� profile – the overall shape of the surface – ignor-ing roughness and waviness variations – is causedby errors in machine tool slideways.

Such surface distinctions tend to be qualitative –not expressible as a number – yet have considerablepractical importance, being an established proce-dure that is functionally sound (Figure 3). Thecombination of these surface texture conditions,together with the surface’s associated “lay”, are ideal-istically shown in Figure 4, where the lay of thesurface can be defined as the direction of the domi-nant pattern. Figure 4 also depicts the classificationof lay, which tends to be either anisotropic – having

directional properties such as feed marks, orisotropic – devoid of a predominant lay direction.The lay of any surface is important when attemptingto characterise its potential functional performance.If the direction of the trace being produced by astylus instrument – record of the stylus motion overthe assessed surface topography – is not taken intoaccount, then a totally misrepresentative reading willresult from an anisotropic surface. This is not thecase when measuring an isotropic surface, forexample a “multi-directional lay” – as indicated inFigure 4. Under this isotropic condition, perhapsthree different measurement paths could be scannedand the worst roughness trace would be utilised to

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1

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6

Any manufacturing process Material shall be removed Material shall not be removed

f e

a

bx

c

d

*The outline represents the six surfaces shown on the 3D-representation (not the front to rear surfaces).

KEY

a = 2D parameter 1b = 2D parameter 2c = 2D parameter 3d = processe = lay patternf = allowancex = not allowed

Figure 3. The composition of the complete graphical symbol for surface texture. [Source: ISO 1302: 2001]

NB: Surfaces exhibiting a defined directionality, or“Lay” must be measured at right angles to this laypattern.

specify the surface. The designer should be awarethat the lay condition and other information can be incorporated into the surface texture symbol (ISO 1302: 2001) – which is often misused – seeFigure 3 for the positioning of this data and othersurface texture descriptors. The surface texturesymbol shown in Figure 4, indicated by “surfacetexture ticks”, highlights the potential process-related lay type and associated directionality (ISO1302: 2001).

Returning to the theme of an isotropic lay condi-tion, if this surface is assessed at a direction not atright angles to the lay, then a totally unrepresenta-tive surface profile will result, which is graphicallyillustrated in Figure 5. As indicated in this figure, asthe trace angle departs to greater obliquity fromcondition A then the surface profile becomes flatonce the direction has reached condition E. Thiswould give a totally false impression of the truesurface topography. If employed in a critical andperhaps highly stressed in-service state, with theuser thinking that this incorrectly assessed surfacewas flat, then, potentially, a premature failure statecould arise. Normally, if the production processnecessitates, for example, a cross-honing operation,

the lay condition would be “crossed” – as shown inFigure 4. Under this roughness state, it is usual tomeasure the surface at 45°, which has the effect ofaveraging out the influence of the two directionsimparted by the cross-honing operation. Wheresurfaces are devoid of a lay direction – as in the caseof “particulate lay” (see Figure 4) from either shot-blasting or the sintering process – then under suchcircumstances a trace will produce the same surfacetexture reading, irrespective of the direction ofmeasurement.

The production of certain milled surfaces cansometimes exhibit roughness and waviness condi-tions at 90° to each other – this is not the same con-dition as “crossed lay” – because the relative heightsand spacings of the two lays differ markedly. Hence,the cusp and chatter marks of the milled topographyshould be measured in opposing directions. When aturned component has had a “facing-off” operationundertaken, and a “circular lay” condition occurs(see Figure 4), then under these circumstances it isnormal to measure the surface texture in a radialdirection, otherwise an inappropriate reading willresult. Conversely, if a “radial lay” occurs – resultingfrom “cylindrically grinding”the end face – it is moreusual to measure surface roughness at a series oftangent positions with respect to the circumferentialdirection.When measuring surface texture in themajority of practical situations it can be achieved bydirect measurement of the profile, positioning theworkpiece in the correct manner to that of the stylusof the surface texture instrument. When the part is


TYPE LAY SYMBOL

Parallel

Perpendicular

Crossed

Multi - directional

Particulate

Circular

Radial

=

X

M

P

C

R

�

Figure 4. The indication of surface ‘lay’ as denoted on engineeringdrawings. [Source: ISO 1302: 2001]

An anisotropic surface exhibiting directional lay

A B C D E

A B C D E

Figure 5. Effect of the relative direction of lay and its associatedinfluence on the measurement of profile shape. (Courtesy of TaylorHobson.)

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MANUFACTURINGPROCESS: 0.005 0.1 0.2 0.4 0.8 1.6 3.3 6.3 12.5 25

SUPERFINISHING

LAPPING

POLISHING

HONING

GRINDING

BORING

TURNING

DRILLING

EXTRUDING

DRAWING

MILLING

SHAPING

PLANING

ROUGHNESS (Ra) in µm

Ra (Nominal) VALUESin µm:

50

25

12.5

6.3

3.2

1.6

0.8

0.4

0.2

0.1

0.05

0.025

N12

N11

N10

N9

N8

N7

N6

N5

N4

N3

N2

N1

ROUGHNESS GRADENUMBER:

INCREASINGROUGHNESS

Figure 6. Anticipated process roughness and respective grades. [Source: ISO 1302: 2001.]

either too large or this is impracticable – due toeither stylus access to the surface or surface inclina-tion – then placing a small portable instrument onthe surface can allow a measurement.Occasions arisewhen even this is not an option and under these cir-cumstances it may be possible to take a “cast replica”of the surface, then present this to the instrument.Some surface texture measuring instrument manu-facturers offer “replica kits” for just this purpose. Itshould be remembered that this replica of the surfaceis an inverted image.

1.2 Establishing the Ranumerical value of surfacetexture from the productionprocess

Numerical data (ISO 1302: 2001) to define the rough-ness grade for surface texture has been established(see Figure 6) which can be related to the method ofproduction. Caution should be made when usingthese values for control of the surface condition,because they can misrepresent the actual state of thesurface topography, being based solely on a derivednumerical value for height. More will be said on thislater. Moreover, the “N-number” has been used toestablish the arithmetic roughness Ra value, thisbeing just one number to cover a spread of potentialRa values for that production process. Nevertheless,this single numerical value has merit, in that itdefines a “global” roughness (Ra) value and accom-panying “N-roughness grade”, that can be used by adesigner to specify a particularly desired surfacecondition being related to the manufacturing pro-cess. The spread of the roughness for a specificproduction process has been established fromexperimental data over the years – covering themaximum expected variance – which can be modi-fied depending upon whether a fine, medium orcoarse surface texture is required. Due to thevariability in the production process and its stoch-astic output, such surface texture values do notreflect the likely in-service performance of the part.Neither the surface topography nor its associatedintegrity has been quantified by assigning to asurface representative numerical parameters. Inmany instances, “surface engineering” is utilised toenhance specific component in-service conditions,but more will be said on this subject toward the endof Chapter 5.

Previously, it was mentioned that with many in-service applications that the accompanying sur-

face texture is closely allied to functional perform-ance, particularly when one or more surfaces are inmotion with respect to an adjacent surface. This sug-gests that the smoother the surface the better,but thisis not necessarily true if the surfaces in question arerequired to maintain an efficient lubrication film.Theapparent roughness of one of these surfaces withrespect to the other enables it to retain a “holdingfilm” in its associated roughness valleys. Yet anotherfactor which may limit the designer from selecting asmooth surface is related to its production cost (seeFigure 7). If a smooth surface is the requirement thenthis takes a significantly longer time to produce thanan apparently rougher surface, which is exacerbatedif this is allied to very close dimensional tolerancing.

1.3 Surface texture roughnesscomparison blocks andprecision reference specimens

In order to gain a basic “feel” for actual replicasurfaces in conjunction with their specific numericalvalue for surface roughness. Then the use of compar-ison blocks allows an efficient and useful means of interpreting the production process with theirexpected surface condition. A designer (Figure 8a)can select a surface using a visual and tactile methodto reflect the required workpiece condition. Corres-pondingly, the machine tool operator can utilisesimilar comparison blocks (see Figure 8b) to estab-lish the same surface condition, without the need tobreak down the set-up and inspect the part with asuitable surface texture measurement instrument.This is a low-cost solution to on-machine inspectionand additionally enables each operator to simply actas an initial source for a decision on the part’ssurface texture condition. Such basic visual andtactile inspection might at first glance seem in-appropriate for any form of inspection today, butwithin its limitations it offers a quick solution tosurface roughness assessment. Tactile and visualsensing is very sensitive to minute changes in thesurface roughness, but is purely subjective in natureand is open to some degree of variation from oneperson to another. Comparison block surface assess-ment is purely a subjective form of attributesampling. Therefore, not only will there be somedivergence of opinion between two operators on theactual surface’s numerical Ra value due to theirdiffering sensual assessments, but also this is only avery rudimentary form of inspection.

Precision reference specimens are manufacturedto exacting and consistent tolerances, particularly


when used to calibrate stylus-based surface texturemeasuring instruments. A range of standard refer-ence specimens can be purchased for this purposeand will act as a “health check” on both the currentstylus condition – whether its point is worn orpartially broken – and indicate if the allied instru-mentation/electronics has “drifted” since the lastcalibration check. This enables the inspector tospeedily and efficiently remedy the situation andbring the instrument back into calibration. Most ofthese calibration reference specimens are manufac-tured from replicas of an original master productionsurface by nickel electroforming; this enables theblock to be a reproduction of the whole surface, withthe finest details being approximately 1 �m in size.Each reference specimen offers exacting uniformityof profile shape. In order to minimise wear on these

reference specimens from frequent use a hard boronnitride layer can be specified.

1.4 The basic operatingprinciple of the pick-up, itsstylus and skid

Prior to describing some of the more sophisticatedinstruments by which the surface is measured, it isworth describing the basic function of a typicalstylus instrument. In Figure 9, a schematic illu-stration is depicted of the basic components for atypical surface texture measuring instrument. The

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Cylindrical grinding

Surface grinding

Reaming

End milling

Turning

Peripheral milling

Shaping and planing

Drilling

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14

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1

0.025 0.05 0.1 0.2 0.4 0.8

Ra Value (µm)1.6 3.2 6.3 12.5 25.0 5.00

Rel

ativ

e P

rodu

ctio

n T

ime,

or

Cos

t

Figure 7. Relative cost, in production time, necessary to produce surface finishes by different production processes. (Courtesy of Taylor Hobson.)


Figure 8. (a) Utilising a comparator gauge to determine the surface finish for a specific manufacturing process. (b) A typical comparator gauge,for both visual and tactile assessment. (Courtesy of Rubert & Co Ltd.)

(a) (b)

Traverseunit

Pick-up Amplifier Filter

Magnificationswitch

Cut-offselector

Motion

Ra

Ra meterStylus

Surface under test

Trace Penunit

Recorder

Figure 9. Schematic diagram illustrating the major constituents of a stylus-type of surface texture measuring instrument. (Courtesy of Taylor Hobson.)

stylus traverses across the surface and the transducerconverts its vertical movements into an electricalsignal. This signal is then amplified for subsequentprocessing, or output to operate a pen recorder. Therequired parameter value is subsequently derivedfrom the filtered signal, having previously been dis-played on screen. In general, the profile is the resultof the stylus tracing the movement across the surfaceunder test, the contacting of consecutive points of theprofile being spaced in time. Therefore this relation-ship between movement and time is closely associ-ated with its “cut-off”.“Cut-off” refers to the limitingwavelength at which components of the profile arepassed nominally unchanged by a filter.

The stylus is normally either conical with a spher-ical tip (see Figure 10), or a four-sided pyramid witha truncated flat tip (Figure 11a). The conical type ofstyli (Figure 10) have a cone angle of either 60° or90°, with a tip radius ranging from less than 0.1 �mto 12 �m in size. A pyramidal stylus tends to beapproximately 2 �m wide in the traverse direction,but is normally wider transversely to the directionof travel, giving the tip greater strength (see Figure11a left). The sharp-pointed 0.1 �m wide pyramidalstylus (Figure 11a right), is utilised on the TaylorHobson “Talystep” and “Nanostep” instruments.However, in use the edges of a pyramidal tip tend tobecome rounded with wear; conversely, the spher-ical tip version develops a flat, so the distinctionbetween the two profile geometries becomes lessmarked with time. If a stylus tip becomes damagedduring use, this results in a considerable increase inits width, leading to potentially very seriousmeasuring errors.

When a comparison is made of the scale of anactual surface under test to that of the stylus tip(Figure 10) against a vertical magnification (Vv) of

×5000 and horizontal magnification (Vh) of ×100,then in this situation the respective size of the stylusis almost indistinguishable from that of a (vertical)straight line or point contact (see Figure 11b). Thissignificant size differential enables the stylus topenetrate into quite narrow valleys, although itsfinite size affects the accuracy with which the surfaceprofile can be traced. These stylus profile and sizelimitations influence the following:

� distortion of peak shape – as the spherical stylustraverses over a sharp peak, the point of contactshifts across the stylus – from one side to theother (Figure 11c). This results in the stylushaving to follow a path which is more roundedthan the peak, but due to the stylus being raisedto its full height when at the crest the true peakheight is measured;

� penetration into valleys – due to the tip’s size, itmay not be able to completely penetrate to deepand narrow valley bottoms (see Figure 12);

� re-entrant features cannot be traced – whenever astylus encounters a re-entrant feature (Figure 12detail) the stylus tip loses partial contact with theprofile and as a result will remove this featurefrom the trace. Typical surfaces that exhibit suchre-entrant characteristics are powder metallurgy(PM) compacts and other porous parts, togetherwith certain cast irons. This means that mis-leading surface texture parameter measurementsmay occur – although recently DIN 4776: 1988 hasdescribed a method of obtaining “distortion-free”assessment for PM parts. If transverse sectionsare taken and positioned within a scanning electron microscope re-entrant features can bevisually revealed.

If the slope of a surface texture feature has asteeper angle than that of the half angle of the sideof a conical stylus tip, then it will lose contact withthe profile, having the same effect as a re-entrantangle on the resulting measurement. The stylus isthe only active contact between the surface and theinstrument and it has been shown above that itsshape and size affect profile trace accuracy. If theforce exerted by the stylus is too great, it may scratchor deform the surface, leading to erroneous results.Conversely, the stylus force must be sufficient toensure that the stylus maintains continuous contactwith the surface at the adopted traverse speed.Metrological instrument manufacturers incorporatethis into the transducer design, with most surfacetexture equipment having a tip radius of between 0.1 and 12 �m, with a stylus force of ≈0.75 mN.This stylus force changes as the tip becomes progres-sively more blunt as it bears on the surface. Aninstrument with very fine tip radius (Figure 10a

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Figure 10. Scanning electron photomicrograph of a stylus (5 �mpoint radius) on a surface. [Courtesy of Hommelwerke GmbH.]

right) must utilise an exceedingly low force, typically≈3 × 10�5 N or less. The transducer assembly canincorporate both a stylus and skid, with the skidoffering a local datum for this transducer and withthat of the surface. Moreover, the skid provides alocal datum for the stylus with respect to its verticaland horizontal motion. Therefore, with the skid’slarge curved radius to that of the relatively smallsurface under test, it rides along the surface beingmeasured (Figure 13), providing a “local datum”. As

long as the skid’s radius is greater than the peakspacing, the apparent line of movement of this skidwill be virtually a straight line. Under such surfacetransducer conditions as the vertical skid movesfrom crest to crest, its relative horizontal skidmotion with respect to the test surface can beignored, as the skid’s vertical motion is virtuallyinsignificant. However, once the crests in the surfaceunder test become more widely spaced, this hori-zontal crest spacing tends to introduce a significant


≈ 2 µm ≈ 3 µm

≈ 0.1 µm

≈ 2 µm

Stylus motion

(a) Typical stylus geometries

(b) Relative size of the stylus against the surface topography

(c) The curve tends to round the peaks (I) and reduce the depth ofthe valleys (II), although the peak height is not affected (III)

Stylus motion

II

I

III

Figure 11. Stylus geometry and its mechanical filtering effect on surface texture. (Courtesy of Taylor Hobson.)

amount of vertical skid motion. If the skid’s verticalmotion affects the subsequent surface textureresults, it is then preferable to use the instrument inthe “skidless mode”, as instruments employing askid should be used for the measurement of rough-ness parameters (ISO 3274: 1996). To achieve skid-less operation and minimise the unwanted affects ofvertical skid motion which might otherwise inter-fere with the results, the skid must be removed, thenby utilising the instrument’s in-built straight edge asa “sliding datum” the surface assessment can beundertaken, as illustrated in Figure 14. More will bementioned on the influence of the skid and its asso-ciated “phase effect” later.

1.5 Filters and cut-off

It was previously suggested that surface geometry iscomprised of roughness, waviness and profile (seeFigure 2). These interrelated factors also tend to havedifferent relationships to the performance of thecomponent. It is normally the case that they areseparated out during analysis. To obtain this sepa-ration on surface texture measuring instruments,selectable filters for roughness and waviness areapplied. In this section, only a superficial treatmentof filtering and its effects will be mentioned, as thiswill be dealt with in greater depth later in thechapter.

In general, selection of the desired filtering canbe established by the following “rules of thumb”:

� roughness filtering would be applied if control isrequired of workpiece performance (for example:resistance to stress failure; wear resistance; fric-tion; reflectivity and lubrication properties);

� waviness filtering might be selected if control isnecessary for workpiece or machine tool per-formance (for example, vibration or noise gener-ation).

Once the type of filter has been chosen then thefilter cut-offs should be selected (see ISO 11562: 1996for more detailed information) with a range,notably:“. . . mm; 0.08 mm; 0.25 mm; 0.8 mm; 2.5 mm;8.0 mm; . . .” (ISO 3274: 1996). However, this can onlybe undertaken when the specific features needing tobe measured are known. Generally, the following criteria can be applied:

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Path traced by a 2.5 µm radius stylusPath traced by a 12.5 µm radius stylus

Re-entrant featureon a surface

Figure 12. Illustrating how the use of a larger-radius stylus reducesthe apparent amplitude of closely spaced irregularities. (Courtesy ofTaylor Hobson.)

Figure 13. Surface texture of component being inspected using askid. (Courtesy of Taylor Hobson.)

Figure 14. A high-quality component’s surface texture beingassessed without a skid which tends to be the “approved method”, oflate. (Courtesy of Taylor Hobson.)

� a 0.08 mm cut-off length should be selected forhigh-quality optical components;

� a 0.8 mm cut-off length should be chosen forgeneral engineering components;

� longer cut-offs are necessary when very roughcomponents are to be measured, or if surfaces forcosmetic appearance are important.

NB A practical guideline is that the cut-off chosenshould be of the order of 10 times the length of thefeature spacings under test. If there is any doubtabout the selection of cut-off, initially measure thesurface in an unfiltered manner and then make aqualified decision from this test.

So far, the term cut-off has been liberally used,but what is it? As an example of cut-off and assuminga perfect filter characteristic, if a high-pass filter hasa cut-off of 0.8 mm, this will only allow wavelengthsbelow 0.8 mm to be assessed, with wavelengthsabove this value being removed. Conversely, when alow-pass filter of 0.8 mm cut-off has been selected,this will only allow wavelengths above 0.8 mm to beassessed. As previously mentioned (ISO 3274: 1996),the internationally recognised cut-off lengths forsurface roughness measurement are given in Table

1. One basic feature of stylus-based instruments isthat the profile is traced by movement across the testsurface, with the consecutive points of the profile incontact being spaced in time. Hence, this relation-ship between movement and time is closely associ-ated with cut-off.

The frequencies present are dependent upon twofactors: traverse speed and spacing irregularities. InFigure 15 (A and B), the frequencies of 100 Hz and50 Hz represent irregularity spacings of 0.01 mmand 0.02 mm respectively. At the same traversespeed, frequencies of 4.0 Hz and 1.25 Hz would begenerated by spacings of 0.25 mm and 0.8 mm. If ahigh-pass electrical filter is used, this will suppressany frequency below 4.0 Hz, enabling only thoseirregularities having spacings of 0.25 mm or less to be represented in the filtered profile. Therefore,this relationship is ideal to obtain a sampling length of 0.25 mm, hence the term “cut-off” length– since the response now cuts off at irregularityspacings of 0.25 mm, denoted by the internationalsymbol, (�c) for cut-off length. By introducingdifferent filters, the most suitable cut-off for thesurface can be selected, where Table 1 acts as a guideto the selection of suitable cut-offs for variousmachining processes.

Until 1990, standard roughness and wavinessfilters were analogue or 2RC (two resistors and twocapacitors) types. Since 1996, the standard (ISO11562: 1996) has specified the digital filter for surfacetexture measurements. For example, if a 0.8 mm cut-off value is utilised, then there is a 50% transmissionof the profile equal to this 0.8 mm. This type offiltering is analogous to a sieve, only allowing valuesbelow the cut-off to be passed through. The mainproblem with utilising an analogue filter is that itassumes that the surface is basically sinusoidal innature, but this rarely is the case. This mismatch withthe “real” surface under test causes the so-called“Gibb’s phenomenon”. The Gibb’s phenomenonresults in an overshooting of the filtered profilewhen analysing certain extreme forms of profile. The“Gibb’s phenomenon” can be explained by thefollowing example.

Filtering is used to determine the mean line of theroughness profile – being identical to the wavinessprofile. An analogue filter determines a profile’s meanline by a “moving average” technique. Hence, at anypoint in time the filter averages the profile previouslytraversed by the stylus. This has been equated to aperson walking backwards! Such a filter cannot antic-ipate what lies ahead of it in the remainder of theprofile, such as abrupt changes in the topography.Under these conditions, it reacts after a significantchange has occurred; this means that the true profileis no longer represented by the mean line, and as aresult the filtered profile will be distorted vertically


Table 1. Typical cut-offs for variously manufactured surfaces

Typical finishing process Meter cut-off (mm)

0.25 0.8 2.5 8.0 25.0

Milling x x xBoring x x xTurning x xGrinding x x xPlaning x x xReaming x xBroaching x xDiamond boring x xDiamond turning x xHoning x xLapping x xSuperfinishing x xBuffing x xPolishing x xShaping x x xElectro-discharge machining x xBurnishing x xDrawing x xExtruding x xMoulding x xElectro-polishing x x

NB The cut-off selected must be one that will give a valid assessment of thesurface characteristic of interest. For example, although a cut-off of 0.8 mm canvalidly be used for almost all of these surfaces, it may not necessarily be suit-able for assessing a particular feature of the texture. This entails examining thesurface and considering the purpose of the measurement before selecting thecut-off. (Courtesy of Taylor Hobson.)

and horizontally shifted. Such an action by the ana-logue filter may lead to serious errors for eitherplateau honed types of surface or PM (porous) typesof topographies.

If a digital filter is employed, such as that shownon the graph in Figure 16(a), then the vertical distor-tions of the profile caused by abrupt changes in theheight of the topography are minimised. The prin-ciple operation of the digital filter can be explainedas below.

Digital profiles are no longer represented by asmooth curve, but instead, are described by a seriesof ordinates (numbers) relating to profile heights atregular intervals. In order to estimate the profile’smean line the filter’s action is to calculate the averageheight at a given point, as the arithmetic average ofthe ordinate points in its vicinity. Hence, if the profileis divided up into “windows” the mean profile heightfor each window can be estimated. A line joins thesewindow averages together, which represents theprofile mean line.

Such a digital filter allows up to 100% transmis-sion of the profile, representing wavelengths shorterthan the actual cut-off length, together with zerotransmission of wavelengths greater than this cut-

off. Figure 16(bi) shows how the unfiltered profileequates to an electrically filtered one – Figure 16(bii)– for the same value of cut-off, but related to 50% ofits depth. The main difference between the (PC)digital filter and the analogue filter is that the formertype evaluates the profile mean around a point –enabling it to anticipate changes in the profile height– whereas the latter (analogue) filter cannot. It ispossible to emulate the analogue filter’s characteris-tics by employing a “weighting function” for eachordinate height when a determination of the arith-metic average or mean point is required. However,unless there is a large variation in the surface topog-raphy, or special processing conditions apply – suchas the “Gibb’s phenomenon” – then the analogue-to-digital differences remain slight.

1.6 Measuring lengths

In order to determine a workpiece’s surface texture,three characteristic lengths are associated with theprofile (ISO 4287: 1997). These are:

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0.01 mm

Surface Profile Electrical WaveformLength traced byStylus in 1 Second

A

B

C

D

Traverse speed: A = 1 mm s–1; B = 1 mm s–1; C = 0.5 mm s–1; D = 2 mm s–1;

0.01 mm

0.01 mm

0.02 mm

1 mm

100 Hz

50 Hz

50 Hz

200 Hz

100 peaks

1 mm

50 peaks

0.5 mm

50 peaks

2 mm

200 peaks

Figure 15. Signal frequency depends on irregularity spacing (compare A and B) and traverse speed (compare A, C and D). (Courtesy of TaylorHobson.)

� sampling length;� evaluation (or assessment) length;� traverse length.

Sampling length (lp, lr and lw)

The surface texture profile illustrated in Figure 17(a)has both roughness and waviness present, with bothpatterns being generally repetitive in nature.Therefore the roughness pattern A over the distanceL might be typical for the whole length of thesurface, only differing in minor detail from thatindicated at B over a similar distance.

NB If a shorter distance T was selected, theroughness patterns at C and D would not be iden-tical. This would give a misleading picture of theirrespective roughness heights.

What was true for the reduced distances alsoapplies to waviness, neglecting the roughness (Fig-ure 17b). This is repetitive over distance U, althoughif the examination is confined to a shorter distanceV then the waviness at E and F appear to bemarkedly different in character. Such a variationdemonstrates why it is necessary to select the lengthof the profile over which a parameter is to be deter-mined, termed its “sampling length”, to suit thesurface under test. Yet another feature concerning


λc = 0.08 0.25

(a) High-pass filter characterisation (Source: ISO 3274: 1996 – abridged graph)

(bi) No filtration

0.8 2.5 8

102

10–2 10–12 4 6 8 1002 4 6 8 1012Sine wavelength (λ) mm

Am

plit

ude

tran

smis

sion

(%

)

Sine wavelength

λc= 0.8 mm

4 6 8 1022 4 6 8

101

8

8

6

6

50%4

4

2

2

1

Waviness depth: 100%

Waviness depth: 50%

(bii) With filtration

Figure 16. Effect of an electrical filter on the surface texture. (Courtesy of Taylor Hobson.)

selection of appropriate lengths can be demon-strated in Figure 17(a). Figure17(a) indicates thatwhile the sampling length L is sufficient to reveal thewhole of the roughness pattern, the waviness hasvery little influence over this length. Even if thesampling length was increased, it would simplyinclude more roughness detail but would have little,if any, effect on a roughness parameter value. In this

case, the waviness would play a greater role and forthis reason it is undesirable to increase the samplinglength much beyond that required to obtain a repre-sentative assessment of roughness.

The sampling length can be defined as the lengthin the direction of the x-axis used for identifying theirregularities that characterise the profile under eval-uation. By specifying a sampling length, this implies

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L L

B

A

T TU

E

F

V

V

DC

(a) Roughness and waviness

(b) Waviness only

Figure 17. Effect of different sampling lengths. (Courtesy of Taylor Hobson.)

that structure in the profile occurring over longerlengths will not be applicable in this particular eval-uation. The sampling length for lr – roughness – isequal (numerically) to the wavelength of the profile�c, whereas the sampling length for lw – waviness –equates to that of the profile filter �f.Virtually all theparameters necessitate evaluation over the samplinglength; however, reliability is improved by taking anaverage of them from several sampling lengths asdepicted by the evaluation length in Figure 18(a).

Evaluation length (ln)

A simplistic diagram of the relationship of the stylusto the material profile/topography for a pre-selectedtraverse length is indicated in Figure 18(a). The eval-uation length can be defined as the total length inthe x-axis used for the assessment of the profile underevaluation (see Figure 18a). As shown, this lengthmay include several sampling lengths – typically five– being the normal practice in evaluating roughness

and waviness profiles. The evaluation length meas-urement is the sum of the individual samplinglengths. If a different number is used for the rough-ness parameter assessment, ISO 4287: 1997 advo-cates that this number be included in the symbol, forexample Ra6. In the case of waviness, no defaultvalue is recommended. From a practical viewpoint,the selection for the correct filter can normally beensured when at least 2.5 times the peak spacingoccurs, with two peaks and valleys within each one.Typically, this would mean that an evaluation lengthof 0.8 mm would be selected, but there are occasionswhen either a larger or smaller evaluation lengthmight be preferable for the surface under test. Themetrologist’s experience and judgement will comeinto play here.

Traverse length

The traverse length can be defined as the total lengthof the surface traversed by the stylus in making a


Material profile

Stylus Motion

Evaluation length (i.e. 5 sampling lengths)

Allowancefor

run-up

Allowancefor

over-travel

1 2 3 4 5

Traversing unit

Traverse length

Ra

(a) Traversing unit (i.e. skidless)

(b) Derivation of the arithmetic roughness parameter Ra

Figure 18. Determining surface texture analysis roughness parameter Ra, together with its arithmetic derivation.

measurement. It will normally be greater than theevaluation length, due to the necessity of allowingrun-up and over-travel at each end of the evaluationlength to ensure that any mechanical and electricaltransients, together with filter edge effects, areexcluded from the measurement (see Figure 18a).Onshorter surfaces, it may be necessary to confine themeasurements to one sampling length, under thesecircumstances the sampling and evaluation lengthsare identical, but the over-travel necessary tocontribute to the traverse length must be retained.

1.7 Filtering effects (�s, �c and �f)

In Figure 19 a flow chart is illustrated showing themanner in which surface assessment occurs, withthe primary profile broken down into filteredelements to obtain the waviness and roughnessprofiles of the workpiece surface. Algorithms enablesuitable characteristic functions and parameters tobe obtained, scaled to an appropriate size. As hasbeen mentioned previously in Section 1.5, filters arevital to any form of surface texture analysis. Today,most forms of filtering are normally electrical orcomputational, although they can occasionally bemechanical for analysis of the range of structure in

the total profile, which can be adjudged to be of mostsignificance in a particular situation. Conversely,the effects of filtering can be considered as a meansof removing irrelevant information, such as instru-ment noise and imperfections. Therefore, filters canselect or reject surface topographical structuredepending upon its scale in the x-axis, in terms of spatial frequencies, or wavelengths. The termslow-pass and high-pass filters refer to whether theyeither reject or preserve surface data. For example,a low-pass filter will reject short wavelengths whileretaining longer ones, whereas a high-pass filter pre-serves shorter-wavelength features while rejectinglonger ones. The term bandpass filter refers to thecombination of a low-/high-pass filter selected torestrict the range of wavelengths, with both high-and low-pass regions being rejected. Filter attenua-tion (rejection) should be somewhat gradual, other-wise significantly differing results occur from almostidentical part surfaces, the exception being when asignificant surface feature causes a slight wavelengthshift.

The term cut-off refers to the 50% transmission(and rejection) wavelength filter, this being specificto the topic of surface texture. In the case of the largemajority of surface texture assessments, it issuggested that when the width of a specific surfacefeature is significant, but its size may only be 1% ofthe overall width, this will make it less important.Under these circumstances that affect feature trans-mission/rejection, it is suggested that bandpass

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Outputscaling

Roughnessalgorithm

Wavinessalgorithm

Primaryprofile

algorithm

Roughnessprofile

Primaryprofile

Wavinessprofile

Profilefilter

λ f

Profile filterλc

Profilerecording

Characteristicfunctions

Parameters ofroughness,waviness

andprimaryprofiles

Figure 19. A flowchart for surface assessment. [Source: ISO 4287: 1997.]

filtering is vital to any potential analysis of surfacetexture.

Profile filter

The “profile filter” can be defined (ISO 4287: 1997)as a filter that separates profiles into long- and short-wave components (see Figure 20a). In particular,three filters can be employed for surface measure-ment (Figure 20a):

� profile filter (�s) – this filter defines where theintersection occurs between the roughness andthe presence of shorter-wavelength componentsin a surface;

� profile filter (�c) – this filter defines the intersec-tion position between the components of rough-ness and waviness;

� profile filter (�f) – filters of this type define theintersection point between waviness and thepresence of any longer wavelengths in a surface.

Primary profile

The primary profile forms the basis for primaryprofile parameter evaluations, being defined as thetotal profile after application of a short-wavelength

(low-pass) filter, with a cut-off �s. The finite size ofa stylus will eliminate any very short wavelengths,which practically is a form of mechanical filtering,being in the main utilised as a default for the �s filter.As the size of styli will vary and the instrument canintroduce vibration and/or supplementary noiseinto the profile signal (having equivalent wave-lengths to that of the stylus dimensions) under thesecircumstances, it is recommended to ignore any �sfiltration along the total profile.

Roughness profile

The roughness profile can be defined as the profilederived from the primary profile by suppressing the long-wave component using a long-wavelength(high-pass) filter, with a cut-off �c. This roughnessprofile provides the foundation for the evaluation ofthe roughness profile parameters and will automat-ically include �f profile filter information, because itis derived from the primary profile.

Waviness profile

The derivation of this waviness profile is the resultof the application of the bandpass filter to select thesurface structure at somewhat longer wavelengths tothat of roughness. The filter �f will suppress anylonger-wave components, namely the profile com-ponent, while the filter �c suppresses the shorter-wave components, such as any of the roughnesscomponents. Hence, the waviness profile forms the basis for the evaluation of the waviness profileparameters.

Roughness profile mean line

The roughness profile mean line is a reference linefor parameter calculation, which corresponds to thesuppression of the long-wave profile component bythe profile filter �c.

Waviness profile mean line

The waviness profile mean line is a reference line forparameter calculation, which corresponds to thesuppression of the long-wave profile component bythe profile filter �f.

Primary profile mean line

The primary profile mean line is a reference line forparameter calculation, being a line determined by


Transmission %

Roughnessprofile

Wavelength

Wavinessprofile

100

50

0

Z Y

X

Surface profile

λs λc λ f

(a)

(b)

Figure 20. (a) Transmission characteristic of roughness and wavi-ness profiles. (b) Surface profile. [Source: ISO 4287: 1997]

fitting a least-squares line of nominal form throughthe primary profile.

Surface profile

In ISO 4287: 1997, the coordinate system is definedby making use of the rectangular coordinate of aright-handed Cartesian set for the surface profile(Figure 20b). Here, the x-axis provides the directionof the trace; the y-axis nominally lies on the real surface, with the z-axis facing in an outwarddirection from the material to the surroundingmedium. Thus, the real surface can be defined as the surface limiting the body and separating it from the surrounding medium. The lay previouslyalluded to in Section 1.1 is normally functionallysignificant for the workpiece, so it is important tospecify it on engineering drawings in terms of thetype of lay and its direction (ISO 1302: 2001 –Appendix B).

1.8 Geometrical parameters

The following discussion is concerned with thecalculation of parameters from the measurementdata. These parameters are all derived after the formhas been removed. It should be stated that any para-meters selected should be appropriate for a givenapplication and that not all of them would be neces-sary in all circumstances. On an engineeringdrawing, a designer may have specified a parameterto define the part’s functional behaviour, whichmeans that this parameter is outside the control ofthe user of the instrument. When surface textureparameters have been specified, the user needs tohave a clear and unambiguous understanding of themanner in which they are calculated.

In understanding and evaluating surfaces, thephilosophy behind the reasons why peaks andvalleys are significant is important, although justhow and what represents a peak/valley is not alwaysclear (see further discussion on this topic in theAppendix). When a surface topography shows thepresence of a peak or valley that is not significant,the decision concerning its importance for in-service functional characteristics is not always asimple matter to establish. In the surface profileshown in Figure 21(a), for example, are both thepeaks here of importance, or even significant? Inorder to minimise any confusion for the user, thelatest standards have introduced the importantconcept that the profile element consists of a peakand valley event. Moreover, associated with this

profile element is a discrimination that prevents any minute, unreliable measurement features fromaffecting the detection of these elements. Several ofthese surface texture-related elements and associ-ated features are described in ISO 4287: 1997,consisting of:

� profile element – the section of a profile thatcrosses the mean line to the point at which it nextcrosses this mean line in the same direction – forexample, from below to above the mean line;

� profile peak – the section of the profile elementthat is above the mean line, namely, the profile bywhich it crosses the mean line in the positivedirection until it once again crosses this meanline, but now in the negative direction;

� profile valley – as described for the “peak” above,but with the direction reversed;

� discrimination level – within a profile it may belikely that a minute fluctuation occurs whichtakes the profile trace across the mean line, thenback again almost immediately. In such a condi-tion the departure of the trace from the mean line is not considered to be a real profile peak or valley. In order to prevent automatic systemsfrom counting small trace departures, allowingthem to only consider those larger surface fea-tures, they specify particular heights and widthsto be counted. Hence, default levels are estab-lished in the absence of other specifications.These default levels are set such that their profilepeak heights or valley depths must exceed 10% ofthe Rz, Wz or Pz parameter value. Furthermore,the width of either a profile peak or valley mustexceed 1% of the sampling length, with bothcriteria being simultaneously met;

� ordinate value Z(x) – this represents the height ofthe assessed profile at any position x, its heightbeing regarded as negative when the ordinate liesbelow the x-axis, and otherwise positive;

� profile element width Xs – this is concerned withthe x-axis segment intersecting with the profileelement (see Figure 21a);

� profile peak height Zp – this represents thedistance between the mean line on the x-axis andthe highest point of the largest profile peak (seeFigure 21a);

� profile valley depth Zv – this represents is thedistance between the mean line on the x-axis andthe lowest point of the deepest valley (see Figure21a);

� profile element height Zt – this equates to the sumof the peak height and valley depth of the profileelement, namely, the sum of Zp and Zv (see Figure21a);

� local slope dZ/dX – this represents the slope of theassessed profile at position xi (see Figure 21b).

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The local slope’s numerical value criticallydepends upon the ordinate spacing and thusinfluences P�q, R�q and W�q;

� material length of profile at level “c” Ml(c) – thisrepresents the section lengths obtained whenintersecting with the profile element by a parallelline to the x-axis at a given level “c” (see Figure21c).

1.9 Surface profile parameters

The following examples of defined parameters canbe calculated from any profile. The designation ofletters follows the logic that the parameter symbol’sfirst capital letter denotes the type of profile underevaluation, for example the Ra is calculated from theroughness profile, while Wa has it origin from thewaviness profile, with the Pa occurring from theprimary profile. In the subsequent sections, the defi-nitions and schematic representations of many ofthese surface profile parameters are described alongwith examples of their usage.


ZpZt

Zv

Mean line

Xs

dZ(x)/dX

dZ(x)/dX

dZ(x)/dX

Sampling length

X

dZ(x)/dX

dZ(x)/dX

dZ(x)/dX

Ml1

Ml (c) = Ml1 + Ml2

Ml2c

(b)

(a)

(c)

Figure 21. (a) Profile length, (b) local slope and (c) material length of a surface trace. [Source: ISO 4287: 1997]

1.9.1 Amplitude parameters (peak-to-valley)

Maximum profile peak height Rp, Wp and Pp

This parameter is represented by the largest peakheight (Zp) within the sampling length, with itsheight being measured from the mean line to the highest point (see Figure 22a). The Rp parameter(equating to roughness) is generally less favoured,with preference given to parameters based on thetotal peak-to-valley height. Often Rp and its associ-ated parameters Wp and Pp are referred to asextreme-value parameters, being somewhat un-representative of the overall surface, because theirnumerical value can vary between respective sam-ples. In order to minimise variation in Rp, it isfeasible to average readings over consecutive samp-ling lengths, although in most cases the valueobtained is numerically too large to offer practicalassistance. The Rp and its Wp and Pp derivatives are

not without some merit, as they can establish un-usual surface features such as either a burr on thesurface or sharp spike, and will indicate the presenceof scratches or cracks – possibly indicative of low-grade material or poor production processing.

Maximum profile valley depth Rv, Wv and Pv

This parameter is represented by the largest valleydepth (Zv) within the sampling length, with itsabsolute value Rp (equating to roughness) beingobtained from the lowest point on the profile fromthe mean line (see Figure 22b). As in the case abovefor peaks, the maximum profile valley depths areextreme-value parameters. In a similar manner toRp, Rv can establish whether there is a tendency toworkpiece cracking, spikes and burrs, detecting suchfeatures on the surface.

Maximum height of profile Rz, Wz and Pz

The maximum height parameter (for example, Rz –for roughness) is the sum of the height of the largestprofile peak height (Zp), together with the largestprofile valley (Zv) within the sampling length (seeFigure 23a). In isolation, the Rz does not provide toomuch useful surface information, and therefore it isoften divided into Rp and Rv, previously described.In fact, in ISO 4287: 1984, the Rz symbol indicatedthe ten point height irregularities, with many of theprevious surface texture measuring instrumentsmeasuring this Rz parameter – see the Appendix formore information regarding this previously utilisedparameter.

Mean height of profile elements Rc, Wcand Pc

Parameters of this type evaluate surface profileelement heights (Zt) within the sampling length (seeFigure 23b) and to obtain this parameter it requiresboth height and spacing discrimination, previouslymentioned. When these values are not specified thenthe default height discrimination used shall be 10%of Rz, Wz and Pz, respectively, with the defaultspacing discrimination being stated as 1% of thesampling length. Both of these height and spacingrequirements must be met. Normally in practice it isextremely rare to utilise this parameter because ofits difficulty in interpretation and, as a result, itwould rarely be used on an engineering drawing.

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Zp1

Zv1 Zv2 Zv3 Zv4 Zv5 Zv6Rv

Zp2

Zp3 Zp4 Zp5

Zp6 Rp

Sampling length

Sampling length

(a)

(b)

Figure 22. (a) Maximum profile peak height and (b) maximumprofile valley depth (examples of roughness profiles). [Source: ISO4287: 1997]

Total height of profile Rt, Wt and Pt

This parameter relates to the sum of the height ofthe largest peak height (Zp) and the largest profilevalley depth (Zv) within the evaluation length. It isdefined over the evaluation length rather than thesampling length and in this manner has no aver-aging effect. This lack of averaging means that anysurface contamination (dirt) or scratches presentwill have a direct effect on the numerical value of,say, Rt.

1.9.2 Amplitude parameters(average of ordinates)

Arithmetical mean deviation of theassessed profile Ra, Wa and Pa

The arithmetic mean parameter is the absolute ordi-nate value Z(x) within the sampling length Thenumerical value of Ra is able to vary somewhatwithout unduly influencing the performance of asurface. Often on engineering drawings a designerwill specify a tolerance band, or alternatively amaximum value for Ra that is acceptable. The math-ematical expression of this parameter is given belowfor these absolute ordinate values as:


Zp1

Zp2

Zp3Zp4 Zp5

Zp6

Zp1 Zp2 Zp3 Zp4 Zp5 Zp6

Zt1 Zt2

Zt3Zt4

Zt5

Zt6

Rz

Sampling length

Sampling length

(a)

(b)

Figure 23. (a) Maximum height of profile and (b) height of profile elements (examples of roughness profiles). [Source: ISO 4287: 1997]

where N = number of measured points in a samplinglength (see Figure 24b).

In Figure 24(a) is illustrated the graphical deriva-tion of this parameter within the sampling length,with the shaded areas of the graph below the centreline in A being repositioned above this centre line inB. Here, the Ra value is the mean line of the resultingprofile indicated in C.

The absolute average roughness over onesampling length is given by the Ra value. This meansthat the influence of a discrete but non-typical peakor valley on the numerical value of Ra is not reallysignificant. Good metrological practice is to ensurethat a number of assessments of Ra occur overconsecutive sampling lengths, enabling the accep-tance of an average of these values. This samplingstrategy ensures that the numerical value of Ra istypical for the inspected surface. As has been previ-

ously mentioned on several occasions, if a defined“unidirectional lay” is present on the surface (Figure4), then any measurements should be undertakenperpendicularly to this “lay” if misinterpretation ofthe surface is to be avoided (Figure 5).

The numerical value of Ra does not impart anyinformation regarding the surface shape, nor ofany irregularities present. In fact, it is quite possibleto have identical Ra values for surfaces that aremarkedly different in their profiles (Figure A in theAppendix) and this will affect their potential in-service performance, with engineering drawingsoften quoting the type of production process (Figure3c). Historically, in Great Britain the most widelyused of all the surface texture parameters has beenRa, but this should not discourage industrial andresearch organisations from using others, as theymay offer more in terms of information regarding asurface’s functional performance.

The mathematical derivation of both the com-monly utilised parameters Ra and Rq are givenbelow (see Figure 24b):

Za � 1N

�N

i�1 �Zi�

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Sampling length (L)

Centre line

Centre line

Ra

Centre lineGraphical derivation of Ra

Derivation of the arithmetical mean deviation

A

(a)

B

C

Sampling length (L)

Y1

Y2

Y3 Y4Y5

Y6Yn

(b)

Figure 24. Determination of Ra and Rq. (Courtesy of Taylor Hobson.)

Ra = |Y1| + |Y2 | + |Y3| . . . + |Yn| /n

Rq = √(Y12 + Y2

2 + Y32 . . . + Yn

2) /n

Root mean square deviation from theassessed profile Rq, Wq and Pq

The root mean square of the ordinate values Z(x)within the sampling length is established by thedepartures from mean line of the profile and can bemathematically expressed in the following way:

1Zq =�——�— ∑N

i=1Z

2iN

If a comparison is made between the arithmeticaverage and the root mean square parameters,the latter has the effect of providing additionalweighting to the numerically greater values ofsurface height. One of the reasons for the harmonybetween both the Ra and Rq parameters is mainlyfrom a historical perspective. The Ra parameter ismuch easier to determine graphically from a profilerecording and for this reason, it was primarilyadopted prior to automatic surface measurementinstruments being developed. Once the roughnessparameters utilising automatic surface textureinstrumentation were made available, the parameterRq had the advantage of being able to neglect thephase effect from the electrical filters, while the Raparameter using arithmetic average will be affectedby these phase effects and cannot be disregarded.To compound the problem, Ra has been virtuallyuniversally adopted for machining specifications to the detriment of Rq. The Rq parameter is stillemployed in many optical applications for theassessment of lenses, mirrors and the like for surfaceoptical quality.

Skewness of the assessed profile Rsk, Wskand Psk

This parameter represents the quotient of the meancube value of the ordinate values Z(x) and the cubeof Pq, Rq or Wq, respectively, within the samplinglength (Figure 25). The skewness is derived from the amplitude distribution curve, representing thesymmetry about the mean line. This parameter cannot distinguish if profile spikes are evenly dis-tributed above or below the mean line, being consid-erably influenced by any isolated peaks or valleyspresent within the sampling length. Skewness can be expressed in mathematical form with Rsk, equat-ing to:

The skewness parameter of an amplitude distribu-tion curve as depicted in Figure 25(a) indicates acertain amount of bias that might be either in anupward or downward direction. The amplitudedistribution curve shape is very informative as to theoverall construction of the surface topography. Ifthis curve is symmetrical in nature, then it indicatessymmetry of the surface profile; conversely, anunsymmetrical surface profile will be indicative of askewed amplitude distribution curve (Figure 25band c). As can be seen in Figure 25(b) and (c), thedirection of skew is dependent upon whether thebulk material appears above the mean line – termednegative skewness (Figure 25c) – or below the meanline – positive skewness (Figure 25b). Utilising thisskewness parameter distinguishes between profileshaving similar if not identical Ra values.

Further, one can deal with this amplitude orheight data statistically, in the same manner as onemight physically measure anthropometric data suchas a person’s average stature, within a specific popu-lation range. As with the statistical dispersion ofpopulation stature, engineering surfaces can exhibita broad range of profile heights.

For example, a boring operation with a relativelylong length-to-diameter ratio may cause deflection(elastic deformation of the boring bar) and occasionthe cutting insert to deflect, producing large peak-to-valley undulations along the bore (waviness).Superimposed onto these longer wavelengths aresmall-amplitude cyclical peaks (periodic oscilla-tions) indicating vibrations resulting from thecutting process. The resultant surface profile for thebored hole would depict the interactions from theboring bar deformations and any harmonic oscilla-tions. This boring bar motion reflected in the profiletrace would exhibit low average profile height, butwith a large range of height values.

Surface texture data can be statistically manipu-lated, beginning with the profile trace’s height, oramplitude distribution curve – this being a graph-ical representation of the distribution of heightordinates over the total depth of the profile. Thecharacteristics of amplitude distribution curves canbe defined mathematically by several terms called“moments”, but more will mentioned concerningthis aspect in the Appendix.

A numerical value can be given to Rsk and in thecase of Figure 25(b) the “positive skewness” mayeventually obtain an adequate bearing surface,although it is unlikely to have oil-retaining abilities.This type of surface can typically be exploited foradhesive-bonding applications. The surface charac-

Rsk � 1

Rq3 1N

�N

i�1 Zi

3


terised by Figure 25(c) might occur in the cases ofporous, sintered or cast-iron surface topography –having comparatively large numerical values ofnegative skewness. The surface is sensitive toextreme ordinate values within the profile undertest; this is due to Rsk being a function of the cubeof the ordinate height. As a result of this peak sensi-tivity, it is a hindrance when attempting to inspectplateau-type surfaces, although the Rsk parameterindicates a reasonable correlation with a compo-nent’s potential load carrying ability, or its porosity.

The shape, or “spikeness” of the amplitude distri-

bution curve can also relay useful information aboutthe dispersion, or “randomness” of the surface pro-file, which can be quantified by means of a para-meter known as kurtosis (Rku).

Kurtosis of the assessed profile Rku, Wkuand Pku

The kurtosis parameter, typified by Rku, is the meanquadratic value of the ordinate values Z(x) and the

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Negative skewness (Rsk) Positive skewness (Rsk)

Amplitudedistributioncurve

(a) Skewness bias

(b) A “locking” surface texture

(c) A “bearing” surface texture

Figure 25. How surface texture topography influences the amplitude distribution curve.

fourth power of Pq, Rq or Wq, respectively, withinthe sampling length. However, unlike the skewnessparameters previously described, namely Rsk and itsderivatives, Rku can detect if the profile peaks aredistributed in an even manner across the samplinglength trace, as well as providing information on theprofile’s sharpness (see Figure 26).

Kurtosis provides a means of measuring thesharpness of the profile, with a “spiky” surface ex-hibiting a high numerical value of Rku (Figure 26c);alternatively, a “bumpy” surface topography willhave a low Rku value (Figure 26b). As a consequenceof this ability to distinguish variations in the actual

surface topography, Rku is a useful parameter in theprediction of in-service component performancewith respect to lubricant retention and subsequentwear behaviour.

It should be mentioned that kurtosis cannotconvey differences between either peaks or valleysin the assessed profile.

The kurtosis parameter indicative of Rku, can bemathematically expressed in the following manner:

Rku � 1

Rq4 1N

�N

i�1 Zi

4


Kurtosis (Rku) > 3

Kurtosis (Rku) < 3

Amplitudedistribution

(a) Kurtosis is influenced by the distribution shape

(b) Material distributed evenly across the whole of the surface topography

(c) Material distributed about the centreline

Figure 26. Variation in surface topography influences the shape and height of the amplitude distribution curve.

Later, the parameters Rsk and Rku will be appliedto specific manufacturing processes to producemanufacturing process envelopes describing thefunctional aspects of a particular generated surfacecondition.

1.9.3 Spacing parameters

Mean width of profile elements Rsm,Wsm and Psm

The mean width parameter of the profile elementwidths Xs within the sampling length relates to theaverage value of the length of the mean line sectionthat contains adjacent profile peaks and valleys(Figure 27). The parameter needs both height andspacing discrimination, and if not specified thedefault height bias utilised shall be 10% of Pz, Rz orWz, respectively. Moreover, the default spacingdiscrimination shall be 1% of the sampling length,with both of these conditions requiring to be met.

The spacing parameters are particularly useful indetermining the feedmarks from a specific machin-ing operation, as they relate very closely to that ofthe actual feed per revolution of either the cutter orworkpiece, depending on which production processwas selected.

NB More is mentioned on spacing parametersand their affects on the surface topography in theAppendix.

1.9.4 Hybrid parameters

Root mean square slope of the assessedprofile R�q, W�q and P�q

The root mean square slope parameter refers to thevalue of the ordinate slope dZ/dX within thesampling length, depending upon both amplitudeand spacing information, hence the term hybridparameter. The slope of the profile is the angle itmakes with a line that is parallel to the mean line,with the mean of the slopes at all points in the profilebeing termed the average slope within the samplinglength. By way of illustration of its use, it might benecessary to determine the developed or actualprofile length, namely the length occupied if all thepeaks and valleys were laid out along a singlestraight line. Hence, the steeper the slope the longerwill be the actual surface length. In practical indus-trial situations, the parameter might be utilised ineither a plating or painting operation, where thesurface length for keying of the coating is a criticalfeature. Moreover, the average slope can be relatedto certain mechanical properties such as hardness,elasticity or more generally to the crushability of asurface. Further, if the root mean square value issmall, this is an indication that the surface wouldhave a good optical reflection property.

NB In the Appendix are listed some of theprevious and current techniques for the assessmentfor these hybrid parameters.

1.9.5 Curves and related parameters

Curves and their related parameters are defined overthe evaluation length rather than the samplinglength.

Material ratio of the profile Rmr(c),Wmr(c) and Pmr(c)

The material ratio of a profile refers to the ratio ofthe bearing length to the evaluation length and isrepresented as a percentage. This bearing length canbe found by the sum of the section lengths obtainedby cutting the profile line – termed slice level – thatis drawn parallel to the mean line at a specified level.The ratio is assumed to be 0% if the slice level is atthe highest peak; conversely, at the deepest valleythis would represent 100%. Parameters Rmr(c),Wmr(c) and Pmr(c) will determine the percentage ofeach bearing length ratio of a single slice level, or

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Xs1 Xs2 Xs3 Xs4 Xs5 Xs6

Sampling length

Figure 27. Width of profile elements. [Source: ISO 4287: 1997]

say, 19 slice levels that are drawn at equal intervalswithin the Rt, Wt or Pt, respectively.

NB More is mentioned on this topic in theAppendix.

Material ratio of the curve of the profile(Abbot–Firestone or bearing ratio curve)

The material ratio curve represents the profile as afunction of level. Specifically, by plotting the bearingratio at a range of depths in the profile, the mannerby which the bearing ratio changes with depthprovides a method of characterising differing shapespresent on the profile (Figure 28a). The bearing areafraction can be defined as the sum of the lengths of individual plateaux at a particular height, normal-ised by the total assessment length – this parameteris designated by Rmr (Figure 28a). The values of Rmrare occasionally specified on engineering drawings,although this may lead to large uncertainties (seeChapter 6, Section 6.4) if the bearing area curve is

referred to by the highest and lowest profile points.In the majority of circumstances mating surfaces

require specific tribological functions; these are thedirect result of particular machining operationalsequences. Normally, the initial production opera-tion will establish the general shape of the surface –by roughing-out – providing a somewhat coarsefinish, with subsequent operations necessary toimprove the finish, resulting in the desired designproperties. This machining strategy provides theoperational sequence that will invariably removesurface peaks from the original process, but oftenleaves any deep valleys intact. This roughing andfinishing machining technique leads to a surfacetexture type that is often termed a stratified surface.In such cases the height distributions are negativelyskewed; therefore this would make it otherwise diffi-cult for an average parameter such as Ra to repre-sent the surface effectively for either its specificationor in the case of quality control matters.

NB This topic is discussed in further detail in theAppendix.


C

Mean line

Evaluation length

C0

Rδc

C1

0 20

0 10 20 30 40 50 60 70 80 90 100

40 60Rmr (c) %

Rmr0 Rmr

80 100

(a)

(b)

Figure 28. (a) Material ratio curve. (b) Profile section level separation. [Source: ISO 4287: 1997]

Profile section height difference R�c,W�c and P�c

This parameter can be represented as the verticaldistance between two section levels of a givenmaterial ratio curve (see Figure 28b).

Relative material ratio Rmr, Wmr andPmr

The relative material ratio can be established at aprofile section level R�c, being related to a referenceC0 (see Figure 28b), where:

C1 = C0 � R�c or (W�c or P�c)

C0 = C(Rmr0, Wmr0, Pmr0)

Rmr refers to the bearing ratio at a predeterminedheight (see Figure 28b). One method of specifyingthe height is to move over to a certain percentage –reference percentage – on the bearing ratio curve,then move down to a certain depth (slice depth),

with the bearing ratio at the corresponding positionhere being the Rmr (Figure 28b). The reason for thereference percentage is to eliminate any spuriouspeaks from the assessment, as they would tend to beworn away during the initial burn-in/running-inperiod. The slice depth will then correspond to asatisfactory surface roughness, or to an acceptablelevel of surface wear.

Profile height amplitude curve

This represents the sample probability density func-tion of the ordinate Z(x) within the evaluation length.The amplitude distribution curve, as it is usuallyknown, is a probability function giving the proba-bility that a profile of the surface has a particularheight at a certain position. Like many proba-bility distributions, the curve normally follows thecontours of a Gaussian – bell-shaped – distribution(Figure 29a). The amplitude distribution curve in-forms the user of how much of the profile is situatedat a particular height, from the aspect of a histogram-like sense.

This curve illustrates the relative total lengths

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Mean line

Amplitude density

Amplitudedistributioncurve

Evaluation length

Evaluation length (E)

Profile graph+y

δy

–y

y Amplitude

density

(b)

(a)

Figure 29. Profile height and amplitude distribution curve. [Source: ISO 4287: 1997]

over which the profile graph will attain any selectedrange of heights that are above or below the meanline (see Figure 29b). The profile’s horizontal lengthsare included within a narrow zone width �y at aheight z and are represented in Figure 29(b) by “a,b, c, d and e”. Therefore, by expressing the sum ofthese lengths as a percentage of the evaluationlength, this will give a measure of the relativeamount of the profile at height z.

This graph is known as the amplitude distribu-tion at height z, so by plotting density against heightthe amplitude over the whole profile can be deter-mined – producing the amplitude density distribu-tion curve.

1.9.6 Overview of parameters

In Table 2 are shown the more recent and previouslyutilised parameters, together with informationconcerning whether the parameter has to be calcu-lated over the sampling or evaluation length.

1.10 Auto-correlation function

Every day of one’s life, the technique of correlationis applied to compare sights, sounds, tastes, objects– the list is almost limitless – this being a process ofcomparison. The auto-correlation function (ACF) isessentially a process of determining the relationshipof any point on the profile to all other points. Some

manufactured surfaces clearly indicate visible repet-itive marks on either the material itself or indirectlyvia the profile graph, while on other surfaces itbecomes difficult to distinguish any repetitive irreg-ularities from random occurrences. This visual diffi-culty is particularly true when the amplitudes of therepetitive irregularities are less than the randomoccurrences. Moreover, the presence of repetitivesurface features – however small – can indicatefactors such as tool wear, machine vibration or defi-ciencies in the machine, with identification of thembeing an important factor. Any random patternoccurring on the surface can reveal, for example,whether a built-up edge condition has transpired onthe cutting tool resulting in a degree of tearing ofthe machined surface – this tends to be of a randomnature and is not predictable.

The extent of this randomness of the surface canbe monitored and assessed by isolating randomfrom repetitive textural patterns, this being achievedby auto-correlation. When a profile is perfectlyperiodic in nature – typified by a sine wave – therelationship of a particular group of points repeatsitself at a distance equal to the wavelength. Con-versely, if the profile under inspection is comprisedentirely from random irregularities, the precise rela-tionship between any specific points will not occurat any position along the trace length, hence anyrepetitive feature or group of features can be identi-fied. Computers equipped with fast digital proces-sors have significantly reduced the tedious task ofdetermining a surface profile’s auto-correlation.

The technique exploited by auto-correlation is tocompare different parts of the surface profile; in this


Table 2. Past and present parameters for surface texture

Parameters 1997 edition 1984 1997 Determined within:edition edition

Evaluation Sampling length length

Maximum profile height Rp Rp XMaximum profile valley depth Rm Rv XMaximum height of profile Ry Rz XMean height of profile Rc Rc XTotal height of profile – Rt XArithmetical mean deviation of the assessed profile Ra Ra XRoot mean square deviation of the assessed profile Rq Rq XSkewness of the assessed profile Sk Rsk XKurtosis of the assessed profile – Rku XMean width of profile elements Sm RSm XRoot mean square slope of the assessed profile �q R�q XMaterial ratio of the profile RMr(c) XProfile section height difference – R�c XRelative material ratio tp Rmr XTen-point height (deleted as an ISO parameter) Rz –

Source: ISO 4287: 1997 (E/F).

manner profile repetitions or similarities can bediscovered. When the profile of the surface displayseither an isotropic or random shape then noportions will be similar, exhibiting low auto-corre-lation function. On the other hand, if an anisotropicor periodic surface topography occurs – for exampleas in single-point turning operations – then repeti-tion of the surface profile occurs and auto-correla-tion will be high.

Figure 30 shows an example of the ACF relatingto specific surface profile conditions. As mentionedabove, the ACF contains information relating to thespacings of peaks and valleys in the profile. An alter-native to the ACF is the equivalent term known asthe power spectrum, or power spectral density, inwhich spacings are replaced by frequencies – onebeing a Fourier transform of the other. For the ACFexamples shown in Figure 30, the scale of the hori-

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Profile:

Amplitudedistribution:

Auto-correlationfunction:

Ra

RtRz Rtm

RqRp

A(β)

A(β)

β∗

β

β

A(β)

β

Rsk = 0Rku = 3

Rsk = –1Rku >3

Rsk = –1Rku >3

SlopeCurvatureProfileLength

Decrement

λa

Sampling length

Peaks per mmHigh Spot CountPeak CountPower SpectrumFourier Analysis

(a)

(b)

(c)

Figure 30. Comparison of surface parameters for typical surfaces showing those currently in use. [After Whitehouse, 1978.]

zontal axis can be the mean distance between peaksor the average distance between mean line crossings.

The ACF is derived from the normalised auto-covariance function (ACVF) – this being as follows:

where

where lm = assessment length, y(x) = profile heightat position x and Rq = rms parameter.

The ACF does not contain information about theamplitude of the profile, with its values ranging fromplus one – giving perfect correlation – to negativeone – this having a correlation of the inverted butshifted profile. Due to the fact that the ACF is inde-pendent of the amplitude of the profile it is morepopular than the ACVF. In the case of an ACF havingan isotropic (random) profile, it quickly decays tozero (Figure 30a), with the profile trace being of anunrepetitive nature. Conversely, the tendency for atruly anisotropic (periodic) generated surface is thatit does not decay to zero, with Figure 30(c) illus-trating some periodicity in its profile trace – indi-cating that decay here is significantly less than thatfor Figure 30(a). Despite the fact that both Figure30(a) and (c) have similar Rz values, their respectiveACF are distinctly different and can be used as ameans to discriminate between surfaces and indicatewhether they will fulfil the desired in-service appli-cations, which might not otherwise be apparent.

Fourier analysis (FFT)

Any surface profile will normally be of somecomplexity, this being comprised of an array ofdiffering waveforms that are superimposed onto oneanother. An actual profile’s specific composition willbe dependent on the shape and size of the wave-forms existing within the profile; both their ampli-tude and frequency, termed “harmonics”, can beestablished by the application of Fourier analysis.

The technique known as a “fast Fourier trans-form” – FFT for short – enables one to establish aseries of sine waves being generated from the surfaceprofile, and when combined together contribute tothe original profile. Individual harmonics representa specific frequency–wavelength, in combinationwith their associated amplitude.

The surface profile depicted in Figure 31(a) wasselected to illustrate a periodic form, which in isola-

tion may mask significant hidden harmonic detailwhich could play an important role in its later in-service application. Results from the FFT analysis ofthe profile (Figure31b) reveal the differing sine waveamplitudes necessary to generate the originalprofile. In this case, the largest sine wave amplitudeequals a value of 0.7 mm, this being termed the“dominant wave”.

It should be emphasised that the informationobtained from the FFT analysis will be exactly thesame as that acquired by the auto-correlationmethod, but obviously it is displayed in a alteredform. Due to the isolation of the harmonics intospecific bands for a particular surface profile, FFTcan impart valuable understanding as to how theproduction process might have been influenced by variables in processing for that product. Forexample, the dominant harmonic in the FFT displayfor a profile might give a valuable insight into thevibrational frequency for a specific machine tool.Knowledge of this vibrational effect on the resultingsurface profile may enable the attenuation of thisvibrational signature by judicious adjustment ofeither cutting data, or specific maintenance to themachine tool to improve the subsequent surfaceprofile’s condition.

1.11 Appearance of peaks andvalleys

For many engineering and statistical graphs nointrinsic relationship exists between the plottedmeasurement units; for example, when plotting therise in temperature of a heat treatment oven againstelapsed time the ordinates would be represented byboth degrees Celsius and hours – two quite dissim-ilar units. As a consequence of these disparate units,acceptance of the shape of the graph is acknow-ledged, whatever scales are applied for the ordinates.It is quite different when dealing with a surfaceprofile graph, where both the horizontal and verticalordinates are represented by the same units (i.e.,length). At first introduction, it may be difficult toappreciate that due to the difference of scale thegraph will not instantaneously give an indication asto the shape of the irregularities. Figure 32 illustratesthe effect, with this disparity being one of the mostdifficult factors in surface texture analysis tocomprehend.

It is very important to note that although thevisual profile’s shape is distorted due to the applica-tion of different horizontal and vertical magnifica-tions, measurements scaled from the graph are

ACVF(�x) � limlm→∞

� lm

0y(x) y(x � �x) dx

ACF(�x) � ACVF(�x)

(Rq)2


correct. Such effects can be visually demonstratedwith reference to the peak angles of the profile illus-trated in Figure 32, indicating how the profile shapevaries as horizontal/vertical magnification is altered.Figure 32(III) verifies this fact, as the horizontalmagnification of the surface profile is increased(Figure 32II), the length X–X expands to X1–X1 andthe peaks; A, B, C and D appear flatter. Increasing the horizontal magnification still further – until it equals the vertical magnification (Figure 32I) –expands the sampling length Y–Y to Y1–Y1. Onceagain, with this still higher magnification, the peaksE and G and valleys F and H now have a much flatterappearance. A point worth making is that the actualdifference in respective heights of correspondingpeaks and valleys in I, II and III are identical.

As a result of the spiky appearance of both the

peaks and valleys on the profile graph, this can leadto considerable confusion when visually assessingthe actual graph. However, the geometric relation-ship between angles on the graph and those thatoccur on the physical profile of the componentunder test are more easily determined. As anexample of this interpretation, Figure 33(a), on theprofile graph, depicts a symmetrical peak with anincluded angle 2. Figure 33(b) exhibits the corre-sponding peak, on the actual surface, having anangle 2. The ratio of the angles is determined by

This ratio is strictly true for symmetrical peaks,although it is only slightly different for asperities of

tan tan

� Vv

Vh

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10(µm)

3

2

1

00.8 0.4 0.3 0.2 0.1

(µm)

5

0

–5

–10

(a) Profile

(b) Wavelength

Figure 31. Fourier analysis of an idealised (i.e. periodic) profile.

an asymmetrical nature. For example, the dataobtained from a profile graph in which the verticaland horizontal magnifications and peak geometrymight be Vv = ×5000, Vh = ×50 and 2 = 10°. Thiswill therefore represent

= 5°

tan = 0.0875

hence

tan = 0.0875 × 5000/50

= 8.75

giving

= 83.5°

Thus

2 = 167°

This example of peak geometry (Figure 33a) repre-sents a fairly sharp peak on the profile graph, butonly a gradual slope – rising and falling at 6.5° fromthe horizontal – on the actual component’s surface(Figure 33b). Due to the fact that it becomes difficultto accurately measure the peak angle on the graph,and it is rare that an accurate assessment of thesurface angles is required, an approximation of 2 :2 is normally sufficient.

Table 3 provides approximate conversions forseveral Vv : Vh ratios.


x5000(I)

(II)

(III)

x5000

x5000

x5000

x1000

Y–1

X–1

Y1

X1

x100

E F G

Y Y

H

A B C D

X X

Figure 32. Diagram illustrating how profile shape varies as the horizontal magnification is reduced: (I) surface profile magnified x5000 equallyin all directions; (II) profile with A Vv: Vh ratio of 5:1; (III) profile graph recorded with a Vv:Vh ratio of 50:1. (Courtesy of Taylor Hobson.)

It has been previously stated by way of a light-hearted analogy for the representation of two roughcontacting surfaces that they resemble “Switzerlandon top of Austria”, although this simply shows theinfluence of the visual aspect of the profile graph. Amore preferable analogy might be “The Netherlandson top of Iowa”, as the peaks on the surface are ingeneral of quite blunt and low aspect.

When considering the profile with its associatedpeaks and valleys, it has been presumed that thepeak height on a profile graph is characterised bythe summit of individual peaks traced by contactwith the stylus for a surface under test. This may be

true for the major ridges for a surface exhibitingmarked directional lay (see Figure 5A) being tracedat 90° to the direction of the dominant surfacepattern lay. Conversely, for a surface displaying ran-dom textural influences, such as the “multi-direc-tional” example in Figure 4, it is extremely unlikelythat a stylus’s path will trace across the summit ofevery peak. In these circumstances, some peaks andvalleys will be displaced from the path of the stylusby varying distances, with the result that the styluswill also traverse across many flanks. Stylus verticaldisplacement, although somewhat less than the fullpeak height or valley encountered, will moreover becorrect for the traced feature. Assumptions made bymany are that every peak on the graph is the summitof a peak on the actual surface, but where randomsurfaces occur there will be sufficient actual sum-mits encountered to prevent any significant inaccu-racy as a result.

1.12 Stylus-based and non-contact systems

Effect of stylus

It should be appreciated by now that the stylus andskid, when employed, are the only parts which arein active contact with the surface under test.Therefore both the shape and dimensions of thispick-up are critical factors and will strongly influ-ence information retrieved from the surface. Thegeometry of a typical stylus – its shape and size –was discussed in Section 1.4 and illustrated in Figure11(a); it influences the accuracy obtainable from the surface. Due to the finite size of the stylus somesurface imperfections, such as visible scratches, are

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2α

2β

(a) Peak on profile graph

(b) Corresponding peak on the surface

Figure 33. Relationship between peak angles on the graph and theactual surface. (Courtesy of Taylor Hobson.)

Table 3. Peak angles (2, Figure 33a) on the surface corresponding to peak angles of 2 on the graph

Ratio: Vv /Vh Peak angle on graph (2, Figure 33)

1° 5° 10° 15° 20° 30° 40° 50°

10 10° 47° 82° 105° 121° 139° 149° 155°25 25° 95° 131° 146° 154° 162° 167° 170°

100 82° 154° 167° 171° 173° 176° 177° 177°250 131° 169° 175° 176° 177° 178° 179° 179°500 154° 175° 177° 178° 178° 179° – –1000 167° 177° 179° 179° 179° – – –2500 174° 179° – – – – – –5000 177° – – – – – – –

Courtesy of Taylor Hobson.

too fine to be completely penetrated, even with the smallest tip available. This is not too much ofa hindrance to assessment as the Ra is an “averagingparameter”, so the omission of the finest texturalfeatures will not unduly affect the resulting value.To illustrate this point, many years ago a series of tests were conducted on ground surfaces byReason et al. (1944), these samples had fourincreasing levels of roughness. The reduction inmeasured Ra value when utilising either a 1.25 �mor 10 �m stylus was 4.5 to 3.25, 8 to 7.5, 11 to 10 and26 to 25 �m, respectively. This small variationoccured despite the fact that the larger stylus waseight times greater than the smaller.

For undistorted surfaces (periodic), there is apredictable relationship between the stylus radiusand the resulting error introduced into the Rareading. Figure 34 charts the approximate values ofthis error, being applicable to regular profiles with150° included angle triangular peaks and valleys –typical of surfaces utilised for calibration standards.

For surfaces other than of this regular triangulatedgeometry, the values tend to be only approximate,although they do indicate the order of any errorlikely to be occasioned. The horizontal ordinates inFigure 34 are the ratio of the stylus tip radius to theactual Ra value of the surface, with the verticalordinates being the amount by which the measuredRa value is too low. The chart demonstrates that onlywhen the tip radius is greater than approximately 20times the Ra value is this error of any significance.By traversing a stylus across a standard incorpo-rating narrow grooves of known widths – 20, 10, 5and 2.5 �m – this is a technique for estimating styluswear or damage. Obviously, the blunter the tip theless distance it can descend into the groove, thispenetration depth being measured from the profilegraph. The effective stylus radius can be establishedfrom the calibration curve supplied with the arte-fact. Stylus cone angle can also be measured by thismethod; because the stylus wears with use, thechange in effective tip size can be monitored.


10080

605040

30

20

108

654

3

2

10.8

0.60.50.4

0.3

0.2

1 2 3 4 5 6 8 10 20 30 40 5060 80100 200

Ratio - Stylus tip radius: Actual Ra of surface

Ra

met

er w

ill r

ead

LO

W b

y th

is %

Figure 34. Error due to finite stylus tip radius, for a specific surface. (Courtesy of Taylor Hobson.)

Illustrative example: When measuring a surface of 0.5 �m Ra with a stylus tip of 5 �m (10:1 ratio) the display will be approximately 2% low.If the stylus has double this radius (i.e., 10 �m) this error increases to 8%.

Stylus force on the surface must not be greatenough to deform or scratch the surface as this maypromote erroneous results. Conversely, the forceimparted by the stylus must be of a sufficient levelto ensure that it maintains continuous contact withthe surface at the desired traverse speed. This factoris important in the design of the pick-up, with mostsurface texture instruments having a stylus tipradius of between 1 and 10 �m. However, the greaterthe radius of the tip, the larger the allowable forcethat can bear on the surface. If a tip radius is small,say 0.1 �m (Figure 11a), then a very low force mustbe used, typically around 0.75 mN.

The conical stylus geometry was previously men-tioned in Section 1.4 and illustrated in Figure 10,invariably having a 90° tip angle. In action (Figure35), the conical tip angle of 90° can easily cope withsurface features such as that shown, having theanisotropic profile of a honed surface. When surfacefeatures become greater than 45° to the horizontal,orthe valley is smaller than, say, 5 �m, then themechanical motion of the tip becomes to some ex-tent distorted, as illustrated in Figure 11(c). Specific-ally, under these conditions, the tip acts in a similarfashion to a low-pass filter with high-frequency fea-tures not being recorded.With a tip angle of 90°, thismeans that the stylus will foul any peak or valleyhaving an included angle of less than 45° – whichmay at first seem a considerable limitation, but inreality does not cause too much of a problem.

Chisel-edge styli (see Figure 11a) are a practicalvariation on the cone-shaped stylus (Figure 35),being particularly successful at entering porous

materials such as sintered parts. One problem asso-ciated with the chisel-type stylus is the difficulty inmaintaining its attitude at right angles to the lay,being more sensitive to error from peaks rather thanvalleys. Stylus misalignment can be minimised bythe application of “smart parameters” that mathe-matically ignore certain features. Normally, it isrecommended to utilise a conventional stylus geom-etry, unless particular problems are encounteredthat may cause the standard stylus to impair thevalidity of the resulting data.

Manufacturers of stylus/skid geometries norm-ally apply identifying marks on the pick-up, or at thevery least on its accompanying transportation case.Table 4(a) illustrates the pick-up markings, whereasTable 4(b) highlights the standard configurations.

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Figure 35. 90° conical stylus tip mechanically tracing across aportion of a honed surface. SEM photomicrograph, X200 magnifica-tion. [Courtesy of PTB Braunschweig/Feinpruf Perthen GmbH.]

Table 4(a). Typical (traceable) markings on pick-up

Identification marks: ±100 5 90 0.8 30/6 1/0

SSttyylluuss ddaattaa::Measuring range (�m) X

Tip Radius (�m) X

Tip angle (°) X

Measuring force (mN) X

SSkkiidd ddaattaa::

Skid radius,longitudinal/traverse X

Distance skid-to-stylus,longitudinal/traverse X

Table 4(b). Configurations for some standard pick-ups

SSttyylluussTip angle (°) 60° ± 5° or 90° ± 5°Tip radius (�m) 2 ± 1 5 ± 2 10 ± 3

Static measuring force (ie at electric zero, mN) � 0.7 � 4 � 16

Variation in static measuring force (mN/m) � 0.035 � 0.2 � 0.8

SSkkiiddDistance from stylus dependent upon pick-up design;

Radius (longitudinal, mm) 0.3 1.3 3 10 30 infinity(lateral, mm) depends upon design of pick-up

Surface roughness (�m) � 0.1

Skid force (N) for:Hard surface � 0.5

Soft surface � 0.25

Linearity of system (%) ± 1

1.12.1 Pick-upThe function of the transducer or pick-up is toconvert the minute vertical movements of the stylus,as it progresses along the surface, into proportionatevariations of an electrical signal. The sensitivitydemanded of the pick-up is such that it should beable to respond to stylus movements of approxi-mately 0.1 nm or better. This output is minute andof necessity must undergo significant amplificationto enable stylus trace movements of between 50,000and 100,000 times greater than the stylus movement(Vv ×50,000 or ×100,000).

In general, pick-ups can be classified into twogroups, depending on their operating principle:

1. Analogue transducers (Figure 36)

� Position-sensitive pick-ups (Figure 36a) give asignal proportional to displacement, even whenthe stylus is stationary. Output is independent ofthe speed at which the stylus is displaced and isonly related to the position of the stylus within apermissible range of vertical movement. A big

advantage of this type of pick-up is that it enablesa true recording of waviness and profile to beobtained.

� Motion-sensitive pick-ups (Figure 36b) producean output only when the stylus is in motion, withthe output being related to the speed at which thestylus is displaced, dropping to zero whenstationary. If displacement is very slow, perhapsdue to widely spaced waviness or to change inform, then the output for practical purposes isalmost zero. This low output means that varia-tions of waviness and form are excluded from theprofile. These pick-ups tend to be utilised ifinstruments do not have recording facilities, suchas some portable equipment.

The variable-inductance pick-up, illustrated inFigure 36(ai), has been widely used for many years.The stylus is situated at one end of a beam pivotedat its centre on knife edges, while at the opposite endan armature is carried which moves between twocoils, changing the relative inductance. This pick-up’s operating principle is as follows: coils areconnected in an AC bridge circuit (Figure 36aii) such


Coils

Ligaments

Modulatedcarrier

Pick-upcoils

Amplifier

Phase detector.demodulator and filter

Knife edge

SkidStylus

Beam

ArmatureCarrier

Oscillator

Silicone fluid

Securing block

Piezo-electric element

Flexible ligament

Stylus arm

Stylus

Spring to give a downward force

Magnet

Magnetic flux

Coil

Springs Stylus

(i) Variable inductance (ii) Schematic diagram of a modulate carrier system

(i) Piezo-electric pick-up (ii) Moving-coil pick-up

(b) Motion-sensitive pick-ups

(a) Position sensitive pick-ups

NB: The skid is not shown, but isfixed to the housing near the stylus

Figure 36. Basic design elements of pick-ups of the analogue transducer configuration. (Courtesy of Taylor Hobson.)

that when the armature is centrally positionedbetween the bridge it is balanced, giving no output.Movement of the armature unbalances the bridge,providing an output proportional to its displace-ment; the relative phase of the signal depends on thedirection of movement. This signal is amplified andcompared with that of the oscillator, to determine inwhich direction it has moved from the central (zero)position. It is necessary to utilise an oscillator toproduce a constant AC output, because the pick-up– unlike a motion-sensitive pick-up (Figure 36b) –does not generate any output; it merely serves tomodify the carrier. Simultaneously, the knife edgesexert light pressure from a very weak spring actingon the beam, enabling subsequent stylus contactwith the surface under test. The ligaments preventunwanted motion of the beam in the horizontalplane, with the result that stylus movement is onlypossible normal to the surface being assessed.

This type of pick-up is also fitted to newer ver-sions of measuring instruments, particularly wherethe range-to-resolution ratio has increased fromaround 1000 to 64,000. Improvements in electronicsfor the latest pick-up designs of this type have obvi-ated the need for reliance on a skid, meaning thatprecise pivot bearings have replaced the knife-edgepivots.

The piezoelectric pick-up (Figure 36b) has beenwidely used in the past, but now it tends to be usedfor the less sophisticated hand-held measuringinstruments. When the stylus deforms the piezo-electric crystal, it has the property of developing a voltage across electrodes, the advantage being thatit is virtually instantaneous. As the stylus follows the contours of the surface, the piezoelectric crystaldistorts by bending a flexure that causes crystalcompression and it becomes charged. The resultingcharge is then amplified and electronically inte-grated, producing signals proportional to the surfaceprofile. A piezoelectric transducer exerts a propor-tionally larger stylus force to that of an equivalentinductive transducer, with the former pick-up poss-ibly damaging softer and more delicate surfaces.

The operating mechanism of this piezoelectrictransducer can be described in the followingmanner: the flexible ligament interposed betweenthe stylus arm and the piezoelectric element hasenough stiffness to transmit normal vertical motionof the stylus to the crystal, but will flex as the stylusis suddenly subjected to instantaneous shock and inthis way protection of the somewhat fragile piezo-electric element is achieved. A light spring forceprovides downward force on the stylus, keeping it incontact with the surface. A small drop of silicone oilis held by capillary force between the securing blockand a thin metal blade fastened to the rear of thehousing, giving the pick-up suitable dynamic char-

acteristics. The silicone fluid exhibits low stiffnessand at lower frequencies; therefore large but slowstylus displacements allow free movement of the farend of the crystal, hence no bending occurs and zerooutput is generated. At higher frequencies the fluidstiffness increases, effectively preventing the localend of the piezoelectric crystal from moving; there-fore the bridge deforms generating an output.

A piezoelectric device is a position-sensitivedevice. A voltage on the electrodes persists while theelement is deformed (providing no current is drawnfrom it), due to practical considerations such asfinite input impedance of the amplifier and cablelosses. These considerations ensure that it can onlybe utilised in the motion-sensitive mode.

The moving-coil transducer pick-up (Figure 36bii)operates on the same principle as a DC generator oran electric dynamo. In operation, as the stylusmotion occurs the coil moves inside a permanentmagnet, inducing a voltage in the coil. This voltageis proportional to the velocity of the coil. This designallows the transducer element (the coil) to becoupled directly to the stylus without the need foran extended arm or hinged beam. Because of itsoverall size it is somewhat restrictive in use and isnot generally popular today.

In a similar fashion to the piezoelectric trans-ducer, the moving-coil pick-up does not measuredisplacement, but velocity. Stylus velocity has to beintegrated in order that the absolute position of thestylus can be determined. As a result of the coilvelocity rather than measurement of stylus displace-ment, integration errors will increase as the signalfrequencies decrease. Hence, this type of pick-up isunsuitable for the measurement of either profile orwaviness (low characteristic frequencies). Thereforethe piezoelectric transducer is only suitable for theassessment of roughness. Yet another disadvantageof the moving coil transducer is its poor linearity. Itshould only be used in the form of a comparator bycomparing similar component surface roughnessesagainst a known roughness calibration standard.

2. Digital transducers (Figure 37)With stylus motion along the surface under test,pulses occur that correspond to multiples of thetransducer resolution which are fed to an up–downelectronic counter that displays the gauge displace-ment, with its range being determined by physicalconstraints of the gauge. Typical range-to-resolutionratios are of the order of 700,000, hence the advan-tage is that there is no need for range switching,enabling the maximum resolution to be availableover the complete operational pick-up range. Thedisplayed displacement is relative to the stylus posi-tion, where the counter is zeroed. This means thatevery time the electronics are switched off and on

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again, the counter must be zeroed at a particulardatum position. In a similar manner, if a certainmaximum stylus speed has been exceeded thecounter may lose count, requiring zeroing again atthe datum position.

The following pick-ups are typical of thosecurrently in general use for surface texture instru-mentation:

� Non-contact laser (Figure 37a): These opticalconfigurations vary depending upon the meas-uring instrument company, but most systemsutilise a miniature Michelson laser interferometerwith a laser wavelength of 632.8 nm to provide

the measurement reference. Interference patternsare detected by multiple photodiodes, enablingan output signal to be interpolated, typicallygiving a basic resolution of 10 nm with an oper-ating range of around 6 mm. A focal point of 2�m is typical, allowing soft or delicate surfaces tobe assessed.

� Phase grating interferometric (Figure 37b). Thispick-up has been developed to complement thelaser interferometric type of pick-up as it offersa greater range, with a corresponding reductionin physical size, by employing a laser diodeinstead of a gas (HeNe) laser source.


OUTPUTBEAMSPLITTER

OUTPUTBEAMSPLITTER

PRISMBEAMSPLITTER

HALF-WAVEPLATE

CYLINDRICALLENS

DEVIATINGPRISM

PIVOTBEARING

STYLUS ARM

SPRING

QUARTER-WAVEPLATE

CONVEXDIFFRACTION

GRATING

DETECTORS

LASER DIODE& COLLIMATOR

(b) Phase grating interferometric (PGI) pick-up. (Coutesy of Taylor Hobson.)

Figure 37. Basic design elements of pick-ups of the digital transducer configuration.

The non-contact laser pick-up (Figure 37a) oper-ates on the following principle: infra-red light isemitted by a laser diode; its path through the opticalsystem to the micro-objective is shown in Figure37(a), with the beam being focused onto the surfaceto a focal point of 2 �m diameter. Light is reflectedback by the workpiece surface, returning along anidentical path, later being deflected onto a detector,whereupon an electrical output is generated thatcorresponds to the distance between the focal pointand the surface feature. A powerful linear motorcontinuously readjusts the hinged measuring leverduring the measuring cycle, enabling the focal pointto coincide with the surface feature(s) beingmeasured. The focus follows the surface as itsmotion translates across that portion of workpieceunder test, in a similar fashion to a stylus-basedpick-up. The vertical movements of the measuringlever are converted into electrical signals by aninductive transducer. Due to the relatively small sizeof the point of focus (approximately 2 �m), quiteminute profile irregularities can be assessed.

Some caution should be expressed in generalabout non-contact pick-ups, as the surface featuresbeing assessed can have a tendency to act assecondary sources of light. When the radius ofcurvature of a part feature is smaller than 10 �m,diffraction effects appear which can affect thebeam’s edge. This is not a serious problem for largesurface features but becomes crucial for finer surfacefinishes, illustrating why optical instruments tend toproduce higher values for surface texture than theirstylus-based equivalents. Other limitations for non-contact pick-ups are that they cannot easily measuresmall bores, they traverse widely changing surfacefeatures, and they cannot “sweep aside” dirt on thesurface, unlike stylus instruments.

The phase grating interferometric pick-up(Figure 37b) has positioned on the end of the armof the pivoted stylus a curved phase grating, whichis the moving element in the interferometer. Thepitch (grating wavelength) provides the measure-ment reference. An interference pattern is detectedby four photodiodes, enabling the output signal tobe measured, giving a basic resolution of 12.8 nmwith a range of 10 mm – ensuring that it is a usefulpick-up for form measurement.

1.12.2 Skid or pick-up operation

Two types of pick-up operation are normallyemployed for surface texture assessment:

� with a skid;� skidless with a reference plane.

The geometry of a skid can vary, from either alarge radius (Figure 38b) to a flat (Figure 38c). Theskid supports the pick-up, which in turn rests on thesurface. The relative motion of the pick-up as ittraverses along the workpiece causes the skid to actas a datum, giving rise to a “floating action” of risingand falling of the pick-up (Figure 38b). The macro-irregularities of the surface, namely of waviness andprofile, means that the stylus with its significantlysmaller radius to that of the skid will follow thissurface topography, sinking into valleys that the skidbridges. However, if the crests and valleys in theworkpiece surface are too widely spaced, then thisdistance with respect to the skid motion (Figure 38a)will also cause the skid to rise and fall and therebylose the datum registration plane (Figure 38a). If thedistance between the stylus tip and the skid (Figure38a) is half the waviness spacing, then these wavi-ness amplitudes are doubled. Conversely, when thedistance of the stylus tip (Figure 38a) correspondsexactly to that of the waviness spacing, then thewaviness is mechanically eliminated. The skid typeof pick-up is only marginally affected by instrumentvibration, because the measurement reference issituated close to the point of measurement. There-fore, the mechanical relationship of the pick-up-to-skid system may be an important factor in its design.If different pick-ups are utilised for the samemeasuring task, then in extreme situations thesemeasured differences could approach that of 100%.

Ideally, the skid and stylus should be coincident,thereby eliminating the “Abbe error”; the Abbe prin-ciple states that the line of measurement and themeasuring plane should be coincident. For practicalreasons, the stylus is slightly displaced from the skidand is situated either in front or behind the stylus.Phasing errors can be induced by the skid (Figure38b), causing distortion of the graphical trace, whileits magnitude depends on the waviness crestspacing. In practice, if the waviness crest spacing isidentical to that of the skid/stylus spacing, the skidwill rise on one crest, with the stylus rising on anadjacent peak. This relative motion completelysuppresses the peak. When the spacings differ, theeffect illustrated in Figure 38(b) occurs, where aspurious valley is introduced into the graph at adistance from the peak, this being equal to theskid/stylus spacing. If two skids are used on eitherside of the stylus, then the “phase effect” of the singleskid/stylus spacing is diminished. In some pick-upsthe line of contact of the skid is laterally offset, whichprevents the skid from burnishing the track(mechanically deforming asperities and giving afalse reading) during repeated traverses; this isparticularly relevant when the instrument is auto-matically setting the vertical magnification (auto-ranging).

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Skid motion

Skid motion

Skid Stylus

Surface

Motion

Motion

Trace

Traverse datum

An independent datum provides a straight reference for the pick-up

Stylus

Optical flat

Datum skid

(a) A rounded skid does not provide a serviceable datum, if the surface irregularities are more widely spaced

(b) The “phase effects” when using a skid

(c) Diagram illustrating an independent datum

Figure 38. Configuration of surface texture instrument and relative motion of the stylus with respect to an independent datum. (Courtesy ofTaylor Hobson.)

The skid acts as a mechanical filter, modifying the profile to a greater or lesser extent. Its radius of curvature, therefore, should be suitably chosen tominimise filtering effects. Generally, if a skid isselected with a radius of curvature of approximately50 mm, this is normally sufficient for general-purpose applications.

The skidless or reference plane technique cantake the form of two distinct types:

1 the pick-up skid travels along a flat surface suchas an adjacent optical flat, or similar and not onthe surface being measured;

2 a shaft which moves in an accurate straight line,with the pick-up being rigidly fastened to it –usually a glass block providing an independentdatum.

The main reason for employing skidless pick-ups are that they do not eliminate the contributionsof waviness and profile errors from the measuredtopography – which the skid obviously does – andoften waviness, in particular, is important to themanufacturing process and must be included in the assessment. The skidless technique provides an undistorted assessment of the actual profile, theproviso being that the reference surface has idealform.

1.12.3 Portable surface textureinstruments

As the assessment of surfaces is not confined tothose inspected in a metrology laboratory and oftenentails the measurement to be made by both produc-tion and maintenance personnel, then some easilyportable yet robust instruments are necessary. Onesuch instrument is that shown in Figure 39. Thisbattery-operated surface texture measuring instru-ment can be used across a wide range of angles and attitudes, increasing the range of versatility ofthe equipment. This instrument has a piezoelectricpick-up which is self-calibrating and can be used inremote operation – split mode – through the infra-red (IrDA) link, up to a distance of 1 m without theinconvenience of cable supply. This is an importantfactor when attempting to measure otherwise in-accessible component features such as bores.

When in transit the stylus has protection, as the“park” position fully protects the stylus assembly.Digital circuitry via surface mount technology pro-vides both reliability and accuracy and the stylusassembly closes up (in its robust case) to fit eitherin the pocket (weight 200 g), or on a belt, which isuseful for off-site surface evaluation in the field. The

large and clear metric or imperial LCD displayprovides simple-to-read surface-related informationand instrumental status data, with the followingspecification:

� “standard” cut-off (0.8 mm ± 15%);� accuracy: Ra (range: 0.1–40 �m ± 5%); Rz (range:

0.1-199 �m ± 5%);� diamond stylus (5 �m radius);� traverse length 5 mm;� minimum bore penetration 65 mm.

Portable and hand-held instruments of this type(within the specification and parameters of theequipment) can establish the surface condition,without the need to break-down assemblies, or thenecessity of removing the surface in question to adedicated and more sophisticated instrument. Suchversatility and portability in surface measurementwhen combined with the confidence in knowing thata representative roughness has been established,albeit for either Ra or Rz, helps in the interpretationof component topographical information fromnormally inaccessible positions, when compared tothat of conventional desk-based equipment. Theyare, however, limited in their surface analysis andparameter scope.

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Figure 39. Portable hand-held surface finish instrument “SurtronicDuo” can be used at any angle/attitude. (Courtesy of Taylor Hobson.)

1.12.4 Surface form measurement

Curved datums

In the previous discussion, all the surfaces have beennominally considered to be flat with only marginalform present. There are occasions when it is neces-sary to measure the surface texture of curvedsurfaces such as balls, rollers, the involute curvatureof gear teeth and fillet radii of crankshafts (seeFigure 40). In the past a wide range of gauges had tobe available with sufficient resolution to assess thesurface texture together with form, while setting upthe surface under test in such a manner that thegeometry of its shape did not influence the actualsurface texture measurement.

If the limiting factor in the determination of thesurface texture was due to a large radius, then thisproblem could be minimised by utilising a short cut-off length and a skid fitted to the gauge to reducethe measurement loop. The skid will induce prob-lems in obtaining a successful and representativesurface texture measurement, if fitted in front orbehind the stylus – the former technique is illus-trated in Figure 41(a). However, the stylus displace-ment from the measuring plane can be negated byintroducing a skid which surrounds the stylus. Thistip projects through the skid’s centre (see Figure41c), thus obeying “Abbe’s principle”. The solutionto curved surface measurement can be addressed byutilising several of the following types of equipment,or techniques:

� as mentioned above – instead of using a straightdatum (skid) the gauge is guided by a curveddatum (Figure 41c);

� the gauge is held stationary and the surface underit is slowly rotated at a peripheral speed sufficientto gather surface data information;

� the gauge is traversed concentrically around thestationary workpiece surface;

� a wide-range gauge is utilised to enable it to allowfor the curvature of the workpiece’s surfaceprofile as it traverses the part.

The inspection of a curved surface offers a par-ticular challenge, which can be achieved by guidanceof the stylus gauge along a curved path having the same radius as the part surface. The curvedsurface measurement condition is attainable ifdatum kits are used (allowing curved surface pathsto be traced by the gauge – see Figure 41b). Thesedatum kits tend to be time-consuming in setting up, necessitating a degree of technical expertise inboth set-up and alignment. The curved surface isrotated within the datum kit’s conical seating againstthe stylus of a gauge, the stylus being incorpor-ated into the conical seat housing (Figure 41b).The advantage of this set-up is that the tip ofthe stylus is always aligned to the centre of the component, with the likelihood of tip flanking on the part being eliminated. Datum kits arenormally only practicable when the radius isconstant during measurement, but if a series ofradii occur then under this situation they are not to be recommended. Today, such datum kits are not normally used due to the necessity of long set-up times.

Form analysis

The introduction of wide-gauge ranges on high-resolution pick-ups and the development of variousform options (reference line fitting) has meant thatguidance of the pick-up along a curved path hasbeen virtually eliminated. Typical of these surfaceform-fitting features that are currently available arethe following software-based options:

� removal of a least-squares best-fit radius;� removal of aspheric form from the raw data –

form error, surface slope error and tilt compar-ison with operator-designed data in the form ofa polynomial expression (see Figure 42a);

� elimination of elliptical/hyperbolic (conic) geo-metry – provides major and minor axes valuesand tilt, with residual surface texture analysisafter removal of best-fit elliptical and hyperbolicforms (see Figure 42b);


Figure 40. Form measurement with an inductive contour pick-up,including “customer-engineered” work-holding, for crankshafts.(Courtesy of Taylor Hobson.)

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Pick-up traverse

d1 d2

Stylus Skid

Light pressure

Surfacecontour

Traverse

Weighted frictionarm

Optical flat datum Precision-ball

Stylus

(a) Stylus displacement solely due to surface curvature (i.e. d1 + d2)

(b) Contour measurement–principle of rotating workpiece instrument

(c) Side skid gauge – the stylus projects through the cylindrical form of the skid

Figure 41. Effect of curved surface measurement. (Courtesy of Taylor Hobson.)

� complex symmetrical profile assessment – via an enhanced “Dual Profile” facility, allows themeasurement profile of a master shape or proto-type component to be saved as a template, en-abling future components to be measured andsimultaneously displayed along with templatedata for immediate comparison (see Figure 42c);

� analysis of gothic arch profiles – frequently em-ployed on the ball tracks for recirculating ball-screws;

� three-dimensional contour analysis – a represen-tative 3D visualisation of the part surface: axono-metric projection, colour height distribution,wear simulation and form removal, with manyadditional features available (this topic is asubject on its own and discussed in Chapter 2).

The number of surface texture parameters avail-able to define a surface’s condition is immense forform-measuring instruments. Typically, these para-meters include 22 profile; 22 waviness; 25 rough-ness; 12 R+W; 9 aspheric parameters; and this

comprehensive list can be enhanced still further. Inaddition to a full range of surface texture parame-ters, form analysis software can provide:

� form error – calculation with reference to best-fitconcave or convex circular arc, straight linemeasurement, including surface roughness detail.Alternatively, referencing to the minimum zone,this being the minimum separation between twoparallel lines containing the data set;

� radius – using the least-squares best-fit, concaveor convex circular arcs can be automaticallycalculated from selected data, with the option ofbeing able to exclude any unwanted surfacefeatures from the selected data. Conversely, theabsolute radius can be set to analyse actual devi-ations from a design master, with other calculatedparameters including its centre coordinate andthe pitch;

� angle – using a straight edge or minimum zonealgorithm, surface tilt can be established and thenremoved, prior to parameter analysis, with other


(a) Aspheric form software (b) Conical form software

(c) Dual profile software

Figure 42. Screen displays of “Windows™-based” software options available for form assessment. (Courtesy of Taylor Hobson.)

calculated values including its intercept andpitch;

� dimension – the linear relationship of surfacefeatures can be assessed and then compared,owing to the ability to calculate both the true X- and Z-coordinate positions.

Contours: profile curving, or an irregular-shaped figure

A typical commercial system is currently availablefor the analysis of contour measurement; assessmentof features such as radii, angles, length and height(see Figure 43 for a typical application) can beachieved with:

� measurement macros – these can be learnt andedited forming user programs for repeatedinspection routines, which minimise repetitiveoperator input (achieved via a series of definable“fastkeys”);

� individual feature tolerancing – allowing indi-vidual sections of the measurement template tobe toleranced with a variety of values (a widetolerance on a flat area of a surface can bedefined, with tighter tolerancing to the radii);

� comparison of DFX files to the contour – ifmeasuring a known contour “best-fit” individualgeometric elements are calculated with referenceto a template and the comparison of each pointin the contour is assessed against the nearestelement in this template;

� geometric element fit to an unknown contour –when measuring components of an unknowncontour, the software finds geometric elementsthat optimise the geometry of the profiledetermining the size, position and relationshipbetween profile features, plus other functionalfactors.

The most recent form and surface textureanalysis equipment has absolute positional control,offering sophisticated high-technology instrumentsproviding complex analytical abilities in a singletraverse of the workpiece. Lately, with the highthermal stability of the pick-up gauge (phase gratinginterferometer – PGI), it typically has a large rangewith around nanometric resolution, equating to arange-to-resolution of 780,000:1. One of the currentdevelopments in stylus protection employs a “snap-off” connector, allowing the stylus to be ejected fromthe gauge if the loading stylus force exceeds safelimits – reducing possible damage to the gaugebecause of operator error. Interchangeable styli canbe fitted to such pick-ups, for better access to thecomponent feature being inspected. If the part is ofa delicate nature and liable to deform, or could beeasily scratched, then non-contact gauge heads canbe utilised. These non-contacting types of gaugescomprise a focus follower with a programmablecontroller for fast, simple use, replacing inductivepick-ups. Non-contact gauges are used where thecomponent surface applications consist of:

� soft and touch-sensitive surfaces – printingpastes and coatings;

� wet or dry solder pastes and printed conductivepastes;

� contact and intra-ocular ophthalmic lenses;� and many other industrial/scientific applications.

Due to variations in the orientation of the work-piece under test to the traverse unit, some of thelatest versions of form analysis instrumentation canbe operated in inverted attitudes, or right-angleattachments can be fitted for measurements betweenshoulders on components, such as on crankshafts(see Figure 40).

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Figure 43. Form and surface measurement instrument “Taly-contour” being utilised to assess a spherical bearing outer race.(Courtesy of Taylor Hobson.)

1.12.5 Non-contact systems

Contact and non-contact operationalaspects on surfaces

As has been previously mentioned, in contactsystems the stylus contacts the surface utilising aprecisely manufactured stylus and, today, it is invari-ably diamond-tipped. However, owing to the stylusgeometry – its shape and size – some styli on certainsurfaces will not be able to penetrate into valleys andas a result create a distorted or filtered measure ofthe surface texture (see Figures 11 and 12). A recentstudy has indicated that the actual radius of curva-ture of a stylus can be very different from itsnominal value, while the effect of stylus forces cansignificantly affect the measured results, with toohigh a force causing surface damage.

The stylus, to enable a representative surface tobe assessed, must traverse across the surfacefollowing a parallel path with respect to the nominalworkpiece surface. The datum in this case wouldmost likely be a mechanical slideway of some sort(see Figure 38). The datum comprises a skid that hasa large radius of curvature (spherical or differentradii in two orthogonal directions), fixed to the endof a hinged pick-up (see Figures 36 and 37). At thefront end of the pick-up body the skid rests on theworkpiece surface; alternatively other designs occur,such as a flat shoe being free to pivot so that it canalign itself to the surface, or two skids are situatedeither side of the stylus. It should be reiterated thatISO 3274: 1996 does not allow the use of a skid,but many are still used in metrological applicationsin industry.

Notwithstanding the long history of stylus-based instrumentation a number of problems exist,associated with either their operation or the inter-pretation of results. For example, none of theseinstruments measure the surface alone: if an inho-mogeneous workpiece is inspected utilising amechanical stylus it responds to the topography andchanges in the surface mechanical properties, suchas its elastic moduli and local hardness. Anotherimportant aspect in contact surface texture inspec-tion techniques is the scale – horizontal and vertical– although it is not common for instrument manu-facturers to incorporate metrology into the scanningaxes of their instruments, with many companiesfailing to calibrate scanning axes.

Stylus-based surface texture instruments have an infrastructure of many specification standards,unlike optical/non-contact instrumentation. Thispoint regarding standards for stylus instrumentsonly embraces two-dimensional measurements and

they have yet to be developed for their three-dimen-sional counterparts. Yet despite this two-dimen-sional standards infrastructure, there is a distinctneed for both good practice and a clear under-standing of which surface texture parameter is mostsuitable for an industrial application to pass downto the shop floor – relating to standards.

For non-contact instrumentation, if one con-siders some form of optical interaction with thesurface that enables local height variations to beestablished, then it will sample a different surfacefrom that of stylus-based instruments. As a practicalexample of this difference, if consideration is givento the optical assessment of metals, their surfacehomogeneity (different phases) could introduceapparent height changes up to 10 nm due to thephase change on reflection; whereas glasses orceramics may have local refractive index changesand contaminant films introducing nanometricchanges. While phase changes at the conductingsurface can introduce variations as a function ofincident angle, surface field anomalies that are theresult of multiple scattering, or sharp points actingas secondary sources of light, together with variousedge and wall effects, will all introduce measurementuncertainty.

It was briefly stated that optical methods do nothave a standards infrastructure, unlike that ofstylus-based surface texture instrumentation,meaning that there exists no formal techniques forcalibrating optical instruments. Therefore, as a resultof this lack of calibration methodology, care shouldbe taken when optical assessment of a range ofsurfaces is to be undertaken, particularly if they areof differing physical surface characteristics. Forexample, if a glass step-height standard is utilised tocalibrate the vertical magnification factor of aninstrument, it would be unwise to measure a metalsurface set at an identical calibration value. More willbe said on the topic of calibration in Chapter 6.

Laser triangulation

The laser triangulation, or chromatic abberrationtechniques can be utilised to measure surface topog-raphy, which are dependent on the sensor modelemployed. Cut-off filters available range from 0.8mm to 8 mm with large measuring envelopes of upto 150 mm by 100 mm, enabling large or multipleartefacts to be scanned within the same measure-ment period. A typical instrument will have avertical range of 300 �m and resolutions of 10 nmfrom a spot size of 2 �m in diameter, with scanningcapabilities of up to 2000 points per second. Themeasuring ranges currently available are from 0.3mm to 30 mm, depending on the sensor model.


One such system has a tested repeatability of 0.03�m, but this claim applies to a specimen having a 2.90 �m Ra roughness, measured with a 2.54 mmcut-off length. Optional equipment can be added to investigate feature location and alignment orvacuum stages can be incorporated to hold awkwardly-shaped artefacts and replication kits canbe supplied to measure inaccessible or difficult toassess surface features.

It is claimed that these systems can measuresurface colour or texture. These instruments offerfast and multiple scanning facilities that reduce thetime taken for each measurement, compared toconventional contact instrumentation. Common toall optical equipment (as described in the followingsection), light scattering causes measurement accu-racy problems in some component surfaces. If afixed resolution occurs for each sensor model, thiswould imply that up to six sensors would be requiredto enable satisfactory coverage of all surfacetextures, or types of measurement needed for acomplete metrological range of applications.

Optical techniques: reflection andscattering

Highly reflective surfaces are normally assumed tobe very smooth, so by measuring reflectivity anindirect technique for measuring roughness can be established. Reflectivity testing is particularlybeneficial where visual appearance is important(cosmetic items), or on soft surfaces such as paper where non-contact measurement is necessary.Advantages of optical methods include assessing andaveraging over an area and high-speed inspection.

Smooth surfaces invariably appear to be visually“glossy” (reflective); conversely, a rough surface has a matt appearance. In the past, the gloss meterprinciple was used to verify how parallel beams ofincidence light at an angle on the surface are reflected.

If a perfectly reflective surface is present (Figure44a), then much of the light will be specularlyreflected (angle of reflection equals angle of inci-dence) and enter the viewing system S, with no lightentering the viewing system at D, being positionedperpendicularly above the surface. However, if aperfectly matt surface is inspected (Figure 44b), thelight is diffusely reflected (scattered in all direc-tions), causing equal amounts of diffused light toenter both S and D. The ratio of specular-to-diffusereflection is a measure of the gloss of the surface.The relative proportions of light entering S and Dcan be measured by either visual means or photo-electric comparison, incorporated into a suitableportable instrument.As it is the ratio of the light thatis measured, any absorption of light by the surfacewill not influence the result, and neither will fluctu-ations in the irradiance distribution of the lamp, ormore specifically today, the laser.

Considerable interest has been shown over theyears in the use of scattering for surface texturemeasurement. In essence, three techniques aregenerally used for scatter-based instrumentaldesign:

1 light scattering theory, when used to construct aninstrument giving absolute measurements ofsurface texture – when a number of conditionsare met;

2 general theoretical approach in instrumentdesign – assumptions are made that have generalconnection with a particular surface textureparameter;

3 application-specific approach, where instrumentdesign is developed to solve an immediateproblem.

In just one example, an integrating sphere (Figure45) can be used to measure gauge block surface

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D

D

S

S

Angle ofincidence

Flat reflective surface

Matt, or rougher surface

Angle ofreflection

Diffuse light

(a) Specular reflection

(b) Diffuse reflection

Figure 44. Diagram illustrating the principle of surface assessmentby specular and diffuse reflection. (Courtesy of Taylor Hobson.)

texture. The instrumental technique measures thetotal intensity of light from a gauge surface, thencompares it with the light intensity that was diffuselyscattered. The ratio of two intensities is termed totalintegrated scatter (TIS) and it is proportional to thesquare of the RMS surface texture parameter Rq.This method relies on a number of assumptions thatmust be met for the type of surface to be meas-ured. The diffuse component of reflected intensity is measured by collecting light in an integratingsphere. An integrating sphere can be practicallyrepresented by a hollow sphere that is coated inter-nally with a highly diffuse reflecting material. Anylight reflected from the inner sphere’s surface givesrise to a constant flux of electromagnetic powerthrough an element of the sphere. This sphere has anumber of ports, allowing radiation both in and out,with the gauge to be irradiated and photodetectorsto detect the intensity of integrated light.

Interference instruments

Surface texture interferometry occurs in severalinstrumental configurations, probably the mostcommon types being interference microscopy,plus full field methods. Becoming popular of late are phase-stepping techniques and swept-/multi-frequency source methods. Today, there are severalcommercially available phase-shifting interferomet-ric microscopes, giving three-dimensional surfaceimaging with very short measuring times. TheNational Physical Laboratory (NPL) has developed a sub-nanometre resolution system that employs amicroscope objective with a numerical aperture of0.5, in conjunction with a birefringent lens providinga focused spot from a laser source and a defocusedorthogonally polarised beam 10 �m in diameter.Fourier analysis has been obtained from surfaces,indicating that with this objective the system pro-duces a surface wavelength range from 0.5 to 15 �m.The trace displayed by the system is an interfero-metrically obtained path difference of the focusedprobe beam and the defocused beam.


Integratingsphere

Scatteredbeams

Scatteredbeams

Inputport

Incidentbeam

Specularbeam

Specimenoversampleport

Baffle

PhotodetectorDetectorport

Outputport

Figure 45. Geometry and layout of an integrating sphere. [Courtesy of Dr R. Leach/NPL.]

As has already been mentioned, light interferencecan be successfully used as a non-contact opticaltechnique to assess surface features. Essentially, theprinciple of interference of light relates to how lightrays are reflected between two surfaces; the differinglight path lengths along various points of the surface

cause phase changes in the light being reflected backto the observer. The result of this reflection will beto promote alternate dark and light interferencefringes. The shape and spacing of these fringes willdepend on the regularity of both the surface and thereference reflector. The surface texture irregularities

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H

E

F

I

G

Objective

Inclined reflector(optical) plate

D C B A

Surface undertest

(a) Basic elements of the instrument

(b) Detail illustrating the formation of multiple beams

A: mercury vapour lamp;B: green filter;C: iris diaphragm;D: lens system;E: semi-reflector;F: objective;G: inclined reflector plate;H: graticule;I: surface under test.

Figure 46. Fizeau-type surface texture interferometer. (Courtesy of Taylor Hobson.)

are reproduced as modifications in the interferencepattern and, when viewed under specific conditions,displacement of the fringes is a measure of theroughness height.

For some interferometer instruments such as theFizeau type, interferometric surface assessmentrelies on the fact that a “wedge of air” occurs on thetest surface, with the resulting interference linesbeing of equal height and their respective heightdifferences given by

Fringe spacing = �/2

where � = wavelength.Under examination, the surface roughness

produces air wedge thickness variations causingdeflection of the interference fringe, from which thetotal height parameter Rt results. Hence the totalheight becomes

Rt = a/A(�/2)

where A = interference fringe, a = fringe deflectionand �/2 = fringe spacing.

The height of irregularities that can be resolvedrange from 0.005 to 1 �m using conventional inter-ferometric methods. The range can be extended byusing the technique of oblique incidence, whichincreases fringe spacings from �/2 to 2�, enablingone to measure a surface roughness height four timeslarger than that measured using a standard interfer-ometric method. Furthermore, if cast replicas of thetest surface are made, then immersing them in fluidsof a suitable refractive index enables transmissioninterferometry to assess roughnesses up to 25 �m.

Maximum contrast is important for optical inter-ferometry, and the wavelength of emitted light mustremain constant to eliminate variations in the phasedifference between interfering beams. Any defects inoptical surface quality within the interferometer canpromote a reduction in fringe contrast, as can vibra-tions of optical components, together with parasiticlight caused by unwanted reflections. Due to thestrongly convergent light utilised in these interfero-metric optical configurations (Linnick and Mirauinterferometers), this can lead to obliquity effects,which can introduce errors in estimation of, say, ascratch depth by as much as 12%. The magnitude oferror is dependent on the numerical aperture of theobjective and the surface’s scratch depths.However, inthe case of more commonly available full field tech-niques this obliquity and hence error is not a problem.

In essence, the Fizeau surface texture interfero-meter is basically a microscope, with a built-inillumination and special-purpose optical system (see Figure 46a). Between the objective and thesurface a semi-reflector G can be positioned, which

may be slightly inclined to the work surface I, allow-ing a wedge-shaped air gap to occur (detailed inFigure 46b). Multiple reflections between the surfaceand the reflecting plate produce good-contrast,sharp fringes (see Figure 47 for typical interfero-metric images) which are viewed in the eyepiece.Utilising a spherical semi-reflecting surface, it is pos-sible to examine three-dimensional curved surfaces,such as precision ball surface finishes (Figure 47c).Multiple reflection (Figure 46a) on the semi-silveredsurface E and the workpiece I means that all on-coming beams are split into several partial beams,which cause interference. Interference fringes thatoccur are both higher in contrast and narrower as the reflection coefficient becomes greater. If too great a reflection coefficient occurs, the contrast willdegrade. Such conditions allow multiple beam reflec-tion to occur only when the distance to the reflectionsurface and that of its test surface is quite small.

Large apertures can be utilised by this Fizeausurface interferometer, enabling full exploitation ofthe light microscope. When employing high aper-tures, the line standard (graduated scale) is depen-dent on the selected aperture and, considering theassociated aperture angle, the fringe spacing is

Fringe spacing = �/2 (2/1+ cos �)

where � is the wavelength, � is a cosine error.Normally, the largest aperture (A) utilised is 0.65,

hence the fringe spacing equation above can besimplified to

Fringe spacing = 1.14�/2

Generally, it can be said that applications of thisparticular Fizeau surface texture interferometerhave limited use, although the technique does havesome merit:

� it can examine a relatively large specimen surfacearea;

� it indicates any form error present;� being a non-contact method, it may be possible

to estimate the scratch depths.

An optical and practical limitation of this type ofinterferometry when applied to precision surfacesoccurs due to visual viewing, which tends to be time-consuming and somewhat fatiguing. By using auto-mated image analysis techniques for detection, thislimitation could be overcome, but at a considerablecost disadvantage to the user.

Although three-dimensional surface textureanalysis will be discussed in Chapter 2, one instru-mental technique has been included in this chapter.An automated surface profiling interferometer is


illustrated in Figure 48 that has a wide range of indus-trial applications, from research to manufacturingprocess control. Of particular relevance is its use insemiconductors, disk drives, printing plates and fuelinjector seals, together with applications where the

surface texture is used to control the product’sperformance. Until recently, microscopes tended tobe utilised purely for attribute sampling, such asimaging surface topographical details, while surfaceprofilers provided accurate measurements to charac-terise the surface details. One of the latest develop-ments in surface texture (white light) interferometersis illustrated in Figure 48, which combines these twotechnologies, providing a fast, quantitative surfacemeasurement on many types of surface topogra-phies. The surface details that can be quantifiedinclude surface roughness, step heights, criticaldimensions and other surface topography featureswithin a matter of seconds.Profile heights that can beassessed range from >1 nm up to 5000 �m, at speci-men translation speeds up to 10 �m/s with a 0.1 nmheight resolution, which is independent of both themagnification and feature height. This interferome-ter can resolve sub-micrometre X- and Y-plane fea-tures on profile areas up to 50 mm2, achieving this byimage stitching. This stitching technique has beendesigned to analyse surface details much larger thanis possible with a single measurement. Stitchingoccurs by taking several measurements of the testspecimen as it is moved by a motorised stage andthen combines – stitches – the multiple data sets intoone surface image. In effect, stitching increases thefield of view, without compromising lateral or verti-cal resolution. The scanning actuator is of a closed-loop piezoelectric variety, employing low-noisecapacitance sensors to ensure that both accurate andrepeatable linear motion occurs over the whole oper-ational range. Other notable modes include both“Phase Stepping Interferometry” (PSI) and “White-Light Scanning Interferometry” (WSI) techniques.

Use of speckle

This technique for surface texture inspection utilisespartially coherent light, with the reflected beamfrom the surface consisting of random patterns ofdark and bright regions termed speckle. The spatialpatterns and contrast of the speckle depend on theoptical system configuration utilised for observationand the condition of coherence of the surfacetexture. Speckle has two important attributes:

� contrast;� number of spots per unit area.

The contrast can be shown to have a relationship tothe surface’s correlation length, whereas the speckledensity is primarily concerned with the imagesystem resolving capacity. Information on the speci-men’s surface can be obtained using the contrast ofspeckle patterns produced in the first instance, near

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Figure 47. Typical interference fringes from a surface texture inter-ferometer, showing both flat and spherical surfaces (Courtesy ofTaylor Hobson).

(a) Lapped surface of a gauge block, showing a scratch. Fringe spacingis 0.25 �m. Due to a scratch extending across adjacent fringes, itsdepth must also be 0.25 �m. (b) Lapped gauge block edge, indicatingedge rounding. (c) Interference patterns on spherical surfaces (i) pitchpolished steel ball; (ii) commercial steel ball; (iii) glass sphere.

(a)

(b)

(c)(i) (ii) (iii)


Figure 48. Automated non-contact three-dimensional surface profiling interferometer. (Courtesy of Zygo Corporation.) (a) Optical configura-tion. (b) View of interferometer. (c) Typical screen displays.

(a)(b)

(c)

the image plane,and secondly,close to the diffractionor defocus plane. Yet another technique utilises thepolychromatic speckle patterns, while others employthe correlation properties of two speckle patterns.From both of these methods, surface texture valuesranging from 0.01 to 25 �m have been estimated.

Optical sectioning

The method of optical sectioning termed theSchmaltz technique after its inventor (sometimestermed the light section microscope) produces virtu-ally identical results to that of physical sectioning,but in a simpler, non-destructive manner. However,the magnification and data obtainable from theprojected image are quite limited, when comparedwith stylus-based surface texture measuring instru-ments. The ratio of vertical to horizontal magnifica-tion is around unity, meaning that the field of viewis small when a large magnification (×400) is used,hence for fine surfaces it is rather limited.

The optical sectioning principle is illustrated inFigure 49(a). The surface to be examined is illumi-nated by a thin band of light delineating a profilesection, which is then viewed at an angle with amicroscope. Typically, illumination and viewingangles are 45° to the work surface producing theclearest profiles (see Figure 49b). For example, theprojected surface indicated in Figure 49(bi) illus-trates an apparent machined profile cusp height of

Cusp height = h × √2

where h is the actual profile height (Rt).Measurements are normally undertaken using

either an eyepiece graticle or an eyepiece incorpo-rating a micrometer for topographical featureassessment.

An alternative technique for optical sectioningcan be achieved by utilising an optical projector, asthis has the added advantage of an enlarged imagebeing projected onto a screen. The surface’s profileheight can then be quickly measured with a speciallyprepared and calibrated template, which compen-sates for any distortion introduced by the viewingangle.

The optical sectioning technique is suitable forsurface topographies having a roughness range of Rtbetween �1 and 200 �m. Moreover, it is eminentlysuitable for the inspection of soft and slightly pliablesurfaces (Figure 49biii, which could be deformed bya stylus), or for estimation of depths of surfacescratches/engraved lines (Figure 49bii).

The reflectance of a surface is a “sensitive func-tion” of its relative roughness, and consequently thewavelength of light is considerably greater than the root mean square value of the surface tex-ture. Hence, the reflectance will depend only on thesurface roughness rather than the peak slope of anyirregularities. Measuring reflectance at two distinctwavelengths enables one to determine the surfaceroughness and slope of asperities (peaks).

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Illumination

Eye

Optical configuration

Surface under inspection

(a) Optical path of Schmaltz microscope

Figure 49. The “Schmaltz technique” – optical sectioning principle and associated projected images. (Courtesy of Taylor Hobson.)

(i) feedmarks from machining, indication cusp heights

(ii) an engraved line on a flat surface

(iii) embossed plastic surface

(b) Optical sectioning images, projected onto a screen:

Performance tests undertaken for the Schmaltz(optical sectioning) microscope (illustrated inFigure 50) show that for an objective of ×60 magni-fication the relative error of indication does notexceed 7.7% over the whole application range (Rtvalues between 0.8 and 3.0 �m).Accepting that prac-tical accuracy limits are in the region of 9%, thenthere is little point in using a ×60 objective, sincethe necessary accuracy can be achieved with the

×30 objective – with the added advantages of a largerfield of view and depth of focus. In the case of the ×30 objective, the relative error of indication doesnot exceed 8.6%. Now, if one enlarges its measuringrange (1.5–10 �m), up to values of Rt of 1.5–14.5 �m,a practical accuracy of ±9% may be obtained. Theobjective having a magnification of ×14 has a rela-tive error of indication within the recommendedmanufacturer’s guidelines, namely, from 3 to 12 �m,


9

8

7

6

5

4

3

2

1

0

-1

-2

10 20 30 40 50 60 70 80 90 100

%100τ/P

×30

×30×14

×10

×7

P

µm

Figure 50. Performance curves for the Schmaltz – optical sectioning – microscope, illustrating the relative error of indication for various micro-scopes. [After Thomas, 1974.]

varying from 6% to 12%. Moreover, if the measuringrange is altered for this ×14 objective to that of Rtranging from 5–65 �m, the value of its relative errorof indication is maintained within the limits of±5%. In a similar manner, for the ×7 magnificationobjective, by enlarging the measuring range from 8 to 100 �m the relative error of indication will stillbe within a ±4% limit.

Scattered light: light-emitting diode(LED) source

Utilising “scattered light” is a fast in-process surfaceroughness technique, which is schematically illus-trated in Figure 51. The parallel light is emitted byan infra-red LED and is projected onto the work-piece surface. For this instrument, the size of thesource’s light spot is approximately 0.8 mm at thefocal point on the surface. Any reflected light tendsto be scattered or diffuse in nature, resulting fromthe roughness of the workpiece surface. The lens willcollimate the light and project it onto an array ofphoto-diodes, from where the variance of the distri-bution of scatter can be established. Any variance isthen normalised, which eliminates intensity varia-tions resulting from the reflected light. Normalisingthe variance compensates for the twin effects ofdifferent levels of reflection and that of workpiece

materials; moreover, this technique eliminates theinfluence from variations in intensities of LED.Other techniques have been developed, for exampleangle-resolved scatter (ARS), but the discussion herewill be confined to the current scattering technique.

Variance in the scatter distribution is termed Rop(the optical roughness parameter). This variability isproportional to the angle of the surface rough-ness. Rop can be utilised to compare the workpiecesurface roughness against a calibrated standard,although this parameter can only be validated whenmeasurement is made under similar conditions. Ifcomponent surfaces are quite smooth, then these areideal conditions for obtaining the highest sensitivityfrom the instrument. Typically, if a component’s gen-eral surface roughness (Ra) lies between 0.05 and 0.5 �m, it is appropriate for evaluation by thistechnique. Any surfaces that might be manufacturedby electrical discharge machining (EDM), electro-polishing, or grinding (pseudo-random productionoperations) are ideal for assessment by the scatteredlight technique, rather than other systematic manu-facturing processes such as turning and milling oper-ations. Only a brief time period is necessary for anobject’s surface measurement by the scattered lightinstrument – typically 300 ms – enabling measure-ment “on the fly” (while the workpiece is in motion).

A practical application of this technique might beto establish the surface roughness of an in situmeasurement for a cold-rolled aluminium strip as itprogresses beneath the focused beam at maximumstrip passing speeds of around 70 km/h. Due to itsability to tolerate relatively fast component motionand quickly estimate surface finish, the scatteredlight technique can achieve 100% inspection on crit-ical surfaces, enabling almost real-time processcontrol for continuous processing operations.

Optical diffraction

The principle behind this instrument’s operation isthe technique of using a surface under test as a phasegrating, enabling the instrument (Figure 52) tocapture the far-field Fraunhoffer diffraction patternon a linear CCD detector array, thus allowing statis-tical assessment of the surface condition.

A schematic diagram of the instrument isdepicted in Figure 52, with a photograph of thecomplete assembly illustrated in Figure 53. Thesystem is based upon two laser diodes having oper-ational wavelengths of 670 nm and 780 nm, respec-tively. These two wavelengths enable diffractionorder numbers to be identified, in conjunction witha low birefringence single-mode fibre terminated byan achromatic collimating lens. The purpose of thisfibre is twofold:

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Rop

Frequencydistribution

Photo-diodearray

Lens

LED

Workpiecesurface

Figure 51. Diagrammatic representation of sensing with scatteredlight.

� to act as a spatial filter, by selectively transmittingthe Gaussian TEM 00 mode;

� providing a convenient method for the produc-tion of spatially coincident wavefronts.

The Gaussian beam for both laser wavefronts isdirected at normal incidence through a cylindricallens onto the workpiece surface. It forms a line imageat the beam waist, so that a restriction of diffractionoccurs only on one plane, enabling a range of metro-logical parameters to be found such as Ra, etc, andthe surface power spectrum. Surfaces can beassessed whether they are random or unidirectionalin nature.

Diffraction patterns are produced from the phasemodulation of the surface and will be focused ontoa 2048 CCD detector. Lastly, data processing isundertaken on a PC, enabling the visualisation ofdiffraction patterns, power spectra and surface para-meters.

With this instrument the surfaces under test mustbe quite smooth, in order to obtain a satisfactoryvisual performance from the equipment. Typical

components that might be inspected with thisinstrument include diamond-machined brass (Navalnon-leaded type), aluminium (grade: 6061 T6) andcopper (OFHC) flats, germanium flats or similarprecision surfaces.

One of the principal reasons for utilising laser-based diffraction techniques is their ability to char-acterise low Rq surfaces, in particular the advantagesobtained from directly filtering the diffractionpattern. Moreover, this instrument has the capabilityof measuring a substantially periodic surface to anRq of approximately 140 nm. In addition, measure-ments of Rq on a rotating surface can be achievedwith no distinction between whether the surface is inmotion or static (unlike a stylus-based instrument).

The surface diffraction physics is rather complexand is therefore beyond the scope of the currentdiscussion on the general operational and perform-ance characteristics of this laser-based instrument.

Microscope applications

A cursory examination of a surface with a micro-scope equipped with a graticle will reveal any promi-nent spacing irregularities. The height of anydominant peak cannot be estimated, although ifsuitable illumination is utilised (see Figure 54 forvarious inspection modes that can be employed)some detail can be visually assessed.

In metallographical inspection of samples, ifdestructive means can be practised to visually assesssurface features at approximately right angles to anyinteresting irregularities, this form of visual inspec-tion reveals considerable information. Rather thansection the material perpendicularly to the surface,a much better and informative strategy is to take ataper section of the surface. With taper sectioning,


Laser Diode670 nm

Laser Diode780 nm

FibreCoupler

Optical Fibre

CCD Array

FocusingOptics

BeamSplitter

MirrorCylindrical Lens

Filter

Sample

Figure 52. Schematic representation of the Talyfine instrument.(Courtesy of Taylor Hobson.)

Figure 53. Assessment of surface texture on a diamond-turnedcomponent, within the range 5–10 nm Rq, utilising a non-contactoptical instrument. (Courtesy of Taylor Hobson.)

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Figure 54. Microscope applications for surface assessment. (Courtesy of Nikon UK Ltd.)

the surface is prepared at a shallow angle (typically11°) perpendicular to the surface (see Figure 161).This slight taper does not unduly modify the shapeof the surface irregularities, but increases theapparent magnification of the surface under test,revealing a considerably greater area for visual ormicro-hardness assessment (more will be said on this latter topic in Chapter 5). Surface prepara-tion is a difficult task, particularly during thepolishing phase prior to suitable etching (normallynecessary for metallographical inspection of metals)as surface profile distortion may occur if sufficientcare is not taken. Sectioning reveals modifications insub-surface microstructural details that might nototherwise be apparent and this will be discussed in Chapter 5 on surface integrity; this may offer

engineering solutions as to reasons why a surfacebehaved in a particular manner in service. Engineer-ing surfaces may fail (in service) for a variety ofunanticipated reasons; these might include high sur-face residual hardness, the introduction of unstablemetallurgical changes sub-surface grains exposed atthe surface occuring under conditions of load ortribological action. Together with a combination ofthese factors (see Figure 55a), their failure modemight need to be investigated.

A stereoscan electron photomicrograph offers amore informative visual three-dimensional image ofthe surface area than can be obtained from a conven-tional optical technique (see Figure 55b), particu-larly when additional aids of soft imaging withtopographical height profiles are utilised, as dis-cussed later in Chapter 3 on surface microscopy.

Optical microscopes have wide-ranging capabili-ties and offer superb yet subtle techniques toenhance surface image quality, including the follow-ing inspection modes (see Figure 54):

� Brightfield – the most frequently used method ofobservation, employing differences in reflectionto obtain natural colour and shape of surface;

� Darkfield – this method becomes of some signif-icance when observing and photomicrographingsurface irregularities, minute flaws, differences inheight levels and samples with low reflectionlevels (paper, plastics, composites and fibres);

� Normarski – this technique can capture the sur-face’s subtle irregularities and flaws as interfer-ence colours, indicating them as three-dimensional forms. Owing to the Normarski’sability to represent very small tilt with sharp dif-ferential contrast, this observational techniquecan detect minute height differences and subtleirregularities in metals, crystalline structures,integrated circuits (IC) and large-scale integrated(LSI) circuits;

� Fluorescence – an epi-fluorescence attachmentallows for detection of positive and negativephoto resists. Selecting from different filtercombinations offers an optimum configurationfor any application, being ideal when trying tolocate resist irregularities and the cause ofparticle generation;

� Simple polarisation – specific optical characteris-tics can be investigated with this method ofpolarised light microscopy. The technique iswidely utilised for geological research, togetherwith evaluation and examination of minerals,plastics, crystal conditions and stress detectionon IC wafers;

� Pinhole aperture – allows high-intensity/-resolu-tion images at large depth of focus, which is ideal for surfaces having multi-layer film three-


Figure 55. Images from a scanning electron microscope (SEM) foroptical assessment of fracture and machined surfaces. (Courtesy ofJeol UK Ltd.)

(a) Mild steel ductile fracture – photomicrograph from an SEM.Magnification ×650; acc. V 15 kV; signal SEI; WD 21 mm; SS 28; pres-sure Pa. (b) Stereo image (left-hand SEM stage tilt – 1.5°) of anaustenitic stainless steel (grade 316) by high-speed machining(milling with a 0.5 mm feedrate). Magnification ×50; acc. V 20 kV;signal SEI; WD 20 mm; SS 30; pressure Pa.

(a)

(b)

dimensional structures. Typically, the aperturediaphragm can be “stopped-down” to around30% of the exit pupil diameter using a ×150 objective, providing large depths of field forsurface inspection.

Many of the latest microscope systems can beused for image capture and processing, enabling theinstrument’s software to “grab” live images from themicroscope via video cameras, scanner computerfiles and archive packages. Such image analysissystems enable image enhancement and manipula-tion (flip and rotate the surface image), with theability to change contrast/brightness, simple thresh-olds, sharpening and smoothing, morphology,component separation, retouching and masking,together with scaling and filtering. Many software-enhancing techniques allow operators to take up to 36 geometrical and analytical measurements,together with reference images for comparison, withWindowsTM-based menus for ease of image and datamanipulation. Such systems can be networked formulti-user applications and sophisticated archivingfacilities, allowing access by different users.

Confocal microscope

Confocal microscopes generally utilise the principleof depth discrimination. Essentially, the imaging and receiving optics are identical, offering excellentproperties. In a similar manner to the so-called“flying spot technique”, the optics project a pointonto the surface, with the reflected light being pickedup by a point detector (see Figure 56). The resultingsignal is utilised to modulate the spot brightness onthe CRT screen, which is scanned in synchronisa-tion with the object under test. Essentially, the lensfocuses a diffraction-limited spot onto the object,with the lens collecting light only from the samevicinity of the surface that was previously illumi-nated. As a consequence of employing the single-point detector, both the image forming/receivingsystems contribute to the signal at the detector.Thus, by rotating the variable aperture over the spec-imen, which itself in some systems rotates, it willbuild up an optical image (via software data capture)of the sample’s surface. By this means, the “flyingspot” covers the complete specimen’s surface to thesame optical magnification and resolution of aconventional microscope, but with the advantage ofa significant improvement of the field of view. Theseimages can be optical slices or sections through thesurface, which can be processed providing non-contact three-dimensional information about thesurface.

1.13 NanotopographicinstrumentsIn the mid-1960s, out of the growing requirement tomeasure very smooth surfaces and thin films, aninstrument was developed having a resolution ofapproximately 0.5 nm combined with a maximummagnification of 1,000,000, a measuring range of 13�m and an arcuate traverse of ±1 mm. Originallysuch instruments were developed in order tomeasure minute step heights, typically around 30nm as illustrated in Figure 57. From this instrumentand others having enhanced design and perform-ance refinements came the current genre of nano-technology equipment, typified by the “Nanostep”shown in Figures 58 and 59 (pioneered by the NPL).Instruments of this level of accuracy and precisionmust be virtually free from thermal expansioneffects; therefore the majority of the components aremanufactured from thermally stable materials, typi-cally glass ceramic “Zerodur™“.

The kinematic (translational component mem-bers) and operational features of the instrument aresuch that the workpiece is supported on a levelling

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Detector

Baffle

Source

Dichroic

Collimatinglens

Focus

Specimensurface

A

B

C

Figure 56. Schematic diagram of an optical profiler. (Courtesy of DrR. Leach/NPL.)

table, which in turn is mounted on a carriage. Thiscarriage is equipped with kinematically positioneddry polymeric pads, forming an interface with ahighly polished precision slideway, giving a lineartranslational motion of 50 mm. The horizontalmicrometer (shown in Figure 58) displaces (via a“slave carriage”) the slideway along its desiredlength of travel, providing minimal disruption to themeasurement process.Anti-vibration mounts isolatethe DC motor/gearbox that drives the micrometerfrom the main structural elements of the instru-

ment, producing ultra-low instrument noise down to0.03 nm under optimum conditions. The motor candrive the micrometer at measurement speeds vary-ing from 0.005 to 0.5 mm/s. The stylus/transducerassembly illustrated in Figure 60 can be verticallypositioned on the workpiece and in contact with itvia the vertical micrometer (depicted in Figure 58),giving a vertical step height range up to 20 �m.Finally, measurement control and signal output areprovided by a suitably configured PC.

The software offers various levels of surface


Step height: α0.03 µm

Trace

Glass substrateSilver deposit

Figure 57. A typical “Talystep” graph of silver deposit on a glass substrate. Thickness of the deposit is approximately 0.03 �m. (Courtesy ofTaylor Hobson.)

Figure 58. Constructional detail of the “Nanostep” and its associatedprecision slideway in low coefficient of expansion (i.e., glass ceramic:“Zerodur”). (Courtesy of Taylor Hobson.)

Figure 59. Detail of the interchangeable “Nanostep” stylus.(Courtesy of Taylor Hobson.)

texture analysis, assessed relative to the best-fitreference line, covering a diverse range of inter-national parameters. Additionally, the form softwareprovides for

� form removal – best-fit form is calculated (least-squares straight line, minimum-zone straight line

or least-squares arc) and then removed, enablingthe texture of the surface to be analysed;

� angle – providing a facility to remove any com-pound surface tilt prior to parameter analysis;

� dimension – provides for the linear relationshipof surface features, which can be assessed andcompared.

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Transducer assembly indicating materials

Column used in measurement loop.

Adaptor plate Ligament pair X

Ligament pair Y

Tube

Coil sub-assembly

Coil holder

Bridge piece

Transducer stem

Transducer stem

Stop

X X

Rollers

Diamond stylus

Leaf spring

Stylus holder

Stylus assembly showing kinematic location.

Contact points ofstem with holder

View in direction X - X

Material:Glass ceramic

Aluminium alloy

Invar

Figure 60. Internal construction of the “Nanostep” instrument. (Courtesy of Taylor Hobson.)

Software has also been developed for this instru-ment enabling it to assess an enhanced dual profile.This provision enables one to measure the profile ofa “master component”, which can then be saved asa template; any subsequent components can then be both measured and simultaneously displayedwith this template for immediate comparison. Astatistical process control software package can beemployed, along with other specialised softwarepackages.

A number of interchangeable styli (see Figure 59)can be fitted to the instrument to suit a range ofdifferent measuring applications, ranging approxi-mately from 1–10 �m conispherical shape to 0.1 ×0.5 �m pyramidical geometry, the latter being usedfor high-resolution work. The stylus force can bevaried between 10 and 700 �N, allowing it to non-destructively measure delicate or easily scratchedcomponents. Once the instrument has been set to therequired depth of measurement, an automaticfacility provides for the raising and lowering of thestylus when repositioning or changing samples. Forthe measurement of ultra-fine surfaces, the instru-ment offers a nominal gauge resolution down to 31pm (with the 2 �m gauge range). Typical perform-ance of the 10 �m conical stylus with an appliedforce of 40 �N can produce a surface roughness Rqvalue of 4.9 nm. Such nano-instrumentation has acomponent capacity of diameter 100 mm, with adepth of 22 mm, covering a large range of precisioncomponents.

Instrument applications are both wide and variedand it might typically be employed for

� ultra-precision bearing and surface defect meas-urement – surface finish/integrity;

� silicon wafer measurement;� integrated circuit production – process monitor-

ing;� magnetic tape measurement;� diamond-turned components – small diameter;� calibration standards;� precision optics;� mirrors for laser gyroscopes;� laser and X-ray mirrors.

In this chapter little or no reference has beenmade to the role of expert systems or neuralnetworks in surface texture analysis. This omissionwas intentional, as the chapter length would other-wise have simply been too long and less specific innature. In Chapter 2 a review of three-dimensionalsurface texture measurements will be made, thenlater on contour/fractal effects will be discussed,which are now becoming an important technologyin describing surfaces.

References

Journal and conference papers

Bell, T. Surface engineering: past, present and future. SurfaceEngineering 6(1), 1990, 31–40.

Bjuggren, M., Krummenacher, L. and Mattsson, L. Noncontactsurface roughness measurement of engineering surfaces bytotal integrated infrared scattering. Precision Engineering 20(1),1997, 33–45.

Bousefield, B. and Bousefield, T. Progress towards a metallographystandard. Metals and Materials March 1990, 146–148.

Brown A.J.C. and Gilbert, F. Industrial applications for optical pro-filometry. Sensor Review January 1990, 35–37.

Caber, P.J. An interferometric profiler for rough surfaces. AppliedOptics 32, 1993, 3438–3441.

Downs M.J., Mason, N.M. and Nelson, J.C.C. Measurement of theprofiles of super-smooth surfaces using optical interferometry.Proceedings of SPIE-1009, 1989, 14–17.

Drews, W.E. Surface measurement: an advanced technology.Quality Progress April 1987, 43–46.

Dyson, J. Interferometry as a Measuring Tool. Machinery Pub. Co.,1970.

Garratt, J. and Bottomly, S.C. Technology transfer in the develop-ment of a nanotopographic instrument. Nanotechnology 1,1990, 38–43.

Garratt J. and Mills, M. Measurement of the roughness of super-smooth surfaces using a stylus instrument. Nanotechnology 7,1996, 13–20.

Gee, M.G. and McCormick, N.J. The application of confocal scan-ning microscopy to the examination of ceramic wear surfaces.Journal of Physics D: Applied Physics 25, 1990, 230–235.

Harvie, A. and Beattie, J.S. Surface texture measurement.Production Engineer, 1978, 25–29.

Hongai, Z., Zhixiang, C. and Riyao, C. The control of roughnesswith expert system controller. Proceedings of the First Inter-national Mach. Mon. and Diagnostics, Las Vegas, 1989, 813–817.

Kuwamura, S. and Yamaguchi, I. Wavelength scanning profilome-try for real-time surface shape measurement. Applied Optics 36,1997, 4473–4482.

Leach, R.K. Measurement of a correction for the phase change onreflection due to surface roughness. Proceedings of SPIE 3477,1998, 138–151.

Leach, R.K. Traceable measurement of surface texture at thenational physical laboratory using Nanosurf IV. MeasurementScience and Technology 11, 2000, 1162–1172.

Leach, R.K. Traceable measurement of surface texture in the opticsindustry. Large Lenses and Prisms Conference, UniversityCollege London, 27–30 March 2001.

Leach, R.K. and Hart, A.. Investigation into the shape of diamondstyli used for surface texture measurement. NPL ReportCBTLM10, April 2001, 1–12.

Mansfield, D. Surface characterisation via optical diffraction. SPIE(International Society for Optical Engineering) Vol. 1573:Commercial Applications of Precision Manufacture at the Sub-Micron Level, 1991, 163–169.

Prostrednik, D. and Osanna, P.H. The Abbott curve: well known inmetrology but not on technical drawings. International Journalof Machine Tools Manufacture 38(5–6), 1998, 741–745.

Schaffer, G.H. The many faces of surface texture. AmericanMachinist, June 1988, 61– 68.

Schneider, U., Steckroth, A. and Hubner, G. An approach to theevaluation of surface profiles by separating them into function-ally different parts. Surface Topography 1, 1988, 71–83.

Stout, K. How smooth is smooth? Surface measurements and theirrelevance in manufacturing. Production Engineer May 1980,17–22.


Thomas,T.R.Trends in surface roughness. International Journal ofMachine Tools Manufacture 38(5–6), 1998, 405–411.

Trumpold, H. and Heldt, E. Why filtering surface profiles. Inter-national Journal of Machine Tools Manufacture 38 (5–6), 1998,639–646.

Ulbricht, R. Die Bestimmung der mittleren räumlichen Licht-intensität durch nur eine. Messung Electrotechnische Zeitschrift29, 1900, 595–601.

Vorburger, T.V. and Teague, E.C. Optical techniques for onlinemeasurement of surface topography. Precision Engineering 3,1981, 63–83.

Westburg, J. Opportunities and problems when standardising andimplementing surface structure parameters in industry. Inter-national Journal of Machine Tools and Manufacture 38(5–6),1998, 413–416.

Whitehouse, D.J. Some ultimate limits on the measurement ofsurfaces using stylus techniques. Measurement and Control 8,1975, 147–151.

Whitehouse,D.J.Beta functions for surface topology? Annals of theCIRP 27, 1978, 491–497.

Whitehouse, D.J. Surfaces: a link between manufacture and func-tion. Proceedings of IMechE 192, 1978, 179–187.

Whitehouse,D.J.Conditioning of the manufacturing process usingsurface finish. Proceedings of the Third Lamdamap Conference,Computational Mechanics July 1997, 3–20.

Whitehouse, D.J. Some theoretical aspects of surface peak para-meters. Precision Engineering 23, 1999, 94–102.

Whitehouse, D.J. Surface measurement fidelity. Proceedings of theFourth Lamdamap Conference,University of Northumbria,WITPress, July 1999, 267–276.

Whitehouse, D.J. Characterizing the machined surface conditionby appropriate parameters. Proceedings of the Third IndustrialTooling Conference, Southampton Institute, Molyneux Press,September 1999, 8–31.

Wyant, J.C. Computerized interferometric measurement of sur-face microstructure. Proceedings of SPIE-2576, 1995, 122–130.

Zahwi,S.and Mekawi,A.M. Some effects of stylus force on scratch-ing surfaces. Eighth International Conference on Metrology andProperties of Engineering Surfaces, University of Huddersfield,26–28 April 2000.

Books, booklets and guides

Bennett, J.M. and Mattsson, L. Introduction to Surface Roughnessand Scattering. Washington, DC: Optical Society of America,1989.

Busch, T. and Wilkie Brothers Foundation. Fundamentals ofDimensional Metrology. Delmar, 1989.

Dagnall, M.A. Exploring Surface Texture. Taylor Hobson Precision,1997.

Dyson, J. Interferometry as a Measuring Tool. Machinery Pub. Co.,1970.

Gayler, J.F.W. and Shotbolt, C.R. Metrology for Engineers. Cassell,1990.

Haycocks, J.A. Novel Probes for Surface Texture Metrology. NPLReport MOM105, July 1991.

Hume, K.J. Engineering Metrology. Macdonald, 1970.Hume, K.J. A History of Engineering Metrology. Mechanical

Engineering Pub., 1980.Leach, R.K. NPL Good Practice Guide No. 37, Measurement of

Surface Texture using Stylus Instruments. NPL, 2001Leach, R.K. and Hart, A. Investigation into the Shape of Diamond

Styli used for Surface Texture Assessment. NPL Report CBTLM10, April 2001.

Mainsah, E., Greenwood, J.A. and Chetwynd, D.G. Metrology andProperties of Engineering Surfaces.Kluwer Academic Pub.,2001.

Mummery, L. Surface Texture Analysis: The Handbook. Hommel-werke GmbH, 1990.

Nicolls, M.O. The Measurement of Surface Finish. DeBeersTechnical Service Centre, DeBeers Industrial Diamond Divi-sion, Charters, UK, 1980.

Reason, R.E. The Measurement of Surface Texture. Cleaver-HumePress, 1960.

Sander, M. A Practical Guide to the Assessment of Surface Texture.Feinpruf GmbH, 1991.

Stover, J.C. Optical Scattering. McGraw-Hill, 1990.Thomas, G.G. Engineering Metrology. Butterworths, 1974.Thomas, T.R. Rough Surfaces. Imperial College Press, 1999.Whitehouse, D.J. and Reason, R.E. The Equation of the Mean Line

of Surface Texture Found by an Electric Wave Filter. Rank TaylorHobson Pub., 1965.

Whitehouse, D.J. Handbook of Surface Metrology. Institute ofPhysics, Bristol and Philadelphia, 1994.

Whitehouse, D.J. Surfaces and their Measurement. Hermes PentonScience, 1991.

Williams, D.C. Optical Methods in Engineering Metrology.Chapman & Hall, 1993.

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